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dissertation entitled

FINGERPRINT CLASSIFICATION
AND MATCHING USING A FILTERBANK

presented by

Salil Prabhakar

has been accepted towards fulﬁllment
of the requirements for

Doctoral

degree in Computer Science
and Engineering

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FINGERPRINT CLASSIFICATION AND MATCHING USING
A FILTERBANK

By

S alz’l Pmbhakar

A DISSERTATION

Submitted to
Michigan State University
in partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Computer Science 85 Engineering

2001

ABSTRACT
FINGERPRINT CLASSIFICATION AND MATCHING USING A
FILTERBANK
By
Salil Pmbhakar

Accurate automatic personal identiﬁcation is critical in a variety of applications
in our electronically interconnected society. Biometrics, which refers to identiﬁca-
tion based on physical or behavioral characteristics, is being increasingly adopted to
provide positive identiﬁcation with a high degree of conﬁdence. Among all the bio-
metric techniques, ﬁngerprint-based authentication systems have received the most
attention because of the long history of ﬁngerprints and their extensive use in foren-
sics. However, the numerous ﬁngerprint systems currently available still do not meet
the stringent performance requirements of several important civilian applications. To
assess the performance limitations of popular minutiae-based ﬁngerprint veriﬁcation
system, we theoretically estimate the probability of a false correspondence between
two ﬁngerprints from different ﬁngers based on the minutiae representation of ﬁn-
gerprints. Due to the limited amount of information present in the minutiae-based

representation, it is desirable to explore alternative representations of ﬁngerprints.

We present a novel ﬁlterbank-based representation of ﬁngerprints. We have used this
compact representation for ﬁngerprint classiﬁcation as well as ﬁngerprint veriﬁcation.
Experimental results show that this algorithm competes well with the state-of-the-
art minutiae-based matchers. We have developed a decision level information fu-
sion framework which improves the ﬁngerprint veriﬁcation accuracy when multiple
matchers, multiple ﬁngers of the user, or multiple impressions of the same ﬁnger are
combined. A feature veriﬁcation and puriﬁcation scheme is proposed to improve the

performance of the minutiae—based matcher.

To My Family

iv

ACKNOWLEDGMENTS

During my four years Of studies at Michigan State University, the sheer joy of work-
ing with my advisor, Dr. Anil K. Jain by far exceeded the excitement Of working
in pattern recognition, the sense Of achievement on completing a Ph.D. thesis, or
watching the school win a NCAA basketball championship. His love for perfection
and interest in detail have supplemented my own quest for knowledge. His advise,
guidance, help, ideas, insights, encouragement, regular reminders of “keep working
hard” and enquiries Of “any new breakthroughs?” were instrumental in making this
thesis possible and shaped my research career. I would like to thank Dr. S. Pankanti
Of IBM T. J. Watson Research Center for numerous discussions, suggestions, insights,
and help, Dr. G. Stockman and Dr. J. Zacks for serving on my Ph.D. committee, Dr.
J. Weng for useful discussions, and Dr. R. Bolle, Manager, Exploratory Computer
Vision Group, IBM T. J. Watson Research Center for his support. I would like to
especially thank my mentor Dr. Lin Hong for his help during my ﬁrst year of graduate
studies.

Special thanks to Arun Ross, Scott Connell, Aditya Vailaya, Nico Duta, Shaoyun
Chen, Wey Hwang, Yonghong Li, Vera Bakic, Paul Albee, Anoop Namboodri, Erin

V

McGarrity, Vincent Hsu, Dan Gutchess, Friederike Griess, Yatin Kulkarni, and others
in the PRIP lab for numerous discussions and encouragement.

I would also like to thank Cathy Davison, Starr Portice, Linda Moore, Debbie
Kruch, Beverly J. Wallace, and Karen Lillis for their administrative help.

My sincere thanks go to my parents for their never-fading love and encouragement,

and to my wife, Chandini, for her understanding and love.

vi

TABLE OF CONTENTS

LIST OF TABLES x
LIST OF FIGURES xiii
1 Introduction 1
1.1 Automatic Identiﬁcation ........................... 1
1.2 Biometrics ................................... 3
1.3 Applications .................................. 4
1.4 Fingerprints .................................. 5
1.5 Fingerprint Formation ............................ 6
1.6 Fingerprint Individuality ........................... 7
1.7 Fingerprint Sensors .............................. 10
1.8 Fingerprint Representation .......................... 14
1.9 Fingerprint Classiﬁcation ........................... 16
1.10 Fingerprint Veriﬁcation ............................ 19
1.11 Information Fusion .............................. 22
1.12 Feature Veriﬁcation .............................. 23
1.13 Challenges in Automatic Fingerprint Identiﬁcation ............ 24
1.14 State-Of-the-art in Fingerprint Identiﬁcation ................ 26
1.15 Thesis Objectives ............................... 27
1.16 Thesis Outline ................................ 29
2 On the Individuality Of Fingerprints 30
2.1 Genetic Factors ................................ 32
2.1.1 Introduction ................................. 32
2.1.2 Experimental Results ............................ 38
2.1.3 Summary .................................. 45
2.2 Environmental Factors ............................ 47
2.2.1 Introduction ................................. 47
2.2.2 Background ................................. 51
2.2.3 A Model of Fingerprint Individuality ................... 62
2.2.4 Experimental Results and Discussions .................. 78
2.2.5 Summary .................................. 84
3 Fingerprint as Oriented Texture 88
3.1 Introduction .................................. 89
3.2 Reference Point Location ........................... 96
3.3 Tessellation .................................. 102

vii

3.4 Filtering .................................... 105

3.5 Feature Vector ................................ 112
3.6 Summary ................................... 116
4 Fingerprint Classiﬁcation 119
4.1 Introduction .................................. 121
4.2 Feature Extraction .............................. 126
4.3 Classiﬁcation ................................. 130
4.4 Experimental Results ............................. 132
4.4.1 Dataset ................................... 132
4.4.2 K -Nearest neighbor classiﬁer ....................... 135
4.4.3 Neural network classiﬁer .......................... 136
4.4.4 Two-stage classiﬁer ............................. 137
4.4.5 Reject option ................................ 141
4.4.6 Support vector machine classiﬁer ..................... 142
4.4.7 Consistency results ............................. 145
4.4.8 Deﬁning New Classes ............................ 145
4.4.9 Dimensionality Reduction Using PCA .................. 147
4.4.10 Dimensionality Reduction Using Feature Clustering ........... 148
4.5 Summary ................................... 150
5 Fingerprint Matching 152
5.1 Introduction .................................. 156
5.2 Feature Extraction .............................. 156
5.3 Matching ................................... 160
5.4 Experimental Results ............................. 162
5.5 Summary ................................... 172
6 Decision-level Fusion in Fingerprint Veriﬁcation 176
6.1 Introduction .................................. 177
6.2 Matcher Combination ............................ 179
6.3 Integration Strategy ............................. 181
6.3.1 Matcher Selection .............................. 181
6.3.2 Non-parametric density estimation .................... 182
6.3.3 Decision Strategy .............................. 183
6.4 Matching Algorithms ............................. 184
6.4.1 Hough Transform Based Matching (Algorithm H ough) ......... 185
6.4.2 String Distance Based Matching (Algorithm String) .......... 185
6.4.3 2D Dynamic Programming Based Matching (Algorithm Dynamic) . . 186
6.4.4 Filterbank Based Matching (Algorithm Filter) ............. 187
6.5 Experimental Results ............................. 187
6.6 Summary ................................... 203

viii

7 Fingerprint Feature Detection and Veriﬁcation

7.1 Introduction ..................................
7.2 Minutia Veriﬁcation .............................
7.2.1 Feature Extraction .............................
7.2.2 Training ...................................
7.2.3 Testing ...................................
7.3 Minutia Classiﬁcation ............................

7.4 Experimental Results .............................
7.5 Summary ...................................

8 Conclusions and Future Work

8.1 Conclusions and Research Contributions

oooooooooooooooooo

8.2 Future Directions ...............................

BIBLIOGRAPHY

ix

204
205
207
207
208
210
210
213
215

217
217
222

227

1.1

1.2

2.1

2.2
2.3

LIST OF TABLES

Performance of ﬁngerprint veriﬁcation systems reported by various com-

panies on their web sites. None Of the companies mention the database
used for Obtaining the performance results, and thus the performance
numbers can not be directly compared. FAR: False Accept Rate; FRR:
False Reject Rate ..............................

Comparison of state-of-the—art fingerprint veriﬁcation algorithms in terms

of equal error rate (ERR) and timing on a database of 800 ﬁngerprints
(image size = 448 x 478 captured by DF-90 optical sensor manufactured
by Identicator Technology). Details Of the evaluation protocol can be
found in [57]. ...............................

False accept and false reject rates with different threshold values for the

twin database ................................

Fingerprint features used in different models .................
Comparison Of probability Of a particular ﬁngerprint conﬁguration using

different models. For a fair comparison, we do not distinguish between
minutiae types. By assuming that an average size ﬁngerprint has 24
regions (R = 24) as deﬁned by Galton, 72 regions (M = 72) as deﬁned
by Osterburg et al., and has 36 minutiae on an average (N = 36), we
compare the probability of Observing a given ﬁngerprint conﬁguration
in the third column of the table. The probability Of observing a ﬁn-
gerprint conﬁguration with N =2 12, and equivalently, R = 8, is given
in braces in the third column. Note that all probabilities represent a

full (N minutiae) match as opposed to a partial match (see Table 2.5).

2.4 The effects of the ﬁngerprint expert misjudgments in using the 12—point

rule. The source of error could be in underestimating the minutiae
detected in the latent print (n) or overestimating the correct num-
ber of matched minutiae (q). m = 12 for all entries. Except for
(m = 12,n = 12,q = 12) entry, all other entries represent incor-
rect judgments by the ﬁngerprint expert. For instance, the entry
( = 12,n = 14,q = 8) in the table indicates that although the ﬁn-
gerprint examiner determined that 12 template minutia unequivocally
matched with all 12 input minutiae, there were indeed 14 input minu-
tiae (2 missed input minutiae) out Of which only 8 correctly matched

27

28

43
56

57

with the corresponding template minutiae (4 incorrect match judgments). 82

2.5 Fingerprint correspondence probabilities Obtained from the proposed in-

dividuality model for different sizes of ﬁngerprint images containing
26, 36 or 46 minutiae. M for the last entry was computed by esti-
mating typical print area manifesting 12 minutia in a 500 dpi optical
ﬁngerprint scan. The entry (35, 12, 12, 12) corresponds to the 12-point
rule. ....................................

2.6 Fingerprint correspondence probabilities Obtained from matching imposter

3.1

4.1

4.2

4.3

4.4

4.5

4.6
4.7
4.8
4.9

ﬁngerprints using an AFMS [11] for the MSU_VERIDICOM and
MSU_DBI databases. The probabilities given in the table are for
matching “exactly q” minutiae. The probabilities for matching “q or
more” minutiae are 3.0x 10'2 and 3.2x 10‘2 for the MSU_VERIDICOM
and MSU_DBI databases, respectively, i.e., of the same order. The
average values for M, m, and n are 28,383, 26, and 26 for the
MSU-VERIDICOM database and 67, 415, 46 and 46 for the MSU_DBI
database, respectively. ..........................

Gabor ﬁlter mask of size 33 x 33, 6 2 0°, f = 0.1, 6,, 2 6y = 4.0. Only a

19 x 19 matrix from the center of the 33 x 33 ﬁlter is shown because
the mask values outside this are zero. Also, only the top left quarter
of the mask is shown due to the symmetry in the X and Y axes of the
0° oriented ﬁlter. The mask values less than 0.05 are set to zero. Each
entry is to be multiplied by 10’3. ....................

Fingerprint classiﬁcation literature survey. The number of classes is de-

noted by C, the classiﬁcation accuracy is denoted by Acc, and the
reject rate is denoted by RR. The classiﬁcation accuracies reported by
the different authors are on different databases with different number
of ﬁngerprints and therefore, they cannot-be directly compared. Most
of the work in ﬁngerprint classiﬁcation is based on supervised learning
and discrete class assignment using knowledge-based features.

Confusion matrix for the K -nearest neighbor classiﬁcation for the ﬁve-class

problem; K = 10. .............................

Confusion matrix for the K -nearest neighbor classiﬁcation for the four-

class problem; K = 10. ..........................

Confusion matrix for the neural network classiﬁcation for the ﬁve-class

problem ...................................

Confusion matrix for the neural network classiﬁcation for the four-class

problem ...................................

Error-reject tradeoff. .............................

A comparison of various ﬁngerprint classiﬁcation algorithms on the NIST

4 database. ................................

xi

83

84

111

123

135

137

137

138

Confusion matrix for the two-stage classiﬁcation for the ﬁve-class problem. 138

Confusion matrix for the two-stage classiﬁcation for the four-class problem. 139

142

5.1

5.2

5.3

6.1

6.2

6.3

6.4

Fingerprint matcher literature survey. The ﬁngerprint matching algo-
rithms are classiﬁed based on the alignment assumed between the tem—
plate and the input ﬁngerprint features. The rotation is denoted by R,
the translation is denoted by T, and the scale is denoted by S .....

False acceptance and false reject rates with different threshold values for
the MSU.DBI database. .........................

Comparison Of the equal error rates (ERR) of the proposed ﬁlterbank-
based technique with a state-of-the—art minutiae—based technique on
two different databases ...........................

Conﬁdence-level classiﬁer combination schemes. A more detailed compar-
ison can be found in [15] ..........................
Combining two ﬁngerprint matchers. CS is the class separation statistic.
CS and p are computed from the training data. Ranks by E ER (Equal
Error Rate) are computed from the independent test data. ......
Comparison of the performance of the best matcher combination with the
best individual matcher. GAR refers to the genuine acceptance rate
that is plotted on the ordinate of the ROC curves. We performed ten
runs of the combination scheme with ten different splits of the database
into training and test sets. The mean (Mean) and variance (Var) of
the GAR values for three ﬁxed values of FAR are reported .......
Equal error rate improvement due to combination Of matchers .......

xii

155

168

172

180

192

198
201

1.1

1.2
1.3

1.4

1.5

1.6
1.7

1.8

2.1
2.2

LIST OF FIGURES

Various electronic access applications in widespread use that require au-
tomatic authentication ...........................

Orientation ﬁeld, thinned ridges, minutiae, and singular points. .....

Fingerprint images captured using (a) inked method (NIST-9 database),
image size = 832 X 768 pixels, (b) Digital Biometrics Optical sensor
(MSU_DBI database), image size = 508 x 480 pixels, and (c) Veridicom
solid-state sensor (MSU_VERIDICOM database), image size = 300 x

300 pixels. All the images have 256 gray levels. ............

Fingerprint sensors. (a) Optical sensor from Digital Biometrics, Inc., and
(b) solid-state sensor from Veridicom, Inc. ...............

Six major ﬁngerprint classes. Twin loop images are labeled as whorl in
the NIST-4 database ............................

System diagram for an automatic veriﬁcation system ............

A general pattern recognition system with proposed feedback in feature
extraction and a new feature reﬁnement stage ..............

An example ﬁngerprint image from the NIST-4 database. The experts
have labeled this image to belong to two classes, right loop, and tented
arch. ....................................

Photograph of identical twin sisters (www.visi.com/~charlesr/).

Fingerprint images of identical twin Sisters captured using an optical scan-
ner from Digital Biometrics Inc., (a) and (b) are two impressions of
the same ﬁnger of one twin and (c) and (d) are two impressions Of
the corresponding ﬁnger of her sibling. Matching score between (a)
and (b) is 487, and between (c) and (d) is 510. The matching score
between (a) and (c) is 24, and the matching score between (b) and (d)
is 4. The ﬁngerprints of both the twins here have the same type (right
loop) and look similar to untrained eyes. Fingerprint experts, as well
as our automatic ﬁngerprint identiﬁcation system can, however, easily
differentiate the twins. ..........................

2.3 Minutiae extraction for twins. (a) and (b) are ﬁngerprint images of an

identical twin and his/ her sibling while the ﬁngerprint in (c) is from
another person. (d), (e), and (f) are the minutiae extracted from (a),
(b), and (c), respectively using the extraction algorithm in [11].

xiii

12

13

17
19

24

25

33

34

36

2.4

2.5

2.6

2.7

2.8

2.9

2.10
2.11

2.12

2.13

2.14

2.15

3.1

3.2

3.3

3.4

3.5

Minutiae matching for (a) twin—nontwin (matching of Figures 2.3(e) and
2.3(f), matching score = 3 on a scale of 0-999) and (b) twin-twin
(matching of Figures 2.3(d) and Figure 2.3(e), matching score = 38
on a scale of 0—999). The “matched” minutiae pairs are shown by
bounding boxes ...............................

Minutiae matching for two impressions of the same ﬁnger shown in Figures
2.2(a) and 2.2(b) (matching score = 487 on a scale of 0—999). The
“matched” minutiae pairs are shown by bounding boxes. .......

(a) Distribution of matching scores for twin-twin imposter, twin-nontwin
imposter, and genuine ﬁngerprint matchings. (b) ROC curves for twin-
twin and twin-nontwin minutiae pattern matchings. ..........

Effect of ﬁngerprint class type on the matching score ............

A ﬁngerprint image of type “right loop”. The overall ridge structure,
singular points, and sweat pores are shown ................

Automatic minutiae matching. Two impressions of the same ﬁnger were
matched in (a) 39 minutiae were detected in input (left), 42 in tem-
plate (right), and 36 “true” correspondences were found. Two different
ﬁngers are matched in (b) 64 minutiae were detected in input (left),
65 in template (right), and 25 “false” correspondences were found. . .

Fingerprint and minutiae. ..........................

Distribution of minutiae distance differences for the genuine ﬁngerprint
pairs in the GT database. ........................

Distributions for minutiae angle differences for the (a) genuine ﬁngerprint
pairs using the ground truth and (b) imposter matchings using the
automatic ﬁngerprint matching system ..................

Area of overlap between the two ﬁngerprints that are matched based on the
bounding boxes of the minutiae features for (a) MSU_DBI database;
(b) MSU-VERIDICOM database. ....................

Distributions for m, n, and q for computation of averages for (a) MSU-DBI
database; (b) MSU_VERIDICOM database. ..............

Comparison Of experimental and theoretical probabilities for the number
of matching minutiae. (a) MSU_DBI database; (b) MSU_VERIDICOM
database. .................................

Flow pattern in a ﬁngerprint image. (a) A section of a ﬁngerprint image,
(b) 3-dimensional surface plot of (a). ..................
Difﬁculty in ﬁngerprint matching. (a) and (b) have the same global con-
ﬁguration but are images of two different ﬁngers .............
Schematic diagram for extraction of generic texture-based representation
for ﬁngerprints. ..............................
Fingerprint Of (a) a child, and (b) an adult. Both the ﬁngerprints were
scanned at 500 dpi. ............................
Concave and convex ridges in a ﬁngerprint image when the ﬁnger is posi-
tioned upright. The reference point is marked by X ...........

xiv

37

37

40

41

48

66
67

73

75

76

79

80

90

92

93

94

96

3.6

3.7
3.8

3.9

3.10

3.11

3.12

3.13

3.14

4.1
4.2
4.3

4.4
4.5

Estimating the reference point. (a) Smoothed orientation ﬁeld overlapped
on the original image, (b) orientation ﬁeld (w=10) shown as intensity
distribution; the background has been segmented, and (c) sine com-
ponent of the orientation ﬁeld; the darkest pixel in the center of the
image marks the detected reference point. Images have been scaled to
the range 0—255 for viewing. ....................... 99

Regions for integrating pixel intensities in E for computing A(z’, j ) . . . . 101

Examples of the results of our reference point location algorithm. The
algorithm fails on very poor quality ﬁngerprints such as (c) and (d). . 103

Reference point (x), the region of interest, and 80 sectors (B = 5, k = 16)
superimposed on a ﬁngerprint ....................... 106

Fingerprints have well deﬁned local frequency and orientation. Ridges in
local regions are shown in (a) and (b). Fourier spectrum of (a) and (b)

are shown in (c) and (d), respectively. ................. 107
Gabor ﬁlters (mask size = 33 x 33, f = 0.1, 6;, = 4.0, 6y 2 4.0). Only 0°
and 90° oriented ﬁlters are shown here. ................. 108

Normalized, ﬁltered, and reconstructed ﬁngerprint images. (a) area Of
interest, (b) normalized image, (c)-(j) 0°, 22.5°, 45°, 90°, 112.5°, 157.5°
ﬁltered images, respectively, (k) reconstructed image with 4 ﬁlters, and
(l) reconstructed image with 8 ﬁlters. While four ﬁlter orientations are
sufﬁcient to capture the global structure of the ﬁngerprint, eight ﬁlter
orientations are required to capture the local characteristics. ..... 110

Examples of 640-dimensional feature vectors. (a) First impression of ﬁnger
1, (b) Second impression of ﬁnger 1, (c) and (d) are the corresponding
FingerCodes, (e) First impression of ﬁnger 2, (f) Second impression of
ﬁnger 2, (g) and (h) are the corresponding FingerCodes. ....... 114

Example of new touchless ﬁngerprint sensor TF S 050 from Biometric Part-
ners, Inc. (http://www.biometricpartners.com/). The touchless sensor
captures a ﬁngerprint from a distance of approximately 50mm. Advan-
tages of touchless technology include capture of larger ﬁngerprint area,
is more hygienic, the sensor does not degrade with repeated use, and
there is no nonlinear distortion due to ﬁnger pressure difference in the
captured image. The image captured by the sensor in (a) is shown in
(b). However, the touchless sensors have their own problems, including

poor quality images. ........................... 118
Pattern area and typelines [68, 104]. .................... 124
Flow diagram of our ﬁngerprint classiﬁcation algorithm. ......... 125
Reference point detected by the algorithm described in Chapter 3 (U),

moved reference point (x), the region Of interest and 48 sectors. . . . 127
Normalized, ﬁltered, and reconstructed ﬁngerprint images. ........ 128
Reconstructed ﬁngerprint images using (a) four ﬁlters, and (b) eight ﬁlters.

Most of the directionality information is captured by four ﬁlters. . . 129

XV

4.6 Fingerprint representation using 192-dimensional feature vectors (In each
representation, the top left disc represents the 0° component, the top
right disc represents the 45° component, the bottom left disc represents
the 90° component, and the bottom right disc represents the 135° com-
ponent). The test image is a right loop. Each disk corresponds to one
particular ﬁlter and there are 48 features (shown as gray values) in
each disk (8 x 6 = 48 sectors) for a total of 192 (48 x 4) features.

130

4.7 Two—stage classiﬁcation scheme using K—N N and neural network classiﬁers. 131

4.8 Example of images in the NIST 4 database with two ground truth labels.
The poor quality ﬁngerprint in (a) is labeled as belonging to both the
arch and tented arch classes, (b) is labeled as belonging to both the
left loop and tented arch classes ......................

4.9 Example Of images which were rejected because a valid tessellation could
not be established. ............................

4.10 K vs. classiﬁcation error for the K -nearest neighbor classiﬁer for the ﬁve-
class problem ................................

4.11 Poor quality images which were correctly classiﬁed. ............

4.12 Poor quality images which were misclassiﬁed as arch. ...........

4.13 Misclassiﬁcation of whorl (twin loop) as (a) right loop (b) left loop. . . .

4.14 Examples of arch-loop misclassiﬁcations; (a) a right loop misclassiﬁed as
an arch; (b) an arch misclassiﬁed as a tented arch ............

4.15 Examples Of images rejected by (10, 5)—NN classiﬁer. ...........

5.1 System diagram of our ﬁngerprint authentication system ..........
5.2 Examples of 640-dimensional feature vectors corresponding to nine differ-
ent impressions of the same ﬁnger. ...................
5.3 The ﬁngerprint image in (b) is obtained by a —22.5° rotation of (a). A
part of the feature vector corresponding to the 0° Gabor ﬁltered image
extracted from (a) is shown in (c) as a gray scale image. The feature
vector in (c) is rotated by —22.5° (R = —1 in Equations (5.2) and
(5.3)) and is shown in (d). (e) shows the feature vector extracted from
the ﬁngerprint image in (b). The feature vectors shown in (d) and (e)
are Similar illustrating that the feature vector for a —22.5° rotation in
the original image approximately corresponds to a unit anticlockwise
cyclic rotation of the feature vector ....................
5.4 A comparison of the quality of inked ﬁngerprints and dab ﬁngerprints. (a)
inked ﬁngerprint, (b) dab ﬁngerprint. ..................
5.5 Examples of images with large deformation due to ﬁnger pressure differ-
ences in the MSU_DBI database. Fingerprint images in (b) and (d)
were taken six weeks after the images in (a) and (c) were acquired,
respectively. ................................
5.6 Examples of rejected images. (a) a-poor quality image, (b) the reference
point is (correctly) detected at a corner of the image and so an appro—
priate region of interest could not be established. ...........

xvi

132

136
139
140
141

142
143

157

159

161

163

164

5.7

5.8

5.9

6.1
6.2

6.3

6.4

6.5

6.6
6.7

6.8

6.9

Errors in matching. Examples of ﬁngerprint images from the same ﬁnger
that were not correctly matched by our algorithm. (a) and (b) do not
match because of the failure of reference point location, (c) and (d) do
not match because of the change in inter ridge distances due to ﬁnger
pressure difference. ............................

Genuine and imposter distributions for the proposed veriﬁcation scheme.
(a) MSU-DBI database, (b) NIST-9 (Vol. 1, CD No. 1). .......

Receiver Operating Characteristic (ROC) curves for two different
(ﬁlterbank-based and minutiae-based) matchers. (a) MSU-DBI
database, (b) NIST-9 (Vol. 1, CD No. 1). FAR and FRR are equal
at all points on the Equal—Error Line. Thus, the point of crossing of
ROC with this line denotes the equal error rate on the ROC ......

Various Multi—modal Biometric Systems [158]. ...............
Performance of individual ﬁngerprint matchers. The ROC curves have
been averaged over ten runs ........................
Normal approximation to the imposter distribution for the matcher Filter.
(a) Imposter and genuine distributions, (b) ROC curves. Visually,
the Normal approximation seems to be good, but causes signiﬁcant
decrease in the performance compared to the nonparametric estimate
of the imposter distribution at low FARs .................
Plot Of joint scores from matchers String and Filter. The solid lines
denote the three sum rule decision boundaries corresponding to three
different thresholds. The dotted lines denote the three product rule
decision boundaries corresponding to three different thresholds.
Two-dimensional density estimates for the genuine and imposter classes
for String + Filter combination. Genuine density was estimated using
Parzen window (h = 0.01) estimator and the imposter density was
estimated using normalized histograms. ................

ROC curves for all possible two-matchers combinations. .........
Comparison of the proposed combination scheme with the sum and the
product rules for the String + Filter combination. ..........
The performance of the best individual matcher Dynamic is compared
with various combinations. The S tring+ Filter is the best two-matcher
combination and String + Dynamic+ Filter is the best overall combi-
nation. Note that addition of the matcher H ough to the combination
String + Filter results in a degradation of the performance. .....
Matching scores for the best combination involving String, Dynamic, and
Filter matchers. Visually, one can see a small overlap between the
genuine (o) and the imposter (*) classes. The class separation statis—
tic is 1.97 for the three-dimensional genuine and imposter densities
estimated from these scores. .......................

6.10 Proposed architecture of multi—modal biometrics system based on several

ﬁngerprint matchers. ...........................

xvii

167

169

170

178

188

189

191

193
194

195

196

197

199

6.11 Performance of matcher combination. (a) & (b) and (c) & (d) were misclas-

siﬁed by the three individual matchers String, Dynamic, and Filter
as impostors, but correctly classiﬁed as genuine by the combination.
Both the minutiae-based and ﬁlterbank-based matchers can not deal
with large nonlinear deformations, however, a combination of matchers
can overcome this. ............................

6.12 Performance improvement by using multiple impressions and multiple ﬁn-

7.1

7.2

7.3

7.4

7.5
7.6
7.7

8.1

gers. (a) Combining two impressions of the same ﬁnger, and (b) com-
bining two ﬁngers of the same person ...................

Sample images from the GT database with varying quality index (Q1).
0 false minutiae were detected in (a), 7 in (b), and 27 in (c) by the
automatic minutiae detection algorithm [11]. .............

Examples Of images in the GT database. The ground truth minutiae
provided by an expert are marked on the image .............

Examples of gray level proﬁles in the neighborhood of (a) minutiae and
(b) non-minutiae. These 32 x 32 subimages, scaled to 8 gray levels, are
used for training an LVQ. ........................

Minutiae detection and classiﬁcation; (a) Minutiae detection using the al-
gorithm in [11] without pruning, (b) results Of minutia-pruning; minu-
tiae marked in white were pruned, (c) result of minutia veriﬁcation
instead Of pruning; minutiae marked in white were rejected, (d) result
of classifying minutiae shown in (b); minutia bifurcations are marked
in black and endings are marked in white. ...............

ROC for ﬁngerprint matching when minutia veriﬁcation is used. .....

ROC for ﬁngerprint matching when minutia classiﬁcation is used.

ROC for ﬁngerprint veriﬁcation when both minutia classiﬁcation and ver-
iﬁcation are used. .............................

The best performance achieved on the MSU-DBI database. The minu—
tiae extraction algorithm Of Jain et a1. [11] was modiﬁed by replacing
its post processing stage with minutiae veriﬁcation stage as described
in Chapter 7. Three different matchers, namely, String, Dynamic,
and Filter, two different ﬁngers, and three different impressions for
each ﬁnger of a person were combined. The genuine distribution was
estimated using 2, 640 matchings and the imposter distribution was es-
timated using 95, 920 matchings. Note that the improvement in perfor-
mance by combining multiple ﬁngers is higher than combining multiple
matchers or multiple templates (impressions). This is because different
ﬁngers provide the most “independent” information. A simple “sum
rule” was used for the combination. ...................

xviii

202

209

212
213
214

215

218

Chapter 1

Introduction

1.1 Automatic Identiﬁcation

With the advent of electronic banking, e-commerce, and smartcards and an increased
emphasis on the privacy and security Of information stored in various databases, auto-
matic personal identiﬁcation has become a very important topic. Accurate automatic
personal identiﬁcation is now needed in a wide range of civilian applications involv-
ing the use Of passports, cellular telephones, automatic teller machines, and driver
licenses. Traditional knowledge-based (password or Personal Identiﬁcation Number
(PIN)) and token-based (passport, driver license, and ID card) identiﬁcations are
prOne to fraud because PINS may be forgotten or guessed by an imposter and the
tokens may be lost or stolen. Therefore, traditional knowledge-based and token-based
approaches are unable to satisfy the security requirements Of our electronically inter-
connected information society (see Figure 1.1). As an example, a large part of the
annual $450 million Mastercard credit card fraud [14] is due to identity fraud. A

1

perfect identity authentication system will necessarily have a biometric component.
Eventually, a foolproof identity authentication systems will have all the three com-
ponents (knowledge-based, token-based, and biometrics). In this thesis, we have only
focused on the biometrics component Of an automatic identiﬁcation system in general,

and a ﬁngerprint-based biometric identiﬁcation system in particular.

 

 

 

 

    

ATM
A Credit
(Sand
Network 4 Electron _ Cellular
Logon Access P 110116

Web
Access

 

Figure 1.1: Various electronic access applications in widespread use that require au-
tomatic authentication.

\\

ﬁx

WM

Thinned ridges Minutiae (0), Core ([3), and Delta (A).

      

Figure 1.2: Orientation ﬁeld, thinned ridges, minutiae, and singular points.

1.2 Biometrics

Biometrics, which refers to identifying an individual based on his or her physiological
or behavioral characteristics has the capability to reliably distinguish between an
authorized person and an imposter. Since biometric characteristics are distinctive,
can not be forgotten or lost, and the person to be authenticated needs to be physically
present at the point of identiﬁcation, biometrics is inherently more reliable and more
capable than traditional knowledge-based and token-based techniques. Biometrics

8180 has a number of disadvantages. For example, if a password or an ID card is

compromised, it can be easily replaced. However, once a biometrics is compromised,
it is not possible to replace it. Similarly, users can have a different password for each
account, thus if the password for one account is compromised, the other accounts
are still safe. However, if a biometrics is compromised, all biometrics—based accounts
can be broken-in. Among all biometrics (e.g., face, ﬁngerprint, hand geometry, iris,
retina, signature, voice print, facial thermogram, hand vein, gait, ear, Odor, keystroke
dynamics, etc. [14]), ﬁngerprint-based identiﬁcation is one Of the most mature and

proven technique.

1.3 Applications

Biometrics has been widely used in forensics applications such as criminal identiﬁca-
tion and prison security. The biometric technology is rapidly evolving and has a very
strong potential to be widely adopted in civilian applications such as electronic bank-
ing, e-commerce, and access control. Due to a rapid increase in the number and use
of electronic transactions, electronic banking and electronic commerce are becoming
one of the most important emerging applications Of biometrics. These applications
include credit card and smart card security, ATM security, check cashing and fund
transfers, online transactions and web access. The physical access control applications
have traditionally used token-based authentication. With the progress in biomet-
ric technology, these applications will increasingly use biometrics for authentication.
Remote login and data access applications have traditionally used knowledge-based

authentication. These applications have already started using biometrics for person

authentication. The use Of biometrics will become more widespread in coming years
as the technology matures and becomes more trust worthy. Other biometric applica-
tions include welfare disbursement, immigration checkpoints, national ID, voter and

driver registration, and time and attendance.

1.4 Fingerprints

Fingerprints are the ridge and furrow patterns on the tip of the ﬁnger [78] and have
been used extensively for personal identiﬁcation Of people [11]. Figure 1.2 shows an
example Of a ﬁngerprint. The biological properties Of ﬁngerprint formation are well
understood and ﬁngerprints have been used for identiﬁcation purposes for centuries.
Since the beginning Of the 20th century, ﬁngerprints have been extensively used for
identiﬁcation of criminals by the various forensic departments around the world [68].
Due to its criminal connotations, some people feel uncomfortable in providing their
ﬁngerprints for identiﬁcation in civilian applications. However, since ﬁngerprint-based
biometric systems Offer positive identiﬁcation with a very high degree of conﬁdence,
and compact solid state ﬁngerprint sensors can be embedded in various systems (e.g.,
cellular phones), ﬁngerprint-based authentication is becoming more and more popular
in a number Of civilian and commercial applications such as, welfare disbursement,
cellular phone access, and laptop computer log-in. The availability of cheap and com-
pact solid state scanners [177] as well as robust ﬁngerprint matchers are two important
factors in the popularity Of ﬁngerprint-based identiﬁcation systems. Fingerprints also

have a number of disadvantages as compared to other biometrics. For example, ap-

proximately 4% Of the population does not have good quality ﬁngerprints, manual
workers get regular scratches on their ﬁngers which poses a difficulty to the match-
ing system, ﬁnger Skin peels off due to weather, ﬁngers develop natural permanent
creases, temporary creases are formed when the hands are immersed in water for a
long time, and dirty ﬁngers can not be properly imaged with the existing ﬁngerprint
sensors. Further, Since ﬁngerprints can not be captured without the user’s knowledge,

they are not suited for certain applications such as surveillance.

1.5 Fingerprint Formation

Fingerprints are fully formed at about seven months of fetus development and ﬁnger
ridge conﬁgurations do not change throughout the life Of an individual except due
to accidents such as bruises and cuts on the ﬁnger tips [63]. This property makes
ﬁngerprints a very attractive biometric identiﬁer. Biological organisms, in general,
are the consequence Of the interaction Of genes and environment. It is assumed that
the phenotype is uniquely determined by the interaction of a speciﬁc genotype and
a speciﬁc environment. Physical appearance and ﬁngerprints are, in general, a part
of an individual’s phenotype. In the case Of ﬁngerprints, the genes determine the
general characteristics of the pattern. Fingerprint formation is Similar to the growth
Of capillaries and blood vessels in angiogenesis [63]. The general characteristics Of the
ﬁngerprint emerge as the skin on the ﬁngertip begins to differentiate. However, the
flow Of amniotic ﬂuids around the fetus and its position in the uterus change during the

differentiation process. Thus, the cells on the ﬁngertip grow in a microenvironment

that is slightly different from hand to hand and ﬁnger to ﬁnger. The ﬁner details of the
ﬁngerprints are determined by this changing microenvironment. A small difference
in microenvironment is ampliﬁed by the differentiation process of the cells. There
are so many variations during the formation Of ﬁngerprints that it would be virtually
impossible for two ﬁngerprints to be alike. But since the ﬁngerprints are differentiated
from the same genes, they will not be totally random patterns either. We could say
that the ﬁngerprint formation process is a chaotic system rather than a random one

[63].

1.6 Fingerprint Individuality

Until recently, the testimony of latent ﬁngerprint examiners was admitted in courts
without much scrutiny and challenge. However, in the 1993 case Of Daubert vs. Mer-
rell Dow Pharmaceuticals, Inc. [50], the Supreme Court ruled that the reliability
of an expert scientiﬁc testimony must be established. Additionally, the court stated
that when assessing reliability, the following ﬁve factors should be considered: (i)
whether the particular technique or methodology in question has been subject to a
statistical evaluation (hypothesis testing), (ii) whether its error rate has been estab-
lished, (iii) whether the standards controlling the technique’s Operations exist and
have been maintained, (iv) whether it has been peer reviewed, and published, and ('0)
whether it has a general widespread acceptance. Subsequently, handwriting identiﬁ—
cation was challenged under Daubert (it was claimed that handwriting identiﬁcation

does not meet the scientiﬁc evidence criteria established in the Daubert case) in sev-

eral cases between 1995 and 2001 and many courts have now decided that handwriting
identiﬁcation does not meet the Daubert criteria. Fingerprint identiﬁcation was ﬁrst
challenged by the defense lawyers under Daubert in the 1999 case Of USA vs. Byron
Mitchell [175] on the basis that the fundamental premises of ﬁngerprint identiﬁcation
have not been objectively tested and its potential error rate is not known. The de-
fense motion to exclude ﬁngerprint evidence and testimony was denied. The outcome
of the USA vs. Byron Mitchell case is still pending. Fingerprint identiﬁcation has
been challenged under Daubert in more than 10 court cases till date since the USA
vs. Byron Mitchell case in 1999 (http://Onin.com/fp/daubertJinks.html).

The two fundamental premises on which ﬁngerprint identiﬁcation is based are: (i)
ﬁngerprint details are permanent, and (ii) ﬁngerprints Of an individual are unique.
The validity Of the ﬁrst premise has been established by empirical Observations as well
as based on the anatomy and morphogenesis of friction ridge skin. It is the second
premise which is being challenged in recent court cases. The notion of ﬁngerprint
individuality has been widely accepted based on a manual inspection (by experts) of
millions Of ﬁngerprints. However, the underlying scientiﬁc basis Of ﬁngerprint individ-
uality has not been rigorously studied or tested. In March 2000, the US. Department
of Justice admitted that no such testing has been done and acknowledged the need
for such a study [174]. In response to this, the National Institute Of Justice issued a
formal solicitation for “Forensic Friction Ridge (Fingerprint) Examination Validation
Studies” whose goal is to conduct “basic research to determine the scientiﬁc validity
of individuality in friction ridge examination based on measurement Of features, quan-

tiﬁcation, and statistical analysis” [174]. The two main topics of basic research under

this solicitation include: (i) measure the amount Of detail in a single ﬁngerprint that
is available for comparison, and (ii) measure the amount of detail in correspondence
between two ﬁngerprints.

What do we mean by ﬁngerprint individuality? The ﬁngerprint individuality prob-
lem can be formulated in many different ways depending on which one of the following
aspects Of the problem is under examination: (i) the individuality problem may be
cast as determining the probability that any two individuals may have sufﬁciently
similar ﬁngerprints in a given target population. (ii) Given a sample ﬁngerprint,
determine the probability Of ﬁnding a sufﬁciently similar ﬁngerprint in a target pop-
ulation.” In this thesis, we deﬁne the individuality problem as the probability of a
false association: given two ﬁngerprints from two different ﬁngers, determine the
probability that they are “sufﬁciently” similar. If two ﬁngerprints originating from
two different ﬁngers are examined at a very high level Of detail, we may ﬁnd that
the ﬁngerprints are indeed different. However, most human experts and automatic
ﬁngerprint identiﬁcation systems (AFIS) declare that the ﬁngerprints originate from
the same source if they are “sufﬁciently” similar. How much similarity is enough
depends on typical (intra—class) variations observed in the multiple impressions of a
ﬁnger. Solutions to the other two problem formulations (i) and (ii) above can be
derived from a solution to the problem considered in this thesis.

The distinctiveness Of ﬁngerprints can be studied by Observing the ﬁngerprints of
genetically related individuals. The closest genetic relationship is found in monozy—
gotic (identical) twins, and therefore, the maximum similarity between ﬁngerprints

iS GXpected to be found among them. A study of identical twin ﬁngerprints can es-

 

tablish performance bounds on the automatic ﬁngerprint veriﬁcation systems. In this
thesis, we have discussed the implications Of the similarity found in identical twin

ﬁngerprints on the performance of automatic ﬁngerprint veriﬁcation systems.

1.7 Fingerprint Sensors

The ﬁngerprint images may be acquired either by an Ofﬂine or an online process.
The ﬁngerprint images acquired by the offline process are known as the “inked”
ﬁngerprints while the images acquired by the online process are known as “live-scan”
ﬁngerprints. Inked ﬁngerprints are of three types: (i) rolled, (ii) dab, and (ii) latent.
In the rolled method of ﬁngerprint acquisition, ink is applied to the ﬁnger and then
rolled on a paper from one side of the nail to the other to form an impression. This
paper is then scanned at 500 dpi resolution by a standard grayscale scanner. The
rolled ﬁngerprints have a larger ridge and furrow area due to the rolling process but
have larger deformations due to the inherent nature of the rolling process. In the dab
method Of ﬁngerprint acquisition, ink is applied to the ﬁnger and then pressed onto a
paper without rolling. The paper is then scanned into a digital image. Typically, dab
inked ﬁngerprints have less nonlinear deformation but smaller area than the rolled
inked ﬁngerprints. Latent ﬁngerprints are formed when the ﬁngers leave a thin layer
of sweat and grease on the surfaces that they touch due to the presence of sweat pores
in our ﬁngertips. Forensic scientists dye this impression which is typically found at
the scene of a crime with color and then scan the ﬁngerprint. .In this thesis, we have

concentrated only on civil applications Of ﬁngerprints and therefore, have not used

10

—¥——_‘___

 

 

the latent ﬁngerprints.

A live-scan ﬁngerprint is Obtained directly from the ﬁnger without the intermediate
use Of paper (at a resolution Of 500 dpi). Typically, live-scan sensors capture a
series of dab ﬁngerprints when a ﬁnger is pressed on the sensor surface. For rolled
live-scan ﬁngerprints, the user rolls her/his ﬁnger from one end of the nail to the
other on the sensor surface and the sensor captures a number of dab ﬁngerprint
images. The rolled ﬁngerprint image is then constructed by mosaicking the multiple
dab images captured during the rolling process. The commercially available live-scan
sensors are based on several different technologies. The Optical ﬁngerprint sensor from
Digital Biometrics Inc. [54] (model FC21RSl) is based on the “optical total internal
reflection” technology. The Thompson-CPS chip-based sensor [163] works on thermal
sensing of temperature difference across the ridges and valleys. The Veridicom [177]
and the Siemens [156] sensors are based on differential capacitance. The pressure-
based and ultrasonic-based ﬁngerprint sensors are available in the market, but they
are not very widely used yet.

A number of commercial systems exist that use ﬁngerprints captured by different
methods. For example, FBI captures ﬁngerprints of known criminals using the inked
rolled method and stores the digitized ﬁngerprint images in its database. A suspect’s
latent ﬁngerprint found at a scene of crime is then matched to the rolled inked ﬁn-
gerprints in the database. As another example, MasterCard instructs the new credit
card applicants tO make an inked rolled impression of their ﬁnger on a paper and mail
the paper to them. The inked rolled ﬁngerprint is then scanned and stored in the

user’s credit card. The user is then veriﬁed at the time of credit card transactions

11

 

 

 

 

[a

 

Figure 1.3: Fingerprint images captured using (a) inked method (N IST—9 database),
image size = 832 x 768 pixels, (b) Digital Biometrics optical sensor (MSU_DBI
database), image size = 508 x 480 pixels, and (c) Veridicom solid—state sensor
(MSU_VERIDICOM database), image size = 300 x 300 pixels. All the images have
256 gray levels.

12

using a dab live-scan ﬁngerprint image obtained with the live—scan ﬁngerprint scanner
attached to the ATM.

An additional point worth mentioning in this section is that the FBI has pre—
scribed a standard resolution of 500ldpi for ﬁngerprint images. A large number of
live ﬁngerprint sensors available in the market today operate at this resolution. Na-
tional Institute of Standards and Technology (NIST) provides a number of ﬁnger-
print databases to the research community for benchmark purposes. A number of
these databases contain inked rolled ﬁngerprints (e.g., NIST—4, NIST-9, etc). These
databases contain ﬁngerprint images scanned at 500 dpi from the paper copy of the
rolled impressions as well as captured by 500 dpi live scanners. A few sensors that
image the ﬁngerprints at a lower resolution are also available in the market. However,
since 500 dpi resolution is the standard, we use ﬁngerprint images scanned only at

this resolution in this thesis.

     

Sensor

 

(b)

Figure 1.4: Fingerprint sensors. (a) Optical sensor from Digital Biometrics, Inc., and
(b) solid-state sensor from Veridicom, Inc.

13

Figure 1.3(a) shows a ﬁngerprint image captured using the inked method. The
N IST 9 database, CD. No. 1, contains 900 ﬁngerprint images captured by this method.
Figures 1.3(b) and (c) Show ﬁngerprint images captured by the optical live—scan sensor
manufactured by Digital Biometrics, Inc. (Figure 1.4(a)) and solid-state live-scan ﬁn-
gerprint sensor manufactured by Veridicom, Inc. (Figure 1.4(b)). The inked method
captures the largest ﬁngerprint area. The chip-based sensors capture only a part of
the whole ﬁngerprint due to their small size. Two images of the same ﬁnger may
capture different parts of the ﬁngerprint. Due to this relatively small overlap between
different images of the same ﬁnger captured with the small sensors, the ﬁngerprint
matching problem is challenging. However, due to their small size (see Figure 1.4),
the solid-state sensors can be easily embedded into laptops, cellular phones, mouse

and ﬁrearms.

1.8 Fingerprint Representation

The popular ﬁngerprint representation schemes have evolved from an intuitive system
developed by forensic experts who visually match the ﬁngerprints. These schemes
are either based on predominantly local landmarks (e.g., minutiae-based ﬁngerprint
matching systems [11, 56]) or exclusively global information (ﬁngerprint classiﬁcation
based on the Henry system [18, 76, 105]). The minutiae—based automatic identiﬁcation
techniques ﬁrst locate the minutiae points and then match their relative placement
in a given ﬁnger and the stored template [11]. A good quality inked ﬁngerprint

image contains between 60 to 80 minutiae, but different ﬁngerprints and different

14

acquisitions of the same ﬁnger have different numbers of minutiae. A graph-based
representation [118, 155, 5] constructs a nearest neighbor graph from the minutiae
patterns. The matching algorithm is based on inexact graph matching techniques.
The point pattern-based representation [11, 26, 96] considers the minutiae points as a
two—dimensional pattern of points. Correlation-based techniques [61, 31] consider the
gray level information in the ﬁngerprint as features and match the global patterns of
ridges and valleys to determine if the ridges align.

The global representation of ﬁngerprints (e.g., whorl, left loop, right loop, arch,
and tented arch) is typically used for indexing [18, 76, 105], and does not offer good
individual discrimination. Further, the indexing efﬁcacy of existing global representa—
tions is poor due to a small number of categories (typically ﬁve) that can be effectively
identiﬁed automatically and a highly skewed distribution of the population in each
category. The global representation schemes of the ﬁngerprint used for classiﬁca—
tion can be broadly categorized into four main categories: (i) knowledge-based, (ii)
structure—based, (iii) frequency-based, and (iv) syntactic. The knowledge-based ﬁn-
gerprint representation technique uses the locations of singular points (core and delta)
to classify a ﬁngerprint into ﬁve major classes (whorl, left loop, right loop, arch, and
tented arch) [18, 105]. A knowledge-based approach tries to capture the knowledge of
a human expert by deriving rules for each category by hand-constructing the models
and therefore, does not require training. Structure-based approach uses the estimated
orientation ﬁeld in a ﬁngerprint image [30, 122]. Frequency-based approaches use the
frequency spectrum of the ﬁngerprints for representation [25]. Hybrid approaches

combine two or more approaches for representation [34, 120].

15

_¥—————

 

 

There are two major shortcomings of the traditional approaches to ﬁngerprint
representation. For a signiﬁcant fraction of the population, the automatic extraction
of representations based on an explicit detection of complete ridge structures in the
ﬁngerprint is difﬁcult. The widely used minutiae-based representation does not uti-
lize a signiﬁcant component of the rich discriminatory information available in the
ﬁngerprints. Local ridge structures cannot be completely characterized by minutiae.
Further, minutiae-based matching has difﬁculty in efﬁciently and robustly matching
two ﬁngerprint images containing different numbers of unregistered minutiae points.

Some applications such as smart cards will also beneﬁt from a compact representation.

1.9 Fingerprint Classiﬁcation

Large volumes of ﬁngerprints are collected and stored everyday in a wide range of
applications, including forensics, access control, and driver license registration. Auto—
matic identity recognition based on ﬁngerprints requires that the input ﬁngerprint be
matched with a large number of ﬁngerprints stored in a database (the FBI database
currently contains more than 630 million ﬁngerprints! [69]). To reduce the search
time and computational complexity, it is desirable to classify these ﬁngerprints in an
accurate and consistent manner such that the input ﬁngerprint needs to be matched
only with a subset of the ﬁngerprints in the database. Fingerprint classiﬁcation is
a technique used to assign a ﬁngerprint into one of the several pre—speciﬁed types
already established in the literature (and used in forensic applications) which can

provide an indexing mechanism. Fingerprint classiﬁcation can be viewed as a coarse

16

 

     

Arch (A) Tented Arch (T)

Figure 1.5: Six major ﬁngerprint classes. Twin loop images are labeled as whorl in
the NIST-4 database.

17

level matching of the ﬁngerprints. An input ﬁngerprint is ﬁrst matched to one of
the pre—speciﬁed types and then it is compared to a subset of the database corre-
sponding to that ﬁngerprint type. To increase the search efﬁciency, the ﬁngerprint
classiﬁcation algorithm can classify a ﬁngerprint into more than one class. For exam-
ple, if the ﬁngerprint database is binned into ﬁve classes, and a ﬁngerprint classiﬁer
outputs two classes (primary and secondary) with high accuracy, then the identiﬁca-
tion system will only need to search two of the ﬁve bins, thus decreasing the search
space 2.5 folds. Continuous classiﬁcation of ﬁngerprints is also very attractive for
indexing where ﬁngerprints are not partitioned in non-overlapping classes, but each
ﬁngerprint is characterized with a numerical vector summarizing its main features.
The continuous features obtained are used for indexing ﬁngerprints through spatial
data structures and for retrieving ﬁngerprints by means of spatial queries [22]. In this
thesis, we have concentrated on an exclusive ﬁngerprint classiﬁcation and classify ﬁn—
gerprints into ﬁve distinct classes, namely, whorl (W), right loop (R), left loop (L),
arch (A), and tented arch (T) (Figure 1.5). The ﬁve classes are chosen based on the
classes identiﬁed by the National Institute of Standards and Technology (NIST) to
benchmark automatic ﬁngerprint classiﬁcation algorithms. The natural proportion of
occurrence of these ﬁve major classes of ﬁngerprints is 0.3252, 0.3648, 0.1703, 0.0616,
and 0.0779 for whorl, right loop, left loop, arch, and tented arch, respectively [173].
There are two main types of features in a ﬁngerprint: (i) global ridge and furrow
Structures which form special patterns in the central region of the ﬁngerprint, and (ii)
1003.1 ridge and furrow minute details (see Figure 1.2). A ﬁngerprint is classiﬁed based

on only the ﬁrst type of features and is uniquely identiﬁed based on the second type

18

of features (ridge endings and bifurcations, also known as minutiae). See Figure 1.2
for examples of ridges, minutiae, orientation ﬁeld and singular points in a ﬁngerprint

image.

1.10 Fingerprint Veriﬁcation

 

Enrollment Module

  

Feature

  
 

. ]
User Interface

  
   

' Extracto System Database

 

Feature

   
   

 

Feature

User Name

 

Matcher .

   

 

Extractor

Authentication Module

Figure 1.6: System diagram for an automatic veriﬁcation system.

A biometric system can be operated in two modes: 1) veriﬁcation mode and 2)
identiﬁcation mode. In the veriﬁcation mode, a biometric system either accepts or
reJ'ects a user’s claimed identity while a biometric system operating in the identiﬁca-
tion mode establishes the identity of the user without a claimed identity. Fingerprint
identiﬁcation is a more difﬁcult problem than ﬁngerprint veriﬁcation because a huge

nuIllber of comparisons needs to be performed in identiﬁcation. In this thesis, we

19

have focused on a biometric system operating in a veriﬁcation mode and an indexing
scheme (ﬁngerprint classiﬁcation) that can be used in an identiﬁcation system. A
number of civilian applications operate in veriﬁcation mode on a regular basis and
perform identiﬁcation only at the time of the user registration to check the integrity
of the database (e.g., ﬁnding duplicates). For example, in an ATM application, after
a user has been registered and issued an ATM card, the acquired ﬁngerprint needs
to be matched only with a single template ﬁngerprint stored on the ATM card on
each transaction. A typical veriﬁcation system can be divided into two modules: (i)
enrollment and (ii) veriﬁcation. The enrollment module scans the ﬁngerprint of a
person through a sensing device and then stores a representation (called template) of
the ﬁngerprint in the database. The veriﬁcation module is invoked during the opera—
tion phase. The same representation which was used in enrollment phase is extracted
from the input ﬁngerprint and matched against the template of the claimed identity
to give a “yes/ no” answer. On the other hand, an identiﬁcation system matches the
input ﬁngerprint with a large number of ﬁngerprints in the database and as a result,
ﬁngerprint classiﬁcation is effective only in an identiﬁcation system and is not an
issue in a veriﬁcation system. In this thesis, we have used the term “identiﬁcation”
in a loose sense for both the ﬁngerprint veriﬁcation and identiﬁcation problems and

the exact meaning of the term can be resolved based on the context.

The biometric veriﬁcation problem can be formulated as follows. Let the stored
biometric signal (template) of a person be represented as S and the acquired signal

(input) for authentication be represented by I. Then the null and alternate hypotheses

20

 

can be stated as:

H0 : I 75 S, input ﬁngerprint is NOT the same as the template,

H1 : I = S, input ﬁngerprint is the same as the template.

The associated decisions are as follows:

D0 : person is an imposter,

D1 : person is genuine.

The veriﬁcation involves matching S and I using a similarity measure. If the similar-
ity/ matching score is less than some decision threshold T, then decide D0, else decide
D1. The above terminology is borrowed from communications theory where we want
to detect a message in the presence of noise. H0 is the hypothesis that the received
signal is noise alone and H1 is the hypothesis that the received signal is message plus
the noise. Such a hypothesis testing formulation inherently contains two types of
errors: Type I: false acceptance (D1 is decided when H0 is true) and Type II: false
rejection (D0 is decided when H1 is true). The two types of errors are also known as

FAR and F RR, deﬁned as:

False Accept Rate = P(D1|w0),

False Reject Rate = P(D0|w1),

21

where wo is the class associated with H0 2 true and wl is the class associated with
H1 = true. The performance of a biometric system is usually speciﬁed in terms of
its FAR. The decision scheme should establish a decision boundary which minimizes
the FRR for the speciﬁed FAR. There is a trade—off between the two types of errors
and both the errors cannot be reduced simultaneously based on the operating point
alone. The given biometric application dictates the FAR and FRR requirements for
the veriﬁcation system. For example, access to an ATM machine generally needs a

small FRR, but access to a secure military installation requires a very small FAR.

1.11 Information Fusion

A number of ﬁngerprint veriﬁcation systems have been developed and tested on large
databases but most of them are not able to meet the rigid performance requirements in
high security applications. Each ﬁngerprint veriﬁcation system uses different feature
extraction and/ or matching algorithms to generate a matching score which is used for
authentication. It is well known in the pattern recognition literature that different
classiﬁers often Inisclassify different patterns [164, 90]. This suggests that different
classiﬁers offer rather complementary information about the given classiﬁcation task.
A combination scheme which harnesses various information sources is likely to improve
the overall system performance. The outputs of various classiﬁers can be combined
to obtain a decision which is more accurate than the decisions made by any one of
the individual classiﬁers. Similar ideas can be used to combine different ﬁngerprint

matching algorithms as described in Chapter 6.

22

1.12 Feature Veriﬁcation

Ideally, we would like to design pattern recognition systems which make decisions
based on all the information available in the input image. However, traditionally, for
simplicity of design, a sequential approach is often adopted to feature extraction and
matching, where each stage transforms a particular component of the information
relatively independently and the interaction between these components of informa-
tion is limited. Often, the rather simplistic model used in each component (stage)
is not sufﬁcient to capture the entire sensed data. One of the problems with the
sequential approach is that the limited use of information in each stage results in
feature extraction and matching performance artifacts. Even though the sequential
approach is efﬁcient from design and processing point of view, it may introduce er-
rors in the feature extraction and recognition stages. We believe that by reexamining
the original image data, some of the errors in the end-to—end sequential processing
can be eliminated, resulting in an improvement in system performance. The main
limitation of the feature veriﬁcation algorithm is that it cannot address the problem
of missed features. Therefore, the feature detection algorithm should be operated
at a very low false reject rate at the expense of higher false accept rate. The false
accepts of the feature extraction algorithm will be veriﬁed by the feature veriﬁcation
algorithm. Performance can also be improved by feature reﬁnement. See Figure 1.7

for our proposed modiﬁcations to a sequential feature extraction system.

23

Feedback

;_..___..__..____'
I
_I

 

 

Feature
Extraction

I

F-----

Sensed image ~—>

 

 

 

 

 

 

 

 

 

I I
l

. | Feature
Matchmg I Reﬁnement '
l I
~ - - - - - '

 

Figure 1.7: A general pattern recognition system with proposed feedback in feature
extraction and a new feature reﬁnement stage.

1.13 Challenges in Automatic Fingerprint Identi-

ﬁcation

Even though several commercial systems exist for ﬁngerprint-based identiﬁcation
[177], the matching accuracy performance is still not acceptable in many emerg-
ing civilian applications. A ﬁngerprint identiﬁcation system involves several stages.
First, the ﬁngerprint image needs to be acquired and Scanned into a digital repre-
sentation. There is a loss of information when the three-dimensional ﬁngerprint is
scanned into a two-dimensional digital image. Placement of the ﬁnger on the sensor,
cuts and bruises on the ﬁnger and ﬁnger pressure differences cause different impres-
sions of the ﬁngerprint to appear different. It is a challenge for the feature extraction

algorithm to reliably extract a robust representation from these images. Due to the

24

noise present in the ﬁngerprint image because of inexact sensing process, there may be
false features detected or important features missed. The matching algorithm should
recover the invariant information from the features such that it outputs a high score
when matching impressions of the same ﬁnger and a low score when matching the im-
pressions of different ﬁngers. If the ﬁngerprint image is of poor quality, a ﬁngerprint
enhancement algorithm should be used to improve the quality of the image. However,
it is very difﬁcult to design a ﬁngerprint enhancement algorithm that is robust to all
types of noise in the sensed ﬁngerprint. An inappropriate enhancement algorithm

may introduce undesirable artifacts into the ﬁngerprint image.

 

Figure 1.8: An example ﬁngerprint image from the NIST-4 database. The experts
have labeled this image to belong to two classes, right loop, and tented arch.

In a veriﬁcation application, it is very important to make a decision in real time
(~ 1 second) so that the veriﬁcation process does not cause inconvenience to the user.
In an identiﬁcation application, the ﬁngerprint matching should be extremely fast due
to the large number of matchings that must be performed. The matching algorithm
should scale well with large databases, both in terms of time and space. Fingerprint

Classiﬁcation can be used to distribute the ﬁngerprints in a ﬁxed number of bins so

25

that the matching algorithm needs to search only a few bins to ﬁnd the correct match.
FBI requirements for a ﬁngerprint classiﬁcation algorithm are 1% error rate with a
maximum of 20% reject rate. Fingerprint classiﬁcation is a difﬁcult problem for both
the automatic systems and the human experts. For example, about 17% of the images
in the NIST-4 database [41] have two different ground truth labels. This means that
even human experts could not agree on the true class of the ﬁngerprint for about 17%
of the ﬁngerprint images in this database containing 4,000 ﬁngerprint images (see

Figure 1.8 for an example).

1.14 State-Of-the-art in Fingerprint Identiﬁcation

A number of systems exist for ﬁngerprint veriﬁcation as well as classiﬁcation. Even
though National Institute of Standards and Technology (NIST) provides a number of
databases for performance evaluation and benchmark, many companies report results
on their proprietary databases and, therefore, their results cannot be independently
veriﬁed and compared. Some of the ﬁngerprint vendors report extremely low er-
ror rates (see Table 1.1) that are not achieved in research laboratories on realistic
databases. As a comparison, a recent evaluation of various ﬁngerprint veriﬁcation
algorithms on a common database in a laboratory environment reports signiﬁcantly
higher error rates (Table 1.2). The details of this performance evaluation can be
found in [57].

A state—of-the-art ﬁngerprint classiﬁcation algorithm [141] reports accuracies of

92.2% for the ﬁve-class classiﬁcation problem with classes deﬁned as arch, tented arch,

26

Table 1.1: Performance of ﬁngerprint veriﬁcation systems reported by various com-
panies on their web sites. None of the companies mention the database used for
obtaining the performance results, and thus the performance numbers can not be
directly compared. FAR: False Accept Rate; FRR: False Reject Rate.

 

 

 

 

 

 

 

 

 

 

 

 

 

Company (web site) Sensor FAR FRR

(‘70) (‘70)
Biolink USA (biolinkusacom) Optical 0.0000001 0.01
Biometricld (biometricidcom) Optical 0.01 0.01
Startek (startek.com.tw) Optical 0.001 3.3
IOSoftware (iosoftwarecom) Optical 0.1 1
Identix (identixcom) Optical 0.0001 1
NEC (nectech.com) Solid-state 0.0002 0.05
Biometrix Int. (biometrixat) Solid-state 0.001 0.0001
Pollex (pollex.ch) Solid-state 0.001 1
Sony (sony.com) Solid-state 0.001 1

 

 

 

 

left loop, right loop, and whorl, and 94.5% for the four-class classiﬁcation, where the
classes arch and tented arch are merged into one. The state-of-the-art classiﬁcation
systems have not met the FBI standards on any public domain database containing

equal number of patterns from each of the ﬁve ﬁngerprint classes.

1.15 Thesis Objectives

Forensic experts who match ﬁngerprints visually have predominantly used minutiae
features for ﬁngerprint matching for over a century. Similarly, forensic experts have
used the locations of singularities in the ﬁngerprints (e.g., core(s) and delta(s)) to
visually classify ﬁngerprints for indexing purposes. Most of the existing automatic
ﬁngerprint veriﬁcation and classiﬁcation systems use representations that are moti-

vated by the representations used by the forensic experts. In this thesis, we have

27

Table 1.2: Comparison of state-of-the-art ﬁngerprint veriﬁcation algorithms in terms
of equal error rate (ERR) and timing on a database of 800 ﬁngerprints (image size =
448 x 478 captured by DF-90 optical sensor manufactured by Identicator Technology).
Details of the evaluation protocol can be found in [57].

 

 

 

 

 

 

 

Algorithm ERR Avg Enroll Time Avg Match Time Reject Rate
(%) (seconds) (seconds) (%)
Sagl 3.64 5.70 2.13 0.00
Sag2 4.01 1.94 1.94 0.00
Cspn 5.33 0.35 0.35 1.81
Cetp 8.29 1.49 1.66 0.00
Cwai 5.90 0.46 0.57 20.86
Krdl 8.03 1.48 1.60 11.98

 

 

 

 

 

 

 

 

theoretically determined the information content of the traditional minutiae-based
representation and established an upper bound on the performance of ﬁngerprint
veriﬁcation systems based on a minutiae representation. As a result of the limited
information content of the minutiae representation, non-minutiae representations of
ﬁngerprints should be explored. In this thesis, we have developed a novel non-minutiae
representation for ﬁngerprints that combines both the global and the local informa-
tion present in a ﬁngerprint. The proposed representation is based on considering
the ﬁngerprint images as oriented textures, is very different from the representations
used by the forensic experts and is more amenable to automatic systems (in terms of
matching speed and storage size). The performance of this representation is evalu-
ated for both ﬁngerprint classiﬁcation and matching applications on large databases.
We have empirically shown that the proposed representation has a discriminatory
power that is comparable to the minutiae-based representation. A combination of a

matcher based on the proposed representation with two other minutiae-based match-

28

ers signiﬁcantly improves the veriﬁcation performance. We have further shown that a
combination of multiple templates and multiple ﬁngers can signiﬁcantly improve the
performance of a ﬁngerprint veriﬁcation system. A feedback and feature reﬁnement
scheme is proposed in a general pattern recognition framework which improves the
performance of a minutiae-based ﬁngerprint veriﬁcation system. Finally, we show
that the use of all the techniques presented in this thesis signiﬁcantly improve the

performance of a ﬁngerprint veriﬁcation system on a large database.

1.16 Thesis Outline

Chapter 2 discusses the individuality of ﬁngerprints. Chapter 3 describes our novel
ﬁlterbank-based ﬁngerprint representation. A classiﬁcation algorithm based on the
prOposed representation is described in Chapter 4. Chapter 5 describes the ﬁlterbank—
based ﬁngerprint veriﬁcation system and compares it with a state-of-the—art minutiae-
ba88d system. Chapter 6 presents a classiﬁer combination strategy geared towards
deCiSion level fusion in ﬁngerprint veriﬁcation systems. The results of combining four
different ﬁngerprint matchers, two ﬁngers of a person and two impressions of the
same ﬁngerprint are presented. Chapter 7 presents results of minutiae veriﬁcation

and Classiﬁcation. Chapter 8 presents conclusions and future directions.

29

Chapter 2

On the Individuality of

Fingerprints

Fingerprint identiﬁcation is based on two basic premises: (i) persistence: the basic
characteristics of ﬁngerprints do not change with time; and (ii) individuality: the
ﬁngerprint is unique to an individual. The validity of the ﬁrst premise has been
established by the anatomy and morphogenesis of friction ridge skin. While the
second premise has been generally accepted to be true based on empirical results, the
underlying scientiﬁc basis of ﬁngerprint individuality has not been formally tested.
AS a result, ﬁngerprint evidence is now being challenged in several court cases. A
SCientiﬁc basis for eStablishing ﬁngerprint individuality will not only determine the
admissibility of ﬁngerprint identiﬁcation in the courts of law but will also establish
an upper bound on the performance of an automatic ﬁngerprint veriﬁcation system.

The distinguishing nature of physical characteristics of a person is due to both
the inherent individual genetic diversity within the human population as well as the

30

 

random processes affecting the development of the embryo [146, 129]. Since two
individuals can be arbitrarily close with respect to their genetic constitution (e.g.,
identical twins), a pessimistic evaluation of identity discrimination based on biomet-
rics may need to rely solely on an assessment of diversity in the traits due to random
process affecting human development. Such an assessment strategy would necessarily
rely on biometric samples from individuals who are identical / similar in their genetic
constitution. Since identical twins have the closest genetics-based relationship, the
maximum Similarity between ﬁngerprints is expected to be found among them. In
Section 2.1, we have quantiﬁed the role of genetic similarity on the similarity of ﬁnger-
prints and shown that a state-of—the—art automatic ﬁngerprint identiﬁcation system
can successfully distinguish identical twins though with a slightly lower accuracy than
nontwins [21]. The implications of the similarity found in identical twin ﬁngerprints
on the performance of ﬁngerprint identiﬁcation systems is discussed.

The environmental factors during the formation of ﬁngerprints play an important
role in the distinctiveness of ﬁngerprints. To quantify the diversity present in ﬁn-
gerprint patters, we study the amount of information available in minutiae points to
eStablish a correspondence between two ﬁngerprint images in Section 2.2. We derive
an expression which estimates the probability of falsely associating minutiae-based
representations from two arbitrary ﬁngerprints. For example, we show that the prob-
aLbility that a ﬁngerprint with 36 minutiae points will share 12 minutiae points with
8mother arbitrarily chosen ﬁngerprint with 36 minutiae points is 6.10 x 10‘8. These
probability estimates are compared with typical ﬁngerprint matcher accuracy results.

0111‘ results Show that (i) contrary to the popular belief, ﬁngerprint matching is not

31

infallible and leads to some false associations, (ii) the performance of automatic ﬁn-
gerprint matcher does not even come close to the theoretical performance, and (iii)
due to the limited information content of the minutiae-based representation, the au-
tomatic system designers should explore the use of non-minutiae-based information

present in the ﬁngerprints.

2. 1 Genetic Factors

2.1 . 1 Introduction

The extent of variation in a physical trait due to random development process differs
from trait to trait. By deﬁnition, identical twins can not be distinguished based on
DNA. Typically, most of the physical characteristics such as body type, voice, and
face are very similar for identical twins and automatic identiﬁcation based on face and
hand geometry is unlikely to distinguish them. See Figure 2.1 for a photograph of an
identical twin pair. It is, however, claimed that identical twins can be distinguished
based on their ﬁngerprints, retina, thermogram, or iris patterns. The focus of this
study is to empirically determine the similarity of ﬁngerprints in identical twins. We
further attempt to assess the impact of this similarity on the performance of automatic
ﬁngerprint-based veriﬁcation systems. Since both, human iris and angiogenesis follow
a development pattern similar to ﬁngerprints, we believe the results of this study
may be qualitatively applicable to other biometric identiﬁers such as iris, retina and

thermogram patterns as well.

32

 

Figure 2.1: Photograph of identical twin sisters (www.visi.com/~charlesr/).

How does one assess whether two ﬁngerprints are identical? In order to reli—
ably establish whether two prints came from the same ﬁnger or different ﬁngers, it
is necessary to capture some invariant representation (features) of the ﬁngerprints:
the features which over a life-time will continue to remain unaltered irrespective of
the cuts and bruises, the orientation of the print with respect to the medium of the
capture, occlusion of a small part of the ﬁnger, the imaging technology used to ac-
quire the ﬁngerprint from the ﬁnger, or the elastic distortion of the ﬁnger during the

acquisition of the print.

An important question in ﬁngerprint matching is: which characteristics of the
ﬁngerprints are inherited? A number of studies have shown a signiﬁcant correlation
in the ﬁngerprint class (i.e., whorl, right loop, left loop, arch, tented arch) of identical
twin ﬁngers; correlation based on other generic attributes of the ﬁngerprint such as

ridge count, ridge width, ridge separation, and ridge depth has also been found to

33

 

Figure 2.2: Fingerprint images of identical twin sisters captured using an optical
scanner from Digital Biometrics Inc., (a) and (b) are two impressions of the same
ﬁnger of one twin and (c) and (d) are two impressions of the corresponding ﬁnger of
her sibling. Matching score between (a) and (b) is 487, and between (c) and (d) is
510. The matching score between (a) and (c) is 24, and the matching score between
(b) and (d) is 4. The ﬁngerprints of both the twins here have the same type (right
loop) and look similar to untrained eyes. Fingerprint experts, as well as our automatic
ﬁngerprint identiﬁcation system can, however, easily differentiate the twins.

34

be signiﬁcant in identical twins. In dermatoglyphics studies, the maximum global
difference between ﬁngerprints has been found among individuals of different races.
Unrelated persons of the same race have very little global similarity in their ﬁnger-
prints, parent and child have some global Similarity as they share half the genes,
siblings have more similarity and the maximum global similarity is observed in the
monozygotic (identical) twins, which is the closest genetic relationship [79].
Monozygotic twins are a consequence of division of a single fertilized egg into
two embryos. Thus, they have exactly identical DNA except for the generally unde-
tectable micromutations that begin as soon as the cell starts dividing. Fingerprints of
identical twins start their development from the same DNA, so they show consider-
able generic similarity [178]. However, identical twins are situated in different parts of
the womb during development, so each fetus encounters slightly different intrauterine
forces from their siblings. As a result, ﬁngerprints of identical twins have different
microdetails which can be used for identiﬁcation purposes [79]. It is claimed that
a trained expert can usually differentiate between the ﬁngerprints of identical twins
based on the minutiae (dis)similarity [79]. Thus, there is anecdotal evidence that
minutiae conﬁgurations are different in identical twins but to our knowledge, no one
has systematically investigated or quantiﬁed how minutiae information in identical
twins is (un)related in the context of an automatic ﬁngerprint-based authentication
system. The multiple ﬁngerprints of a Single individual also share common genetic
information and a very common development environment. However, this chapter
focuses on analyzing the similarity in ﬁngerprint minutiae patterns in identical twin

ﬁngers.

35

 

Figure 2.3: Minutiae extraction for twins. (a) and (b) are ﬁngerprint images of an
identical twin and his/ her sibling while the ﬁngerprint in (c) is from another person.
(d), (e), and (f) are the minutiae extracted from (a), (b), and (c), respectively using

the extraction algorithm in [11].

36

 

It! ‘ x ”a ”I! is”
Ai‘je it Ber! t
2 P , ){ﬂ . “his r “(at ﬁt“
i’ ~~ r
x I... l, I x ‘9 ti 7‘; El
’. x: :4

Figure 2.4: Minutiae matching for (a) twin-nontwin (matching of Figures 2.3(e) and
2.3(f), matching score = 3 on a scale of 0—999) and (b) twin-twin (matching of Figures
2.3(d) and Figure 2.3(e), matching score = 38 on a scale of 0—999). The “matched”
minutiae pairs are shown by bounding boxes.

 

Figure 2.5: Minutiae matching for two impressions of the same ﬁnger shown in Figures
2.2(a) and 2.2(b) (matching score = 487 on a scale of 0—999). The “matched” minutiae

pairs are shown by bounding boxes.

37

Using an automatic ﬁngerprint biometric system [11], we study the (dis)similarity
between identical twin ﬁngerprints and compare it to the (dis)similarity between two
arbitrary ﬁngerprints. We have conﬁrmed the claim that the identical twin ﬁnger-
prints have a large class correlation, i.e., if one of the identical twin’s ﬁngerprint is
a whorl then it is very likely that the other twin’s ﬁngerprint will also be of whorl
type. We also analyze the correlation between the ﬁngerprint class and the minu-
tiae matching score between two randomly chosen ﬁngerprints. Finally, we stipulate
the implications of the extent of the similarity in identical twin ﬁngerprints to the

performance of a ﬁngerprint—based person veriﬁcation system.

2.1.2 Experimental Results

A randomly chosen subset of the rolled identical twin ﬁngerprints collected for the
National Heart, Lung, and Blood Institute (N HLBI) twin study [66, 168] is used in
our experiments. The ﬁngerprints were acquired using the methods documented in
[169]. The ﬁngerprints of the index ﬁngers of 100 pairs of identical twins were scanned
using an IBM ﬂatbed color scanner in grayscale mode at 500 dpi resolution. Some
of the original ﬁngerprints were in ink while others were taken on a sensitized paper
with ink-less fluid. The latter tend to fade with time. Due to differences in paper
quality and degradation of the print over time, several of these ﬁngerprints are of
poor quality. We rejected some of the very poor quality ﬁngerprints and used only
94 pairs of identical twin ﬁngerprints in our study. See Figures 2.3(a) and (b) for

examples of ﬁngerprint images in our twin database.

38

To study the similarity of identical twin ﬁngerprints, we matched every ﬁngerprint
in our twin database with every other ﬁngerprint. See Figure 2.3 for an example
of minutiae extraction for twin ﬁngerprints. Figures 2.4 and 2.5 show examples of
matching twin-nontwin ﬁngerprints, twin-twin ﬁngerprints, and two impressions of the
same ﬁnger of a person. In Figure 2.6(a), the dash line shows the twin-twin imposter
distribution of matching scores computed by matching a ﬁngerprint with his/her
identical twin sibling (twin-twin match), while the solid line shows the twin-nontwin
imposter distribution of matching scores between a person’s ﬁngerprint and everyone
else except his/ her twin (twin-nontwin match). The twin-twin imposter distribution
was estimated using 188 (94 X 2) matchings between the 94 twin ﬁngerprint pairs in our
identical twin database whereas the twin-nontwin imposter distribution was estimated
using 17, 484 (94 x 93 x 2) matchings. Figure 2.6(a) shows that the twin-twin imposter
distribution is slightly shifted to the right of the twin-nontwin distribution indicating
that twin-twin ﬁngerprints are generally more similar than twin-nontwin ﬁngerprints.
The twin-twin and twin-nontwin distributions are found to be signiﬁcantly different
(greater than 99.99% conﬁdence) using the Kolmogorov-Smirnov test [179].

The genuine distribution of matching scores is estimated by matching multiple
ﬁngerprint images of the same ﬁnger. Since we had access to only a single impression
of the ﬁngers in our twin database, we had to synthesize the genuine distribution for
twin-twin matching. Since the identical twin ﬁngerprint images in our database were
obtained by rolling inked ﬁngers of the subjects by fairly experienced ﬁnger-printers,
we expect the genuine distribution characteristics of the twin database to closely

correspond to that obtained from a standard public domain ﬁngerprint database

39

 

60' . . a w veer: . e -
—- random

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I“ —— twin-nontwin
‘ - twin-twin
50 ~
40 ~
0
U)
a
33° ‘
o
a.
20 ~
10 ~
0 ‘A—Ws— \ In . .. m
101
Matching Score
(a)
10 T . . .
99.5- .
99- , ’ , , - — — :
5‘5 , , ' ’ ’ ' ’ l
2 98.5 r I .
E /
a: 98“ . I a
O /
a / ’
0.97 5 - , , , , ' ’ I a
I
g 97- : 4
.3; ,1
a , , ,
g 96.5 ~ , «
(D , ,
96:” ~
— twin—nontwin
95'5 ~ ~ twin-twin "
—+-— Equal-Error Line
95 1 1 *ﬁ 1 I
0 2 4 6 8 10
False Acceptance Rate (%)
(b)

Figure 2.6: (a) Distribution of matching scores for twin-twin imposter, twin-nontwin
imposter, and genuine ﬁngerprint matchings. (b) ROC curves for twin-twin and twin-
nontwin minutiae pattern matchings.

40

n.‘ -."7u-|—_ —— —

 

 

100 T T T I

99.5 - -

:0
Pro
auto
II

\
\
l

(D
m
f
\
\
I

(D .
\J
l
\
\
\

Genuine Acceptance Rate (%)
(D (D
p) \I
01 01
\
\

‘D
a)
r
\
\
u

 

// —-— between different classes
95.5 r I — — within same class
I —+—— Equal-Error Line

0 2 4 6 8 1 0
False Acceptance Rate (%)

 

 

 

 

 

 

Figure 2.7: Effect of ﬁngerprint class type on the matching score.

(e.g., N IST9 CD No. 1) [42]. This database, consisting of 1, 800 ﬁngerprint images
taken from 900 independent ﬁngers, two impressions per ﬁnger, was used to compute
the genuine distribution which is shown in Figure 2.6(a). This genuine distribution
along with the two “imposter” distributions in Figure 2.6(a) were used to generate the
Receiver Operating Characteristics (ROC) [172, 92] curves shown in Figure 2.6(b).
Figure 2.6(b) shows that, due to the similarity of twin ﬁngerprints, the ability of
the system to distinguish identical twins is lower than its ability to distinguish twin—
nontwin pairs. However, contrary to claims made in the popular press [53], the
automatic ﬁngerprint identiﬁcation system can still be used to distinguish between
identical twins without a drastic degradation in performance. See Figure 2.2 for an
illustration. Table 2.1 shows the trade—off between FARS and F RRS of twin-twin and

twin-nontwin matchings for different thresholds on the matching score.

41

To quantify the performance degradation of a ﬁngerprint veriﬁcation system due
to the inherent twin-twin similarity in ﬁngerprints, we assume that twin-nontwin
imposter distribution is representative of the matchings between unrelated people
(nontwins). Suppose a ﬁngerprint veriﬁcation was set to operate at a decision thresh-
old of T to satisfy the speciﬁed FAR requirements. Now, suppose that identical twins
use this automatic ﬁngerprint identiﬁcation system. Since the twin-twin imposter
distribution in Figure 2.6(a) is slightly to the right of the twin-nontwin distribution,
this will increase the FAR of the system but will have no effect on the FRR. The
FAR for identical twins is generally 2% to 6% higher than twin-nontwin matchings
depending on the system operating point (different thresholds). The quantitative
implication of this in the performance of a ﬁngerprint matching system is as follows.
Suppose our system is developed on ﬁngerprints of unrelated people (nontwins) and
is set to operate at, say, a threshold of 20 which corresponds to an FAR of ~ 1% (see
row 2 of Table 2.1). Now, if 1 million unrelated people (nontwins) used the system,
then, based on our empirical distributions, 10,000 people will be falsely accepted
while 22, 000 people will be falsely rejected. However, if 500, 000 identical twin pairs
(1 million twins) used the system operating at the same threshold of 20, then 48, 000
of these will be falsely accepted while 22,000 people will be falsely rejected. Notice
the increase in the false acceptance rate from 1.02% to 4.79%.

To safeguard against twin fraud, we can set the operating point of our system
pessimistically at a threshold of 26 which corresponds to an FAR of ~ 1% for twin-
twin matchings and an FAR of ~ 0.3% for twin-nontwin matchings. This raises

the FRR to ~ 3.5% as opposed to 2.2% when operating at a threshold of 20. This

42

Table 2.1: False accept and false reject rates with different threshold values for the
twin database.

 

 

 

 

 

Threshold F RR FAR (twin—twin) FAR (twin-nontwin)
T (%) (%) (%)
16 1.05 8.51 2.20
20 2.20 4.79 1.02
24 3.00 2.13 0.48
26 3.49 1.06 0.29

 

 

 

 

 

 

means that in the worst case scenario (when all the people accessing the system
are twins), the system will falsely accept 10,000 people out of one million at the
expense of falsely rejecting 35,000 people. In the best case (when there are no twins
accessing the system), only 3, 000 people will be falsely accepted while falsely rejecting
35, 000 people. In practice, the system will falsely accept between 3, 000 and 10, 000
people (between 0.3% and 1% ), depending upon the fraction of twins in our sample
population of 1 million while falsely rejecting 35, 000 people.

Dermatoglyphics studies have suggested that there is a large correlation between
the ﬁngerprint types of identical twins. To conﬁrm this claim, we manually classiﬁed
the 94 pairs of identical twin ﬁngerprints in our database into ﬁve classes (right loop,
left loop, whorl, arch, and tented arch). The class correlation between the index
ﬁngers of identical twins is found to be 0.775 (fraction of identical twin pairs whose
index ﬁngerprints have the same class label). The natural proportion of occurrence
of each of the ﬁve major classes of ﬁngerprints in the index ﬁnger is 0.3252, 0.3648,
0.1703, 0.0616, and 0.0779 for whorl (W), right loop (R), left loop (L), arch (A),
and tented arch (T), respectively [173]. If we randomly choose two index ﬁngerprint

images from a large database, the probability that these two ﬁngerprints will have

43

 

the same class label is equal to 19%,, +ij +19% +10% +10%, i.e., 0.2718, where pw, pg, 191,,
19,4, and pT, are the probabilities of a ﬁngerprint chosen at random belonging to the
class of whorl, right loop, left loop, arch, and tented arch, respectively. Thus, there is
only 0.2718 chance that two randomly chosen index ﬁngers will have the same type
which is much lower than the 0.775 chance that the ﬁngerprints of two identical twins
will have the same class label.

We believe that the global similarity of ﬁngerprints (shown as class similarity) is,
to a certain extent, responsible for the local similarity (shown in the matching per-
formance). Consider two ﬁngerprints that belong to the same class (e.g., right loop).
Since the minutiae can exist only along the ridges (although at random locations),
the matching score between these two ﬁngerprints is likely to be higher than the
matching score between two sets of random point patterns. To study the correlation
of class information with the matching performance, we used the NIST4 database [41]
which has 4, 000 ﬁngerprint images collected from 2, 000 independent ﬁngers with 800
ﬁngerprints from each of the ﬁve classes.

We computed the genuine distribution from 3,600 matchings between the two
impressions of the same ﬁnger from 1, 800 good quality ﬁngerprint pairs from the
NIST4 database. The between-class and within-class distributions were computed
from about 130, 000 matchings each. The ROCs for between-class and within-class
matchings are shown in Figure 2.7. Note that the matching performance is better for
ﬁngerprints belonging to different classes compared to ﬁngerprints belonging to the
same class. Also, the magnitude of the shift between the two ROCs in Figure 2.7 is

of the same order of magnitude as the one manifested in Figure 2.6(b). Thus, we

44

have shown that the minutiae-based similarity in identical twin ﬁngerprints, is of the
same order as the similarity between unrelated people who have the same ﬁngerprint
class label. Hence, the larger similarity observed in identical twins is due to the high

class correlation in their ﬁngerprint types.

2.1.3 Summary

One out of every eighty births results in twins and one third of all the twins are
monozygotic (identical) twins [86]. Some identical twins have been reported to be
involved in fraud, which can be called “twin fraud”, since people mistake the identities
of the identical twins. The childhood mischief by the identical twins of switching
places on their teachers and taking each other’s exams may grow into serious criminal
activities in adulthood such as buying a single insurance for identical twin siblings
or claiming welfare beneﬁts twice when only one sibling is unemployed. There have
been cases reported where an identical twin was sentenced for a crime that was
committed by his/ her sibling [53]. Fertility treatments have resulted in an increase in
the identical twin birth rate (in fact, according to a study by Robert Derom [53], the
identical twin birth rate is about twice as high for women who use fertility drugs).
Further, because of the medical advances in the treatment of premature babies, the

population of identical twins is increasing.

We have shown that even though identical twin ﬁngerprints have large class cor-
relation, they can still be distinguished using a minutiae-based automatic ﬁngerprint

identiﬁcation system; though with a slightly lower accuracy than nontwins. Our re-

45

sults suggest that the marginal degradation in performance may be related to the

dependence of the minutiae distribution on ﬁngerprint class.

What are the implications of our empirical results in person identiﬁcation ap—
plications? In authentication applications, marginal degradation in accuracy perfor-
mance will have almost no effect on “evil” twins posing as impostors. In large scale
ﬁngerprint based identiﬁcation applications, a small degradation in authentication
accuracy may imply a signiﬁcant degradation in the recognition accuracy. Further,
if the degradation in the performance is dependent on the class correlation which in
turn depends on the genetic constitution (as suggested by the dermatoglyphics stud-
ies), it may imply that beneﬁts reaped by composition of ten-ﬁnger information may
have been overestimated in the literature. Further, the magnitude of performance
degradation of a minutiae-based ﬁngerprint matcher may depend upon the genetic
relationship among a target population corpus. Both of these effects may need further
investigation; more research is necessary for class-independent minutiae-based match—
ers. Since the accuracy performance of a minutiae-based ﬁngerprint matcher degrades
with genetic Similarity in the population, alternate independent representations of ﬁn—
gerprints should be explored that can be combined with the minutiae representation
to yield a more accurate automatic ﬁngerprint matching system. Finally, ﬁngerprint
classiﬁcation applications used for the binning of population to increase efﬁciency of

ﬁngerprint based search may not be very efﬁcient in genetically related population.

46

m‘.

2.2 Environmental Factors

2.2.1 Introduction

Our interest in the ﬁngerprint individuality problem is twofold. Firstly, a scientiﬁc
basis (reliable statistical estimate of the matching error) for ﬁngerprint comparison
can determine the admissibility of ﬁngerprint identiﬁcation in the courts of law as
an evidence of identity. Secondly, it can establish an upper bound on the perfor—
mance of an automatic ﬁngerprint veriﬁcation system. Here, we develop a ﬁngerprint
individuality model that attempts to estimate the probability of a false association.
We use this model to establish an upper bound on the performance of a ﬁngerprint
veriﬁcation system [11].

In order to solve the individuality problem, we need to ﬁrst deﬁne a priori the
representation of a ﬁngerprint (pattern) and the metric for the similarity. Finger-
prints can be represented by a large number of features, including the overall ridge
flow pattern, ridge frequency, location and position of singular points (core(s) and
delta(s)), type, direction, and location of minutiae points, ridge counts between pairs
of minutiae, and location of pores (see Figures 2.8(a) and (b)). All these features
contribute in establishing ﬁngerprint individuality. In this study, we have chosen
minutiae representation of the ﬁngerprints because it is utilized by forensic experts,
has been demonstrated to be relatively stable and has been adopted by most of the
automatic ﬁngerprint matching systems.

Given a representation scheme and a similarity metric, there are two approaches

for determining the individuality of the ﬁngerprints. In the empirical approach, repre-

47

Ending Core

 

Delta Pores _Ridge_
Bifurcatlon

Figure 2.8: A ﬁngerprint image of type “right loop”. The overall ridge structure,
singular points, and sweat pores are shown.

sentative samples of ﬁngerprints are collected and using a typical ﬁngerprint matcher,
the accuracy of the matcher on the samples provides an indication of the uniqueness
of the ﬁngerprint with respect to the matcher. There are known problems (and costs)
associated with collection of the representative samples. In a theoretical approach to
individuality estimation, one models all realistic phenomenon affecting inter-class and
intra—class pattern variations. Given the similarity metric, one could then, theoreti-
cally estimate the probability of a false association. Theoretical approaches are often
limited by the extent to which the assumed model conforms to the reality. In this

work, we emphasize the theoretical formulation of the ﬁngerprint individuality model

48

based on a number of parameters derived from a database of ﬁngerprint images. We
also juxtapose the probabilities obtained from individuality model with the empirical
matcher accuracy results.

Minutiae patterns are generated by the underlying ﬁngerprints which are smoothly
ﬂowing oriented textures. The minutiae points are not randomly distributed since the
positions are determined by the ridges (see Figure 2.9). Further, the orientations of
nearby minutiae are strongly correlated. Thus, the conﬁguration space spanned by
the minutiae pattern is smaller than that spanned by a pattern of (directed) random
points. This typically implies that the probability of ﬁnding sufﬁciently similar prints
from two different ﬁngers is higher than that of ﬁnding sufﬁciently similar sets of
random (directed) point patterns. In our study, we have imposed realistic ﬁngerprint
structural (e.g., ridge/valley position, ridge orientation) constraints on a random
point conﬁguration space to derive a more effective estimate of the probability of
false association.

The total number of degrees-of-freedom of the pattern space (e. g., minutiae conﬁg-
uration space) does not directly relate to the discriminability of the different patterns
(e.g., minutiae from different ﬁngers). The effective estimation of discriminatory in-
formation can only be achieved by taking into account intra-pattern variations [16].
There are several sources of variability in the multiple impressions of a ﬁnger [11]:
non-uniform contact (with the sensor), irreproducible contact, inconsistent contact,
and imaging artifacts. This variability in multiple impressions of a ﬁnger manifests
itself in (i) detection of spurious minutiae or missing genuine minutiae, (ii) displace-

ment / disorientation (also called deformation) of the genuine detected minutiae, and

49

‘1 o‘-.-'I.'. -‘l

 

(iii) transformation of the type of minutiae (connective ambiguity). This entails de-
signing a similarity metric (matcher) that accommodates these intra—class variations.
As a result, the probability of false association increases signiﬁcantly.

Most of the earlier approaches did not explicitly incorporate these (intra—class)
variabilities into their individuality models (see [47] for a critical review of several
models) and, therefore, overestimate the ﬁngerprint individuality. Since most of the
existing models of individuality do not address the problems associated with oc-
currence of spurious minutiae or missing genuine minutiae, they do not provide a
systematic framework to address issues related to a partial representational match
between two ﬁngerprints (e.g., what is the probability of ﬁnding 7 matched minutiae
in two ﬁngerprints with 18 and 37 minutiae, respectively?) This is very important
in an automatic ﬁngerprint matching system (feature extraction algorithms are not
as accurate as a well-trained ﬁngerprint expert in detecting minutiae) and in match-
ing latents (where a print depicting a small portion of a ﬁnger is matched against a
print depicting a full ﬁnger). Although, in a manual ﬁngerprint matching procedure,
the likelihood of detecting false minutia is signiﬁcantly smaller than that in an auto—
matic system, the prints imaged from different portions of ﬁngers may give rise to the
variability in the number of detected minutia. Our approach not only explicitly mod-
els the situation of partial representational match but also incorporates constraints
on the conﬁguration space due to intra-pattern variations (e.g., number of minutia,
minutia position/ orientation, image area) based on empirical estimates derived from
the ground truth data marked on ﬁngerprints obtained in a realistic environment.

The rest of the Chapter is organized as follows. Section 2.2.2 presents a summary

50

of major ﬁngerprint individuality studies and compares the probability of a ﬁnger-
print conﬁguration obtained by different models. Section 2.2.3 presents the proposed
ﬁngerprint individuality model, and section 2.2.4 presents the results. Summary and

discussions are presented in section 2.2.5.

2.2.2 Background

The early individuality studies typically focused on a predominantly minutiae-based
representation; some studies explicitly factored in ﬁngerprint class (e.g., right loop,
left loop, whorl, arch, tented arch, etc.) information. The type, direction, and lo-
cation of minutiae were the most commonly used features in the early individuality
studies. See Table 2.2 for a comparison of the features used in ﬁngerprint individual-
ity models. The types of minutiae used varies from one study to other: some studies
used two minutia types (ending and bifurcation) whereas others used as many as 13
types of events (e.g., empty cell, ridge ending, ridge fork, island, dot, broken ridge,
bridge, spur, enclosure, delta, double fork, trifurcation, multiple events) [94]. Later
models considered additional features to determine the probability of occurrence of a

particular ﬁngerprint conﬁguration (e.g., ridge counts [47], sweat pores [29]).

Most of the early individuality studies examined the distinctiveness of a por-
tion/ feature of the ﬁngerprint. Under simplifying assumptions (e.g., implicit assump-
tions about statistical independence of events and the corresponding event distribu-
tions are identical), these studies estimated the distinctiveness of the entire ﬁngerprint

(total pattern variation) by collating the distinctiveness in the feature extracted from

51

ﬁngerprints (total feature variation). We will refer to these total pattern variation-
based ﬁngerprint individuality estimates as the probability of ﬁngerprint conﬁguration.

‘ A summary of these studies is presented below.

The ﬁngerprint individuality problem was ﬁrst addressed by Galton in 1892 [70],
who considered a square region spanning six-ridges in a given ﬁngerprint. He assumed
that, on an average, a ﬁngerprint can be covered by 24 such six-ridge wide independent
square regions. Galton estimated that he could correctly reconstruct any of the
regions with a probability of %, by looking at the surrounding ridges. Accordingly,
the probability of a speciﬁc ﬁngerprint conﬁguration, given the surrounding ridges
is (%)24. He multiplied this conditional (on surrounding ridges) probability with the
probability of ﬁnding the surrounding ridges to obtain the probability of occurrence
of a ﬁngerprint as

1 1 1 2“
P(Fingerprint Conﬁguration) 2 E x ﬂ x (2) = 1.45 x 10‘“, (2.1)

where % is the probability of occurrence of a speciﬁc ﬁngerprint type (such as arch,
tented arch, left loop, right loop, double loop, whorl, etc.) and 5&7). is the probability
of occurrence of the correct number of ridges entering and exiting each of the 24
regions. Eq. (2.1) gives the probability that a particular ﬁngerprint conﬁguration in
an average size ﬁngerprint (containing 24 regions deﬁned by Galton) will be observed
in nature. Roxburgh [170], Pearson [98], and Kingston [39] objected to Galton’s
assumption that the probability of occurrence of any particular ridge conﬁguration

in a six—ridge square is %, and claimed that Eq. (2.1) grossly underestimated the

52

 

ﬁngerprint individuality (i.e., overestimated the probability of occurrence). Pearson
[98] argued that there could be 36 (6 x 6) possible minutiae locations within one of
Galton’s six-ridge-square regions, leading to a probability of occurrence of a particular
ﬁngerprint conﬁguration of

1 1 1 2“
P(Fingerprint Conﬁguration) = 16 x 25—6 x (36) = 1.09 x 10"“. (2.2)

A number of subsequent models (Henry [64], Balthazard [176] (cf. [47]). Bose [47],
Wentworth and Wilder [36], Cummins and Midlo [79], and Gupta [161]) are interre-
lated and are based on a ﬁxed probability, p, for the occurrence of a minutiae. They

compute the probability of a particular N —minutiae ﬁngerprint conﬁguration as
P(Fingerprint Conﬁguration) = pN . (2.3)

In the following, we provide the values of p used in various studies. In most cases,

the authors do not present any details on how they arrived at their choice of p.

0 Henry [64] chose p = i and added 2 to the number of minutiae, N, if the
ﬁngerprint type and core-to-delta ridge count could be determined from the

given (latent) ﬁngerprint.

o Balthazard [176] also set p = 211-, under the assumption that there are four types
of equally likely minutiae events: (i) fork (bifurcation) to the right, (ii) fork to

the left, (iii) ending to the right, and (iv) ending to the left.
0 Bose [47] adopted p = %, under the assumption that there are four possibilities

53

in each square region of one ridge-interval width in a ﬁngerprint: (i) a dot, (ii)

a fork, (iii) an ending, and (iv) a continuous ridge.
0 Wentworth and Wilder [36] chose 5% as the value of p.

o Cummins and Midlo [79] adopted the same value of p as Wentworth and Wilder,
but introduced a multiplicative constant of % to account for the variation in

ﬁngerprint pattern type.

0 Gupta [161] estimated the value of p as 116 for forks and endings, and Till—0 for the

less commonly occurring minutiae types, based on 1,000 ﬁngerprints. He also

used a ﬁngerprint—type-factor of ﬂ and correspondence—in-ridge-count-factor of

i
10'

Because of the widely varying values of p used in the above studies, the probability
of a given ﬁngerprint conﬁguration also dramatically varies from one model to the
other.

Roxburgh [170] proposed a more comprehensive analysis to compute the probabil—
ity of a ﬁngerprint conﬁguration. His analysis was based on considering a ﬁngerprint
as a pattern with concentric circles, one ridge interval apart, in a polar coordinate
system. Roxburgh also incorporated a quality measure of the ﬁngerprint into his
calculations. He computed the probability of a particular ﬁngerprint conﬁguration to
be:

C Q N
P(Fingerprint Conﬁguration) = (F) (W) , (2.4)

where P is the probability of encountering a particular ﬁngerprint type and core type,

54

Q is a measure of quality (Q = 1.5 for an average quality print, Q = 3.0 for a poor
quality print), R is the number of semicircular ridges in a ﬁngerprint (R = 10), T is
the corrected number of minutiae types (T = 2.412), and C is the number of possible
positions for the conﬁguration (C = 1). Amy [102] (cf. [47]) considered the variability
in minutiae type, number, and position in his model for computing the probability of
a ﬁngerprint conﬁguration. He further recognized that K multiple comparisons of the
ﬁngerprint pair (e.g., each hypothesized orientation alignment, each reference point

correspondence) increase the possibility of false association which is given by

P(False Association) 2 1 — (1 — P(Fingerprint Conﬁguration))K . (2.5)

Kingston’s [39] model, which is very similar to Amy’s model, computes the probability
of a ﬁngerprint conﬁguration based on the probabilities of the observed number of

minutiae, observed positions of minutiae, and observed minutiae types as follows:

N
P(Fingerprint Conﬁguration) 2 (e'y)(yN/Nl)(P1) 11(1),)
i=2

(0.082)
[s — (2' -— 1)(0.082)]’

(2.6)

 

where y is the expected number of minutiae in a region of given size S (in mm?) and

P,- is the probability of occurrence of a particular minutiae type.

Most of the models discussed above implicitly assume that ﬁngerprints are being
matched manually. The probability of observing a given ﬁngerprint feature is esti-
mated by manually extracting the features from a small number of ﬁngerprint images.

Champod and Margot [37] used an AF IS to extract minutiae from 977 ﬁngerprint im-

55

Table 2.2: Fingerprint features used in different models.

 

 

Author

Fingerprint features used

 

Galton (1892)

ridges, minutiae types

 

Pearson (1930)

ridges, minutiae types

 

Henry (1900)

minutiae locations,
types, core-to—delta ridge count

 

Balthazard (1911)

minutiae locations, two types,
and two directions

 

Bose (1917)

minutiae locations and three types

 

Wentworth & Wilder (1918)

minutiae locations

 

Cummins & Midlo (1943)

minutiae locations, types,
core-to-delta ridge count

 

Gupta (1968)

minutiae locations and types,
types, ridge count

 

Roxburgh (1933)

minutiae locations, two minutiae types,

two orientations, ﬁngerprint and core types,
number of possible positionings, area,
ﬁngerprint quality

 

Amy (1948)

minutiae locations, number,
types, and orientation

 

Trauring (1963)

minutiae locations,
two types, and two orientations

 

Kingston (1964)

minutiae locations,
number, and types

 

Osterburg et al. (1980)

minutiae locations and types

 

 

Stoney et al. (1986)

 

minutiae locations,

distribution, orientation, and types, variation
among prints from the same source, ridge
counts, and number of alignments

 

56

 

Table 2.3: Comparison of probability of a particular ﬁngerprint conﬁguration using
different models. For a fair comparison, we do not distinguish between minutiae
types. By assuming that an average size ﬁngerprint has 24 regions (R = 24) as
deﬁned by Galton, 72 regions (M = 72) as deﬁned by Osterburg et al., and has 36
minutiae on an average (N = 36), we compare the probability of observing a given
ﬁngerprint conﬁguration in the third column of the table. The probability of observing
a ﬁngerprint conﬁguration with N = 12, and equivalently, R = 8, is given in braces
in the third column. Note that all probabilities represent a full (N minutiae) match
as opposed to a partial match (see Table 2.5).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Author P(Fingerprint Conﬁguration) N =36,R=24,M=72
(N=12,R=8,M=72)
R .—
Galton (1892) T16 x g x (%) 1.45 x 10 11
(9.54 x 10‘7)
Pearson (1930) % x if)? x (Ill—6)“ 1.09 x 10‘41
(8.65 x 10’”)
Henry (1900) (%)” 1.32 x 10-23
(3.72 x 10‘9)
Balthazard (1911) (21)“ 2.12 x 10-22
(5.96 x 10-8)
Bose (1917) (%)” 2.12 x 10—22
(5.96 x 10’8)
Wentworth & Wilder (1918) (%)]V 6.87 x 10"62
(4.10 x 10‘21)
Cummins & Midlo (1943) % x (%)N 2.22 x 10-63
(1.32 x 10’22)
Gupta (1968) 1%, x 1—10 x (315)“ 1.00 x 10-38
(1.00 x 10’”)
1 1.5 N _47
Roxburgh (1933) m x (——10x2'412) 3.75 x 10
(3.35 x 10-18)
Trauring (1963) (0.1944)N 2.47 x 10‘26
(2.91 x 10‘9)
Osterburg et al. (1980) (0.766)M’N(0.234)N 1.33 x 10“27
(3.05 x 10‘15)
Stoney (1985) g x 0.6 x (0.5 x 104$)”-I 1.2 x 10-80
(3.5 x 10‘26)

 

 

 

57

ages scanned at a relatively high resolution of 800 dpi. They generated frequencies
of minutiae occurrence and minutiae densities after manually verifying the thinned
ridges produced by the AFIS to ensure that the feature extraction algorithm did not
introduce errors. They considered minutiae only in concentric bands (ﬁve ridges wide)
above the core and acknowledged that their individuality estimates were conservative
(i.e., provided an upper bound). As an example, they estimated the probability of
occurrence of a seven-minutiae conﬁguration (ﬁve endings and two bifurcations) as
2.25 x 10‘5.

Osterburg et al. [94] divided ﬁngerprints into discrete cells of size 1 mm x 1 mm.
They computed the frequencies of 13 types of minutiae events (including an empty
cell) from 39 ﬁngerprints (8,591 cells) and estimated the probability that 12 ridge
endings will match between two ﬁngerprints based on an average ﬁngerprint area of
72 mm2 as 1.25 x 10‘2”. Sclove [157] modiﬁed Osterburg et al.’s model by incor-
porating the observed dependence of minutiae occurrence in cells and came up with
an estimate of probability of ﬁngerprint conﬁguration that is slightly higher than
that obtained by Osterburg et al. Stoney and Thornton [47] criticized Osterburg et
al.’s and Sclove’s models because these models did not consider the ﬁngerprint ridge
structure, distortions, and the uncertainty in the positioning of the grid. Stoney and
Thornton [47] critically reviewed earlier ﬁngerprint individuality models and proposed
a detailed set of ﬁngerprint features that should be taken into consideration. These
features included ridge structure and description of minutiae location, ridge counts
between pairs of minutiae, description of minutiae distribution, orientation of minu-

tiae, variation in minutiae type, variation among ﬁngerprints from the same source,

58

number of positions (different translations and rotations of the input ﬁngerprint to
match with the template), and number of comparisons performed with other ﬁnger-

prints for identiﬁcation.

Stoney’s [49] model is different from other models in that it attempts to character-
ize a signiﬁcant component of pairwise minutiae dependence. Stoney [49] and Stoney
and Thornton [47] studied probabilities of occurrences of various types of minutiae,
their orientation, number of neighboring minutiae, and distances/ ridge counts to the
neighboring minutiae. Given a minutiae set, they calculated the probability of a
minutiae conﬁguration by conjoining the probabilities of the individual events in the
conﬁguration. For instance, they proposed a linear ordering of minutiae in a minutia
conﬁguration and recursively estimated the probability of a n-minutiae conﬁguration
from the probability of a (n — 1)-minutiae conﬁguration and the occurrence of a new
minutiae of certain type/orientation at a particular distance/ridge counts from its
nearest minutiae within the (n — 1)-minutiae conﬁguration. The model also incor-
porated constraints due to connective ambiguity and due to minutia-free areas. The
model corrected for the probability of false association by accounting for the various
possible linear orderings which could initiate/ drive the search for correspondence. A
sample calculation for computing the probability of a false association using Stoney’s

model is given below.

a

_ l
P(False Association) = 1 _ (1 _ 0.6 * (0.5 x 10.3)(N 1))

N _
z 3— x 0.6 * (0.5 x 10—3)‘N 1) . (2.7)

59

For the sake of simplicity, we have considered only a rudimentary version of Stoney’s
model for the above computation; it is arbitrarily assumed that the probability of
a typical starting minutia is 0.6, a typical neighboring minutia places an additional
constraint of 5 X 10‘3 on the probability, and there are no constraints due to connective
ambiguity, minutia-free areas or minutia-free borders are assumed. Finally, it is
(arbitrarily) assumed that one in every ﬁve minutia can potentially serve as a starting
point for a new search. We believe that a more realistic estimation of the individuality
based on Stoney’s model would not deviate from the simplistic estimation presented
here by more than a couple of orders of magnitude.

Stoney and Thornton identiﬁed weaknesses in their model and acknowledged that
one of the most critical requirements, i.e., consideration of variation among prints
from the same source, is not sufﬁciently addressed in their model. Their tolerances
for minutiae position were derived from successive printings under ideal conditions
and are far too low to be applicable in actual ﬁngerprint comparisons.

The models discussed above (including Amy’s model of false association due to
multiple comparisons) concentrated mainly on measuring the amount of detail in a
single ﬁngerprint (i.e., estimation of the probability of a ﬁngerprint conﬁguration).
These models did not emphasize the intra—class variations in multiple impressions of a
ﬁnger. We will refer to the quantiﬁcations of ﬁngerprint individuality which explicitly
consider the intra-class variations as the probability of correspondence. ’I‘rauring [125]
was the ﬁrst to concentrate explicitly on measuring the amount of detail needed to
establish correspondence between two prints from the same ﬁnger using an AFIS and

observed that corresponding ﬁngerprint features could be displaced from each other

60

by as much as 1.5 times the inter-ridge distance. He further assumed that (i) minu-
tiae are distributed randomly, (ii) there are only two types of minutiae (ending and
bifurcation), (iii) the two types of minutiae are equally likely, (iv) the two possible
orientations of minutiae are equally likely, and (v) minutiae type, orientation, and po-
sition are independent variables. Tfauring computed the probability of a coincidental

correspondence of N minutiae between two ﬁngerprints to be:

P(Fingerprint Correspondence) 2 (0.1944)N. (2.8)

Stoney and Thornton’s [47] criticism of the Trauring model is that he did not consider
ridge count, connective ambiguity, and correlation among minutiae location. Further,
they claim that Trauring’s assumption that the minutiae types and orientations are
equally probable is not correct. The probabilities of observing a particular minutiae

conﬁguration from different models are compared in Table 2.3.

There have been a few studies which empirically estimate the probability of ﬁnd-
ing a ﬁngerprint in a large database that successfully matches the input ﬁngerprint.
Meagher et al. [151] (for more details see Stiles [123]) matched about 50,000 rolled
ﬁngerprints belonging to the same ﬁngerprint class (left loop) with each other to
compute the impostor distribution. However, the genuine distribution was computed
by matching each ﬁngerprint image with itself; this ignores the variability present in
different impressions of the same ﬁnger. Further, they assumed that the impostor and
the genuine distributions follow a Gaussian distribution and computed the probability

of a false association to be 10—97. This model grossly underestimates the probability

61

of a false association because it does not consider realistic intra-class variations in

impressions of a ﬁnger (see also, Stoney et al. [47] and Wayman [91]).

2.2.3 A Model of Fingerprint Individuality

We have developed a model to obtain a realistic and more accurate probability of
correspondence between ﬁngerprints. The probabilities obtained using this model will
be compared against empirical values using an automatic ﬁngerprint matching system
(AFMS) [11] (an AFIS is used for identiﬁcation; an AF MS is used for veriﬁcation).

To estimate the probability of correspondence, we make the following assumptions:

1. We consider only minutiae features since (i) most of the discriminatory power of
the AFMS is based on minutiae features, and (ii) for an objective measurement
of individuality, it is necessary that the representation be consistently repro-
ducible, easily localized, and quantiﬁed. Minutiae features have been shown
to be stable and practical systems have demonstrated a reliable extraction of
minutia representation from ﬁngerprints of reasonable image quality. Only ridge
endings and ridge bifurcations are considered because the occurrence of other
minutiae types such as islands, dots, enclosures, bridges, double bifurcations,
trifurcations, etc. is relatively rare. Additionally, we do not distinguish be—
tween the two types of minutiae because ridge endings and ridge bifurcations
can not be accurately discriminated. Since minutiae can reside only on ridges
which follow certain overall patterns in a ﬁngerprint, the minutiae directions are

not completely independent of the minutiae locations. We implicitly model the

62

statistical dependence between minutiae directions and locations in our model.
Finally, we have not considered the pairwise minutiae features such as ridge

counts in the present analysis.

. We assume a uniform distribution of minutiae in a ﬁngerprint with the re-
striction that two minutiae cannot be very close to each other. While minu-
tiae locations are not uniformly distributed, our assumption approximates the
slightly overdispersed uniform distribution found by Stoney [48]. Sclove [157]
showed that the minutiae tend to cluster. We have not explicitly modeled the
clustering tendency of minutiae. Therefore, the assumption of independence
of minutiae locations will bias the estimate of the probability of a false asso—
ciation towards higher values. However, it is a common practice in ﬁngerprint
individuality studies to make conservative (higher) estimates of the probability
of correspondence. Both Sclove [157] and Osterburg et al. [94] discuss how
these conservative estimates favor a suspect in a criminal investigation, in the
sense that it gives the suspect the beneﬁt of the doubt by lowering the certainty

attached with the ﬁngerprint matching.

. Correspondence of a minutiae pair is an independent event and each corre—
spondence is equally important. Fingerprint matching systems weigh different
correspondence based on their position (e. g., correspondences involving minu-
tiae from peripheral pattern area are weighted less than those minutiae located
in the center of the ﬁngerprint). Similarly, it is possible to weight spatially

diverse correspondences more than all correspondences localized in a narrow

63

spatial neighborhood. Our analysis currently ignores such dependencies among

the minutiae correspondences.

. We do not explicitly take into account ﬁngerprint image quality in individu-
ality determination. It is very difﬁcult to reliably assign a quality index to a
ﬁngerprint because image quality is a subjective concept. Our approach to in-
corporating image quality in ﬁngerprint matching assumes that only a subset
of the true minutiae in a ﬁngerprint will be detected. All correspondences are
considered reliable and no certainty is associated with a correspondence based
on the ﬁngerprint image quality. In good quality ﬁngerprints, one could use
conﬂicting evidence (when a minutia in input does not match any minutiae in
template) to reject the hypothesis that the input and the template ﬁngerprints
are the same. However, there will be some errors in identifying minutiae in ﬁn-
gerprints with poor quality. Therefore, we explicitly consider only the positive
evidence from a minutiae correspondence; the negative information from the

conﬂicting evidence (e.g., a minutia that does not match) is ignored.

. Ridge widths are same across the population and spatially uniform in the same
ﬁnger. This assumption is justiﬁed because the pressure variations could make
non-uniform ridge variations uniform and vice versa. Further, there may be

only limited discriminatory information in the ridge frequency.

. The analysis of matchings of different impressions of the same ﬁnger binds the
parameters of the probability of matching minutiae in two ﬁngerprints from

different ﬁngers.

64

7. We assume that there exists one and only one alignment between the template

and the input minutiae sets.

The ﬁngerprint correspondence problem involves matching two ﬁngerprints; one
is called the template (stored in the system) and the other is called the input (which
needs to be veriﬁed). We assume that a reasonable alignment has been established
between the template and the input. The alignment of the input minutiae set with the
template minutiae set is done so that the minutiae correspondences can be determined
in a small tolerance. In manual ﬁngerprint matching, this alignment is typically
based on aligning the ﬁngerprint singularities (core(s) and delta(s)) and ridges. An
automatic system may seek an alignment that maximizes a given objective function
(such as the number of matching minutiae). This assumption may not be valid when
matching a partial (latent) ﬁngerprint with a full print in the database, as there may
be several “reasonable” alignments possible. When multiple alignments are indeed

warranted by a situation, the probability of false association increases (see Eq. (2.5)).

Given an input ﬁngerprint containing n minutiae, our goal is to compute the
probability that any arbitrary ﬁngerprint (template in a database of ﬁngerprints)
containing m minutiae will have exactly q corresponding minutiae with the input.
Since we only consider ﬁngerprint minutiae which is deﬁned by its location, (:13, y),
and by the angle of the ridge on which it resides, 6, the input and the template

minutiae sets, T and I, respectively, are deﬁned as:

65

_._——-~—‘——

~—

 

Figure 2.9: Automatic minutiae matching. Two impressions of the same ﬁnger were
matched in (a) 39 minutiae were detected in input (left), 42 in template (right),
and 36 “true” correspondences were found. Two different ﬁngers are matched in
(b) 64 minutiae were detected in input (left), 65 in template (right), and 25 “false”
correspondences were found.

66

Area of Tolerance (C) Image Area
\ /

 

9

 

 

 

I \
Minutia Area of Overlap (A)

Figure 2.10: Fingerprint and minutiae.

'i
ll

{{I1,y1.91},{12.y2,92}. ...,{rm,ym,0m}} , (2.9)

N
ll

{Ix/1: yi. 0’1}, {$3, yin 9’2}, {mini/1v 01d}- (210)

Once an alignment between the input minutiae set and the template minutiae set
is established, we develop our individuality model. Let us ﬁrst model the intra—class

variation. A minutiae j in the input ﬁngerprint is considered as “corresponding” or

67

“matching” to the minutiae i in the template, if and only if

 

\/(171— $3)? + (y1- — yj)2 _<_ r0, and (2.11)

min<l6:—0.l,36o—Iez— .0 s a... (2.12)

where r0 is the tolerance in distance and 60 is the tolerance in angle. Both manual
and automatic ﬁngerprint matchings are based on some tolerance both in minutiae
location and angle to account for the variations in different impressions of the same
ﬁnger. Eq. (2.12) computes the minimum of |t91 — (9,] and 360 — I61 — 63-] because the

angles are mod 360 (the difference between angles of 2° and 358° is only 4°).

Let A be the total area of overlap between the input and the template ﬁngerprints
after a reasonable alignment has been achieved. The probabilities that any arbitrary
minutiae in the input will match any arbitrary minutiae in the template, only in
[terms of location, and only in terms of direction, are given by Eqs. (2.13) and (2.14),
respectively. Eq. (2.13) assumes that (:r,y) and (.v’,y’) are independent and Eq.

(2.14) assumes that 9 and 0’ are independent.

 

f tolerance 7er C
P {_ .2 {_ .2< = 8188.0 =—0=— 2.13
(\/(:r, :13,) + (y, y]) _ r0) total area of overlap A A’ ( )
angle of tolerance _ 260

total angle _ IEO

 

 

P(minaoz —6.I.360- I6: - .0 s 60) = (214)

First we will develop our ﬁngerprint correspondence model when only minutiae loca-
tions alone are matched and then introduce the minutiae angles later in the formula-

tion. If the template contains m minutiae, the probability that only one minutia in

68

the input will correspond to any of the m template minutiae is given by if. Now,

given two input minutiae, the probability that only the ﬁrst one corresponds to one

of the m template minutiae is the product of the probabilities that the ﬁrst input
mC

minutiae has a correspondence (—A—) and the second minutiae does not have a cor-

respondence it? . Thus, the probability that exactly 1 of the 2 input minutiae
A C

matches any of the m template minutiae is 2 X -":4—0 X -AA‘—_’"§, since either the ﬁrst input

minutiae alone may have a correspondence or the second input minutiae alone may
have a correspondence. If the input ﬁngerprint has n minutiae, the probability that

exactly one input minutia matches one of the m template minutiae is

mam- 7: (m7?) (%). (2...)

The probability that there are exactly p corresponding minutiae between the n input

minutiae and m template minutiae is then given by:

" (“a <——<".::20> 0:12:32»

 

 

 

 

 

p tdfms
(37321—5) (iii: 11100 l ((A - (xiii—13:13; me); “'1‘”
n-p terms

The ﬁrst p terms in Eq. (2.16) denote the probability of matching p minutiae between
the template and the input; and remaining n — p terms express the probability that

n — p minutiae in the input do not match any minutiae in the template. Dividing the

69

numerator and denominator of each term in Eq. (2.16) by C, we obtain:

p(A,C,m,n,p) = n (g) (LEE—12) (Si—p" 1)) x
p C C
A

 

 

 

 

 

 

 

 

C (p-l)
<><><>
Letting M = %, we get
77. m m— ) m— — )
”(M’m’n’p’z p (MW—i) (lied—11>)
M—m M—(m—l) (M—(m—(n— —1))
(M—p)(M—(p+1))‘“( M—(n-li l “'18)

By assuming that M is an integer (which is a realistic assumption because A >> C),

we can write the above equation in a compact form as:

n! .M—n!
p(M,m,n.p)=——— ( )

ml

 

 

 

 

. (M — m)!
p!(n — p)! X M! X (m — p)! X «M — m) — (n — p>>!' (2'19)
Rearranging the terms,

_ m! X (M — m)! (M — n)!nl
”(M’m’n’pl ‘ pi<m — p)! (n —p>!<(M — m) — (n — p»! X

M! , (2.20)

70

which ﬁnally reduces to:

p(M,m, n,p) = . (2.21)

 

Eq. (2.21) deﬁnes a hyper-geometric distribution. To get an intuitive understand-
ing of the probability model for the minutiae correspondence in two ﬁngerprints,
imagine that the overlapping area of the template and the input ﬁngerprints is di-
vided into M non-overlapping cells. The shape of the individual cells does not matter,
just the number of cells. Now consider a deck of cards containing M distinct cards.
Each card represents a cell in the overlapping area. There is one such deck for the
template ﬁngerprint and an identical deck for the input ﬁngerprint. If m cards are
drawn from the ﬁrst (template) deck without replacement, and n cards are drawn
from the second (input) deck without replacement, the probability of matching ex-
actly q cards among the cards drawn is given by the hyper-geometric distribution in

Eq. (2.21) [83].

The above analysis considers a minutiae correspondence based solely on the minu-
tiae location. Next we consider a minutiae correspondence that depends on minutiae
directions as well as minutiae positions. For the sake of this analysis, let us assume
that the minutiae directions are completely independent of the minutiae positions and

matching minutiae position and minutiae direction are therefore independent events.

71

Let I be such that P(min(|61— ,] ,360 — [61— 63]) S 60) 2: -1- in Eq. (2.14). Given n
input and m template minutiae, the probability of p minutiae falling into the similar
positions can be estimated by Eq. (2.21). Once p minutiae positions are matched,

the probability that q (q S p) minutiae among them have similar directions is given

p (ac—1)“?

where 1 is the probability of two position-matched minutiae having a similar direction

by

and 151-1 is the probability of two position-matched minutiae taking different directions.

Therefore, probability of matching q minutiae in both position as well as direction is

 

given by
K m 1W — m \l
min (m,n) p In _ p p 1 q l _ 1 p—q
F" M q

 

 

Until now, we have assumed that the minutiae locations are uniformly distributed
within the entire ﬁngerprint area. Since A is the area of the overlap between the
template and the input ﬁngerprints, the ridges occupy approximately £3— of the area,
with the other half being occupied by the valleys. Since the minutiae can lie only on
ridges, i.e., along a curve of length 1%, where w is the ridge period, the value of M in

Eq. (2.23) should therefore be changed from M = A/ C to M = 521453, where 2r0 is

72

the length tolerance in minutiae location.

Parameter Estimation

Our individuality model has several parameters, namely, r0, l, w, A, m, n, and q.
The value of I further depends on 60. The values of r0, l, and w are estimated in
this section for a given sensor resolution. To compare the values obtained from the
theoretical model with the empirical results, we will estimate the values of A, m, and

n from two different databases in the next section.

 

f T I f

0.16 _
0.14r _

0.12i ‘

p
u...
I
1

Probability
.0
O
on

 

.0
8
l

.o
5?.
I
l

0.02 - 1

 

 

 

0 4 l l
0 20 40 60 80 1 00

«x — x)2 + (v - y)"’»"2

Figure 2.11: Distribution of minutiae distance differences for the genuine ﬁngerprint
pairs in the GT database.

The value of re should be determined to account for the variation in the different
impressions of the same ﬁnger. However, since the spatial tolerance is dependent
upon the scale at which the ﬁngerprint images are scanned, we need to calculate

it for the speciﬁc sensor resolution. We used a database (called GT) consisting of

73

450 mated pairs of ﬁngerprints acquired using a high quality (Identicator [81]) op-
tical scanner at a resolution of 500 dpi. The second print in the mated pair was
acquired at least a week after the ﬁrst print. The minutia were manually extracted
from the prints by a ﬁngerprint expert. The expert also determined the correspon-
dence information for the detected minutiae. Using the ground truth correspondence
information between duplex (two) pairs of corresponding minutiae, a rigid transfor-
mation between the mated pair was determined. The overall rigid transformation
between the mated pair was determined using a least square approximation of the
candidate rigid transformations estimated from each duplex pairs of the corresponding
minutiae. After aligning a given mated pair of ﬁngerprints using the overall transfor-

mation, the location difference (r’ — 2:, y’ — y) for each corresponding minutia pair was

 

computed; distance (\/(:c’ — :12)2 + (y’ — y)2) estimates for all minutiae in all mated
ﬁngerprint pairs were pooled to obtain a distribution for the distance between the

corresponding minutiae (see Figure 2.11). We are seeking that value of r0 for which

 

P (\/(:r’ — :13)2 + (y’ — y)2 S r0) 2 0.975, i.e., the value of r0 which accounts for at

least 97.5% of variation in the minutiae position of genuine ﬁngerprint matchings.

 

Thus, r0 is determined from the distribution of \/(:1:’ — :13)2 + (y’ — y)2 estimated in
Figure 2.11 and is found to be 15 pixels for ﬁngerprint images scanned at 500 dpi
resolution.’

To estimate the value of l, we ﬁrst estimate the value of 60. The value of 60 can
also be estimated using the database CT. After aligning a given mated pair of ﬁn-
gerprints using the overall transformation, we seek that value of 60 which accounts

for 97.5% variation in the minutia angles in the genuine ﬁngerprint matchings, i.e.,

74

 

0.1

0.09

0.08

0.07

0.03
0.02

0.01

 

 

 

6O 80 100 120 140 160 180
min(|9'-9|,360—|9’-6|)

 

 

0.018 1 I I I I I I r

I
1

0.016

I
1

0.014

I
1

0.012

0.01 - -

Probability

0.008 r .

.0
I
1

0.004 r -

0.002 ~ ,

 

 

 

 

0 J 1 l l l l 1 l
0 20 40 60 80 1 00 1 20 140 1 60 1 80

min(| 0'— 0 |, 360-| 0'- 0 |)
(b)

Figure 2.12: Distributions for minutiae angle differences for the (a) genuine ﬁnger-
print pairs using the ground truth and (b) imposter matchings using the automatic
ﬁngerprint matching system.

75

 

 

| — MSU_DBI]

0.025 r
0.02 r

' 0.015 r

Probability

0.01 r

0.005 r

 

 

 

l

0 2O 40 60 80 1 00 1 20
Area of overlap in 1000 pixels

 

 

 

(a)
[— MSU_VER|DICOM ]
0.06 ~ .

 

0.05 r

Probability
.0 .o
O O
(a) «b

.0

0

I0
I

0.01 ~

 

 

 

o 1 l l
0 10 20 30 40 50
Area of ovedap in 1000 pixels

0))

Figure 2.13: Area of overlap between the two ﬁngerprints that are matched based
on the bounding boxes of the minutiae features for (a) MSU-DBI database; (b)
MSU_VERIDICOM database.

 

76

we seek that value of 60 for which P(min(|61 - 6]] ,360 — |61 — 6j|) S 60) 2 0.975.
The distribution, P (min (|6’ - 6| ,360 — |61 -— 6j|)) for the genuine ﬁngerprint match-
ings in CT is shown in Figure 2.12(a). Note that the minimum of the distribution
occurs at 90° and the distribution between 90° and 180° is monotonically increasing.
The area under this density from 90° to 180° is about 0.5% of the total area and
quantiﬁes the “connective ambiguity” (transformation of a ridge ending and a ridge
bifurcation and vice versa due to ﬁnger pressure variations). We believe that since
the connective ambiguity is small (about 0.5%), it could be ignored. The value for
60 for which P(min (|6’ — 6| ,360 — |6’ — 6|) 3 60) 2 0.975 is found to be 60 = 22.5°.
In the second step, we determine the distribution P (min (|6’ — 6| ,360 — |6’ — 6|)) for
the imposter ﬁngerprint matchings. Since we do not have correspondences marked
by an expert between imposter ﬁngerprint pairs, we depend on our ﬁngerprint
matcher to establish correspondences between minutiae in imposter pairs. Thus,
our estimation of l is slightly dependent on the automatic ﬁngerprint matcher used
but we believe that the value estimated here is very close to the true value of l.
The distribution P (min (|61 — 631,360 — |61 — 6j|)) estimated by using our matcher
on the GT database is shown in Figure 2.12(b) from which we determined that
P(min(|61- 6]] ,360 — |61 — 931) S 225°) 2 0.267, i.e., l = 3.75. Note that under
the assumption that minutiae directions are uniformly distributed and the minutiae
directions for the minutiae that match in their location are independent, we obtain
l = 5% = 8. If minutiae orientations (0—180) are considered instead of directions

((0-360) , the value for l determined from the experiments is 2.4 as opposed to a value

of 4 determined under the assumption stated above.

77

The value of U) was taken as reported by Stoney [48]. Stoney estimated the value
of ridge period as 0.463 mm / ridge from a database of 412 ﬁngerprints. For ﬁngerprint
sensors with a resolution of 500 dpi, the ridge period converts to ~ 9.1 pixels/ ridge.

Thus, 212 ~ 9.1.

2.2.4 Experimental Results and Discussions

Fingerprint images were collected in our laboratory from 167 subjects using an optical
sensor manufactured by Digital Biometrics, Inc. (image size = 508 X 480, resolution
2 500 dpi). Single impressions of the right index, right middle, left index, and left
middle ﬁngers for each subject were taken in that order. This process was then
repeated to acquire a second impression. The ﬁngerprint images were collected again
from the same subjects after an interval of six weeks in a similar fashion. Thus, we
have four impressions for each of the four ﬁngers of a subject. This resulted in a
total of 2,672 (167 X 4 X 4) ﬁngerprint images. We call this database MSU,DBI.
A live feedback of the acquired image was prOvided and the subjects were guided
in placing their ﬁngers in the center of the sensor in an upright orientation. Using
the protocol described above, we also collected ﬁngerprint images using a solid-state
ﬁngerprint sensor manufactured by Veridicom, Inc. (image size = 300 X 300, resolution
= 500 dpi). We call this database MSU_VERIDICOM. A large number of impostor
matchings (over 4, 000, 000) were generated using the automatic ﬁngerprint matching
system [11].

The mean values of m and n for impostor matchings were estimated as 46 for the

78

 

.0

o

N
I
1

 

 

 

0 HA I

0 20 40 60 80 100
Number of minutiae

(a)

0.07 . . , , r

 

0.06 r

0.05|

p
0
#

r

Probability
.0
o
m

9

o

N
I

0.01 r

 

 

 

i L

 

0 A J l 1
0 1 0 20 30 40 50 60

Number of minutiae
(b)

Figure 2.14: Distributions for m, n, and q for computation of averages for (a)

MSU.DBI database; (b) MSU-VERIDICOM database.

79

 

 

A ——+— Empirical
0.251 I \ —- Theoretical _

 

 

 

0.2l' l \

Probability
.0
at

.0
A
I‘

0.05 ~

 

 

 

 

O
I
1

o ' 5 10 15 20

 

 

l
/

0-3 I \ —+— Empirical
’ ‘ — — Theoretical

 

 

 

0.25 - ’ l

.0
N
I

Probability
.0
61

0.1L ,

0.05 r \

 

\
1 1 l”—! l L

0 2 4 6 8 10 12
Number of matching minutiae (q)

0))

Figure 2.15: Comparison of experimental and theoretical probabilities for the number
of matching minutiae. (a) MSU.DBI database; (b) MSU-VERIDICOM database.

 

 

80

MSU_DBI database and as 26 for the MSU.VERIDICOM database from the distribu-
tions of m, n (Figures 2.14(a) and (b)). The average value of A for the MSU_DBI and
the MSU.VERIDICOM databases are 67,415 pixels and 28, 383 pixels, respectively.
The value of the overlapping area A was estimated in the following fashion. After
the template and the input ﬁngerprints were aligned using the estimated transforma-
tion, a bounding box A,- of all the corresponding minutiae in the input ﬁngerprint
was computed in the common coordinate system. Similarly, a bounding box A; of
all the corresponding minutiae in the template ﬁngerprint was also computed in the
common coordinate system. The intersection A of these two bounding boxes A,- and
A for each matching was then estimated. The estimates of A for all the matchings
performed in the database were pooled to obtain a distribution for A (see Figures
2.13 (a) and (b)). An arithmetic mean of the distribution was used to arrive at an
estimate of A.

The probabilities of a ﬁngerprint correspondence obtained for different values of
M, m, n, and q are given in Table 2.5. The values obtained from our model shown in
Table 2.5 can be compared with values obtained from the previous models in Table
2.3 for m = 36, n = 36, and q = 36,12.

Typically, a match consisting of 12 minutiae points (the 12—point rule) is con-
sidered as sufﬁcient evidence in many courts of law. Assuming that an expert can
correctly glean all the minutia in the latent, a 12-point match with the full-print tem-
plate (see the ﬁrst row, last column entry in Table 2.4) is an overwhelming amount of
evidence, provided that there is no contradictory minutia evidence in the overlapping

area. The value of A was computed for 500 dpi ﬁngerprint images from the minutiae

81

Table 2.4: The effects of the ﬁngerprint expert misjudgments in using the 12-point
rule. The source of error could be in underestimating the minutiae detected in the
latent print (n) or overestimating the correct number of matched minutiae (q). m = 12
for all entries. Except for (m = 12, n = 12, q = 12) entry, all other entries represent
incorrect judgments by the ﬁngerprint expert. For instance, the entry (m = 12, n =
14, q = 8) in the table indicates that although the ﬁngerprint examiner determined
that 12 template minutia unequivocally matched with all 12 input minutiae, there
were indeed 14 input minutiae (2 missed input minutiae) out of which only 8 correctly
matched with the corresponding template minutiae (4 incorrect match judgments).

 

 

 

 

 

 

q 8 9 10 11 12
TI.

12 6.19 x 10-10 4.88 x 10-12 1.96 x 10-14 3.21 x 10-17 1.22 x 10'-20
13 1.58 x 10-9 1.56 x 10-11 8.42 x 10-14 2.08 x 10-16 1.58 x 10:lg
14 3.62 x 1033 4.32 x 10:11 2.92 x 10-13 9.66 x 10-16 1.11 x 10-18
15 7.63 x 10-9 1.06 x 10-10 8.68 x 10-13 3.60 x 10-15 5.53 x 10-18
16 1.50 x 10-8 2.40 x 10-10 2.30 x 10-12 1.45 x 10-14 2.21 x 10-17

 

 

 

 

 

 

 

 

density of 0.246 minutiae / mm2 estimated by Kingston (cf. [48]) from 100 ﬁngerprints;
thus M = 35. Since latents are typically of very poor quality, it is possible that there
could be an error in judgment of existence of minutiae in the latent or their possible
match to the minutiae in the template print. The effect of such misjudgments on the
chance of false associations is rather dramatic. For instance, imposing two incorrect
minutiae match judgments lowers the probability of the match from 1.22 X 10‘20 to
1.96 X 10"14 and ignoring two genuine minutiae present in the input (latent) print
lowers the probability from 1.22 X 10‘20 to 1.11 X 10‘”. Thus, the misjudgment of
a false minutiae match has signiﬁcantly more impact that that of missing genuine
minutiae in the input latent print.

Figures 2.15(a) and (b) show the distribution of the number of matching minutiae
computed from the MSU_DBI and MSU-VERIDICOM databases using an automatic

ﬁngerprint matching system (AFMS) [11], respectively. These ﬁgures also show the

82

Table 2.5: Fingerprint correspondence probabilities obtained from the proposed in-
dividuality model for different sizes of ﬁngerprint images containing 26, 36 or 46
minutiae. M for the last entry was computed by estimating typical print area man-
ifesting 12 minutia in a 500 dpi optical ﬁngerprint scan. The entry (35, 12, 12,12)
corresponds to the 12-point rule.

 

 

 

 

 

 

 

 

 

M, m, n, q P(Fingerprint Correspondence)
104, 26, 26, 26 5.27 X 10'40
104, 26, 26, 12 3.87 x 10-9
176, 36, 36, 36 5.47 X 10‘59
176, 36, 36, 12 6.10 x 10-8
248, 46, 46, 46 1.33 X 10”77
248, 46, 46, 12 5.86 X 10’7
70, 12, 12, 12 1.22 x 10—70

 

 

 

 

theoretical distributions obtained from our model described in Section 2.2.3 for the
average values of M, m, and n computed from the databases. The empirical dis-
tribution is to the right of the theoretical distribution, which can be explained by
the following factors: (i) some true minutiae are missed and some spurious minu-
tiae are detected by the automatic system due to noise in the ﬁngerprint images and
the imperfect nature of the automatic algorithms. Spurious minutiae may also be
detected because of cuts and bruises on the ﬁngertips; (ii) the automatic matching
algorithm cannot completely recover the non-linear deformation present in the ﬁn-
gerprint images; so the alignment between the input and template has some error.
(iii) automatic feature extraction introduces error in minutiae location and orienta-
tions. (iv) the matcher seeks that alignment which maximizes the number of minutiae
correspondences. Consequently, the chance of false associations increases.

The theoretical curve is the upper bound on the performance of a minutiae-based
automatic ﬁngerprint veriﬁcation system which means that it is possible to improve

the system to match the theoretical curve. At the same time, the automatic sys-

83

tem can not perform better than the theoretical limit because of limited information
content in the minutiae—based matching.

Table 2.6 shows the empirical probability of matching 10 and 15 minutiae in
MSU.VERIDICOM and MSU_DBI databases, respectively. The typical values of m
and n were estimated from their distributions by computing the arithmetic means.
The probabilities of false correspondence for these values of m, n and q, are reported
in the third column of Table 2.6. Admittedly, this is an approximate procedure but
we do not expect signiﬁcant deviations from our probability estimates even when the

exact procedure for estimating the probability is adopted.

Table 2.6: Fingerprint correspondence probabilities obtained from matching imposter
ﬁngerprints using an AFMS [11] for the MSU.VERIDICOM and MSU_DBI databases.
The probabilities given in the table are for matching “exactly q” minutiae. The
probabilities for matching “q or more” minutiae are 3.0 X 10’2 and 3.2 X 10"2 for the
MSU.VERIDICOM and MSU_DBI databases, respectively, i.e., of the same order.
The average values for M, m, and n are 28, 383, 26, and 26 for the MSU.VERIDICOM
database and 67,415, 46 and 46 for the MSU-DBI database, respectively.

 

 

 

 

 

Database m,n,q P(False Correspondence)
MSU-VERIDICOM 26, 26, 10 1.7 x 10-2
MSU_DBI 46, 46, 15 1.4 X 10‘?2

 

 

 

2.2.5 Summary

One of the most fundamental questions one would like to ask about any practical
biometric authentication system is: what is the inherent discriminable information
available in the input signal? Unfortunately, this question, if at all, has been answered
in a very limited setting for most biometrics modalities, including ﬁngerprints. The

inherent signal capacity issue is of enormous complexity as it involves modeling both

84

the composition of the population as well as the interaction between the behavioral
and physiological attributes at different scales of time and space. Nevertheless, a
ﬁrst-order approximation to the answers to these questions will have a signiﬁcant
bearing on the acceptance of ﬁngerprint- (biometrics) based personal identiﬁcation
systems into our society as well as determining the upper bounds on scalability of
deployments of such systems.

Estimating ﬁngerprint individuality essentially involves determining the discrim-
inatory information within the input measurements (ﬁngerprint images) to resolve
the identities of the people. The empirical and theoretical methods of estimating
individuality serve complementary goals. Empirical observations lead us to charac-
terize the constraints on the discriminatory information across different ﬁngers as
well as the invariant information among the different impressions of the same ﬁnger;
the theoretical modeling/ generalization of these constraints permits a prediction of
the bounds on the performance and facilitates development of constructive methods
for an independent empirical validation. Historically, there has been a disconnect in
the performance evaluations of practical ﬁngerprint systems and theoretical perfor-
mance predictions. Further, the data-dependent empirical performance evaluations
themselves have varied quite dramatically.

The model proposed here is relatively simple. It ignores most of the known (weak)
dependencies among the features and does not directly include features such as ridge
counts, ﬁngerprint class, ridge frequencies, permanent scars, etc. For these reasons, we
suspect that the proposed model does not yet compete in predicting the performance

of human ﬁngerprint expert matcher. Yet, we believe that the individuality estimates

85

predicted by the present model are signiﬁcantly closer to the performance of practical
automatic ﬁngerprint matchers on realistic data samples than other models reported
in the literature.

While the individuality of the minutiae based ﬁngerprint representation based on
our model is lower than the previous estimates, our study indicates that the likelihood
of an adversary guessing someone’s ﬁngerprint pattern (e.g., requiring matching 20
or more minutia from a total of 36) is signiﬁcantly lower than a hacker being able to
guess a six-character alpha-numerical case-sensitive (most probably weak) password
by social engineering techniques (most common passwords are based on birthday,
spouse’s name, etc.) or by brute force. Obviously, more stringent conditions on
matching will provide a better cryptographic strength at the risk of increasing the
false negative error rate.

If a typical full dab ﬁngerprint contains 46 minutiae, there is an overwhelming
amount of information present in the minutiae representation of ﬁngerprints for man-
ual identiﬁcation (the probability of a false correspondence between two ﬁngerprints
from different users containing 46 minutiae each is 1.33 X 10‘”). However, an auto-
matic system that makes its decision based on 12 minutiae correspondences is utilizing
only a limited amount of information (the probability of a false correspondence for
matching 12 minutiae between two ﬁngerprints from different users containing 46
minutiae each is 5.86 X 10’7). Due to this limited amount of information present in
the minutiae representation of ﬁngerprints, it is desirable to explore alternate com-
plementary representations of ﬁngerprints for automatic matching. In Chapter 3, we

describe such an alternate texture-based representation of ﬁngerprints and empirically

86

Show that it has a discriminatory power similar to the minutiae—based representation.

87

 

Chapter 3

Fingerprint as Oriented Texture

Traditionally, there are two main types of features in ﬁngerprints: (i) global ridge and
furrow structures which form a special pattern in the central region of the ﬁngerprints,
and (ii) minute details associated with local ridges and furrows. A ﬁngerprint is
typically classiﬁed based on only the ﬁrst type of features and uniquely identiﬁed
based on the second type of features. The minutiae-based representation is the most
popular representation of ﬁngerprints as it has a long history of use by the forensic
experts who visually match ﬁngerprints. Forensic experts also use other features such
as ridge count between pairs of minutiae and ridge width in conjunction with minutiae
for identiﬁcation purposes. However, automatic processing of ﬁngerprints allows the
use of Cartesian coordinates and Euclidean distances in establishing the similarity
between ﬁngerprints. Similarly, the use of an alternate representation of ﬁngerprint
that has good discriminatory power is also feasible for automatic systems. Chapter
2 has established an upper bound on the performance of minutiae-based ﬁngerprint
matching systems due to the limited amount of information content present in the

88

minutiae-based representation. As a result, it is desirable to explore an alternate
independent representation of ﬁngerprints that can complement the minutiae-based
representation. This complementary representation should combine both the global
and the local information sources in a ﬁngerprint to obtain a rich representation.
This representation should not only take into account the local anomalies in the
ridge structure (e.g., minutiae), but also, for instance, the global pattern of ridges
and furrows, inter-ridge distances, and overall patterns of ridge ﬂow. Further, it
is an added advantage to design representations which can be automatically and
reliably extracted from the ﬁngerprint and whose extraction will degrade gracefully

with deterioration in the quality of the ﬁngerprints.

3. 1 Introduction

The smooth ﬂow pattern of ridges and valleys in a ﬁngerprint can be viewed as an
oriented texture ﬁeld [28] (see Figure 3.1). The image intensity surface in ﬁngerprint
images is comprised of ridges whose directions vary continuously, which constitutes an
oriented texture. Most textured images contain a limited range of spatial frequencies,
and mutually distinct textures differ signiﬁcantly in their dominant frequencies [2, 84,
10]. Textured regions possessing different spatial frequency, orientation, or phase can
be easily discriminated by decomposing the image in several spatial frequency and
orientation channels. For typical ﬁngerprint images scanned at 500 dpi, there is very
little variation in the spatial frequencies (determined by inter-ridge distances) among

different ﬁngerprints. This implies that there is an optimal scale (spatial frequency)

89

 

Figure 3.1: Flow pattern in a ﬁngerprint image. (a) A section of a ﬁngerprint image,
(b) 3-dimensional surface plot of (a).

90

for analyzing the ﬁngerprint texture. Every pixel in a ﬁngerprint image is associated
with a dominant local orientation and a local measure of coherence of the ﬂow pattern.
A symbolic description of a ﬁngerprint image can be derived by computing the angle
and coherence at each pixel in the image. Fingerprints can be represented/ matched
by using quantitative measures associated with the ﬂow pattern (oriented texture) as
features.

Analysis and modeling of oriented textures is an important research problem with
a wide variety of practical applications [28]. Previous attempts at describing oriented
textures have used either exclusively local or predominantly global features. Examples
of local representations include Poincaré indices, winding numbers, and information
related to singularities and anomalies. The primary limitation of the local approaches
to representation of an oriented texture is that it does not efﬁciently capture the gross
discriminatory information. Local information also tends to be unstable and noise
prone. Examples of global representations include directional co-occurrence matri-
ces, phase portraits of the orientation ﬁelds, and autocorrelation methods. Jain and
Farrokhnia [10] derived a global representation of texture by decomposing the input
image into different frequency and orientation components using a Gabor ﬁlterbank.
They applied this representation to successfully classify and segment textured images.
The global representations, although efﬁcient, do not capture all the discriminatory
information. For example, the global conﬁguration of the two ﬁngerprints shown in
Figure 3.2 is the same but the prints are different due to different conﬁguration of the
local anomalies. Discriminating individual members of such a texture family based

on global representations alone is not feasible.

91

.. ~A‘L3'i' _i’

 

 

Figure 3.2: Difﬁculty in ﬁngerprint matching. (a) and (b) have the same global
conﬁguration but are images of two different ﬁngers.

Daugman [86] derived a translation and scale invariant texture representation
(called IrisCode) for the human iris by an ordered enumeration of multi—scale quadra—
ture Gabor wavelet coefﬁcients of the visible iris texture. Daugman’s iris texture rep-
resentation is not rotation invariant. But large rotations in human iris do not occur
due to the restricted movement of the head. Small amounts of rotation were handled
in the the matching phase by a rotation of the IrisCode itself. Our representation for
oriented texture of ﬁngerprints was inspired by Daugman’s work on iris recognition
and the success of the Gabor ﬁlterbank as reported by Jain and Farrokhnia [10] . We
propose a generic scheme for representing ﬁngerprint texture that relies on extracting
one (or more) invariant points of reference of the ﬁngerprint texture based on an anal—
ysis of its orientation ﬁeld. A predetermined region of interest around the reference

point is tessellated into cells. Each cell is then examined for the information in one

92

or more different, orientation speciﬁc, spatial frequency channels. An ordered enu-
meration of the features thus extracted from each cell is used as the representation of
the ﬁngerprint (see Figure 3.3). Thus, the representation elements capture the local

information and the ordered enumeration of the tessellation captures the invariant

global relationships among the local patterns.

Number, Type
& Bandwidth
of Filters
I

Number of Type, Shape & Cells v Cell Features

Reference Extent of
Frames Tessellation 3’1 ﬂ
: 1
' I
.. V :5
D» B a
E 3'“ E e
m
gag ’ e g
i: 5’ :r.
' | |—> I: -> 1 1 e
Ereggggf. Tessellation *- Cj comPOSltlon a
Determma Ion
+CD
\_J

 

 

Figure 3.3: Schematic diagram for extraction of generic texture-based representation
for ﬁngerprints.

It is desirable to obtain representations for ﬁngerprints which are scale (due to
pressure and sensor resolution), translation, and rotation invariant. Scale invariance
is not a signiﬁcant problem since most ﬁngerprint images could be scaled as per the dpi
speciﬁcation of the sensors. Figure 3.4 shows that a child’s ﬁngerprint has a smaller

area when both the ﬁngerprints were scanned at the same dpi resolution. When a

93

 

 

 

Figure 3.4: Fingerprint of (a) a child, and (b) an adult. Both the ﬁngerprints were
scanned at 500 dpi.

94

child grows up, the scale difference between his ﬁngerprints acquired at different ages
may result in a ﬁngerprint mismatch. Periodically updating the ﬁngerprint template
will alleviate this problem. The translation invariance is accomplished by locating
the reference point. The representation proposed here is not rotation invariant and so
the rotation is handled by a rotation of the representation in the matching stage. A
circular tessellation is deﬁned so that a rotation in the ﬁngerprint image corresponds
to a cyclic rotation of the elements of the representation. The local discriminatory
information in the sector needs to be decomposed into separate components. A Ga-
bor ﬁlterbank is one of the well-known techniques to capture useful information in
speciﬁc bandpass channels as well as to decompose this information into orthogonal
components in terms of spatial frequencies. The four main steps in our representation
extraction algorithm are: (i) determine a reference point for the ﬁngerprint image,
(ii) tessellate the region around the reference point, (iii) ﬁlter the region of interest
in eight different directions using a bank of Gabor ﬁlters (eight directions are required
to completely capture the local ridge characteristics in a ﬁngerprint while only four
directions are required to capture the global conﬁguration [18]), and (iv) compute the
average absolute deviation from the mean (AAD) of gray values in individual sectors
in ﬁltered images to deﬁne the feature vector, also called the FingerCode (similar to

the IrisCode introduced by Daugman [86]).

95

Concave ridges Convex ridges

Figure 3.5: Concave and convex ridges in a ﬁngerprint image when the ﬁnger is
positioned upright. The reference point is marked by X.

3.2 Reference Point Location

Fingerprints have many conspicuous landmarks and any combination of them could be
used for establishing a reference point. We deﬁne the reference point of a ﬁngerprint
as the point of maximum curvature of the concave ridges (see Figure 3.5) in the

ﬁngerprint image.

Many previous approaches to determination of a reference point (re, ye) critically
relied on the local features like Poincaré index [97] or some other similar properties
of the orientation ﬁeld. While these methods work well for good quality ﬁngerprint
images, they fail to correctly localize reference points in poor quality ﬁngerprints
with cracks and scars, dry skin, or poor ridge and valley contrast. Recently, Hong
and Jain [105] have attempted to judiciously combine the orientation ﬁeld information
with available ridge details for ﬁngerprint classiﬁcation. However, their method does
not reliably handle poor quality ﬁngerprints when the orientation ﬁeld is very noisy

and it can be misled by poor structural cues in the presence of ﬁnger cuts and bruises

96

on the skin.

In order that a reference point algorithm gracefully handle local noise in a poor
quality ﬁngerprint, the detection should necessarily consider a large neighborhood
in the ﬁngerprint image. On the other hand, for an accurate localization of the
reference point, the approach should be sensitive to the local variations in a small
neighborhood. To meet these conﬂicting requirements of an accurate and reliable
localization, we propose a new method of reference point determination based on
multi-resolution analysis of the orientation ﬁelds. This method locates the reference
point more precisely than the algorithm proposed by Hong and Jain [105].

Given an M X N ﬁngerprint image, I, its orientation ﬁeld, (9, is deﬁned as an
P X Q image, where C(i, j ) represents the local ridge orientation at pixel (i, j ), P S
M ,Q S N. Local ridge orientation is usually speciﬁed for a block rather than at
every pixel in the image I. The ﬁngerprint image is divided into a set of to X 11) non-
overlapping blocks and a single orientation is deﬁned for each block (see Figures 3.6
(a) and (b)); P = [%|,Q = [1:1]. Note that there is an ambiguity by a factor of
7r in ﬁngerprint orientation, i.e., local ridges oriented at g and ridges oriented at 321
cannot be differentiated from each other. A number of methods have been developed
to estimate the orientation ﬁeld in a ﬁngerprint [119, 162, 120, 28]. The least mean

square orientation estimation algorithm [108] used here has the following steps:
1. Divide I, the input ﬁngerprint image, into non-overlapping blocks of size 212 X 11).

2. Compute the gradients 6I(i, j) and 6y(i, j ) at each pixel (i, j). Depending on

the computational requirement, the gradient operator may vary from the simple

97

Sobel operator to the more complex Marr-Hildreth Operator [59].

3. Estimate the local orientation of each block centered at pixel (i, j ) using the

following equations [28]:

 

1+1;- j+%
V1(2,]) = 28x(u,v)8y(u,v), (3 1)
u=1—% v=]-—%
1+3;- j+%
VyfiJ) = (530410) — 3301. 71)), (3 2)
u=z—% U=]—%
. 1 _ V i,
00.9) = 5m 4511. 1]), (3.3)

where C(i, j) is the least square estimate of the local ridge orientation of the
block centered at pixel (i, j). Mathematically, it represents the direction that
is orthogonal to the dominant direction of the Fourier spectrum of the to X w

window.

A summary of our reference point location algorithm is presented below:

1. Estimate the orientation ﬁeld (9 as described above using a window size of to X 11;.

2. Smooth the orientation ﬁeld in a local neighborhood. Let the smoothed ori-
entation ﬁeld be represented as (9’. In order to perform smoothing (low-pass
ﬁltering), the orientation image needs to be converted into a continuous vector

ﬁeld, which is deﬁned as follows:

(1),,(i,j) = cos(2(9(i,j)), and (3.4)

<I>y(i,j) = sin(2(9(i,j)), - (3.5)

98

 

(C)

Figure 3.6: Estimating the reference point. (a) Smoothed orientation ﬁeld overlapped
on the original image, (b) orientation ﬁeld (w=10) shown as intensity distribution; the
background has been segmented, and (c) sine component of the orientation ﬁeld; the
darkest pixel in the center of the image marks the detected reference point. Images
have been scaled to the range 0—255 for viewing.

99

where (1),, and (by, are the :1: and y components of the vector ﬁeld, respectively.

A low-pass ﬁltering of the resulting vector ﬁeld is performed as follows:

twp/2 Imp/2

61(23):) = Z Z W(u,v)<l>x(i—uw,j—vw) and (3.6)

u=-w¢/2 v=—w¢/2
106/2 Ive/2

<I>1(i,j) = Z Z W(u,v)<I>y(i—uw,j—vw), (3.7)

u=—w¢/2 v=—w¢/2

where W is a 10¢, X 164. low-pass ﬁlter with unit integral. Note that the smoothing
operation is performed at the block level. For our experiments, we used a 5 X 5

mean ﬁlter. The smoothed orientation ﬁeld (9’ at (i, j) is computed as follows

C'(i,j) = étan‘l(

(1)1032)

(P;(i.i))° (3'8)

 

. Compute 8, an image containing only the sine component of 0’.

£(i,j) = sin (C'(i,j)). (3.9)

. Initialize A, a label image used to indicate the reference point.

. For each pixel (i, j) in 8, integrate pixel intensities (Sine component of the
orientation ﬁeld) in regions R1 and R11 shown in Figure 3.7 and assign the

corresponding pixels in A the value of their difference.

4032') = 280.1) — 280.1). (3.10)
RI

RI!

100

The regions R1 and R1 1 (see Figure 3.7) were determined empirically by applying
the reference point location algorithm over a large database. The radius of the
semi—circular region was set equal to the window size 11). The geometry of regions
R1 and R” is designed to capture the maximum curvature in concave ridges
(see Figure 3.5). Although this approach successfully detects the reference point
in most of the cases, including double loops (see Figure 3.8 (a)), the present
implementation is not very precise and consistent for the arch type ﬁngerprints
because it is difﬁcult to localize points of high curvature in arch type ﬁngerprint

images.

 

Figure 3.7: Regions for integrating pixel intensities in 8 for computing A(i, j).

C}

K]

. Find the maximum value in A and assign its coordinate to the core, i.e., the

reference point.

. For a ﬁxed number of times, repeat steps 1-6 by using a window size of 112’ X w’,

where w’ < w and restrict the search for the reference point in step 6 in a local

neighborhood of the detected reference point. In our experiments, we used three

101

iterations with w = 15, 10, and 5 pixels respectively, and hence the precision of

the detected reference point is 5 pixels.

Figure 3.8 shows the results of our reference point location algorithm for four
different images. The reference point location algorithm performs extremely well for
good quality ﬁngerprint images of whorl, left loop, right loop, and arch types. This
algorithm has higher error in consistently locating the reference point in the arch type
ﬁngerprints due to the absence of singular points in arch type ﬁngerprint images. The
algorithm fails for very poor quality ﬁngerprints because of the errors in orientation

ﬁeld estimation.

3.3 Tessellation

Let I(:1:, y) denote the gray level at pixel (1:, y) in an M X N ﬁngerprint image and let
(are, ye) denote the reference point. The region of interest in the ﬁngerprint is deﬁned
as the collection of all the sectors S,, where the i’” sector S,- is computed in terms of

parameters (r, 6) as follows:

3.- = {(5159) lb(Ti +1) S r < b(T.- + 2),

6.so<6.+1,1555N.15y3M}, (3.11)

102

/-\«
name-unv-

, ”ru' 3"

 

(C)

Figure 3.8: Examples of the results of our reference point location algorithm. The
algorithm fails on very poor quality ﬁngerprints such as (c) and (d).

103

where

 

T,- = i div k, (3-12)
6,- = (2' mod 1:) x (27r/k), (3.13)
r = We — :17.)2 + (y — yc)2. (3-14)
0 = tan-1((y — yc)/(:r - are». (3-15)

b is the width of each band, It is the number of sectors considered in each band, and
i = 0, ..., (B X k — 1), where B is the number of concentric bands considered around
the reference point for feature extraction. The parameter B depends on the area of
the ﬁnger imaged. For example, at the same resolution of 500 dpi, a larger ﬁnger area
will be captured in a 640 X 480 pixel image than in a 320 X 320 pixel image. Thus the
parameter B depends on the image size and the dpi resolution of the sensor. The width
of the concentric bands is deﬁned by the parameter b and depends on the dpi resolution
of the sensor. The width of the bands should capture one ridge and valley pair on
an average. For ﬁngerprint images scanned at 500 dpi, we choose b = 20. A band
with a width of 20 pixels is necessary to capture a single minutia in a sector, allowing
our low-level features to capture this local information. If the sector width is more
than 20 pixels, then the local information is modulated by more global information.
The innermost band (circle) is not used for feature extraction because the sectors in
the region near the reference point contain very few pixels and, therefore, the feature
extraction in this region is not very reliable. A circular tessellation is chosen because a

rotation of the ﬁngerprint will correspond to the rotation of the tessellation. The value

104

, 1n."

‘0 7"

of 1: controls the capture of the global versus the local information in a ﬁngerprint
and depends upon the application. For example, more global information is required
by the ﬁngerprint classiﬁcation algorithm, and so, a lower k value is chosen. On
the other hand, the ﬁngerprint veriﬁcation application needs to capture more local
information in the ﬁngerprints and hence requires a higher value of k. The values
for these parameters, B, b, and It were determined empirically to obtain the best
performance for the ﬁngerprint classiﬁcation and matching applications. Both the
classiﬁcation and the matching algorithms based on the FingerCode representation
are able to handle small changes in these parameters without a signiﬁcant degradation
in performance. A large change in the parameter values is also handled gracefully
with a decrease in performance proportional to the change in the parameter values.
The value of B should be set in such as way as to capture maximum ridge and valley
details without rejecting a large number of ﬁngerprint images. The value of It should
be chosen based on the tradeoff between local and global information required for a
particular application, the value of b should be chosen based on the dpi resolution
of the sensor and the average inter-ridge distance in ﬁngerprint images. Once the

parameter values are chosen for an application, they remain constant.

3.4 Filtering

Fingerprints have local parallel ridges and valleys, and well-deﬁned local frequency
and orientation (see Figure 3.10). Properly tuned Gabor ﬁlters [86, 88] can remove

noise, preserve the true ridge and valley structures, and provide information contained

105

 

Figure 3.9: Reference point (X), the region of interest, and 80 sectors (B = 5, k = 16)
superimposed on a ﬁngerprint.

in a particular orientation in the image. A minutia point can be viewed as an anomaly
in locally parallel ridges and it is this information that we are attempting to capture

using the Gabor ﬁlters.

Before ﬁltering the ﬁngerprint image, we normalize the grey level intensities in the
region of interest in each sector separately to a constant mean and variance. Normal-
ization is performed to remove the effects of sensor noise and gray level background
due to ﬁnger pressure differences. Let I (:r, y) denote the gray value at pixel (:12, y), M,-
and V,, the estimated mean and variance of grey levels in sector Si, respectively, and

N,(a:,y), the normalized gray—level value at pixel (r,y). For all the pixels in sector

106

 

(C)

Figure 3.10: Fingerprints have well deﬁned local frequency and orientation. Ridges
in local regions are shown in (a) and (b). Fourier spectrum of (a) and (b) are shown
in (c) and (d), respectively.

3,, the normalized image is deﬁned as:

M0+ MW, if I(x,y)>M,-

Nita?!) = (3.16)
M0_ W, otherwise,

where M0 and V0 are the desired mean and variance values, respectively. Normal-
ization is a pixel—wise operation which does not change the clarity of the ridge and
valley structures. If normalization is performed on the entire image, then it cannot

compensate for the intensity variations in different parts of the image due to the ﬁn—

107

0.5\.-""‘"”

04.-

 

  

 

, 20 —15
. ,-v ‘ -20

(a) 0° orientation

0.51m-

.
' O O O
-0-
--O O
-0- o ..

 

 

(b) 90° orientation

Figure 3.11: Gabor ﬁlters (mask size = 33 X 33, f = 0.1, (5I = 4.0, by = 4.0). Only
0° and 90° oriented ﬁlters are shown here.

108

ger pressure differences. A separate normalization of each individual sector alleviates
this problem. Figure 3.12 shows an example of this normalization scheme. For our
experiments, we set the values of both M0 and V0 to 100. The values of M0 and V0
should be the same across all the training and test sets.

An even symmetric Gabor ﬁlter has the following general form in the spatial

domain:

_1 $12 yl2 I
C(r,y;f, 6) = erp{—2—[ﬁ- + E]}cos(27rfr ), (3.17)
x y
:r' = rsin6 + ycos6, (3.18)
y’ = :rcos6 — ysin6, (3.19)

where f is the frequency of the sinusoidal plane wave along the direction 6 from the
:c-axis, and 6,, and 6,, are the space constants of the Gaussian envelope along :1: and y
axes, respectively. The spatial characteristics of Gabor ﬁlters can be seen in Figure
3.11.

We perform the ﬁltering in the spatial domain with a mask size of 33 X 33. Figure
3.11 shows that the ﬁlter values outside this 33 X 33 mask are close to zero. To speed
up the ﬁltering process, we convolve a pixel only with those values in the ﬁlter mask
whose absolute value is greater than 0.05. This speeds up the convolution process
signiﬁcantly while maintaining the information content as the convolution with small
values of the ﬁlter mask does not contribute signiﬁcantly to the overall convolution

output. We also make use of the symmetry of the ﬁlter to speed up the convolution.

109

I
i"

I
l , .

, i;
’1... My,» {fl/‘12,
I?“ 1.! _.' . I

.a<;;:\l :.\
)1,“ . #3153
. r -' 1 {wtml

.11.;
(" "‘ J .5111
Iﬁlk§$§§éjﬂﬂl

 

Figure 3.12: Normalized, ﬁltered, and reconstructed ﬁngerprint images. (a) area
of interest, (b) normalized image, (c)-(j) 0°, 225°, 45°, 90°, 112.5°, 157.5° ﬁltered
images, respectively, (k) reconstructed image with 4 ﬁlters, and (l) reconstructed
image with 8 ﬁlters. While four ﬁlter orientations are sufﬁcient to capture the global
structure of the ﬁngerprint, eight ﬁlter orientations are required to capture the local
characteristics.

110

Table 3.1: Gabor ﬁlter mask of size 33 X 33, 6 = 0°, f = 0.1, 6,, = 6,, = 4.0. Only a
19 X 19 matrix from the center of the 33 X 33 ﬁlter is shown because the mask values
outside this are zero. Also, only the top left quarter of the mask is shown due to the
symmetry in the X and Y axes of the 0° oriented ﬁlter. The mask values less than
0.05 are set to zero. Each entry is to be multiplied by 10’3.

57 62 64 62 57 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 -51 -59 —65 -67
0 0 —57 ~85 -120 -160 -199 -232 -255 —263
0 -62 -99 -149 -210 -278 —346 -404 -444 -458
0 -66 -106 -159 -224 -297 -370 -433 -475 -490
0 0 -50 -76 —106 -141 -176 -205 -225 -233
0 0 59 89 125 166 206 241 265 273

62 106 170 255 359 476 592 692 760 784

80 135 216 325 458 607 755 882 969 1000

One such mask for the 0°-oriented Gabor ﬁlter is shown in Table 3.1. However,
convolution with Gabor ﬁlters is still the major contributor to the overall feature
extraction time (approx. 3 seconds of CPU time for convolution of a circular area of
radius 120 pixels with 8 Gabor ﬁlters on a SUN ULTRA 10 workstation).

In our experiments, we set the ﬁlter frequency f to the average ridge frequency
(1 / K), where K is the average inter-ridge distance. The average inter-ridge distance
is approximately 10 pixels in a 500 dpi ﬁngerprint image. If f is too large, spurious
ridges are created in the ﬁltered image whereas if f is too small, nearby ridges are
merged into one. Different ﬁlter directions (6) include 0°, 22.5°, 45°, 675°, 90°,
112.5°, 135°, and 157.5° with respect to the :r-axis. The normalized region of interest
in a ﬁngerprint image is convolved with each of these eight ﬁlters to produce a set
of eight ﬁltered images. A ﬁngerprint convolved with a 0°-oriented ﬁlter accentuates

those ridges which are parallel to the r-axis and smoothes the ridges in the other

111

directions. Filters tuned to other directions work in a similar way. These eight
directional-sensitive ﬁlters capture most of the global ridge directionality information
as well as the local ridge characteristics present in a ﬁngerprint. We illustrate this
through reconstructing a ﬁngerprint image by adding together all the eight ﬁltered
images. The reconstructed image is similar to the original image without a signiﬁcant
loss of information (Figure 312(1)). Empirically, we have determined that at least
four directional ﬁlters are required to capture the entire global ridge information in
a ﬁngerprint (Figure 312(k)), but eight directional ﬁlters are required to capture
the local characteristics. By capturing both the global and local information, the
veriﬁcation accuracy is improved’although there is some redundancy among the eight
ﬁltered images. If 6,, and 6y (standard deviations of the Gaussian envelope) values are
too large, the ﬁlter is more robust to noise, but is more likely to smooth the image
to the extent that the ridge and valley details in the ﬁngerprint are lost. If 61 and 6,,
values are too small, the ﬁlter is not effective in removing the noise. The values for
6,, and 6y were empirically determined and each is set to 4.0 (about half the average

inter-ridge distance).

3.5 Feature Vector

It is difﬁcult to rely on features that are extracted based on explicit detection of
structural features in ﬁngerprints, especially in poor quality images. Features based
on statistical properties of images are likely to degrade gracefully with the image

quality deterioration. For this study, we use grayscale variance-based features. The

112

average absolute deviation of the gray levels from the mean value in an image sector
is indicative of the overall ridge activity in that sector which we claim to be useful
for ﬁngerprint classiﬁcation and veriﬁcation. Similar features were successfully used
earlier by Jain and Farrokhnia [10] for texture classiﬁcation and segmentation. Our
empirical results on ﬁngerprint classiﬁcation and veriﬁcation applications show that

this simple statistical feature performs extremely well.

Let Fw(a:,y) be the 6-direction ﬁltered image for sector 8,. Now, V i E
{0,1,...,79} and 6 E {0°,22.5°,45°,67.5°,90°,112.5°,135°,157.5°}, the feature

value, V19, is the average absolute deviation from the mean deﬁned as:

1
V219 = 7:; (Z (Fidel!) — Pull) , (3-20)

where n,- is the number of pixels in S, and P,-g is the mean of pixel values of F.9(SE, y) in
sector 5,. The average absolute deviation of each sector in each of the eight ﬁltered
images deﬁnes the components of our 640-dimensional feature vector. The feature
vectors for some example images in the MSU_DBI database are shown as grayscale

images in Figure 3.13.

The average absolute deviation (AAD) features give slightly better performance
than variance features in our experiments. The number of ﬁlter orientations required
was empirically determined. In the ﬁngerprint veriﬁcation application, using eight
orientation ﬁlters resulted in a better performance than when only four orientation
ﬁlters were used. A further increase in the number of ﬁlters did not provide any

increase in the veriﬁcation performance. Similarly, using eight ﬁlters instead of four

113

 

Figure 3.13: Examples of 640-dimensional feature vectors. (a) First impression of
ﬁnger I, (b) Second impression of ﬁnger 1, (c) and (d) are the corresponding F inger-
Codes, (6) First impression of ﬁnger 2, (f) Second impression of ﬁnger 2, (g) and (h)
are the corresponding FingerCodes.

114

ﬁlters did not improve the performance of the ﬁngerprint classiﬁcation algorithm (see

Chapter 4.

The 640-dimensional feature vectors (FingerCodes) for ﬁngerprint images of two
different ﬁngers from the MSU-DBI database are shown as gray level images with eight
disks, each disk corresponding to one ﬁltered image in Figure 3.13. The gray level
in a sector in a disk represents the feature value for that sector in the corresponding
ﬁltered image. Note that Figures 3.13(c) and (d) appear to be visually similar as
are Figures 3.13(g) and (h), but the corresponding disks for two different ﬁngers look

very different.

The translation is handled by a single reference point location during the feature
extraction stage. Our representation scheme is able to tolerate the imprecision in
the reference point estimates of up to 10 pixels (approximately 1 inter-ridge distance
unit) away from its “true” location. A circular tessellation is chosen because the
sector size increases as we go farther away from the center and handles the error
in center location better. The present implementation of feature extraction assumes
that the ﬁngerprints are vertically oriented (ﬁngertip pointed straight up). In reality,
the ﬁngerprints in our database are not exactly vertically oriented; the ﬁngerprints
may be oriented up to i45° away from the assumed vertical orientation. The circular
tessellation assists in obtaining a representation corresponding to a rotation of the
ﬁngerprint image by a cyclic rotation of the values in the feature vector. We use this
cyclic rotation of the feature vector to partially handle the rotation in the matching

stage.

115

a- h... n _1'

 

3.6 Summary

Chapter 2 establishes an upper bound on the performance of the minutiae—based au-
tomatic ﬁngerprint identiﬁcation systems due to the limited information content of
the minutiae representation. This was a powerful motivation for exploring a novel
and rich alternate representation for ﬁngerprints. The proposed ﬁlterbank-based rep-
resentation for ﬁngerprints was motivated by Daugman’s work on Iris recognition
[86] that quantiﬁed the textural information present in the human iris using a Ga-
bor ﬁlterbank in a small IrisCode. Gabor ﬁlterbank has also been successfully used
in texture classiﬁcation and segmentation tasks [10]. Since ﬁngerprint images can be
viewed as a textured pattern, it is appropriate to use this ﬁlterbank-based representa-
tion for ﬁngerprints. Our proposed ﬁlterbank-based representation has the desirable
property of capturing both the local minute details and the global pattern informa-
tion in a ﬁngerprint. One of the main advantages of this representation is that a
single representation can be used for ﬁngerprint classiﬁcation as well as matching. As
a comparison, earlier approaches to ﬁngerprint representation are either exclusively
local (e.g., minutiae) or exclusively global (e.g., orientation ﬁeld). The exclusively lo—
cal representation is traditionally used for ﬁngerprint matching while the exclusively
global representation is used for ﬁngerprint classiﬁcation. Additionally, the compact-
ness of the ﬁlterbank representation is very attractive for credit card or smart card
applications where the amount of available storage is limited. The good discrimina-
tory power of the representation is demonstrated by the classiﬁcation and veriﬁcation

applications in Chapters 4 and 5, respectively. The current implementation of the

116

._.17

"1

 

feature extraction is computationally expensive due to the image convolution op-
erations. It is possible to signiﬁcantly enhance the Speed of the feature extraction
algorithm by implementing the convolution operation via a dedicated DSP chip. For
an example, a DSP implementation of the FingerCode extraction algorithm using an
Analog Devices Share (Super Harvard Architecture Computer) DSP 21062 EZ—LAB
Development board developed by Bittware, Inc. was reported in [115] and the feature
extraction time was reduced by an order of magnitude. The primary advantage of
our approach is its computationally attractive matching/ indexing capability. As far
as the ﬁngerprint database is concerned, the feature extraction is an off-line process
and if the normalized (for orientation and size) FingerCodes of all the enrolled ﬁn-
gerprints are stored as templates, the classiﬁcation or veriﬁcation effectively involves
a “bit” comparison with the test image. As a result, the identiﬁcation time would be
relatively insensitive to the database size because “bit” comparison is an extremely
fast operation. Further, our approach for representation extraction and matching
is more amenable to hardware implementation than, say, a string-based ﬁngerprint
matcher.

There are a number of limitations of our approach to ﬁngerprint representation.
The implementation of the representation extraction algorithm that is based on a ref-
erence point in the ﬁngerprint image rejects about 5% of the images (in the NIST-9
database) due to failure of the reference point location on poor quality ﬁngerprint
images. An alignment based on the minutiae points or orientation ﬁeld in an image is
expected to overcome this problem but the resulting representation is not translation

and rotation invariant and thus, is not very attractive for indexing purposes. More-

117

 

 

Figure 3.14: Example of new touchless ﬁngerprint sensor TFS 050 from Biometric
Partners, Inc. (http://www.biometricpartners.com/). The touchless sensor captures
a ﬁngerprint from a distance of approximately 50mm. Advantages of touchless tech-
nology include capture of larger ﬁngerprint area, is more hygienic, the sensor does not
degrade with repeated use, and there is no nonlinear distortion due to ﬁnger pressure
difference in the captured image. The image captured by the sensor in (a) is shown in
(b). However, the touchless sensors have their own problems, including poor quality
Images.

over, the ﬁlterbank representation is not invariant to nonlinear deformations which is
an inherent property of the touch-based ﬁngerprint sensing process. The new gener—
ation of touchless sensors (see Figure 3.14) do not suffer from nonlinear deformations
in the captured ﬁngerprint image but there are additional degrees of freedom in the
translation (translation in z—axis results in a scaling in two-dimensional projection)

and rotation variance.

118

Chapter 4

Fingerprint Classiﬁcation

Fingerprint classiﬁcation provides an important indexing mechanism in a ﬁngerprint
database. An accurate and consistent classiﬁcation can greatly reduce ﬁngerprint
matching time for a large database. We present a ﬁngerprintclassiﬁcation algorithm
which is able to achieve an accuracy which is comparable to the algorithms reported in
the literature. In 1899, Edward Henry and his two assistants established the “Henry
System” of ﬁngerprint classiﬁcation [78]. The Henry system classiﬁes ﬁngerprints
into three main categories: (i) loop, (ii) whorl, and (iii) arch. Each category is then
further divided resulting in a total of more than twenty categories. Federal Bureau
of Investigation (FBI) follows Henry system of classiﬁcation but recognizes only eight
different types of ﬁngerprint: radial loop, ulnar loop, double loop, central pocket
loop, plain arch, tented arch, plain whorl, and accidental. Due to the small interclass
separability of these types ﬁngerprint types, it is extremely difficult to design an eight-
class classiﬁer with high accuracy. As a result, most automatic systems reduce the
number of ﬁngerprint types to a subset of classes deﬁned in the Henry system. For

119

v.7

 

example, academic institutes have typically concentrated on a ﬁve-class classiﬁcation
that includes whorl, left loop, right loop, arch, and tented arch, while the commercial
systems typicallyprovide ulnar, radial loops, accidental, whorl, double loop, and arch
classiﬁcation [78].

Fingerprint classiﬁcation remains a very difﬁcult problem for both human experts
and automatic systems because of large variations in ﬁngerprint conﬁgurations. A
substantial amount of experience is required for a forensic expert to reach a satisfac-
tory level of performance in ﬁngerprint classiﬁcation. Fingerprints have a continuum
in the pattern space. For example, there is a continuum of patterns between the
two extremes of a “true” arch and a “true” loop. As a result, there exists patterns
which lie on any arbitrarily drawn class boundary drawn for an exclusive classiﬁca-
tion. Due to the fuzzy boundaries between the large number of ﬁngerprint classes,
NIST [41] chose a ﬁve-element subset in the Henry system of ﬁngerprint classiﬁcation
for automatic system development. These ﬁve classes are whorl, right loop, left loop,
arch, and tented arch. Our automatic system classiﬁes ﬁngerprints into these ﬁve
categories. The algorithm uses the novel representation (FingerCode) described in
Chapter 3 and is based on a two-stage classiﬁer to make a decision. Our approach
has been tested on 4, 000 images in the NIST-4 database. For the ﬁve-class problem,
a classiﬁcation accuracy of 90% is achieved (with a 1.8% rejection during the feature
extraction phase). For the four—class problem (arch and tented arch combined into
one class), we are able to achieve a classiﬁcation accuracy of 94.8% (with 1.8% re-
jection). By incorporating a reject option in the classiﬁer, the classiﬁcation accuracy

can be increased to 96% for the ﬁve-class classiﬁcation task, and to 97.8% for the

120

...,“.b

four-class classiﬁcation task after a total of 32.5% of the images are rejected.

4. 1 Introduction

Several approaches have been developed for automatic ﬁngerprint classiﬁcation.
These approaches can be broadly categorized into four main categories: (i) knowledge-
based, (ii) structure-based, (iii) frequency-based, and (iv) syntactic. The knowledge-
based ﬁngerprint classiﬁcation technique uses the locations of singular points (core
and delta) to classify a ﬁngerprint into the ﬁve above-mentioned classes [97, 105].
A knowledge—based approach tries to capture the knowledge of a human expert by
deriving rules for each category by hand-constructing the models and therefore, does
not require training. Accuracies of 85% [97] and 87.5% [105] have been reported
on the NIST-4 database [41] using these approaches. A structure-based approach
uses the estimated orientation ﬁeld in a ﬁngerprint image to classify the ﬁngerprint
into one of the ﬁve classes. An accuracy of 90.2% with 10% rejection is reported
on N IST—4 [43]. The neural network used in [43] was trained on images from 2, 000
ﬁngers (one image per ﬁnger) and then tested on an independent set of 2, 000 images
taken from the same ﬁngers. The error reported is thus optimistically biased. A
later version of this algorithm [76] was tested on the NIST-14 database which is a
naturally distributed database resulting in a better performance (in a naturally dis-
tributed database, the number of ﬁngerprint images for a particular ﬁngerprint type
is proportional to the probability of occurrence of that type in nature). A further

enhancement of this algorithm was reported in [44, 45]. However, this performance

121

 

improvement should be expected since the NIST-14 database contains only a small
percentage of arch-type ﬁngerprints which pose the most difﬁcultly for ﬁngerprint
classiﬁers, and the neural network used in the algorithm implicitly takes advantage
of this information. A similar structure-based approach which uses hidden Markov
models for classiﬁcation [30] depends on a reliable estimation of ridge locations which
is diﬂicult in noisy images. In another structure—based approach, B-spline curves are
used to represent and classify ﬁngerprints [122]. A syntactic approach uses a formal
grammar to represent and classify ﬁngerprints [46]. quuency—based approaches use
the frequency spectrum of the ﬁngerprints for classiﬁcation [25]. Hybrid approaches
combine two or more approaches for classiﬁcation [34, 120]. These approaches show
some promise but have not been tested on large databases. For example, Chong et
al. [122] report results on 89 ﬁngerprints, Fitz and Green [25] on 40 ﬁngerprints, and
Kawagoe and Tojo [120] on 94 ﬁngerprints. Recently, Cappelli et al. [141] proposed a
ﬁngerprint classiﬁcation algorithm based on the multi—space KL transform applied to
the orientation ﬁeld. This algorithm reports about 2% better accuracy than our algo-
rithm on the N IST-4 database. See Table 4.1 for a comparison of different ﬁngerprint
classiﬁcation algorithms.

Most of the information about a ﬁngerprint category is contained in the central
part of the ﬁngerprint, called the pattern area [68]. The pattern area is the area be-
tween the two innermost ridges (known as typelines) that form a divergence tending
to encircle or encompass the central portion of the ﬁngerprint as shown in Figure 4.1.
The knowledge-based techniques which use both the core and delta points for classiﬁ-

cation require that these singular points be present in the image. The dab ﬁngerprint

122

Table 4.1: Fingerprint classiﬁcation literature survey. The number of classes is de-
noted by C, the classiﬁcation accuracy is denoted by Acc, and the reject rate is
denoted by RR. The classiﬁcation accuracies reported by the different authors are
on different databases with different number of ﬁngerprints and therefore, they can-
not be directly compared. Most of the work in ﬁngerprint classiﬁcation is based on

supervised learning and discrete class assignment using knowledge-based features.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Authors C Features Method Acc.
(RR)
Kawagoe and Tojo 1984 7 Singular points Rule-based 91.5%
(0%)
Blue et al. 1994 5 Orientation ﬁeld Neural network 92.8%
(0%)
Wilson et al. 1994 5 Orientation ﬁeld Neural network 90.2%
(10%)
Candela et al. 1995 6 Orientation ﬁeld Neural network 92.2%
(0%)
Pal and Mitra 1996 5 Orientation ﬁeld Neural network 82+%
(0%)
Fitz and Green 1996 3 FFT Nearest-neighbor 85 %
(0%)
Karu and Jain 1996 5 Singular points Rule-based 85%
(0%)
Senior 1997 4 Ridge lines Hidden Markov Model 90%
(0%)
Chong et al. 1997 5 Ridge lines Rule-based 96.5%
(0%)
Hong and Jain 1999 5 Singular points Rule-based 87.5%
and ridge lines (0%)
Proposed 1999 5 Gabor response Combination 90%
(1.8%)
Cappelli et al. 2000 5 Orientation ﬁeld Combination 99%
(20%)

 

123

 

 

Figure 4.1: Pattern area and typelines [68, 104].

images obtained by optical scanners do not always capture the entire ﬁngerprint and
often have the delta point(s) missing. Also, the core or delta point(s) are difﬁcult to
detect in noisy ﬁngerprint images. There is, however, sufﬁcient information available
in the ridge pattern itself to classify a ﬁngerprint. While the structure-based approach
does not depend upon the core or delta points, it requires a reliable estimate of the
orientation ﬁeld which is very difﬁcult to obtain in low quality ﬁngerprint images.
We propose a ﬁngerprint classiﬁcation algorithm (Figure 4.2) based on our ﬁl-
terbank ﬁngerprint representation scheme which is directly derived from local ridge
structures. The representation does not use the core, delta, and orientation ﬁeld,
explicitly. It is more capable of tolerating poor image quality, which is a major dif—
ﬁculty in ﬁngerprint classiﬁcation. The main steps of our classiﬁcation algorithm
are as follows: (i) Locate a reference point in the input image and deﬁne a spatial
tessellation (sectors) of the region around the reference point; (ii) decompose the
input image into a set of component images, each of which preserves certain ridge
orientation information; compute the standard deviation of the component images in

each sector to generate the feature vector (called F ingerCode); (iii) feed the feature

124

Decompose Input Image Compute S.D.

     
  

Ian Image Normalize Each Sector

Find Registration Point Tessellate Image Space

192-dimensional FingerCode

 

Fingerprint Two-stage
‘—
Category Classiﬁer

 

 

 

 

Figure 4.2: Flow diagram of our ﬁngerprint classiﬁcation algorithm.

125

vector into a multi-stage classiﬁer; in our algorithm, a two—stage classiﬁer is used.
This two-stage classiﬁer uses a K -nearest neighbor classiﬁer in its ﬁrst stage and a
set of neural network classiﬁers in its second stage to classify a feature vector into
one of the ﬁve ﬁngerprint classes.

In the following sections, we will present the details of our ﬁngerprint classiﬁcation

algorithm.

4.2 Feature Extraction

The category of a ﬁngerprint is determined by its global ridge and furrow structures.
A valid feature set for ﬁngerprint classiﬁcation should be able to capture this global
information effectively. The ﬁlterbank—based ﬁngerprint representation developed in
Chapter 3 is able to represent both the minute details and the global ridge and
furrow structures of a ﬁngerprint. For the purpose of classiﬁcation, we adapt our
representation such that it is very effective in representing the global ridge and furrow
structures and is invariant to individual minute details.

The representation scheme developed in Chapter 3 has certain parameters which
are adapted to our ﬁngerprint classiﬁcation algorithm. We choose the tessellation
parameter B, the number of concentric bands to be 6 based on the size of the images
in the NIST 4 database (512 X 512). Number of sectors in each band is chosen to be
eight (k = 8). This results in large sectors which are capable of capturing the global
information in the ﬁngerprints. Thus, a total of 8 X 6 = 48 sectors (So through S47)

are deﬁned. Since most of the category information is present in the part below the

126

core point in the ﬁngerprints (different ﬁngerprint types have similar ridge structure
in the part above the core point), we move the reference point down by 40 pixels
with respect to the core point detected by the reference point detection algorithm in

Chapter 3.

 

Figure 4.3: Reference point detected by the algorithm described in Chapter 3 (Cl),
moved reference point (X), the region of interest and 48 sectors.

A ﬁngerprint image is convolved with four Gabor ﬁlters (6 = 0°, 45°, 90°, and 135°)
to produce the four component images. Thus, our feature vector is 192—dimensional
(48 X 4). Our experimental results indicate that the four component images capture
most of the ridge directionality information present in a ﬁngerprint image and thus
form a valid representation. We illustrate this by reconstructing a ﬁngerprint image

by adding together all the four ﬁltered images. The reconstructed image is similar

127

 

. ‘5

Component image 135° Reconstructed image

Figure 4.4: Normalized, ﬁltered, and reconstructed ﬁngerprint images.

128

 

Figure 4.5: Reconstructed ﬁngerprint images using (a) four ﬁlters, and (b) eight
ﬁlters. Most of the directionality information is captured by four ﬁlters.

to the original image without a signiﬁcant loss of information (Figure 4.4). Using
additional ﬁlters does not necessarily improve the directionality information in the
reconstructed image (see the comparison of reconstruction using four ﬁlters with
reconstruction using eight ﬁlers in Figure 4.5). Since convolution with Gabor ﬁlters
is an expensive operation, the use of additional ﬁlters will increase the classiﬁcation
time without necessarily improving the classiﬁcation accuracy.

In each component ﬁltered image, a local neighborhood with ridges and furrows
that are parallel to the corresponding ﬁlter direction exhibits a. higher variation,
whereas a local neighborhood with ridges and furrows that are not parallel to the
corresponding ﬁlter tends to be diminished resulting in a lower variation. The spatial
distribution of the variations in local neighborhoods of the component images thus
constitutes a characterization of the global ridge structures which is captured by
the average absolute deviation of grayscale values from the mean (AAD features)

(Equation (3.20)).

129

 

((1) Left Loop (e) Arch (f) Tented Arch

Figure 4.6: Fingerprint representation using 192-dimensional feature vectors (In each
representation, the top left disc represents the 0° component, the top right disc rep—
resents the 45° component, the bottom left disc represents the 90° component, and
the bottom right disc represents the 135° component). The test image is a right loop.
Each disk corresponds to one particular ﬁlter and there are 48 features (shown as
gray values) in each disk (8 X 6 = 48 sectors) for a total of 192 (48 X 4) features.

4.3 Classiﬁcation

Automatic classiﬁcation of ﬁngerprints is a difficult problem because of the small
interclass variability and large intraclass variability among the ﬁve classes under
consideration. In order to simplify the classiﬁcation task, we decompose the ﬁve-class
problem into a set of 10 two-class problems. Further, we use a two—stage classiﬁer for
ﬁngerprint classiﬁcation. In the ﬁrst stage, we use a K -nearest neighbor classiﬁer to

ﬁnd the two most probable classes for a given input pattern. The K -nearest neighbor

130

192-dimensional test pattern

 

Training Phase

I 7
Training set E L K-nearest neighbor
r classifier

wl R I LI Al T : ﬁrstrecall secon recall

 

 

 

 

 

 

 

 

 

 

 

V {WyRLATl {W,R,L,A,T}

 

 

 

Neural networks

W
W
W
i m
3 m
W
—'—.DA_—TLl——» {W.R.L.A.T}

 

 

 

 

 

 

 

 

 

 

 

Multiplexer

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 4.7: Two—stage classiﬁcation scheme using K-NN and neural network classiﬁers.

decision rule ﬁrst ﬁnds the K nearest neighbors of the test pattern in the feature space
and then assigns the test pattern to the class which is most frequently represented
among the K nearest neighbors. The top two categories can be retrieved from the
K -N N classiﬁer corresponding to the classes which have the highest and the second
highest count among the K nearest neighbors, i.e., the ﬁrst recall and the second
recall. In the second stage of the classiﬁer, 10 (CS) neural networks are trained to
solve each of the 10 two—class problems. The second stage uses the ﬁrst and second

recalls to select the speciﬁc neural network which has been trained to distinguish

131

between the corresponding pair of classes and the input pattern is then sent to the
' selected neural network for further classiﬁcation. This neural network makes the ﬁnal

decision between these two classes.

4.4 Experimental Results

4.4.1 Dataset

 

(b)

 

Figure 4.8: Example of images in the NIST 4 database with two ground truth labels.
The poor quality ﬁngerprint in (a) is labeled as belonging to both the arch and tented
arch classes, (b) is labeled as belonging to both the left loop and tented arch classes.

The NIST-4 database consists of 4, 000 ﬁngerprint images (image size is 512 x 480)
from 2, 000 ﬁngers. Each ﬁnger has two impressions (first and second). Each image
is labeled with one or more of the ﬁve classes (W, R, L, A, and T). About 17% of the

ﬁngerprint images in the NIST 4 database are labeled with two labels which shows

that there is disagreement among the human experts about the true class of a large

132

 

Figure 4.9: Example of images which were rejected because a valid tessellation could
not be established.

number of ﬁngerprints. The fraction of images with more than one label can also
be interpreted as a measure of human accuracy in classifying ﬁngerprints. On this
basis, we can say that there is about 17% error in classifying ﬁngerprints by human
experts. The accuracy of the current automatic ﬁngerprint classiﬁcation system is of
the same order. See Figure 4.8 for examples of ﬁngerprint images that were assigned
two different labels. To simplify the training procedure, we make use of only the ﬁrst
label of a ﬁngerprint to train our system. For testing, however, we make use of all
the true labels assigned to a ﬁngerprint and consider the output of our classiﬁer to be
correct if the output matches any one of the labels. This is in line with the common
practice used by other researchers in comparing the classiﬁcation results on the NIST-
4 database. The images in the NIST-4 database are numbered f0001 through f 2000
and 30001 through 32000. Each number represents a fingerprint from a different
ﬁnger. We form our training set with the ﬁrst 2, 000 ﬁngerprints from 1, 000 ﬁngers

(f0001 to f1000 and 30001 to 31000) and the test set contains the remaining 2,000

133

ﬁngerprints (f 1001 to f2000 and 31001 to 32000). The natural proportion (prior
probabilities) of ﬁngerprints belonging to each class is 0.279, 0.317, 0.338, 0.037, and
0.029 for the classes W, R, L, A, and T, respectively [43]. Classiﬁcation accuracies
can be signiﬁcantly increased by using datasets whose records follow the natural
distribution of ﬁngerprint classes because the more common types of ﬁngerprints
(loop and whorl) are easier to recognize. However, we do not use datasets with
a natural class distribution. Twenty eight ﬁngerprints from the training set were
rejected by our feature extraction algorithm because the reference point was detected
at a corner of the image and, therefore, a valid tessellation could not be established
for these images (Figure 4.9). Thirty ﬁve ﬁngerprints were rejected from the test
set for the same reason. So, our training set contains 1, 972 ﬁngerprint images and
the test set contains 1, 965 ﬁngerprint images. The thirty ﬁve images rejected from
the test set of 2, 000 ﬁngerprints amounts to a reject rate of 1.8%. We report the
results of our ﬁngerprint classiﬁcation algorithm on the NIST-4 database for the
ﬁve-class ﬁngerprint classiﬁcation problem. Since ﬁngerprint classes A (arch) and
T (tented arch) have a substantial overlap, it is very difﬁcult to separate these two
classes. Therefore, we also report our results for the four-class classiﬁcation problem,
where classes A and T have been merged into one class. By incorporating a rejection
option, classiﬁcation accuracy can be increased. We report the improvement in error
rates at different rejection rates for both the ﬁve-class and the four-class classiﬁcation

problems.

134

4.4.2 K -Nearest neighbor classiﬁer

The K -nearest neighbor classiﬁer results in an accuracy of 85.4% for the ﬁve-class
classiﬁcation task when 10 nearest neighbors (K = 10) are considered. Classiﬁcation
accuracy does not always increase with increasing K; there exists an optimal value
of K which is a function of the number of available training samples (Figure 4.10)
[8]. For the four-class classiﬁcation task (where classes A and T were collapsed into
one class), an accuracy of 91.5% is achieved. The confusion matrix for the K -nearest
neighbor classiﬁcation for the ﬁve-class problem is shown in Table 4.2. The diagonal
entries in this matrix Show the number of test patterns from different classes which
are correctly classiﬁed and the off-diagonal entries denote the number of classiﬁcation
errors. Since a number of ﬁngerprints in the NIST-4 database are labeled as belonging
to two different classes, row sums of the confusion matrices in Tables 4.2, 4.4, and 4.6

are not identical.

Table 4.2: Confusion matrix for the K -nearest neighbor classiﬁcation for the ﬁve-class
problem; K = 10.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Assigned class
True class W R L A T
W 320 38 31 6 0
R 1 368 2 10 21
L 0 1 359 13 8
A 1 3 7 422 20
T 0 15 16 95 208

 

135

 

 

I
I

22

-"' N N
(O O —‘
I l r
1 1 1

Error (%)

_L
m
l
i

I
l

17

I
I

16

I
l

15

 

 

 

14 l l l l J
0

Figure 4.10: K vs. classiﬁcation error for the K -nearest neighbor classiﬁer for the
ﬁve-class problem.

4.4.3 Neural network classiﬁer

We trained a multi-layer feed-forward neural network using a quick propagation train-
ing algorithm [154]. The neural network has one hidden layer with 20 neurons, 192
input neurons corresponding to the 192 features, and 5 output neurons corresponding
to the ﬁve classes. We obtained an accuracy of 86.4% for the ﬁve—class classiﬁcation
task. For the four-class classiﬁcation task, an accuracy of 92.1% is achieved. The

confusion matrix for the neural network classiﬁcation is shown in Table 4.4.

136

Table 4.3: Confusion matrix for the K -nearest neighbor classiﬁcation for the four-class
problem; K = 10.

 

 

 

 

 

 

Assigned class
True class W R L A + T
W 320 38 31 6
R 1 368 2 32
L 0 1 359 21
A + T 1 18 23 745

 

 

 

 

 

 

 

 

Table 4.4: Confusion matrix for the neural network classiﬁcation for the ﬁve-class
problem.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Assigned class
True class W R L A T
W 352 29 10 2 2
R 6 374 1 9 17
L 10 2 353 10 7
A 0 6 8 384 48
T 1 16 19 64 235

 

 

4.4.4 Two-stage classiﬁer

The objective here is to perform a “simple” classiﬁcation task using a K -NN classiﬁer
and then use a bank of two-class neural network classiﬁers to handle more subtle

discriminations. The ﬁrst stage uses the K -nearest neighbor (K 10) classiﬁer
to yield the two most probable classes. We observed that 85.4% of the time, the
class with the maximum vote among the K nearest neighbors is the correct class
and 12.6% of the time, the class with the second highest vote is the correct class.
In other words, the K -nearest neighbor classiﬁer yields the top two classes with an

accuracy of 98%. This result itself can be used to accurately classify ﬁngerprints into

two out of the ﬁve classes. Each ﬁngerprint will have an entry in two of the ﬁve

137

Table 4.5: Confusion matrix for the neural network classiﬁcation for the four-class

 

 

 

 

 

 

problem.
Assigned class
True class W R L A + T
W 352 29 10 4
R 6 374 1 26
L 10 2 353 17
A + T 1 22 27 731

 

 

 

 

 

 

 

 

partitions of the database and the matching is required to be performed only in the
corresponding two partitions of the database. The second classiﬁcation stage uses 10
different neural networks for 10 different pairwise classiﬁcations of ﬁve classes. These
neural networks have 192 input neurons, 20 — 40 hidden neurons in one hidden layer,
and 2 output neurons. Each neural network is trained using the patterns from only
the two corresponding classes in the training set. For example, the neural network
which distinguishes between R and W is trained using only the patterns labeled R

and W in the training set.

Table 4.6: Confusion matrix for the two-stage classiﬁcation for the ﬁve-class problem.

 

 

 

 

 

 

 

 

Assigned class
True class W R L A T
W 366 16 8 4 1
R 3 372 1 8 17
L 6 0 364 6 7
A 2 1 3 405 39
T 0 6 14 55 261

 

 

 

 

 

 

 

 

 

This two-stage classiﬁer yields an accuracy of 90% for the ﬁve-class classiﬁcation
task and an accuracy of 94.8% is achieved for the four-class classiﬁcation task. The

confusion matrix for the two—stage classiﬁer for the ﬁve-class and four-class classiﬁ-

138

Table 4.7: Confusion matrix for the two—stage classiﬁcation for the four—class problem.

True class

 

AM

(a) Arch (b) Left Loop

Figure 4.11: Poor quality images which were correctly classiﬁed.

cations are shown in Tables 4.6 and 4.7 respectively. These classiﬁcation accuracies
do not take into account the prior class probabilities. The equal number of samples
for each class in the N IST-4 database provides a relatively larger number of samples
of the rare classes (arch and tented arch). However, in an operational system, the
number of ﬁngerprints for a class will be proportional to the natural distribution of
ﬁngerprints. We can estimate the performance of our two-stage ﬁngerprint classiﬁer
on a naturally distributed database from the confusion matrices in Tables 4.6 and
4.7 by multiplying the error rate for each class with its prior probability. The es-

timated classiﬁcation accuracy on a naturally distributed database is 93.0% for the

139

   

‘l:

ht Loop

     

(a) Whorl ‘ I?” I (b)Rg

Figure 4.12: Poor quality images which were misclassiﬁed as arch.

ﬁve-class problem and 93.9% for the four-class problem. Although our classiﬁer is
robust to noise and is able to correctly classify most of the poor quality ﬁngerprints
in the NIST-4 database (Figure 4.11), it fails on some very bad quality ﬁngerprint
images where no ridge information is present in the central part of the ﬁngerprint
(Figure 4.12). In poor quality ﬁngerprints it is very difﬁcult to detect the reference
point correctly (Figure 4.9 (b)). Our classiﬁer also fails to correctly classify twin loop
images which are labeled as whorl in the N IST—4 database. For these images, our
reference point location algorithm picks up the upper core and on considering that
as the center, the image looks like a loop in the region of interest which leads to a
misclassiﬁcation of W as L or R. See Figures 4.13 for these misclassiﬁcations. About
3% of the errors result from loop-arch misclassiﬁcation because of the subtle difference
between loop and arch types (see Figure 4.14(a)). The A—T misclassiﬁcation accounts
for about 5% of the errors. An example of this type of confusion is shown in Figure

4.14(b).

140

         

(a) Whorl as Right Loop (b) Whorl as Left Loop

Figure 4.13: Misclassiﬁcation of whorl (twin loop) as (a) right loop (b) left loop.
4.4.5 Reject option

Classiﬁcation accuracies can be further increased by incorporating a reject option. We
use the (K, Kl)-nearest neighbor classiﬁer [145] for rejection and the proposed two-
stage classiﬁer for classiﬁcation. If the number of training samples from the majority
class among the K nearest neighbors of a test pattern is less than K’ (K ’ < K), we
reject the test pattern and do not attempt to classify it. Most of the rejected images
using this scheme are of poor quality (Figures 4.15 (a) and (b)). Other rejected images
are those images which “appear” to belong to different classes. For example, for the
ﬁngerprint image shown in Figure 4.15 (c), 3 of its nearest neighbors belong to class
R, 3 to class A and 4 to class T. By rejecting 19.5% of the images for the ﬁve-class
problem, the classiﬁcation accuracy can be increased to 93.5% and for the four-class

classiﬁcation problem, the accuracy can be increased to 96.6% (Table 4.8).

141

  

«mar ""

(a) Right loop (b) Arch

   

Figure 4.14: Examples of arch-loop misclassiﬁcations; (a) a right loop misclassiﬁed
as an arch; (b) an arch misclassiﬁed as a tented arch.

Table 4.8: Error-reject tradeoff.

 

4.4.6 Support vector machine classiﬁer

For comparison purposes, we also used a support vector machine (SVM) classiﬁer
for our ﬁngerprint classiﬁcation problem. Support vector machines are kernel-based
classiﬁers that have gained a signiﬁcant popularity in recent years due to their supe-
rior performance demonstrated on a number of practical classiﬁcation applications.
The SVM classiﬁers are binary classiﬁers which seek that hyperplane as the decision
boundary which maximizes the margin between the two classes. The parameters of a

support vector machine classiﬁer are the type of kernel, kernel parameters, and a con-

142

 

(C)
Figure 4.15: Examples of images rejected by (10, 5)-N N classiﬁer.

143

Table 4.9: A comparison of various ﬁngerprint classiﬁcation algorithms on the NIST
4 database.

 

 

 

 

 

 

 

 

 

 

 

Algorithm Year 5—class accuracy 4-class accuracy

% (reject rate %) % (reject rate %)
Wilson et a1. [43] 1993 90.2 (10) NA
Karu et al. [97] 1996 85.5 91.1
Hong et al. [105] 1999 87.2 92.3
Proposed 1999 90.0 (1.8) 94.8 (1.8)
Cappelli et al. [141] 1999 92.2 94.5

 

stant c that controls the trade-off between the training error and the margin. We used
the SVM Torch package [144] for our ﬁngerprint classiﬁcation problem. The best accu-
racy of 86.1% for the ﬁve-class classiﬁcation task was achieved when a Gaussian kernel
of standard deviation 10 and c = 100 was used. For a four-class problem, an accuracy
of 91.8% is achieved using the same parameters. An n-class classiﬁcation problem is
solved by considering n one-against-the—others support vector machine classiﬁers. The
number of support vectors generated in the ﬁve-class classiﬁcation task for the whorl—
against-the others classiﬁer was 239, the left loop-against-the—others classiﬁer was 325,
the right loop—against-the-others was 380, the arch—against-the—others was 427, and
the tented arch-against-the-others was 638. Thus the total number of support vectors
used by the multi—class SVM was 2, 009. Consequently, the SVM classiﬁer is slower
than the K -nearest neighbor classiﬁer while providing no signiﬁcant improvement in

classiﬁcation accuracy.

144

4.4.7 Consistency results

In the ﬁngerprint classiﬁcation task, another metric of performance evaluation is the
classiﬁer consistency. The purpose of the ﬁngerprint classiﬁcation task is to index the
ﬁngerprint database such that the input ﬁngerprint needs to be compared only with
a subset of the database. Suppose a ﬁngerprint (let us say, of type arch) is “wrongly”
classiﬁed (let us say, to type left loop) during the indexing. However, if the input
ﬁngerprint is another impression of the same ﬁnger, and is again misclassiﬁed as the
same category (left loop), the indexing scheme would still be effective. The best
consistency results for 967 pairs of ﬁngerprints in the test set was achieved using a
16—nearest neighbor classiﬁer as 82.6% for the ﬁve-class classiﬁcation and 89.8% for
the four-class classiﬁcation. The classiﬁcation results stated in Table 4.8 made use of
the multiple labels of the ﬁngerprint images in the NIST-4 database. However, if we
strictly consider only the ﬁrst label of the ﬁngerprint images in the NIST-4 database
for a fair comparison, the K -nearest neighbor ﬁngerprint classiﬁer gives a ﬁve-class
classiﬁcation accuracy of 79.8% and four-class classiﬁcation accuracy of 88.3%. Thus,
the consistency result is 2.8% (82.6% — 79.8%) better than the accuracy result for the

ﬁve-class problem and 1.5% (89.8% — 88.3%) better for the four-class problem.

4.4.8 Deﬁning New Classes

The ﬁve ﬁngerprint classes, i.e., whorl, left loop, right loop, arch, and tented arch,
used in this chapter are based on the Henry system of classiﬁcation which has been

in use for more than one hundred years. These classes used in the forensic domain

145

may not be the best separable categories in our ﬁlterbank—based feature space. It is
possible to deﬁne new classes such that the ﬁngerprints belonging to different classes
are compact and well separated in the feature space. We ﬁrst assumed that the
“clusters” formed by the ﬁngerprint patters in the FingerCode-space are essentially
spherical. As a result, we used a standard k-means clustering algorithm that uses
Euclidean distance metric on the training data to detect clusters in the feature space.
The clusters thus detected do not have any physical meaning in terms of ﬁngerprint
patterns and deﬁne non-intuitive ﬁngerprint categories. Since the k-means clustering
algorithm depends on the initialization of cluster centers, we performed multiple (20)
runs of the k-means algorithm with different initializations and chose the clustering
with the minimum squared error. The best consistency results on the 967 pairs of
test images were 73.8% (using a 7-nearest neighbor classiﬁer) when ﬁve clusters were
deﬁned and 82.2% (using a 12-nearest neighbor classiﬁer) when four clusters were
deﬁned. On changing the distance metric for the k—means algorithm from Euclidian
distance to Mahalanobis distance [145], the k-means algorithm seeks hyper-elliptical
clusters instead of spherical cluster. We achieve sightly higher consistency results
of 76.2% for the four-class problem and 85.2% for the ﬁve-class problem by using
the Mahalanobis distance. This suggests that the shape of the clusters formed in
the F ingerCode feature space is closer to elliptical than spherical. However, the
consistency results when the classes were deﬁned using a clustering of the data are
inferior as compared to the consistency results when the classes were deﬁned by a
ﬁngerprint expert. This implies that the ﬁngerprints do not form well deﬁned clusters

in the F ingerCode feature space and an exclusive classiﬁcation of ﬁngerprints has

146

limitations because of the inherent overlap between the ﬁngerprint classes. Therefore,
a continuous classiﬁcation of ﬁngerprints should be explored. A successful continuous

ﬁngerprint classiﬁer is developed by Lumini et al. in [22].

4.4.9 Dimensionality Reduction Using PCA

The training and the test sets contain about 2, 000 samples each while our feature
vector is 192-dimensional. It is desirable to have a large number of representative
samples per class (e.g., ten times) with respect to the feature dimension for good
generalization of a practical classiﬁcation system [145]. Since the collection of a
large number of representative samples is expensive, we used the principal component
analysis (KL transform) to reduce the dimensionality of the feature vector and used
a K-nearest neighbor algorithm classiﬁer. While an accuracy of 85.4% was achieved
with this KL—KN N classiﬁer when all the 192 features were used, we achieved an
accuracy of 85.1% when only 96 features were used (8—nearest neighbor classiﬁer),
84.3% when 72 features were used (IO-nearest neighbor classiﬁer), and 83% when 48
features were used (12—nearest neighbor classiﬁer). Thus, with a slight degradation
in performance, we were able to reduce the feature vector size to 1 / 4th of its original
value. A similar behavior was observed in the classiﬁer consistency results as well.
The consistency was 81.1% for 96 features, 81.0% for 72 features, and 79.2% for 48

features.

Cappelli et al. [141] used a Multi-space KL transform for feature reduction. The

central idea of this approach is to ﬁnd one or more KL subspaces for each class that

147

are well-suited in representing the ﬁngerprints in that class. They used a ﬁxed number
of subspaces for each class. The selection of the number of subspaces for a class was
ad-hoc and was based on the authors’ perception of complexity of that class (arch,
left loop, right loop, whorl, and tented arch, were assigned 1, 2, 2, 3, and 1 subspaces,
respectively). An accuracy of over 99% with 20% reject rate was reported on the
naturally distributed NIST-14 database using a combination of six classiﬁers including
the Multi—KL—KN N classiﬁer which was the best individual classiﬁer. The accuracy on
the NIST-4 database that contains equal number of ﬁngerprint images from the ﬁve
classes was not reported and is expected to be inferior due to inclusion of large number
of more difﬁcult arch and tented arch type ﬁngerprint images. We used a similar idea
to develop a Multi—KL-KN N classiﬁer based on the ﬁlterbank representation. We
used an equal number of subspaces for all the ﬁve classes (one for each class) because
the complexity of each class in not known apriori in the ﬁlterbank representation. We
were able to achieve a ﬁve-class classiﬁcation accuracy of 85.1% when only 96 features
were used for each class, an accuracy of 84.9% was achieved when 72 features were
used, and an accuracy of 83.2% was achieved when only 48 features were used. This
shows that Multi-KL—KNN classiﬁer performs marginally better than the KL-KNN

classiﬁer but not as good as without dimensionality reduction.

4.4.10 Dimensionality Reduction Using Feature Clustering

Although the feature dimension reduction using principal component analysis is useful

as the ﬁnal classiﬁer is based on fewer features and as a consequence, is faster, the

148

feature extraction time is not reduced. All the 192 features are ﬁrst extracted from
the ﬁngerprint images and then the feature vector is reduced by'projecting it to the
new space. In order that the feature extraction time is reduced, we need to “select”
a subset of features while maintaining the classiﬁcation accuracy. For this purpose,
we used a standard k-means clustering algorithm to cluster the features into 96 and
48 clusters, respectively. Due to very few number of samples in each cluster, the
clustering results are not used directly for feature reduction. We observe that the
corresponding feature values for the same location but different orientation cluster
together. This means that there is some redundancy in the different directions (4
in our case) used for the Gabor ﬁlters during the feature extraction. However, each
direction yields some extra information such that the classiﬁcation accuracy increases
by using more directions. The increase in the classiﬁcation accuracy that results from
using more number of orientation speciﬁc ﬁlters result in increased computation time
for feature extraction. Depending on the application, the tradeoff between accuracy
and time can be selected. For example, using a K -nearest neighbor classiﬁer, an
accuracy of 85.4% is achieved by using 4 directions, an accuracy of 82.0% is achieved
when 2 directions are used and an accuracy of 65% is achieved when only one direction
is used. A similar behavior was observed in the classiﬁcation consistency results as
well. The consistency was 82.6% for four directions, 79.1% for two directions, and

61.9% when only one direction was used.

149

u a na- -- u_ _: _7

4.5 Summary

We have developed a ﬁngerprint classiﬁcation algorithm that uses the ﬁlterbank-based
representation and outputs an accuracy comparable to the state-of-the—art algorithms
reported in the literature on the NIST-4 database. Our feature vector, called Fin-
gerCode, captures the ﬁngerprint class information and is robust to noise which is
reﬂected in the high classiﬁcation accuracy. We have tested our algorithm on the
NIST-4 database and a very good performance has been achieved (90% for the ﬁve-
class classiﬁcation problem and 94.8% for the four-class classiﬁcation problem with
1.8% rejection during the feature extraction phase). However, this algorithm suf-
fers from the requirement that the region of interest be correctly located, requiring
the accurate detection of reference point in the ﬁngerprint image. Our system takes
about 3 seconds on a Sun Ultra-10 machine to classify one ﬁngerprint. Since image
decomposition (ﬁltering) steps account for 90% of the total compute time, special
purpose hardware for convolution can signiﬁcantly decrease the overall time for clas-
siﬁcation. Most of the work in ﬁngerprint classiﬁcation has concentrated on features
(e.g., location of singular points, orientation ﬁeld) that the forensic scientists have
used for a long time. These classiﬁers perform discrete classiﬁcation of ﬁngerprint
images into one of the predetermined classes. Since there exits a continuum of ﬁnger—
print patterns between these discrete predetermined classes, the automatic systems
based on simple features such as singular points or orientation ﬁeld will have a lim-
ited performance irrespective of the location and shape of the decision boundary

When performing discrete classiﬁcation. By attempting to design features which are

150

parameterized, rich and completely data driven, such as the ones proposed in this
thesis, we can apply advanced pattern recognition and clustering techniques instead
of simple hand-crafted rules to gain performance improvement. We believe that the
FBI requirement of 1% error with 20% reject rate is very challenging to meet. The
algorithms that have reported a performance close to or surpassing this requirement
[44, 141] have reported their results on a naturally distributed database and have thus
taken the advantage of the fact that the less frequently occurring classes are more
difﬁcult to classify. We have shown that the simple variance-based features proposed
in this thesis work quite well. However, we expect that better performance can be
achieved by extracting richer, more discriminatory features from the ﬁltered images

in the feature extraction algorithm.

151

Chapter 5

Fingerprint Matching

The distinctiveness of a ﬁngerprint can be determined by the overall pattern of ridges
and valleys as well as the local ridge anomalies (minutiae points). Although the ridges
possess the discriminatory information, designing a reliable automatic ﬁngerprint
matching algorithm is very challenging due to the nonlinear deformation and noise in
ﬁngerprint images (see Figure 3.2).

The existing popular ﬁngerprint matching techniques can be broadly classiﬁed
into two categories: (a) minutiae-based and (b) correlation—based. The minutiae-
based techniques typically match the two minutiae sets from two ﬁngerprints by ﬁrst
aligning the two sets and then counting the number of minutiae that match. A typ-
ical minutiae extraction technique performs the following sequential operations on
the ﬁngerprint image: (2') ﬁngerprint image enhancement, (z'z') binarization (segmen-
tation into ridges and valleys), (iii) thinning, and (w) minutiae detection. Several
commercial [112] and academic [131, 11] algorithms follow these sequential steps for
minutiae detection. Alternative techniques for minutiae detection directly operate

152

on the gray scale ﬁngerprint image itself and detect minutiae by adaptively tracing
the gray scale ridges in the ﬁngerprint images [56, 181]. The alignment between the
input and the template ﬁngerprints can be obtained using one or more of the ﬁnger-
print features. For example, an alignment can be achieved based on the orientation
ﬁeld of the ﬁngerprints, the location of singular points such as the core and the delta
[95], ridges [11], inexact graph-matching on the minutiae graphs [5], Hough trans-
form [131], point patterns [128]), etc. The number of matched minutiae in certain
tolerances is typically normalized by the total number of minutiae in the two sets to
account for the falsely detected and missed minutiae during the feature extraction.
One of the main difﬁculties in the minutiae-based approach is that it is very difﬁcult
to reliably extract minutiae in a poor quality ﬁngerprint image. A number of image
enhancement techniques can be used to improve the quality of the ﬁngerprint image
prior to minutiae extraction (e.g., [108]).

Correlation-based techniques match the global pattern of ridges and furrows to
see if the ridges align. The simplest technique is to align the two ﬁngerprint images
and subtract the input from the template to see if the ridges correspond. However,
such a simplistic approach suffers from many problems including the errors in esti-
mation of alignment, non-linear deformation in ﬁngerprint images, and noise. An
auto—correlation technique has been proposed by Sibbald [31] that computes the cor-
relation between the input and the template at ﬁxed translation and rotation incre-
ments. If the correlation exceeds a certain threshold, the two ﬁngerprints are declared
to originate from the same ﬁnger. A variant of the correlation technique is to perform

the correlation in the frequency domain instead of the spatial domain by performing

153

a two-dimensional fast Fourier transform (FFT) on both the input and the template
ﬁngerprints. The sum of the pixel-to—pixel multiplication of the two frequency do-
main representations of the ﬁngerprint images is then compared to a threshold to
make a decision. One of the advantages of performing correlation in the frequency
domain is that the frequency representations of the ﬁngerprints are translation in-
variant. One of the major disadvantages, however, is the extra computation time
required to convert the spatial image to a frequency representation. The frequency
domain correlation matching can also be performed optically [137, 38, 73]. The input
and the template ﬁngerprints are projected via laser light through a lens to produce
their Fourier transform and their superposition leads to a correlation peak whose
magnitude is high for the matching pair and low otherwise. The main advantage of
performing optical correlation is the speed; the main disadvantage is that optical pro-
cessors have very limited versatility (programmability) (cf. [112]). A modiﬁcation of
the spatial correlation-based techniques is to divide the ﬁngerprint images into grids
and determine the correlation in each sector instead of the whole image [61, 103].
The correlation-based technique overcomes some of the limitations of minutiae-based
approach. For example, the minutiae extraction algorithm detects a large number
of spurious minutiae and misses genuine minutiae in very noisy ﬁngerprint images.
Correlation-based techniques are less sensitive to the noise in ﬁngerprint images but
have problems of their own. For example, correlation-based techniques are more sen-
sitive to an error in estimation of the alignment between the two ﬁngerprints. Also,
the correlation-based techniques cannot easily deal with the non-linear deformation

present in the ﬁngerprint images. Additionally, the correlation-based techniques typi-

154

cally have larger template size. See Table 5.1 for a comparison of different ﬁngerprint

matching algorithms.

Table 5.1: Fingerprint matcher literature survey. The ﬁngerprint matching algorithms
are classiﬁed based on the alignment assumed between the template and the input
ﬁngerprint features. The rotation is denoted by R, the translation is denoted by T,
and the scale is denoted by S.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Author (Year) Alignment Features Used
Kovacs-Vajna [186] (2000) nonlinear minutiae and its
16 x 16 grayscale
neighborhood
Jiang et al. [182] (2000) R + T + S minutiae
Almansa and Cohen [1] (2000) nonlinear minutiae
Jain et al. [19] (2000) R + T texture features
O’Gorman [112] (1999) R + T in local regions minutiae
Jain et al. .11] (1997) R + T + nonlinear thin ridges, minutiae
Sibbald [31] (1997) R + T grayscale intensity
Ratha et al. [131] (1996) R + T + S minutiae
Maio et al. [58] (1995) R + T minutiae, core, delta
Coetzee and Botha [103] (1993) R + T minutiae and
frequency-domain
features
Marsh and Petty [137] (1991) R + T grayscale intensity
Driscoll et al. [61] (1991) R + T grayscale intensity

 

The ﬁlterbank-based representation described in Chapter 3 does not fall either
into the minutiae-based or the correlation-based matching categories. The proposed
technique is a feature-based technique that captures both the local and the global
details in a ﬁngerprint as a compact ﬁxed length feature vector (FingerCode). The
ﬁngerprint matching is based on the Euclidean distance between the two correspond-
ing FingerCodes and hence is extremely fast. We are able to achieve a veriﬁcation
accuracy superior to the results of a typical state-of-the—art minutiae-based algorithm

[11] in terms of equal error rates (see Table 5.3) and only marginally inferior at very

155

low false accept rates on two different databases. Finally, we Show that the matching
performance can be improved by combining the decisions of the matchers based on

complementary (minutiae-based and ﬁlter-based) ﬁngerprint information.

5.1 Introduction

It is desirable to explore representation schemes which combine global and local infor-
mation in a ﬁngerprint. Our novel, relatively short, ﬁxed length code representation
for the ﬁngerprints, called FingerCode is suitable for matching as well as storage on
a smartcard. The matching reduces to ﬁnding the Euclidean distance between these
FingerCodes and hence the matching is very fast and the representation is amenable

to indexing.

5.2 Feature Extraction

We have used the proposed ﬁlterbank-based representation described in Chapter 3
with the values of the parameters described below. In our initial experiments with
MSU_DBI database (image size = 508 x 480 pixels, scanned at 500 dpi), we considered
ﬁve concentric bands (B = 5) for feature extraction. Each band is 20—pixels wide (b
= 20), and segmented into sixteen sectors (k = 16) (Figure 3.9). Thus, we have a
total of 16 x 5 = 80 sectors (So through 579) and the region of interest is a circle
of radius 120 pixels, centered at the reference point. Eighty features for each of the

eight ﬁltered images provide a total of 640 (80 x 8) features per ﬁngerprint image.

156

Comfpute A.A.D.
eature

Input Image Normalize each sector Filtering

Locate the reference point Divide image in sectors

Template FingerCode

 

Matching result

Figure 5.1: System diagram of our ﬁngerprint authentication system.

157

Each feature can be quantized into 256 values and requires 1 byte of storage, so the
entire feature vector requires only 640 bytes of storage. Note that these parameters of
the tessellation depend upon the image resolution and size. In our second experiment
with N IST-9 database (image size = 832 x 768 pixels, scanned at 500 dpi), we used
7 concentric bands (B = 7), b = 20, and k = 16, giving us an 896 byte FingerCode.
The 640-dimensional feature vectors (FingerCodes) for nine different impressions
of the same ﬁnger are shown as gray level images with eight disks, each disk corre-
sponding to one ﬁltered image in Figure 5.2. The gray level in a sector in a disk
represents the feature value for that sector in the corresponding ﬁltered image. The
nine ﬁngerprint images of the different impressions of the same ﬁnger differ from each
other in translation, rotation, non-linear deformation, image intensities in different
part of the ﬁngerprint, and noise. A simple correlation—based technique that subtracts
the input image from the template is unlikely to succeed due to the large intra—class
variation in different impressions of the same ﬁnger. The tessellation scheme of the
proposed ﬁlterbank-based algorithm is able to handle small errors in the location of
the reference point for translation invariance of the representation. One can see that
the representations for the nine impressions of the same ﬁnger visually look very sim-
ilar. However, the feature values in different impressions are not exactly the same.
This difference results from the image rotation and non-linear deformation. However,
the gray scale intensity-based feature (variance) is able to handle small rotation and
non-linear deformation in each sector. The Euclidean distance between these nine
FingerCodes ranges from 10 and 40 (normalized to a scale of 0—100) which quantiﬁes

the typical intra—class variability in a single user. The Euclidean distance between the

158

FingerCodes from different ﬁngers range from 30 to 100 on the same scale quantifying

the typical inter-class variability in the representation.

 

(g) (h) (0

Figure 5.2: Examples of 640-dimensional feature vectors corresponding to nine dif-
ferent impressions of the same ﬁnger.

159

5.3 Matching

Fingerprint matching is based on ﬁnding the Euclidean distance between the corre-
sponding FingerCodes. The translation invariance in the FingerCode is established by
identifying the reference point. However, F ingerCodes are not rotationally invariant.
The approximate rotation invariance is achieved by cyclically rotating the features in
the FingerCode itself. A single-step cyclic rotation of the features in the FingerCode
described by Eqs. (5.1)-(5.3) corresponds to a feature vector which would be obtained
if the image was rotated by 22.5°. A rotation by R steps corresponds to a R x 225°
rotation of the image. A positive rotation implies counterclockwise rotation while a
negative rotation implies clockwise rotation. See Figure 5.3 for an illustration. The

FingerCode obtained after R steps of rotation is given by

vi? 2 Vi’9’a (5'1)
2' = (2' + k — R) mod k + (2' div k) x k, (5.2)
9' = (9 + 180° + 22.5° x (—R)) mod 180°, (5.3)

where V5 is the rotated FingerCode, V219, is the original FingerCode, k (= 16) is the
number of sectors in a band, 2' E [0, 1,2, ...79], and 6 6 [0°, 225°, 45°, 675°, 90°,

112.5°, 135°, 157.5°].

For each ﬁngerprint in the database, we store ﬁve templates corresponding to the
following ﬁve rotations of the corresponding FingerCode: K52, V51, V13, ‘45, and

14.3. We use only ﬁve values of parameter R (—2, —1,0, 1, 2) because the ﬁngerprint

160

 

(d)

Figure 5.3: The ﬁngerprint image in (b) is obtained by a —22.5° rotation of (a). A
part of the feature vector corresponding to the 0° Gabor ﬁltered image extracted
from (a) is shown in (c) as a gray scale image. The feature vector in (c) is rotated
by —22.5° (R = —1 in Equations (5.2) and (5.3)) and is shown in (d). (e) shows the
feature vector extracted from the ﬁngerprint image in (b). The feature vectors shown
in (d) and (e) are similar illustrating that the feature vector for a —22.5° rotation in
the original image approximately corresponds to a unit anticlockwise cyclic rotation
of the feature vector.

images in both the MSU_DBI and NIST-9 databases do not have more than :l:45°
rotation. For databases that have more rotation in the ﬁngerprint images, a higher
range for the parameter R may be used. The input FingerCode is matched with
the ﬁve templates stored in the database to obtain ﬁve different matching scores.
The minimum of these ﬁve matching scores corresponds to the best alignment of
the input ﬁngerprint with the database ﬁngerprint. Since a single cyclic rotation
of the features in the FingerCode corresponds to a rotation of 225° in the original

image, we can only generate those representations of the ﬁngerprint which are in

161

multiples of 225°. Due to the nature of the tessellation, our features are invariant to
only small perturbations that are less than :tll.25°. Therefore, we generate another
feature vector for each ﬁngerprint at the time of user enrollment which corresponds
to a rotation of 11.25°. The original image is rotated by an angle of 11.25° and its
FingerCode is generated. Five templates corresponding to the various rotations of
this F ingerCode are also stored in the database. Thus, the database contains 10
templates for each ﬁngerprint. These 10 templates correspond to all the rotations of
the ﬁngerprint image in multiples of 11.25°. This takes care of the ﬁngerprint rotation
while matching the input FingerCode with the stored templates. The ﬁnal matching
distance score is taken as the minimum of the ten scores obtained by matching the
input FingerCode with each of the 10 templates. This minimum score corresponds
to the best alignment of the two ﬁngerprints being matched. Since the template
generation for storage in the database is an off-line process and the matching process
is extremely fast, the veriﬁcation time still depends on the time taken to generate a

single template for the test image.

5.4 Experimental Results

Our MSU.DBI database consists of a total of 2,672 ﬁngerprint images from 167
subjects. A live feedback of the acquired image was provided during the data capture
and the volunteers guided the subjects in placing their ﬁngers in the center of the
sensor and in an upright position. Due to this assistance provided to the subjects,

most of the ﬁngerprints were reasonably well centered. Despite the supervised image

162

acquisition, there is a signiﬁcant intra—class deformation and up to i45° deviation
from the assumed vertical upright orientation in the acquired images. However, these
images are of better quality than the traditional inked ﬁngerprints (see Figure 5.4).
The ﬁngerprint images which were captured after a period of six weeks have signiﬁcant
nonlinear distortions due to ﬁnger pressure differences (see Figures 5.5 and 5.7(c) and

(d)). This presents a challenge to all the ﬁngerprint matching algorithms.

 

Figure 5.4: A comparison of the quality of inked ﬁngerprints and dab ﬁngerprints.
(a) inked ﬁngerprint, (b) dab ﬁngerprint.

We have also evaluated our system on 1, 800 images of the public domain database
NIST-9 (Vol. 1, CD. No. 1) which contains 1,800 ﬁngerprint images (image size =
832 x 768 pixels) from 900 different ﬁngers. The complete NIST-9 ﬁngerprint database
contains 1,350 mated ﬁngerprint card pairs (13,500 ﬁngerprint image pairs) that
approximate a natural distribution of the National Crime and Information Center

ﬁngerprint classes. The database is divided into multiple volumes. Each volume has

163

 

Figure 5.5: Examples of images with large deformation due to ﬁnger pressure differ-
ences in the MSU_DBI database. Fingerprint images in (b) and (d) were taken six
weeks after the images in (a) and (c) were acquired, respectively.

three compact discs (CD’S). Each CD contains 900 images of card type 1 and 900
images of card type 2. Fingerprints on the card type 1 were scanned using a rolled
method, and ﬁngerprints on card type 2 were scanned using a live-scan method.
Matching ﬁngerprint images in the NIST—9 database is more difficult compared to
the live—scan ﬁngerprint images because the two impressions from the same ﬁnger in

the NIST—9 database are captured using different methods (rolled and live—scan) and

164

 

hence the two images of the same ﬁnger differ signiﬁcantly in their ridge structures. A
large number of N IST-9 images are of poorer quality and these images often contain
extraneous objects like handwritten characters and other artifacts common to inked
ﬁngerprints.

One hundred images (approximately 4% of the database) were rejected from the
MSU_DBI database because of the following reasons: (2) the reference point was
located at a corner of the image and therefore an appropriate region of interest (tes-
sellation) could not be established, (22) the quality of the image was poor based on
the quality index of the images. See Figure 5.6 for examples of images which were
rejected. A total of 100 images (approximately 5.6% of the database) were rejected
from the N IST-9 database based on the same criteria. The quality index was deter-
mined using a quality checker algorithm [147] that estimates the dryness of the ﬁnger
(or smudginess of the ﬁngerprint image) and the extent to which the surface of the
ﬁnger tip is imaged. The estimate of the dryness / smudginess is based on the variance
of the grayscale in the captured image.

To establish the veriﬁcation accuracy of our ﬁngerprint representation and match-
ing approach, each ﬁngerprint image in the database is matched with all the other
ﬁngerprints in the database. A matching is labeled correct if the matched pair is
from the same ﬁnger and incorrect, otherwise. None of the genuine (correct) match-
ing scores was zero indicating that the images from the same ﬁnger did not yield an
identical FingerCode because of the rotation, distortion, and inconsistency in refer-
ence point location. For the MSU_DBI database, a total of 3, 306, 306 matchings were

performed. The probability distribution for genuine (correct) matches was estimated

165

I‘m— _

 

Figure 5.6: Examples of rejected images. (a) a poor quality image, (b) the reference
point is (correctly) detected at a corner of the image and so an appropriate region of
interest could not be established.

with 7,472 matches and the imposter distribution was estimated with 3,298,834
matches. Figure 5.8 (a) shows the two distributions. For the NIST—9 database, a to-
tal of 722, 419 matchings were performed and the genuine and imposter distributions
were estimated with 1, 640 and 720, 779 matching scores, respectively. Figure 5.8 (b)
shows the imposter and genuine distributions for the NIST—9 database. If the Eu-
clidean distance between two FingerCodes is less than a threshold, then the decision
that “the two images come from the same ﬁnger” is made, otherwise a decision that
“the two images come from different ﬁngers” is made. Different decision thresholds
lead to different values of FAR and FRR (see Table 5.2).

A Receiver Operating Characteristic (ROC) curve is a plot of Genuine Acceptance
Rate (1-FRR) against False Acceptance Rate for all possible system operating points
(i.e., matching distance threshold) and measures the overall performance of the sys-

tem. Each point on the curve corresponds to a particular decision threshold. In the

166

 

 

Figure 5.7: Errors in matching. Examples of ﬁngerprint images from the same ﬁnger
that were not correctly matched by our algorithm. (a) and (b) do not match because
of the failure of reference point location, (c) and (d) do not match because of the
change in inter ridge distances due to ﬁnger pressure difference.

167

Table 5.2: False acceptance and false reject rates with different threshold values for
the MSU.DBI database.

 

 

 

 

Threshold value False Acceptance Rate (%) False Reject Rate (%)
30 0.10 19.32
35 1.07 7.87
40 4.59 2.83

 

 

 

 

 

ideal case, both the error rates, i.e., FAR and F RR should be zero and the genuine
distribution and imposter distribution should be disjoint. In such a case, the “ideal”
ROC curve is a step function at the zero False Acceptance Rate. On the other ex-
treme, if the genuine and imposter distributions are exactly the same, then the ROC
is a line segment with a slope of 45° with an end point at zero False Acceptance Rate.
In practice, the ROC curve behaves in between these two extremes. An Equal Error
Rate (EER) is deﬁned as that operating point where the two types of errors, FAR
and F RR, are equal. Figures 5.9 (a) and (b) compare the ROCS of a state-of-the—art
minutiae-based matcher [11] with our ﬁlter-based matcher on the MSU_DBI and the
N IST—9 databases, respectively. The ROC curves show that our system performs bet-
ter than the minutiae-based system when the system performance requirements are
less demanding on FAR (FAR greater than 2%) on both the databases. A number of
applications including bank’s ATM machines usually have such FAR requirements.
However, at very low FARs, our system performs worse than the minutiae—based ap-
proach. Our system also performs better than the minutiae-based system at the equal
error rate (see Table 5.3).

Most of the false accepts in our system occur among the same “type” (class) of

ﬁngerprints; a whorl is confused with another whorl and not a loop. This conﬁrms

168

 

 

Genuine ‘

01
I

.5
I
1

Imposter

Percentage (%)
w

M
I
l

 

 

 

0O 20 4O 60 80 1 00

Normalized matching distance

(a)

 

01
I

Genuine ]

Imposter

Percentage (%)
.5

(D
T
1

 

 

 

,A. . A1 .

O 20 4O 60 80 1 00
Normalized matching distance

(b)

Figure 5.8: Genuine and imposter distributions for the proposed veriﬁcation scheme.
(a) MSUDBI database, (b) NIST-9 (Vol. 1, CD No. 1).

 

169

 

100 I W I I I I I I I

I

96 , .,.—-~ ~" ‘ ’ -

I

94 _I'l ~

92

I
'\
1

~
\

90-

86- -

Genuine Acceptance Rate (%)

 

—— Filter—based

82 ~-~- Minutiae—based
+ Equal-Error Line

80 l 1 l l 1 l 1 l J

1 2 3 4 5 6 7 8 9 10
False Acceptance Rate (%)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(a)

100 . a a a

95" f
g3 90~ ,, , ’ ’ '
a: I"
13 ,>’
I: 85” /' ‘
8 .I'
s z
E 80 7’ .
g .
a) 751 -
.E !
2 .'
8 7o} -

i
55' —— Filter-based
‘--- Minutiae-based
—l— Equal—Error Line
60 l l l J
0 2 4 6 8 10
False Acceptance Rate (%)
(b)

Figure 5.9: Receiver Operating Characteristic (ROC) curves for two different
(ﬁlterbank-based and minutiae-based) matchers. (a) MSU_DBI database, (b) NIST-9
(Vol. 1, CD No. 1). FAR and FRR are equal at all points on the Equal-Error Line.
Thus, the point of crossing of ROC with this line denotes the equal error rate on the
ROC.

170

that the proposed approach does capture the global information as well as the local
information and hence is suitable for indexing as shown in Chapter 4. However, this
is a shortcoming in terms of veriﬁcation. The imposter distributions in Figure 5.8 are
wider than the typical imposter distribution in a minutiae—based approach. This also
suggests that FingerCodes capture more global information; at a global information
level, there is more similarity in ﬁngerprints from different ﬁngers. Since FingerCodes
also capture local information, there is more variation in imposter scores which results
in a wider imposter distribution than the minutiae-based technique. The genuine dis-
tribution for the minutiae-based approach is typically very wide because the matching
score depends heavily on the quality of the ﬁngerprint image. The ﬁlterbank-based
approach, on the other hand, has a relatively narrower genuine distribution due to
its superior ability to deal with noise in the ﬁngerprint image. As a result of this
difference in the characteristics of the genuine and the imposter distributions, when
the threshold is changed from a value corresponding to a very low FAR to high FARS,
the FRR for the minutiae-based approach drops very rapidly and then stabilizes. On
the other hand, the F RR for the ﬁlterbank-based approach drops slowly but steadily
with increasing FAR leading to a crossover of its ROC with the minutiae-based ROC
(see Figures 5.9(a) and (b)). This implies that the ﬁlterbank-based approach is supe-
rior to the minutiae—based approach at high FARS due to its ability to gracefully deal
with large amount of noise in the ﬁngerprint images. The ﬁlterbank-based approach
is inferior to the minutiae—based approach at low FARs because it is capturing more
global information and is not able to distinguish between ﬁngerprints that have a very

similar global structure. This suggests that the FingerCode representation captures

171

 

discriminatory information that is complementary to the information used by pop-
ular minutiae-based ﬁngerprint matchers. An added advantage of such independent
knowledge is that a combination of the two approaches, i.e., ﬁlterbank-based and
minutiae-based, can signiﬁcantly improve the overall performance of the veriﬁcation

system. This will be further discussed in Chapter 6.

Table 5.3: Comparison of the equal error rates (ERR) of the proposed ﬁlterbank-
based technique with a state-of-the-art minutiae-based technique on two different
databases.

 

 

 

 

Database Minutiae-based (%) F ilterbank-based (%)
(reject rate (%)) (reject rate (%))

MSU_DBI 3.9 (0) 3.5 (4.0)

NIST-9 7.1 (0) 6.7 (5.6)

 

 

 

 

 

5.5 Summary

We have developed a novel ﬁlter-based representation technique for ﬁngerprint veri-
ﬁcation. The technique exploits both the local and global characteristics in a ﬁnger-
print image to make a veriﬁcation. Each ﬁngerprint image is ﬁltered in a number of
directions and a ﬁxed—length feature vector is extracted in the central region of the
ﬁngerprint. The feature vector (FingerCode) is compact and requires only 640 (or
896, depending on image size) bytes. The matching stage computes the Euclidean
distance between the template FingerCode and the input FingerCode. With increas-
ingly cheaper CPU cycles and use of special purpose DSP chips, the computation
time in FingerCode extraction will become a nonissue. On MSU_DBI database of

2, 672 ﬁngerprints from 167 different subjects, 4 impressions per ﬁnger, we are able

172

m).

to achieve a veriﬁcation accuracy better than a state-of-the-art minutiae—based ﬁn-
gerprint matcher in terms of Equal Error Rate (EER) and only marginally inferior at
very low FARs (when the reject rate is not considered). A similar performance is ob-
served on the more challenging NIST-9 database. This shows that the discriminatory
power of the proposed representation is comparable to that of the minutiae-based
representation. Note that the performance of neither the minutiae-based system nor
the ﬁlterbank-based system is even close to the theoretical performance upper bound
established in Chapter 2.

The ﬁlterbank approach suffers from a number of disadvantages and more research
is needed in the following areas to improve the representation and matching: (2) The
registration is based on the detection of the reference point. Even though our multi-
resolution reference point location algorithm is accurate and handles the poor quality
ﬁngerprint images gracefully, it fails to detect the reference point in very low quality
images leading to either a rejection of the image or even worse, a false rejection in the
veriﬁcation system. A ﬁlterbank approach that aligns the ﬁngerprints based on the
minutiae information can achieve a more reliable registration and will not reject any
images due to the absence of the reference point. However, the representation thus
extracted will not be translation and rotation invariant resulting in a longer match-
ing time. (22) The current implementation of the ﬁlterbank representation is not
rotational invariant. The rotation is handled in the matching stage by rotating the
FingerCode itself. However, due to quantization of the rotation space and generation
of multiple alignment hypotheses, the false accepts increase. This problem can be

addressed by estimating'a frame of reference of the ﬁngerprints. However, estimation

173

of a frame of reference in the ﬁngerprints is a difﬁcult problem because all ﬁngerprints
have circular ridges in the portion above the core point. (222) Due to skin elasticity,
there is non-linear distortion in the ﬁngerprint images and even if the ﬁngerprints are
registered in location and orientation, all ridges in all sectors may not align. This
problem can be partially addressed by estimating the local ridge frequency in each
sector and normalizing each sector to a constant ridge frequency. (22)) the Finger—
Code representation does not have any explicit procedure to handle the noise in the
ﬁngerprint images due to the dryness/smudginess of the ﬁnger. Although the sec-
tors are normalized to a constant mean and variance and then ﬁltered using a bank
of Gabor ﬁlters, large amount of noise changes the gray-level image characteristics
and causes problems in the quantiﬁcation of discriminatory information in sectors.
The simple variance-based features proposed in this thesis perform well, have good
discriminatory power, and degrade more gracefully than the minutiae-based features
with noise in the ﬁngerprint images. However, we believe that extraction of richer
and more discriminatory features from the sectors in the ﬁltered images should be
explored to improve the matching performance. (12) The current implementation of
ﬁlterbank representation extraction takes longer than a typical minutiae-extraction
algorithm. Approximately 99% of the total compute time for veriﬁcation (~ 3 sec-
onds on a SUN ULTRA 10) for the images in the MSU_DBI database is taken by the
convolution of the input image with 8 Gabor ﬁlters. The convolution operation can
be made signiﬁcantly faster by dedicated DSP processors or performing the ﬁltering
in the frequency domain. If the reference point is correctly located, the features are

translation invariant and the rotation handled in the matching stage is very fast. As

174

'— ——~W- r

a result, the matching process is extremely fast. (v2) The current matching algorithm
is very simple, an implementation of a smarter matching algorithm should be able
to improve the veriﬁcation performance. For example, the match resulting from each
sector can be weighed differently based on image quality and a quantitative measure
of the nonlinear distortion in the sector. The veriﬁcation system should also beneﬁt

from a matcher that can handle conflicting information in the ﬁngerprints.

175

Chapter 6

Decision-level Fusion in

Fingerprint Veriﬁcation

The current ﬁngerprint veriﬁcation systems do not meet the low FAR requirements
of several civilian applications due to the nonlinear deformation and noise present
in ﬁngerprint images. An efﬁcient and effective method to improve the veriﬁcation
performance is to combine multiple ﬁngerprint matchers, multiple templates, and
multiple ﬁngers. We propose a combination scheme that is optimal (in the Neyman-
Pearson sense) when sufﬁcient data are available to obtain reasonable estimates of
the joint densities of classiﬁer outputs. Four different ﬁngerprint matching algorithms
are combined using the proposed scheme to improve the accuracy of a ﬁngerprint
veriﬁcation system. Experiments conducted on the MSU_DBI database conﬁrm the
effectiveness of the proposed integration scheme. At the same FAR, the FRR improves
by ~ 3% at all operating points as compared to the best individual matcher. We

further show that a combination of multiple impressions or multiple ﬁngers improves

176

77“.

the FRR by more than 4% and 5%, respectively at the same FAR at all operating
points. Analysis of the results provide some insight into the various decision-level

classiﬁer combination strategies.

6. 1 Introduction

In some applications with a stringent performance requirement (e.g., very low FAR),
no single biometric can meet the requirements due to the inexact nature of sensing,
feature extraction, and matching processes. This has generated interest in designing
multimodal biometric systems [107]. Multimodal biometric systems can be designed
to operate in one of the following ﬁve scenarios (see Figure 6.1): (2) Multiple sen-
sors: for example, optical, ultrasound, and capacitance based sensors are available
to capture ﬁngerprints. (22) Multiple biometric system: multiple biometrics such as
ﬁngerprint and face may be combined [65, 90, 13]. (222) Multiple units of the same
biometric: one image each from both the irises, or both the hands, or ten ﬁngerprints
may be combined [17]. (22)) Multiple instances of the same biometric: for exam-
ple, multiple impressions of the same ﬁnger [17], or multiple samples of the voice,
or multiple images of the face may be combined. (21) Multiple representations and
matching algorithms for the same input biometric signal: for example, combining
different approaches to feature extraction and matching of ﬁngerprints [20]. The ﬁrst
two scenarios require several sensors and are not cost effective. Scenario (222) causes
an inconvenience to the user in providing multiple cues and has a longer acquisition

time. In scenario (22)), only a single input is acquired during veriﬁcation and matched

177

with several stored templates acquired during the one—time enrollment process. Thus,
it is slightly better than scenario (222). In our opinion, scenario (2)), combination of
different representation and matching algorithm, is the most cost-effective way to

improve biometric system performance.

Multiple Sensor System

Multiple Matcher System

i 7: \. .\.\
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W {Ir/l r?

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: I].

          

BIOMETRIC
SYSTEMS

    
 

Minutiae-Based Filter- Based ’
Fingerprint

Multiple Finger System

 

Figure 6.1: Various Multi-modal Biometric Systems [158].

We propose to use a combination of four different ﬁngerprint-based biometric sys-
tems where each system uses different feature extraction and / or matching algorithms
to generate a matching score which can be interpreted as the conﬁdence level of
the matcher. The proposed combination scheme operates at the decision-level. A
combination at the feature level can result in a larger improvement. However, the
feature extraction algorithms from different ﬁngerprint veriﬁcation system designers

use proprietary code and typically only the conﬁdence from the matcher is available.

178

A combination at the decision level is preferred over a combination at the abstract or
the rank level because of more information being contained in the conﬁdence value
of a matcher. We combine the four different matching scores from four different
matchers available to us to obtain the lowest possible FRR for a given FAR.

We also compare the performance of our integration strategy with the sum and
the product rules [90]. Even though we propose and report results in scenarios (222),

(22’) and (2)), our combination strategy could be used for scenarios (2) and (22) as well.

6.2 Matcher Combination

A comprehensive list of classiﬁer combination strategies can be found in [15, 90]. Jain
et al. [15] summarize and categorize various classiﬁer combination schemes based on
architecture, selection and training of individual classiﬁers, and the characteristics of
the combiner. A summary of various classiﬁer combination schemes is shown in Table
6.1 [15]. However, a priori it is not known which combination strategy works better
than the others and if so under what circumstances.

In this chapter we will restrict ourselves to a particular decision-level integration
scenario where each classiﬁer may select its own representation scheme and produces
a conﬁdence value as its output. A theoretical framework for combining classiﬁers in
such a scenario has been developed by Kittler et al. [90]. The well known sum rule
computes the sum of the aposteriori probabilities for each of the classes generated
by individual classiﬁers generated by each matcher/ classiﬁer and makes the decision

in favor of the class with the maximum sum. The product rule computes the prod-

179

Table 6.1: Conﬁdence-level classiﬁer combination schemes. A more detailed compar-
ison can be found in [15].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Combination Scheme Trainable Adaptable
Sum, mean, median No No
Product, min, max No No
Generalized ensemble Yes No
Adaptive weighting Yes Yes
Stacking Yes N o
Logistic Regression Yes N o
Dempster-Shafer N o No
Mixture of local experts (MLE) Yes Yes
Hierarchical MLE Yes Yes
Bagging Yes No
Boosting Yes No
Neural tree Yes N o

 

 

not of the aposteriori probabilities for each of the classes and makes the decision in
favor of the class with the maximum product. The product rule implicitly assumes
an independence of classiﬁers. The sum rule further assumes that the aposteriori
probabilities computed by the respective classiﬁers do not deviate dramatically from
the prior probabilities. The max rule, min rule, median rule, and majority vote rule
have been shown to be special cases of the sum and the product rules [90]. Making
these assumptions simpliﬁes the combination rule but does not guarantee optimal re-
sults and hinders the combination performance. We follow Kittler et al.’s framework

Without making any assumptions about the independence of various classiﬁers.

180

6.3 Integration Strategy

Let us suppose that the test pattern Z is to be assigned to one of the two possible
classes, wo and wl. Let us assume that we have N classiﬁers, and the 2th classiﬁer
outputs a single conﬁdence value 6,- about class 2111 (the conﬁdence for the class 2110
will be 1 — 0,), 2 = 1, 2, .., N. Let us assume that the prior probabilities for the two
classes are equal. The classiﬁer combination task can now be posed as an independent
(from the original N classiﬁer designs) classiﬁer design problem with two classes and

N features (6,, 2 = 1,2, ..,N).

6.3. 1 Matcher Selection

It is a common practice in classiﬁer combination to perform an extensive analysis of
various combination strategies involving all the N available classiﬁers. In feature se-
lection, it is well known that the most informative d—element subset of N conditionally
independent features is not necessarily the union of the d individually most informa—
tive features [85, 77, 166, 75]. Cover [167] argues that no non-exhaustive sequential
d—element selection procedure is optimal, even for jointly normal features. He further
showed that all possible probability of error orderings can occur among subsets of
features subject to a monotonicity constraint. The statistical dependence among fea-
tures causes further uncertainty in the d—element subset composed of the individually
best features. One could argue that the combination strategy itself should pick out
a subset of the classiﬁers that should be combined. However, we know in practice

that the “curse of dimensionality” makes it difﬁcult for a classiﬁer to automatically

181

delete less discriminative features [8, 160]. Therefore, we propose a classiﬁer selection
scheme prior to classiﬁer combination. We also propose to use the class separation
statistic [82] as the feature effectiveness criterion. This statistic, CS, measures how
well the two classes (imposter and genuine, in our case) are separated with respect

to the feature vector, X “, in a d-dimensional space, Rd.

0806’) = /. Ip<Xdeo> — p(Xdlwllldx. (6.1)

where p(Xdlwo) and p(Xdlwl) are the estimated distributions for the mo (imposter)

and 201 (genuine) classes, respectively. Note that 0 3 CS 3 2.

We will use the class separation statistic to obtain the best subset of matchers

using an exhaustive search of all possible 2N — 1 matcher subsets.

6.3.2 Non-parametric density estimation

Once we have selected the classiﬁer subset containing (1 (d S N, N = 4 in our case)
classiﬁers, we develop our combination strategy. We do not make any assumptions
about the form of the distributions for the two classes and use non-parametric methods
to estimate the two (imposter and genuine) distributions. We will later show that
this method is superior to a parametric approach which assumes a speciﬁc form of

the density.

The Parzen window density estimate of a d—dimensional density function based

182

on n i.i.d. observations (training samples) and a Gaussian kernel is given by [145]:

1 1 t —1
X)=nhd§:{(—_—— 27r ﬁlms mp]_W(X_Xi) 2 (X—Xj)]}, (6-2)

where h is the window width. The covariance matrix, 23, of the kernel is estimated
from the n training samples and h oc 72%]. The value of h is usually determined
empirically. A large value of h means a large degree of smoothing and a small value
of h means a small degree of smoothing of the estimated density. A rule of thumb
states that for a small (large) number of training samples (n), window width should
be large (small). Further, for a ﬁxed 22, the window width should be large (small) for
large (small) number of features (d). When a large number of training samples are
available, the density estimated using Parzen window approach is very close to the

true density.

6.3.3 Decision Strategy

Bayes decision rule [145] is “optimal” for given prior probabilities and the class con-
ditional densities. Bayes decision rule minimizes the total classiﬁcation error (FAR
+ FRR) , that is, no other decision rule can yield a lower total error than the Bayes
decision rule. However, in a ﬁngerprint veriﬁcation system, usually there is a con-
straint on the FAR dictated by the application of the veriﬁcation system. In the
case when the FAR is required to be below a prespeciﬁed value, the Neyman-Pearson
decision rule is preferred which minimizes the FRR for a given FAR. The ﬁngerprint

veriﬁcation is formulated as a hypothesis testing problem and the likelihood ratio

183

L = P(Xdlw0)/P(Xd|w1) is used to construct the decision rule in our two-class prob-
lem: Decide DO (person is an imposter) for low values of L; decide D1 (person is
genuine) for high values of L. If L is small, the input is more likely to come from
class ml; the likelihood ratio test rejects the null hypothesis for small values of L. The
N eyman-Pearson lemma states that this test is optimal, that is, among all the tests
with a given signiﬁcance level, a (FAR), the likelihood ratio test has the maximum
power (l-FRR). For a speciﬁed a, /\ is the smallest constant such that P{L g A} S a.
The type II error ([3) is given by P{ L > /\}. If we choose /\ = 1, the Neyman—Pearson
decision rule is equivalent to the Bayes decision rule under a 0 — 1 loss function and
equal priors. Since the designers of the veriﬁcation system do not know in advance
the particular application that the system will be used for, it is a common practice
to report the performance of the system for a range of different FARs. We plot ROC
curves using several different FARs and their corresponding FRR values obtained for

a range of thresholds (values of A).

6.4 Matching Algorithms

We have used four different ﬁngerprint matching algorithms which can be broadly
classiﬁed into two categories: (2) minutiae-based, and (22) ﬁlter-based. The three

minutiae-based and one ﬁlter-based algorithms are summarized in this section.

184

6.4.1 Hough Transform Based Matching (Algorithm H ough)

The ﬁngerprint matching problem can be regarded as template matching [131]: given
two sets of minutia features, compute their matching score. The two main steps of the
algorithm are: (2) Compute the transformation parameters 6m, 6y, 0, and s between the
two images, where (5,, and 6,, are translations along :1:— and y- directions, respectively,
6 is the rotation angle, and s is the scaling factor; (22) Align two sets of minutia points
with the estimaoted parameters and count the matched pairs within a bounding box;
(222) Repeat the previous two steps for the range of allowed transformations. The
transformation that results in the highest matching score is believed to be the correct
one. The ﬁnal matching score is scaled between 0 and 99. Details of the algorithm

can be found in [131].

6.4.2 String Distance Based Matching (Algorithm String)

Each set of extracted minutia features is ﬁrst converted into polar coordinates with
respect to an anchor point. The two-dimensional (2D) minutia features are, therefore,
reduced to a one-dimensional (1D) string by concatenating points in an increasing
order of radial angle in polar coordinates. The string matching algorithm is applied
to compute the edit distance between the two strings. The edit distance can be easily
normalized and converted into a matching score. This algorithm [11] can be summa-
rized as follows: (2) Rotation and translation are estimated by matching ridge segment
(represented as planar curve) associated with each minutia in the input image with

the ridge segment associated with each minutia in the template image. The rotation

185

and translation parameters that result in the maximum number of matched minutiae
pairs within a bounding box was used to deﬁne the estimated transformation and
the corresponding minutiae are labeled as anchor minutiae, A1 and A2, respectively.
(22) Convert each set of minutia into a 1D string using polar coordinates anchored
at A1 and .42, respectively; (222) Compute the edit distance between the two 1D
strings. The matched minutiae pairs are retrieved based on the minimal edit distance
between the two strings; (2v) Output the normalized matching score (in the range of
0-99) which is the ratio of the number of matched-pairs and the number of minutiae

points.

6.4.3 2D Dynamic Programming Based Matching (Algo-

rithm Dynamz’c)

This matching algorithm is a generalization of the above mentioned string-based algo-
rithm. The transformation of a 2D pattern into a 1D pattern usually results in a loss
of information. Chen and Jain [152] have shown that ﬁngerprint matching using 2D
dynamic time warping can be done as efficiently as 1D string editing while avoiding
the above mentioned problems with algorithm Str2ng. The 2D dynamic time warp-
ing algorithm can be characterized by the following steps: (2) Estimate the rotation
between the two sets of minutia features as in Step 1 of algorithm S tr2ng; (22) Align
the two minutia sets using the estimated parameters from Step 1; (222) Compute the
maximal matched minutia pairs of the two minutia sets using 2D dynamic program-

ming technique. The intuitive interpretation of this step is to warp one set of minutia

186

to align with the other so that the number of matched minutiae is maximized; (2v)
Output the normalized matching score (in the range of 0-99) which is based on only
those minutiae that lie within the overlapping region. A penalty term is added to

deal with unmatched minutia features.

6.4.4 Filterbank Based Matching (Algorithm F2lter)

Chapter 5 describes our ﬁlterbank-based ﬁngerprint veriﬁcation algorithm. The dis-

tance score was inverted and normalized to a matching score between 0 and 99.

6.5 Experimental Results

One hundred images (about 4% of the database) were removed from the total of
2, 672 images in the MSU_DBI database because the ﬁlter-based ﬁngerprint matching
algorithm rejected these images due to failure in locating the center or due to a poor
quality of the images. We matched all the remaining 2, 572 ﬁngerprint images with
each other to obtain 3,306,306 (2572 x 2571/2) matchings and called a matching
genuine only if the pair contains different impressions of the same ﬁnger. Thus, we
have a total of 3, 298, 834 (3, 306,306 — 7, 472) imposter and 7, 472 genuine matchings
per matcher from this database. For the multiple matcher combination, we randomly
selected half the imposter matching scores and half the genuine matching scores for
training (the Neyman-Pearson decision rule) and the remaining samples for test.
This process was repeated ten times to obtain ten different training sets and ten

corresponding independent test sets. All performances will be reported in terms of

187

ROC curves computed as an average of the ten ROC curves corresponding to the
ten different training and test sets. For the multiple impression and multiple ﬁnger
combinations, the same database of 3, 298,834 imposter and 7, 472 genuine matchings
computed using the Dynamic matcher was used because it is the best individual

matcher at low FARS.

 

 

 

 

 

 

 

 

 

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(D + Dynamic
7 -a—- String '
+ Hough
-9— Filter
—+— Equal-Error Line
70 M l l l I I
0 1 2 3 4 5 6 7

False Acceptance Rate (%)

Figure 6.2: Performance of individual ﬁngerprint matchers. The ROC curves have
been averaged over ten runs.

The ROC curves computed from the test data for the four individual ﬁngerprint
matchers used in this study are shown in Figure 6.2. The class separation statistic
computed from the training data was 1.88, 1.87, 1.85 and 1.76 for the algorithms
Dynamic, String, Filter, and H ough, respectively, and is found to be highly cor-
related to the matching performance on the independent test set. Figure 6.2 shows
that matcher Filter is better than the other three matchers at high FARs while it

has the worst performance at very low FARs. Matcher H ough is the worst at most

188

 

 

 

 

 

 
 
     
  

 

 

  

 

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False Acceptance Rate (%)

(b)

Figure 6.3: Normal approximation to the imposter distribution for the matcher
Filter. (a) Imposter and genuine distributions, (b) ROC curves. Visually, the Normal
approximation seems to be good, but causes signiﬁcant decrease in the performance
compared to the nonparametric estimate of the imposter distribution at low FARs.

189

operating points except at very low FARs. At an equal error rate of about 3.5%, the
matchers Dynamic, String, and Filter perform at the same level while the matcher
H ough has an equal error rate of about 6.4%.

In general, biometrics applications demand very low error rates (e. g., FAR=0.01%
and FRR=1.0%). Small errors in estimation of the imposter and genuine distribu-
tions can signiﬁcantly effect the performance of a system. We will demonstrate this
by approximating the imposter density with a normal density and using the empirical
genuine density. This is because, visually, the imposter density looks like a normal
density while the genuine density does not resemble a normal density. Consider the
empirical genuine density and a normal approximation to the imposter density for
the algorithm Filter shown in Figure 6.3(a). One would expect to get very accurate
estimates of the parameters of a one-dimensional density from over 1.6 million data
points. In fact, visually the normal approximation to the imposter density seems to
ﬁt the empirical density very well (see Figure 6.3(a)). As far as the equal error rate
is concerned, using either the normal approximation or the nonparametric approxi-
mation of the imposter density give similar results. However, a signiﬁcant decrease in
performance is observed at low FARs when a normal approximation to the density is
used in place of the nonparametric estimate (see Figure 6.3(b)). This is because the
normal approximation to the imposter density has a heavier tail than the empirical
density. To achieve the same low value of FAR, the system will operate at a higher
threshold when the normal approximation to the density is used compared to when
the nonparametric estimate of the density is used. The FRR, which is the area under

the genuine density curve below the threshold, increases signiﬁcantly. So, we would

190

like to stress that a parameterization of the density should be done with care.

 

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01
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'4o ' 0
Normalized Matching Score (Filter)

Figure 6.4: Plot of joint scores from matchers String and Filter. The solid lines
denote the three sum rule decision boundaries corresponding to three different thresh-
olds. The dotted lines denote the three product rule decision boundaries correspond—
ing to three different thresholds.

Next, we combine the four available ﬁngerprint matchers in pairs of two. It is
well known in classiﬁer combination studies that the independence of classiﬁers plays
an important role in performance improvement [15]. A plot of the scores in a two-
dimensional space from the training data for the String + Filter combination is

shown in Figure 6.4. The correlation coefﬁcient, p, between the matching scores can

be used as a. measure of diversity between a pair of matchers [110]. A positive value

191

Table 6.2: Combining two ﬁngerprint matchers. CS is the class separation statistic.
CS and p are computed from the training data. Ranks by EER (Equal Error Rate)
are computed from the independent test data.

 

 

 

 

 

 

 

 

Combination CS (rank) rank by EER p

String + Filter 1.95 (1) 1 0.52
Dynamic + Filter 1.95 (1) 2 0.56
String + Dynamic 1.94 (3) 4 0.82
H ough + Dynamic 1.93 (4) 3 0.80
Hough + Filter 1.91 (5) 6 0.53
Hough + String 1.90 (6) 5 0.83

 

 

 

 

 

 

of p is directly proportional to the measure of “dependence” between the scores from
the two matchers. Table 6.2 lists the correlation coefﬁcients for all possible pairings
of the four available ﬁngerprint matchers. It can be observed from this table that
the minutiae-based ﬁngerprint matchers have more dependence among themselves
than with the ﬁlter-based ﬁngerprint matcher. This is because the minutiae—based
matchers are using the same features (minutiae set) and differ only in the matching
algorithm.

To combine two ﬁngerprint matchers, we ﬁrst estimate the two—dimensional gen-
uine and imposter densities from the training data. The two-dimensional genuine
density was computed using the Parzen density estimation method. The value of
window width (h) was empirically determined to obtain a smooth density estimate
and was set at 0.01. We used the same value of h for all the two-matcher combina-
tions. As a comparison, the genuine density estimates obtained from the normalized
histograms were extremely peaky due to unavailability of sufﬁcient data (only about
3, 780 genuine matching scores were available in the training set to estimate a two-

dimensional distribution in 10, 000 (100 x 100) bins). However, for estimation of the

192

_ Imposter

O)
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Percentage (%)

N

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Figure 6.5: Two—dimensional density estimates for the genuine and imposter classes
for String + Filter combination. Genuine density was estimated using Parzen win-
dow (h = 0.01) estimator and the imposter density was estimated using normalized
histograms.

two—dimensional imposter distribution, over 1.6 million matching scores were avail—
able. Hence, we estimated the two—dimensional imposter distribution by computing

a normalized histogram using the following formula:

10)=(X“’|w0 if“ (X, X), (6.3)

where 6 is the delta function that equals 1 if the raw matching score vectors X and
X, are equal, 0 otherwise. Here n is the number of imposter matchings from the
training data. The computation time for Parzen window density estimate depends
on n and so, it is considerably larger than the normalized histogram method for large

n. The smooth estimates of the two-dimensional genuine and imposter densities for

193

 

 

 

 

 

 

 

 

100 I I I I I T f I T
99 *
.’~’.F‘M'—N—‘ F”..—
3 ﬂ/x/l ,_-
2., 98 , ,/.—/ -
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s 96 r
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c 94 / 43— String + Filter
8 ,1 + Dynamic + Filter
," -6— String + Dynamic
/ --— Hough + Dynamic
93 2 —e— Hough + String
+ Hough + Filter
—+— Equal—Error Line
92 l l l l l l I I; 1
O 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

False Acceptance Rate (%)

Figure 6.6: ROC curves for all possible two-matchers combinations.

String + Filter combination are shown in Figure 6.5. The class separation statistic
for all pairs of matcher combination is shown in the second column of Table 6.2; the
number in parenthesis is the predicted ranking of the combination performance based
on CS. The actual ranking of performance obtained from the independent test set is
listed in the third column marked ROC (see Figure 6.6 for ROC curves). As can be
seen, the predicted ranking is very close to the actual rankings on independent test

data.

The following observations can be made from the two-matcher combinations:

0 Classiﬁer combination improvement is directly related to the “independence”

(lower values of p) of the classiﬁers.

o Combining two weak classiﬁers results in a large performance improvement.

194

 

100 I T f 1— T T T' I I

99*- n

(O
on
I

(D
\l
I

1

(D
01
I

(D
h
L

 

Genuine Acceptance Rate (%)
(O
O)

 

-8— Proposed combination
—9— Sum rule

+ Product rule

—i—- Equal-Error Line

<0
0)

 

 

 

 

 

92 l l l l 1 l
O 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

False Acceptance Rate (%)

Figure 6.7: Comparison of the proposed combination scheme with the sum and the
product rules for the String + Filter combination.

a Combining two strong classiﬁers results in a small performance improvement.
0 The two individually best classiﬁers do not form the best pair.

The proposed combination scheme either outperforms or maintains the perfor-
mance of the sum rule and outperforms the product rule in all the two-, three-, and
four-matcher combinations. However, we provide illustrations of the comparison in
two-matcher combinations as it is easier to visualize the decision boundaries in two
dimensions. We choose the String + Filter combination which involves a strong and
a weak classiﬁer. The results of this combination and a comparison with the sum and

the product rules is shown in Figure 6.7. By assuming that the errors in estimation

195

 

 

 

 

 

 

 

 

 

 

1 00 i I I f If I I I I
n W
99 ~ -
<3 _
a! 98 l’ _/ ‘
2 /
g .
8 97k .
c -
g gel .
<
m 95
.E l
E
o 94 -
(D + Dynamic
—8— String + Filter L
93 —e— Hough + String + Filter
—~— String + Dynamic + Filter
-+- Equal-Error Una

 

o 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
False Acceptance Rate (%)

Figure 6.8: The performance of the best individual matcher Dynamic is compared
with various combinations. The String + Filter is the best two-matcher combination
and String + Dynamic + Filter is the best overall combination. Note that addition
of the matcher H ough to the combination String + Filter results in a degradation
of the performance.

of aposteriori probabilities (matching scores) are very small, Kittler et al. [90] math-
ematically showed that the sum rule is less sensitive to these errors than the product
rule. In our case, instead of considering the scores from two classiﬁers as estimates
of aposteriori probability, we consider them as features in a separate classiﬁcation
problem. In such a case, the decision boundaries corresponding to the sum and the
product rules can be drawn and visualized. In Figure 6.4 the decision boundaries cor-
responding to three different thresholds are shown for the sum and the product rules
by solid and dotted lines, respectively. The product rule has a strong bias for low
values of the two component classiﬁer outputs. This is undesirable in most practical

situations and the product rule is not expected to perform well in most cases. The

196

_a

00

80

60

40

20

Dynamic matching score

1 oo
80 100
so so
40
are . 20
b/Og

      

8,050

 

40 e
o

.. 20 . “g $0

0 0 310‘“

800,9 Finer ‘“

Figure 6.9: Matching scores for the best combination involving String, Dynamic, and
Filter matchers. Visually, one can see a small overlap between the genuine (0) and the

imposter (*) classes. The class separation statistic is 1.97 for the three-dimensional
genuine and imposter densities estimated from these scores.

sum rule decision boundary is always a line with 135° slope and sum rule performs
well only when combining two classiﬁers of equal strength (two weak or two strong
classiﬁers). When a weak and a strong classiﬁers are combined, the decision boundary
bends towards the axis of the strong classiﬁer. A weighted sum rule weights the de-
cisions from different classiﬁers differently for combination. Thus, the weighted sum
rule can adapt the slope of its decision boundary but the decision boundary is still
linear. The proposed technique can produce a decision boundary that is non-linear
and is expected to perform better than the sum and the product rules. However, the
disadvantage of the proposed technique is that it requires sufﬁcient training data to
obtain reasonable estimates of the densities while the sum rule is a ﬁxed rule and does

not require any training. The weighted sum rule can perform better than the sum

197

Table 6.3: Comparison of the performance of the best matcher combination with the
best individual matcher. GAR refers to the genuine acceptance rate that is plotted on
the ordinate of the ROC curves. We performed ten runs of the combination scheme
with ten different splits of the database into training and test sets. The mean (Mean)
and variance (Var) of the GAR values for three ﬁxed values of FAR are reported.

 

 

 

 

 

 

FAR GAR GAR GAR
Dynamic String + Dynamic + Filter Improvement
(%) Mean (%) (Var (%)) Mean (%) (Var (%)) (%)
1.00 95.53 (0.08) 98.23 (0.02) 2.70
0.10 92.96 (0.05) 96.16 (0.04) 3.20
0.01 90.25 (0.04) 93.72 (0.05) 3.47

 

 

 

 

 

 

rule but it is difﬁcult to determine the weights. In summary, the proposed matcher
combination scheme outperforms the commonly used sum rule and the product rule
(Figure 6.7).

Finally, we combine the matchers in groups of three and then combine all the four
matchers together. From the tests conducted on the independent data set, we make

the following observations (see Figure 6.8).

0 Adding a matcher may actually degrade the performance of classiﬁer combina-
tion. This degradation in performance is a consequence of lack of independent
information provided by the classiﬁer being added and ﬁnite size of the training

and test sets.

0 Matcher selection based on a “goodness” statistic is a promising approach.

0 Performance of combination of matchers is signiﬁcantly better than the best

individual matcher.

Among all the possible subsets of the four ﬁngerprint matchers, the class separa-

198

 
   
  
 
 
    
   

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System Database

Figure 6.10: Proposed architecture of multi—modal biometrics system based on several

ﬁngerprint matchers.

tion statistic is the maximum for String + Dynamic + Filter combination. Hence,
our feature selection scheme selects this subset for the ﬁnal combination and rejects
the matcher Hough. This is consistent with the nature of the H ough algorithm,
which is basically the linear pairing step in algorithms String and Dynamic, without
the capability of dealing with elastic distortions. Therefore, H augh does not provide
“independent” information with respect to String and Dynamic matchers. Figure
6.9 shows the small overlap in the scores from the genuine and the imposter classes for

the best combination involving ﬁngerprint matchers String, Dynamic, and Filter.

199

'7 ’ loco,
a”. n v,»
' r7“

 

(c) Finger 2, Impression 1 (d) Finger 2, Impression 2

 

Figure 6.11: Performance of matcher combination. (a) & (b) and (c) & (d) were mis-
classiﬁed by the three individual matchers String, Dynamic, and Filter as impostors,
but correctly classiﬁed as genuine by the combination. Both the minutiae-based and
ﬁlterbank—based matchers can not deal with large nonlinear deformations, however,
a combination of matchers can overcome this.

200

The performance of the various matcher combinations on an independent test set
supports our claim that String + Dynamic + Filter is the best combination. Figure
6.11 shows two pairs of images which were misclassiﬁed as impostors by all the three

individual algorithms but correctly classiﬁed by the combined system.

Table 6.4: Equal error rate improvement due to combination of matchers.

 

String Dynamic Filter Combination
Equal Error Rate (%) 3.9 3.5 3.5 1.4

 

 

 

 

 

 

 

 

The performance of the combined system is more than 3% better than the best
individual matcher at low FARS (see Table 6.3). The equal error rate is more than 2%
better than the best individual matcher (see Table 6.4). The matcher combination
takes about 0.02 seconds on an Sun Ultra 10 in the test phase. This additional
computational burden will have almost no effect on the overall matching time which
will still be bounded by the slowest individual matcher (Filter) which takes about
3 seconds. Based on the experimental results presented above, we propose a multi-
matcher biometric system design in Figure 6.10.

The performance improvement due to combination of two impressions of the same
ﬁnger and the combination of two different ﬁngers of the same person using the pro-
posed strategy is shown in Figures 6.12(a) and (b), respectively. The best individual
matcher Dynamic was used in these experiments. The correlation coefficient be-
tween the two scores from two different impressions of the same ﬁnger is 0.42 and
between two different ﬁngers of the same person is 0.68 and is directly related to the

improvement in the performance of combination. The CS for individual impressions

201

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

99 - l
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—9— First impression alone
—8— Second impression alone
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m ' 1 ¥ 1 l t ‘F 4 L I
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
False Acceptance Rate (%) '
(a)
1 I I I I T I T l I
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—+— Equal-Error Line
m 1 1 1 EL 4 I I I I
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

False Acceptance Rate (%)

(b)

Figure 6.12: Performance improvement by using multiple impressions and multiple
ﬁngers. (a) Combining two impressions of the same ﬁnger, and (b) combining two
ﬁngers of the same person.

202

is 1.84 and 1.87, respectively, and for the combination CS value is 1.95. The CS
for individual ﬁngers is 1.87 and 1.86, respectively, and for the combination the CS
value is 1.98. Combination of two impressions of the same ﬁnger or two ﬁngers of the
same person using the proposed combination strategy is extremely fast. Therefore,

the overall veriﬁcation time is the same as the time taken by the matcher Dynamic.

6.6 Summary

We have presented a scheme for combining multiple matchers at decision-level in
an optimal fashion. Our design emphasis is on matcher selection before arriving
at the ﬁnal combination. It was shown that one of the ﬁngerprint matchers in the
given pool of matchers is redundant and no performance improvement is achieved by
utilizing this matcher in the combination. This matcher was identiﬁed and rejected by
the matcher selection scheme. In case of a larger number of matchers and relatively
small training data, a matcher may actually degrade the performance when combined
with other matchers, and hence matcher selection is essential. We demonstrate that
our combination scheme improves the false reject of a ﬁngerprint veriﬁcation system
by more than 3% with no signiﬁcant computational overhead. We also show that
combining multiple impressions instances of a ﬁnger or multiple ﬁngers is a viable
way to improve the veriﬁcation system performance. We observe that independence
among various matchers is directly related to the improvement in performance of the

combination.

203

Chapter 7

Fingerprint Feature Detection and

Veriﬁcation

Raw image data offer rich source of information for feature extraction and matching.
For simplicity of pattern recognition system design, a sequential approach consisting
of sensing, feature extraction and matching is conventionally adopted where each
stage transforms a particular component of information relatively independently. The
interaction between these modules is limited to one-way ﬂow of control. Some of
the errors in the end-to—end sequential processing can be easily eliminated especially
for the feature extraction stage by revisiting the original image data. We propose
a feedback path for the feature extraction stage, followed by a feature reﬁnement
stage for improving the matching performance. This performance improvement is
illustrated in the context of a minutiae-based ﬁngerprint veriﬁcation system. We
show that a minutia veriﬁcation stage based on reexamining the gray-scale proﬁle
in a detected minutia’s spatial neighborhood in the sensed image can improve the

204

7 C

 

 

matching performance by ~ 2.2% equal error rate (point on the ROC where FAR
is equal to FRR) on the GT database. Further, we show that a feature reﬁnement
stage which assigns a class label to each detected minutia (ridge ending and ridge
bifurcation) before matching can also improve the matching performance by ~ 1%
equal error rate. A combination of feedback (minutia veriﬁcation) in the feature
extraction phase and feature reﬁnement (minutia classiﬁcation) improves the overall

performance of the ﬁngerprint veriﬁcation system by ~ 3%.

7.1 Introduction

  

       

» .. ' ...... H , . " , _
(a) Q1 = 0.96 (b) Q1: 0.53 (0) Q1: 0.04

 

 

Figure 7.1: Sample images from the GT database with varying quality index (QI). 0
false minutiae were detected in (a), 7 in (b), and 27 in (c) by the automatic minutiae
detection algorithm [11].

Most of the existing automatic ﬁngerprint veriﬁcation systems ﬁrst detect the
minutiae in a ﬁngerprint image and then match the input minutiae set with the stored

template [11, 56]. A typical algorithm described in [11] uses a sequential approach to

205

 

feature extraction. The feature extraction ﬁrst binarizes the ridges in a ﬁngerprint
image using masks that are capable of adaptively accentuating the local maximum
gray-level values along a direction normal to the local ridge direction. Minutiae are
determined as points that have either one neighbor (ridge ending) or more than two
neighbors (ridge bifurcation) in the skeletonized image (see Figure 1.2). However,
the orientation estimation in a poor quality image is extremely unreliable, resulting
in the detection of many false minutiae (see Figure 7.1). Several researchers have
proposed minutia-pruning in the post-processing stage to delete spurious minutiae
[11, 52, 136] but the pruning is based on rather ad-hoc techniques. In this chapter,
we propose a feedback system for minutiae extraction which is based on an analysis
of the gray scale proﬁle in the neighborhood of potential minutiae. We also propose
a feature reﬁnement stage where the minutiae are classiﬁed into two major classes:
ridge bifurcation and ending. The goal of the proposed feedback system (which we
call minutia veriﬁcation) is to learn the characteristics of minutiae in gray level images
which can then be used to verify each detected minutia. This step can be used to
replace the rather ad—hoc minutia-pruning stage used in [11]. Each detected minutia
is ﬁltered through this veriﬁcation stage and is either accepted or rejected based on
the learnt gray level characteristics in the neighborhood of a minutia. The minutia
classiﬁer is based on supervised Learning Vector Quantization (LVQ) [165]. We chose
to use LVQ for our classiﬁcation problem due to its fast learning speed and good
performance. Also, public domain LVQ software can be downloaded from the web.
We Show that the feature reﬁnement (minutia classiﬁcation into bifurcation and

ending) can further improve the matching performance. We use a rule-based classiﬁer

206

to classify a minutia into the two categories. The matching algorithm proposed in
[11] is modiﬁed to match minutiae of the same type in the sensed image and the
template. The modiﬁcation of minutia matching algorithm used in [11] with minutia

veriﬁcation and minutia classiﬁcation signiﬁcantly improves the matching accuracy.

7.2 Minutia Veriﬁcation

Our minutia veriﬁcation algorithm can be divided into three stages; (i) feature ex-

traction, (ii) training (learning the minutiae characteristics), and (iii) veriﬁcation.

7 .2.1 Feature Extraction

We use the minutiae detection algorithm developed by Jain et al. [11] for our study.
Each detected minutia has the following three attributes: the :c and y position and
the direction of the ridge on which the minutia resides. We extract a 64 x 64 region
centered at the :1: and y position of the minutia and oriented in the direction of the
minutia. A minutia is captured in a 32 x 32 block in ﬁngerprint images scanned
at 500 dpi. A larger region of 64 x 64 was chosen to avoid the boundary problems
in ﬁltering. The extracted region is normalized to a constant mean and variance to
remove the effects of sensor noise and gray-scale deformation because of ﬁnger pressure
variations. In our experiments, we set the values of both the mean and variance to
100. We enhance the contrast of the ridges by ﬁltering each 64 x 64 window with an
appropriately tuned Gabor ﬁlter [19]. We set the frequency, f, of the Gabor ﬁlter to

the average ridge frequency (1 / K ), where K is the average inter-ridge distance. The

207

 

average inter-ridge distance is approximately 10 pixels in a 500 dpi ﬁngerprint image.
The values of parameters 6,, and 6,, for Gabor ﬁlters were empirically determined and
each is set to 4.0 (about half the average inter-ridge distance). Since the extracted
region is in the direction of the minutia, the ﬁlter is tuned to 0° direction. We perform
the ﬁltering in the spatial domain with a mask size of 33 X 33. The Gabor response
for each pixel in the region is scaled to eight gray levels. We extract a 32 x 32 region
(see Figure 7.3) from the center of the 64 x 64 region to avoid boundary problems
in normalization and ﬁltering and concatenate the rows of the window to form a

1, 024-dimensional feature vector.

7.2.2 Training

In the training phase, minutiae and non-minutiae feature vectors are fed to a Learning
Vector Quantizer to learn the characteristics of minutiae and non-minutiae regions.
For the training phase, we need ground truth for the minutiae and non—minutiae
points in a large number of ﬁngerprints. So, we use the GT database that contains
900 ﬁngerprint images from 269 different ﬁngers and have the ground truth minu-
tiae information provided by a ﬁngerprint expert (see Figure 7.2). Other ﬁngerprint
databases that we have access to do not have the associated minutiae ground truth
marked in them. The multiple impressions for each ﬁnger in the GT database were
taken at different times. The images are of different sizes but all the images have
been scanned at 500 dpi resolution with 256 gray levels. We use the ﬁrst 450 images

for training and the remaining 450 images from different ﬁngers for testing.

208

 

Figure 7.2: Examples of images in the GT database. The ground truth minutiae
provided by an expert are marked on the image.

We extract approximately 15, 000 feature vectors (each feature vector has 1,024
components) corresponding to all the true minutiae from the 450 images in the train-
ing database. We also extracted an equal number of negative samples (non-minutiae)
by randomly sampling the images in the training set and making sure that there is
no minutia in its immediate 32 x 32 neighborhood. For the true minutia, we use
the direction of the minutia provided by the expert. For the negative examples, we
compute the direction of the 32 x 32 block using the hierarchical orientation-ﬁeld
algorithm [11]. See Figure 7.3 for examples of minutiae and non-minutiae gray level

proﬁles.

209

7.2.3 Testing

We use two methods to test the LVQ-based minutiae vs. non-minutiae classiﬁer. In
the ﬁrst method, we evaluate the classiﬁer usingthe ground truth minutia information
in the test database. In the second method, we extract the minutiae from the test
database using the minutiae extraction algorithm described in [11]. An automatically
detected minutia may be slightly perturbed from its original location because of the
noise introduced during the binarizing and thinning processes. So, we extract twenty
ﬁve 32 x 32 windows in the neighborhood of each detected minutia and verify the
presence of minutiae in each window. The decisions from the veriﬁcation of these 25
windows are combined in a simple manner. if the classiﬁer yields a positive veriﬁcation
for any of the 25 windows, the minutia is accepted. Figures 7.4 (a)-(c) compare the
minutiae detection without pruning, with pruning, and with pruning replaced with

minutia veriﬁcation for a good quality ﬁngerprint.

7 .3 Minutia Classiﬁcation

The American National Standards Institute proposes four classes of minutia: ending,
bifurcation, trifurcation, and undetermined [23]. The most discriminable categories
are ridge ending and bifurcation. A number of ﬁngerprint matching algorithms do
not even use minutia type information because of the difﬁcultly in designing a robust
classiﬁer to identify minutiae type. However, we show that a consistent classiﬁcation
of minutia can indeed improve the overall matching performance. We use a rule-based

minutiae classiﬁcation scheme. In minutiae extraction algorithm, if a pixel in the

210

 

 

Figure 7.3: Examples of gray level proﬁles in the neighborhood of (a) minutiae and
(b) non-minutiae. These 32 x 32 subimages, scaled to 8 gray levels, are used for
training an LVQ.

thinned image has only one neighbor then the minutia is classiﬁed as an ending, and
if a pixel has more than 2 neighbors, then the minutia is classiﬁed as a bifurcation.
The matching algorithm in [11] is modiﬁed to match minutiae endings only with
minutiae endings and minutiae bifurcations only with minutiae bifurcations. In our
experience, there are signiﬁcantly more endings present in a typical ﬁngerprint than
bifurcations (according to a study conducted by Osterburg [94], the probability of
occurrence of ridge endings is more than twice the probability of occurrence of ridge

bifurcations). See Figure 7.4 (d) for minutia classiﬁcation results.

211

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Figure 7.4: Minutiae detection and classiﬁcation; (a) Minutiae detection using the
algorithm in [11] without pruning, (b) results of minutia-pruning; minutiae marked
in white were pruned, (c) result of minutia veriﬁcation instead of pruning; minutiae
marked in white were rejected, (d) result of classifying minutiae shown in (b); minutia
bifurcations are marked in black and endings are marked in white.

212

 

 

 

 

 

 

 

 

100 r , ﬁ ﬁ
95: ’,j”’

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False Acceptance Rate (%)

Figure 7.5: ROC for ﬁngerprint matching when minutia veriﬁcation is used.

7 .4 Experimental Results

We ﬁrst evaluated the performance of a minutiae-based ﬁngerprint veriﬁcation sys-
tem [11] which incorporates the minutiae vs. non-minutiae classiﬁer. Approximately
15,000 1, 024-dimensional feature vectors each for minutiae and non-minutiae were
extracted from the the training database to design the LVQ classiﬁer. The classiﬁer
was tested on an independent test set containing 450 images. The best performance
of ~ 95% on the training data and ~ 87% on the test data was achieved with one
hundred code book vectors per class. A real test for the utility of the minutiae veriﬁ-
cation module is the gain in matching accuracy when this module is incorporated in
the matcher. So, we replaced the minutia-pruning stage in the algorithm in [11] with
the proposed minutia veriﬁcation stage. In the ROC curves shown in Figure 7.5, the
dotted line represents the matching accuracy on the test set and the solid line repre-

sents the performance when the pruning stage in [11] is replaced with the proposed

213

 

 

 

 

 

 

 

 

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. - - Without minutia type infomiation
I —-+— Equal-Error Line
75 1 1 1 1
O 2 4 6 8 10

False Acceptance Rate (%)

Figure 7.6: ROC for ﬁngerprint matching when minutia classiﬁcation is used.

minutia veriﬁcation scheme. These ROC curves show that the overall performance of

the ﬁngerprint veriﬁcation system increases by ~ 3% equal error rate.

The beneﬁts of using minutia type information is illustrated in Figure 7.6. The
solid line in the ﬁgure represents the performance when the minutia type information
is used. Figure 7.7 shows the performance improvement when both minutia veriﬁca-
tion and minutiae classiﬁcation are incorporated in the matcher. The classiﬁcation is
done before the veriﬁcation but the classiﬁcation information is not used during the
veriﬁcation. The performance of the ﬁngerprint veriﬁcation system in [11] is signiﬁ-

cantly improved by using the proposed minutia classiﬁcation and minutiae veriﬁcation

modules.

214

 

 

 

 

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False Acceptance Rate (%)

Figure 7.7: ROC for ﬁngerprint veriﬁcation when both minutia classiﬁcation and
veriﬁcation are used.

7 .5 Summary

We have shown that the performance of a minutiae-based ﬁngerprint veriﬁcation sys-
tem can be improved by providing feedback in feature extraction (veriﬁcation of each
detected minutia by an analysis of grey-level proﬁle in its spatial neighborhood in
the original image). Performance can also be improved if the features are reﬁned
and more discriminable attributes (minutia type information) can be extracted and
utilized in matching. The minutiae veriﬁcation approach suffers from the problem of
missed minutiae, i.e., the true minutiae in the ﬁngerprint image that are missed by the
feature extraction algorithm can not be recovered by the minutiae veriﬁcation algo-
rithm. Minutiae veriﬁcation algorithm can only reject the falsely detected minutiae.
Therefore, the minutiae detection algorithm should be operated at a very low false

reject rate. We have accomplished this by removing the post-processing stage from

215

 

the feature extraction algorithm. However, there are still many missed minutiae in
the ﬁngerprint images that can not be recovered. The minutiae veriﬁcation algorithm
can also be applied on the whole or a subset of the image for minutiae detection.
The minutiae detection algorithm will essentially need to examine a large number
of candidates in the ﬁngerprint image. With the current accuracy of the minutiae
veriﬁcation algorithm of ~ 85%, a large number of errors will be made in the minutiae
detection task. As a result, techniques to improve the current minutiae veriﬁcation
task should be explored further. In our training of the minutiae veriﬁcation algo-
rithm, the minutiae examples are representative of the total pattern variation in the
minutiae types. However, the non-minutiae examples selected from random locations
in the ﬁngerprint images may not be representative of all the non-minutiae patterns.
A more representative non-minutiae training set or a more clever method of using
the training patterns for a more effective training should be explored to improve the

performance of the minutiae veriﬁcation algorithm.

216

 

Chapter 8

Conclusions and Future Work

8.1 Conclusions and Research Contributions

This thesis has concentrated on ﬁngerprint-based biometric identiﬁcation systems.
Further, we have focused only on the core technology of ﬁngerprint feature extrac—
tion, classiﬁcation, and matching. There are a number of other very important issues
in a ﬁngerprint-based identiﬁcation system including encryption, security of the ﬁn-
gerprint template, detection of fake ﬁngers, and privacy concerns. These issues need
to be addressed in a systematic way in developing a foolproof ﬁngerprint-based iden-
tiﬁcation system for a wide-scale deployment but are out of the scope of this thesis.
The core ﬁngerprint identiﬁcation technology, i.e., ﬁngerprint feature extraction, clas-
siﬁcation, and matching, are extremely important but challenging problems and even
though several commercial systems exist for ﬁngerprint veriﬁcation, the performance
(veriﬁcation accuracy and time) needs to be improved for a wide adoption in authen-
tication applications. One of the most fundamental questions one would like to ask

217

 

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on

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\i

Genuine Accpetence Rate (%)
8 8

9

 

 

+ Individual best matcher (Dynamic)
93 r —€r— Combining three matchers ‘
-e— Combining two fingers

—x— Combining three templates (impressions)

 

 

 

 

 

 

1o 10’1 10° 101
False Acceptence Rate (%)

Figure 8.1: The best performance achieved on the MSU_DBI database. The minutiae
extraction algorithm of Jain et al. [11] was modiﬁed by replacing its post process-
ing stage with minutiae veriﬁcation stage as described in Chapter 7. Three different
matchers, namely, String, Dynamic, and Filter, two different ﬁngers, and three
different impressions for each ﬁnger of a person were combined. The genuine dis-
tribution was estimated using 2,640 matchings and the imposter distribution was
estimated using 95,920 matchings. Note that the improvement in performance by
combining multiple ﬁngers is higher than combining multiple matchers or multiple
templates (impressions). This is because different ﬁngers provide the most “indepen-
den ” information. A simple “sum rule” was used for the combination.

218

about a ﬁngerprint authentication system is: what is the inherent discriminable infor—
mation available in the ﬁngerprints? Unfortunately, this question, if at all, has been
answered in a very limited setting. In this thesis, we have quantitatively analyzed ge-
netic and environmental factors inﬂuencing the information content in minutiae—based
representation of ﬁngerprints. This analysis established a performance limitation on
automatic minutiae-based ﬁngerprint identiﬁcation due to the limited amount of in-
formation present in minutiae representation. Automatic ﬁngerprint identiﬁcation
system designers, should therefore, explore non-minutiae—based ﬁngerprint represen-
tations.

We have developed a novel ﬁlterbank-based representation for ﬁngerprints. This
representation is compact and has good discriminatory power. We have used this rep-
resentation to achieve ﬁngerprint classiﬁcation and matching accuracies in line with
the best accuracies reported in the literature. The primary advantage of our approach
is its computationally attractive matching/ indexing capability. For instance, if the
translation and orientation normalized FingerCodes of all the enrolled ﬁngerprints
are stored as templates, the identiﬁcation effectively involves a “bit” comparison.
As a result, the identiﬁcation time would be relatively insensitive to the database
size. Further, our approach for feature extraction and matching is more amenable
to hardware implementation than, say, a string—based minutiae matcher. We have
proposed a general system design for decision-level matcher fusion that uses the opti-
mal Neyman-Pearson decision rule and outperforms the combination strategies based
on the assumption of independence among the matchers. We have proposed a multi-

modal biometric system design based on multiple ﬁngerprint matchers. The use of the

219

proposed combination strategy in combining multiple matchers signiﬁcantly improves
the overall accuracy of the ﬁngerprint-based veriﬁcation system. The effectiveness of
the proposed integration strategy is further demonstrated by building multi-modal
biometric systems that combine two different impressions of the same ﬁnger or ﬁnger-
prints of two different ﬁngers. The proposed feature reﬁnement and feedback stages in
a minutiae-based feature extraction algorithm has been shown to improve the veriﬁ-
cation performance. The various techniques proposed in this thesis have signiﬁcantly
improved the overall performance of the ﬁngerprint veriﬁcation system (see Figure
8.1) and have contributed signiﬁcantly in improving the state-of-the-art in ﬁngerprint
veriﬁcation.

There are still a number of challenges in ﬁngerprint veriﬁcation. For example,
almost all current ﬁngerprint capture devices can be spoofed by some kind of a fake
ﬁnger (e.g., tight ﬁtting latex glove having an impression of somebody else’s ﬁnger-
print). Fingerprint liveness detection is a difﬁcult problem because the vital signs or
liveliness identiﬁers often turn out to be more behavioral characteristics and tend to
be volatile. However, the ﬁngerprint capture devices and veriﬁcation systems should
strive to make it increasingly difﬁcult to fake a ﬁnger by incorporating anti-spooﬁng
measures into the hardware and software. The current combined (minutiae-based and
ﬁlterbank-based) veriﬁcation system still cannot deal with very poor quality ﬁnger-
prints and large nonlinear distortion. An estimated 4% of the population including
old people, asian women, and manual workers do not have good quality ﬁngerprints
and this poses a challenge to the matching system. Although, our ﬁngerprint ver-

iﬁcation system has no difficulty in identifying children of any age, our tests were

220

conducted over a short period of time (three months). Children’s ﬁngers grow in size
with age and the ridge characteristics such as the inter-ridge distance changes. If a
child registers into the system today, the veriﬁcation system will have difﬁculty in
identifying him/ her in a few years with the same template. This problem can be
addressed by either a regular update of the child’s template in the database or by

incorporating the ﬁnger growth invariance into the matcher.

If we put all the advantages and disadvantages of ﬁngerprint as a biometrics in
perspective, we believe that the core technology of ﬁngerprint veriﬁcation (one-to—one
matching) has achieved a performance (error rates and timing) that may be sufﬁcient
for several civilian applications and in the near future we should see ﬁngerprints beings
increasingly used in authentication systems as the cost of the ﬁngerprint devices
reduces further. The ﬁngerprint classiﬁcation (indexing) and identiﬁcation (one—to—
many matchings), on the other hand, have not reached sufﬁciently high accuracy for
a wide-scale deployment. If an identiﬁcation system has N users in the database,
then N ﬁngerprint matching are needed to be performed without any indexing. An
efﬁcient indexing technique should be able to reduce the number of matchings to N’
where N’ S N. However, the foundation of an identiﬁcation system lies on the core
technology of ﬁngerprint feature extraction and matching. Therefore, the feature
extraction and matching algorithms need to be further improved in order to be used
in identiﬁcation systems. A number of future research directions to improve the

ﬁlterbank-based as well as minutiae-based systems are given in the following section.

221

8.2 Future Directions

Our research can be expanded in the following areas:

0 The registration in the FingerCode extraction is based on the detection of the
reference point. Even though our multi-resolution reference point location algo-
rithm is accurate and handles the poor quality ﬁngerprint images gracefully, it
fails to detect the reference point in very low quality images leading to either a
rejection of the image or even worse, a false rejection in the veriﬁcation system.
A more robust feature extraction algorithm should not rely on a single refer-
ence point alone. As a possible solution, multiple reference point candidates
can be located and representations corresponding all of these reference points
can be stored as multiple templates. At the time of veriﬁcation, match the
input representation with each of the multiple representations and output the
maximum matching score. As another possible solution, an alignment can be
established using the minutiae features in a ﬁngerprint. Such a system will not
reject any images due to the absence of the reference point and perform well for
the medium quality ﬁngerprint images where the extracted minutiae can still be
used to achieve an alignment. However, the representation thus extracted will
not be translation and rotation invariant resulting in a longer matching time.
To deal with very poor quality ﬁngerprint images where an alignment based
on the detected minutiae points can not be established, an alternate alignment
technique based on some other features of ﬁngerprints such as the orientation

ﬁeld should be explored.

222

o The current implementation of the ﬁlterbank representation is not rotation in—
variant. The rotation is handled in the matching stage by rotating the F inger-
Code itself. However, due to quantization of the rotation space and generation
of multiple alignment hypothesis, the false accepts increase. This problem can
be addressed by estimating a frame of reference of the ﬁngerprints. However, es-
timation of a frame of reference in the ﬁngerprints is a difﬁcult problem because

all ﬁngerprints have circular ridges in the portion above the reference point.

0 Due to skin elasticity, there is non-linear distortion in the ﬁngerprint images
and even if the ﬁngerprints are registered in location and orientation, all ridges
in all sectors may not align. This problem can be partially addressed by esti-
mating the local ridge frequency in each sector and normalizing each sector to a
constant ridge frequency. To further address the non—linear distortion problem,
the tessellation can be distorted in a non-linear way according to the ﬁngerprint

distortion model proposed in [142].

e The FingerCode representation does not have any explicit procedure to han-
dle the noise in the ﬁngerprint images due to the dryness/smudginess of the
ﬁnger. Although the sectors are normalized to a constant mean and variance
and then ﬁltered using a bank of Gabor ﬁlters, large amount of noise changes
the gray-level image characteristics and causes problems in the quantiﬁcation of
discriminatory information in sectors. The simple variance-based features pro-
posed in this thesis perform well, have good discriminatory power, and degrade

more gracefully than the minutiae-based features with noise in the ﬁngerprint

223

 

images. However, we believe that extraction of richer and more discriminatory
features from the sectors in the ﬁltered images should be explored to improve

the matching performance.

The current implementation of ﬁlterbank representation extraction takes longer
than a typical minutiae-extraction algorithm. The convolution operation can be
made signiﬁcantly faster by dedicated DSP processors or performing the ﬁltering
in the frequency domain. These implementation issues need to be addressed to

make the FingerCode matching system real-time.

The current matching algorithm is very simple. An implementation of a smarter
matching algorithm should be able to improve the veriﬁcation performance. For
example, the match resulting from each sector can be weighed differently based
on image quality and a quantitative measure of the nonlinear distortion in the
sector. The veriﬁcation system should also beneﬁt from a matcher that can

handle conflicting information in the ﬁngerprints.

The current minutiae veriﬁcation algorithm is applied on the minutiae extracted
using the algorithm in [11] that detects the minutiae in the thinned binarized
ﬁngerprint ridges. The minutiae patterns that are learnt during the training
can be used to detect the minutiae in the gray scale ﬁngerprint image directly.
However, the current implementation of the minutiae veriﬁcation algorithm can
not be used for the minutiae detection problem due to its poor accuracy. For
example, consider a 320 x 320 pixels ﬁngerprint image scanned at 500 dpi res-

olution. Our minutiae veriﬁcation algorithm samples a 32 x 32 region around

224

each minutiae and cannot tolerate more than 8—pixel displacement in the minu-
tiae location. Therefore, at least 400 (4 X W) candidate minutiae locations
in the ﬁngerprint image will need to be sampled. With the current 87% accu-
racy of our minutiae veriﬁcation algorithm, there will be 52 errors made by the
minutiae identiﬁcation algorithm in the image. In a typical 320 x 320 ﬁngerprint
image scanned at 500 dpi resolution containing 30 — 40 minutiae on an average,
52 errors can result in missing all the correct minutiae on one extreme to a false
detection of 52 minutiae on the other extreme. Therefore, techniques to improve
the accuracy of the minutiae veriﬁcation algorithm should be explored. At the

same time, an intelligent scheme to apply the minutiae veriﬁcation algorithm

to only selected locations instead of the whole image should also be explored.

The design of a core point learning and veriﬁcation algorithm similar to the
minutiae learning and veriﬁcation algorithm described in this thesis should be
explored to verify the detected reference point in the ﬁlterbank representation
extraction algorithm. The current limitation in developing such an algorithm

is the unavailability of large number of ground truth core examples.

A number of people have speculated upon the nature of invariant information
in the ﬁngerprints. In particular, different researchers have granted a varying
degree of latitude in the transformation invariance of the minutiae and based
their matching algorithms on this hypotheses. For instance, some assume mostly
rigid global transformation, others similarity transformation, while some others

non-linear local transformations. However, there is no study supporting the ba-

225

 

sis for these hypotheses on which the entire matcher design relies. A study and
quantization of minutiae transformation invariance information will be bene-
ﬁcial for the minutiae-based algorithms. Also, an estimate of the minutiae
transformation invariance could also form a basis for the transformation invari-
ance information for the ﬁngerprints themselves. This study could be conducted
using the GT database which has 900 ﬁngerprint images that have the minutiae
location, orientation and correspondences between a pair of ﬁngerprints marked

by an expert.

226

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