Fingerprint Recognition: Models and Applications
By
Soweon Yoon

A Dissertation
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
Computer Science – Doctor of Philosophy
2014

Abstract
Fingerprint Recognition: Models and Applications
By
Soweon Yoon
Fingerprint recognition has been successfully used in law enforcement and forensics to
identify suspects and victims for over a century. Recent advances in automated fingerprint
identification systems (AFIS), coupled with the growing need for reliable person recognition, have resulted in an increased deployment of AFIS in broad applications such as border
control, employment background checks, secure facility access, and user authentication in
laptops and mobile devices. Despite the success of fingerprint recognition technique in many
large-scale and diverse person identification applications, several challenging issues in fingerprint recognition still need to be addressed. First, the persistence and uniqueness of
fingerprints—the fundamental premises for fingerprint recognition—remain as presumptions
rather than facts with solid scientific underpinnings. Although some studies have addressed
the uniqueness of fingerprints, there has been no systematic study reported on the persistence of fingerprints. Given a large longitudinal fingerprint database, we have analyzed it
with a multilevel statistical model to assess the impact of time interval between a genuine
fingerprint pair on the corresponding match score and identification decision. Second, an
appropriate mathematical model for fingerprint orientation field is necessary in addressing
a number of challenging problems, including feature extraction (e.g., orientation field and
minutiae) from noisy or partial fingerprints, detecting abnormality in fingerprint patterns,
and representing fingerprints in a compact form. To this end, we have developed a global
orientation field model in the form of ordinary differential equations which is constrained
by the number of singular points in a fingerprint. The model represents the global orientation field with a small number of polynomial terms and outputs fingerprint-like orientation
fields with the specific number of singular points after fitting an input pattern. We use

this model to check the fingerprint-ness of the input image and ensure the integrity of exemplar fingerprint databases. Third, given that automatic latent fingerprint matching is
difficult due to poor quality of latent fingerprints found at crime scenes, we have developed
a semi-automatic latent enhancement method. The proposed algorithm is based on robust
orientation field estimation that is able to (i) reduce human intervention in feature markup
and (ii) improve automatic feature extraction and matching accuracy of latents. Fourth,
fingerprint obfuscation or alteration is a type of attack on AFIS that is of concern to law
enforcement and border crossing agencies. We show that the fingerprint matching accuracy
can greatly deteriorate when the altered fingerprints are presented to AFIS. To address this
deficiency of AFIS, we have (i) analyzed the types of fingerprint obfuscation, (ii) developed
a detection algorithm for altered fingerprints by measuring the abnormality in orientation
field and minutiae distribution, and (iii) proposed a restoration and matching algorithm to
possibly link an altered fingerprint to its pre-altered mate. By addressing these contemporary problems, this dissertation has advanced our understanding of fingerprint recognition
and enabled development of robust and accurate fingerprint recognition algorithms.

Acknowledgments

I thought that being a Ph.D. was to become an independent researcher. I do not dare
say that I have matured into an independent researcher at this time as I finish my Ph.D.
study. However, my six years at MSU gave me courage to step out into the wilderness and
explore.
I am most grateful to my advisor, Dr. Anil K. Jain. He is not only a perfect advisor for
me, but also a great mentor to me. He has been always supportive of my research, open to
my gut feelings when determining research directions, and respected my way of conducting
research with great patience. He opened up many opportunities for me during the course of
study and let me experience the real world, instead of just sitting in the lab without knowing
what is happening out there. I also appreciate his warmth and compassion as a person. He
was there whenever I needed any help, sometimes even before I was aware that I needed
help.
Jianjiang Feng, a great researcher and my model Ph.D., made my Ph.D. life complete.
His flawless papers and brilliant ideas thrilled me. I can say, without hesitation, that the
happiest moment during my Ph.D study was when I worked together with Dr. Jain and
Jianjiang. I have really enjoyed doing research and learned how research should be done.
I was very lucky that I joined the PRIP lab along with four other rookies—Alessandra,
Brendan, Serhat, and Kien. We went through formalities necessary to complete the study by
checking on each other, traveled together to conferences and meetings, and shared joy and
frustration we had. Alessandra, who is thoughtful and conscientious in nature, was not just
a colleague in the lab, but a friend to me. Brendan’s confidence and energy motivated me to
endeavor to become more active and optimistic. I would like to thank Serhat for becoming
a companion in the last tough year of Ph.D. study. I also thank: Jung-Eun, Unsang, Pavan,
Abhishek, Radha, Koichiro, Sunpreet, Scott, Lacey, Charles, Kai, Hu, Di, Qijun, Heeseung,
iv

Eryun, Tim, Shengcai, Zhifeng, Maria Teresa, Hyunju and Dongoh. I heartily wish Jung-Eun
all the best.
I appreciate Dr. George Stockman, Dr. Yiying Tong, Dr. Arun Ross and Dr. Lalita
Udpa for serving as my Ph.D. committee members. Karthik Nandakumar, Prof. Christophe
Champod and Prof. Jaihie Kim greatly encouraged me by giving valuable advice and having
constructive discussions.
I would like to thank the following organizations and people for supporting the research
projects I have participated in: FBI Biometric Center of Excellence (BCoE), NSF Center for
Identification Technology Research (CITeR), Captain Greg Michaud, Lt. Gary Daniels and
Lt. Scott Hrcka in the Forensic Science Division at Michigan State Police, Jean-Christophe
Fondeur and Vincent Bouatou at Morpho, and Ming Hsieh, Anne Wang and Dr. Lester Li
at 3M Cogent Inc.
My all-time mentors and best friends, Ho Gi and Jae Kyu—your honesty and enthusiasm
for research as well as life, sometimes against all odds, always inspire me to become a better
researcher and a better person.
Finally, I thank my parents and sisters who truly understand me and respect my thoughts
and decisions all the time.

v

Table of Contents

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

ix

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . .
1.1 Friction Ridge Pattern for Human Identification . . . . . . . . .
1.1.1 Friction Ridge Pattern: Fingerprints and Palmprints . . . . .
1.1.2 Premises of Fingerprints for Human Identification . . . . . . .
1.1.3 Applications of Fingerprint Recognition . . . . . . . . . . . .
1.2 Fingerprint Representation . . . . . . . . . . . . . . . . . . . . .
1.2.1 Level-1 Features: Orientation Field and Pattern Type . . . .
1.2.1.1 Orientation Field . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1.2 Pattern Types . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2 Level-2 Features: Minutiae . . . . . . . . . . . . . . . . . . . .
1.2.3 Level-3 Features: Pores, Dots, and Incipient Ridges . . . . . .
1.3 Fingerprint Matching . . . . . . . . . . . . . . . . . . . . . . . .
1.3.1 Types of Fingerprints . . . . . . . . . . . . . . . . . . . . . .
1.3.1.1 Exemplar Fingerprints . . . . . . . . . . . . . . . . . . . . .
1.3.1.2 Latent Fingerprints . . . . . . . . . . . . . . . . . . . . . .
1.3.2 Exemplar Fingerprint Matching . . . . . . . . . . . . . . . . .
1.3.2.1 Quality Assessment . . . . . . . . . . . . . . . . . . . . . .
1.3.2.2 Feature Extraction . . . . . . . . . . . . . . . . . . . . . . .
1.3.2.3 Verification and Identification . . . . . . . . . . . . . . . . .
1.3.3 Latent Fingerprint Matching . . . . . . . . . . . . . . . . . .
1.3.3.1 Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.3.3.2 ACE-V Methodology . . . . . . . . . . . . . . . . . . . . . .
1.3.3.3 Performance Evaluation . . . . . . . . . . . . . . . . . . . .
1.4 Challenges in Fingerprint Recognition . . . . . . . . . . . . . .
1.4.1 Persistence and Uniqueness of Fingerprints . . . . . . . . . . .
1.4.2 “Lights-Out” Latent Identification . . . . . . . . . . . . . . .
1.4.3 Vulnerability of Automated Fingerprint Identification Systems
1.5 Dissertation Contributions . . . . . . . . . . . . . . . . . . . . .

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Chapter 2 Longitudinal Study of Fingerprint Recognition
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Longitudinal Data Analysis . . . . . . . . . . . . . . . . . . .
2.2.1 ANOVA-based Approach . . . . . . . . . . . . . . . . . . . .
2.2.2 Multilevel Statistical Model . . . . . . . . . . . . . . . . . .
2.2.2.1 Parameter Estimation Method . . . . . . . . . . . . . . .
vi

2.3 Multilevel Model for Longitudinal Fingerprint Data . . . . .
2.3.1 Longitudinal Fingerprint Database . . . . . . . . . . . . .
2.3.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Longitudinal Analysis of Genuine Fingerprint Match Scores
2.4.1 Modeling of Genuine Match Scores . . . . . . . . . . . . .
2.4.1.1 Assessment of Goodness-of-Fit . . . . . . . . . . . . . .
2.4.1.2 Validation of Model Assumptions . . . . . . . . . . . . .
2.4.1.3 Parameter Estimation and Hypothesis Test . . . . . . .
2.4.1.4 Genuine Match Score Trends of Individual Subjects . . .
2.5 Longitudinal Analysis of Fingerprint Matching Accuracy . .
2.5.1 Multilevel Model for Binary Responses . . . . . . . . . . .
2.5.2 Trend of True Acceptance Rate over Time . . . . . . . . .
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 3 Fingerprint Orientation Field Modeling . . . . .
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Fingerprint Orientation Field Models . . . . . . . . . . . . . .
3.2.1 Local Orientation Field Extraction . . . . . . . . . . . . . .
3.2.2 Global Orientation Field Models . . . . . . . . . . . . . . .
3.2.2.1 Approximation Method . . . . . . . . . . . . . . . . . . .
3.2.2.2 Deterministic Mathematical Models . . . . . . . . . . . .
3.3 Global Orientation Field Modeling . . . . . . . . . . . . . . .
3.3.1 From Rational Polynomial Function to Ordinary Differential
3.3.2 Generalized Orientation Field Model . . . . . . . . . . . . .
3.3.2.1 Constraints on Singularity . . . . . . . . . . . . . . . . . .
3.3.2.2 Parameter Estimation . . . . . . . . . . . . . . . . . . . .
3.3.3 Defining Fingerprint Pattern: Fingerprint-ness . . . . . . .
3.3.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . .
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chapter 4 Latent Fingerprint Enhancement
4.1 Introduction . . . . . . . . . . . . . . . . . . .
4.2 Manual Markups of Latents . . . . . . . . . .
4.3 Orientation Field Estimation . . . . . . . . .
4.3.1 Orientation Element Computation . . . . .
4.3.2 Orientation Field Model . . . . . . . . . . .
4.3.3 Orientation Element Grouping . . . . . . .
4.3.4 Hypotheses Generation . . . . . . . . . . . .
4.4 Fingerprint Enhancement . . . . . . . . . . .
4.5 Experimental Results . . . . . . . . . . . . . .
4.5.1 Database . . . . . . . . . . . . . . . . . . .
4.5.2 Performance Evaluation . . . . . . . . . . .
4.6 Summary . . . . . . . . . . . . . . . . . . . .

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Chapter 5 Fingerprint Obfuscation . . . . . . . . . . . . . . . . . . . . . . . . . 127
vii

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Analysis of Altered Fingerprints . . . . . . . . . . . . . . . .
5.2.1 Altered Fingerprint Database . . . . . . . . . . . . . . . .
5.2.2 Vulnerability of Fingerprint Identification Systems . . . .
5.2.3 Types of Altered Fingerprints . . . . . . . . . . . . . . . .
5.2.3.1 Obliteration . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3.2 Distortion . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.3.3 Imitation . . . . . . . . . . . . . . . . . . . . . . . . . .
5.2.4 Effectiveness of Fingerprint Quality Assessment Algorithm
5.3 Detection of Altered Fingerprints . . . . . . . . . . . . . . .
5.3.1 Abnormality in Orientation Field . . . . . . . . . . . . . .
5.3.1.1 Orientation Field Approximation . . . . . . . . . . . . .
5.3.1.2 Feature Extraction . . . . . . . . . . . . . . . . . . . . .
5.3.2 Abnormality in Minutiae Distribution . . . . . . . . . . .
5.3.3 Experimental Results . . . . . . . . . . . . . . . . . . . . .
5.3.3.1 Finger-Level Evaluation . . . . . . . . . . . . . . . . . .
5.3.3.2 Subject-Level Evaluation . . . . . . . . . . . . . . . . .
5.4 Matching of Altered Fingerprints . . . . . . . . . . . . . . .
5.4.1 Restoration of Altered Fingerprints . . . . . . . . . . . . .
5.4.2 Matching of Altered Fingerprints . . . . . . . . . . . . . .
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 6 Conclusions and Future Research . . . . . . . . . . . . . . . . . . . 169
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
6.2 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

viii

List of Tables

Table 2.1

Models with different combinations of covariates. . . . . . . . . . . . . . .

50

Table 2.2

Goodness-of-fit of the models shown in Table 2.1. . . . . . . . . . . . . . .

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Table 2.3 Parameter estimates and 95% confidence intervals in Model BT with bootstrapping when a single finger is used for recognition. . . . . . . . . . . . . .

59

Table 2.4 Parameter estimates and 95% confidence intervals in Model BA with bootstrapping when a single finger is used for recognition. . . . . . . . . . . . . .

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Table 2.5 Parameter estimates and 95% confidence intervals in Model BQ with bootstrapping when a single finger is used for recognition. . . . . . . . . . . . . .

59

Table 2.6 Parameter estimates and 95% confidence intervals in Model D with bootstrapping when a single finger is used for recognition. . . . . . . . . . . . . .

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Table 2.7 Parameter estimates and 95% confidence intervals in Model BT with bootstrapping when the match scores from ten fingers are fused by a sum rule. .

61

Table 2.8 Parameter estimates and 95% confidence intervals in Model BA with bootstrapping when the match scores from ten fingers are fused by a sum rule. .

61

Table 3.1 Global fingerprint orientation field models. Note that n is the order of the
basis function or polynomial and Ns is the number of singular points detected
in the image. If the model requires singular points as input, the number of
singular points is not included in the number of parameters to be estimated.

82

Table 5.1

High Profile Cases of Fingerprint Alteration . . . . . . . . . . . . . . . . . 129

Table 5.2

Exclusive Categorization of the Altered Fingerprints into Three Types . . 136

Table 5.3 NFIQ Distribution for False Positive Cases at the False Positive Rate of
1% by the Proposed Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 152

ix

List of Figures

Figure 1.1 The FBI’s tenprint card (from NIST SD29 [1]). . . . . . . . . . . . . . .

2

Figure 1.2 A. E. H. Herschel’s fingerprints [73] at (a) age 7, (b) age 17, and (c) age
40. The pairwise match scores (i.e., similarity between a pair of fingerprints)
from a state-of-the-art fingerprint matcher for these three fingerprints are: (a)
vs. (b) 6,217; (a) vs. (c) 5,032; (b) vs. (c) 5,997; the maximum impostor score
of (a) against 10,000 fingerprints in NIST SD4 [2] is 3,325 and that of (b) is
2,935. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

Figure 1.3 Fingerprints from the index fingers of identical twins [81]. (a) The first
impression of the index finger of a twin, (b) the second impression of the same
finger of the twin, and (c) an impression of the index finger of her sibling. The
match score of (a) and (b), which is a genuine match, is 487 from the matcher
used in [81] while the match score of (a) and (c), which is a twin-impostor
match, is only 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

Figure 1.4 Fingerprint features at three different levels of detail. (a) Rolled fingerprint
in NIST SD29 [1], (b) Level-1 features: orientation field and singular points
(cores marked as circles and deltas marked as triangles), (c) Level-2 features:
minutiae, and (d) Level-3 features: incipient ridges. . . . . . . . . . . . . . .

7

Figure 1.5 Orientation field and vector field around singular points. (a) Orientation
fields of cores with different orientations, (b) vector fields of the corresponding
cores, (c) orientation fields of deltas with different orientations, and (d) vector
fields of the corresponding deltas. A core in the orientation field corresponds
to a source or a sink with |A| > 0 in the vector field while a delta in the
orientation field corresponds to a saddle in the vector field which has |A| < 0.

9

Figure 1.6 Fingerprint pattern types. (a) Arch, (b) left-loop, (c) right-loop, (d)
tented-arch, (e) whorl, and (f) twin-loop. Core is marked as yellow circle, and
delta is marked as red triangle. . . . . . . . . . . . . . . . . . . . . . . . . .

10

Figure 1.7 Minutia types in a fingerprint. (a) Ridge ending and (b) ridge bifurcation. 11
Figure 1.8 Level-3 features in a fingerprint. (a) Pores, (b) incipient ridges, (c) dots,
and (d) ridge edge protrusion. . . . . . . . . . . . . . . . . . . . . . . . . . .

12

Figure 1.9 Three types of impressions of the same finger. (a) Rolled fingerprint, (b)
plain fingerprint in NIST SD29 [1], and (c) latent fingerprint in NIST SD27 [3]. 13
x

Figure 1.10 Challenging latent fingerprint images in NIST SD27 [3]. (a) Partial area,
(b) unclear ridge structure, (c) overlapped with other fingerprints, and (d)
complex background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

15

Figure 1.11 Fingerprints of various quality levels: (a) NFIQ of 1, (b) NFIQ of 3, and
(c) NFIQ of 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

17

Figure 1.12 Fake fingerprints. (a) Gummy fingerprint: (Left) pressing a finger on
the softened plastic [19, 94], (Center) the mold generated from a finger [21],
(Right) a gummy fingerprint from the mold [4], and (b) dummy finger [5]. . .

24

Figure 1.13 Photographs of altered fingerprints. (a) Transplanted friction ridge skin
from sole of the feet [6], (b) fingers that have been bitten [122], (c) fingers
burnt by acid [67], and (d) stitched fingers [23]. . . . . . . . . . . . . . . . .

25

Figure 2.1 Fingerprint pairs with minutiae correspondences labeled by Galton in his
study on fingerprint persistence [61]. (a) A pair of fingerprints with 13-year
time interval showing perfect minutiae correspondences, and (b) a pair of
fingerprints from another finger of the same subject with one minutia missing
in the later age impression (denoted as ‘A’). . . . . . . . . . . . . . . . . . .

30

Figure 2.2 Cross-sectional analysis versus longitudinal analysis of balanced but timeunstructured longitudinal data (adapted from [49]). For this dataset (two
measurements for each of 5 subjects), (a) the cross-sectional analysis that discards subject labels on data makes an inference that the measurement values
tend to decrease with respect to subject’s age, while (b) the longitudinal analysis interprets the data as the measurement values tend to increase with respect
to age. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

35

Figure 2.3 Six different impressions of the right index finger of a subject in the longitudinal fingerprint database. . . . . . . . . . . . . . . . . . . . . . . . . . .

43

Figure 2.4 Statistics of the longitudinal fingerprint database used in this study. Histograms of (a) the number of tenprint cards per subject, (b) time span of data
collection for a subject, (c) age at the first and last tenprint acquisitions, (d)
gender, and (e) race. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

44

Figure 2.5 Normal probability plots of (a) residuals at level 1 (εi,jk ), (b) randomeffects for intercept at level 2 (b0i ), and (c) random-effects for slope at level 2
(b1i ) of Model BT fitting the match scores obtained from COTS-1 . . . . . .

53

Figure 2.6 Normal probability plots of (a) residuals at level 1 (εi,jk ), (b) randomeffects for intercept at level 2 (b0i ), and (c) random-effects for slope at level 2
(b1i ) of Model BT fitting the match scores obtained from COTS-2. . . . . . .

54

xi

Figure 2.7 Population-mean trends of genuine match scores and 95% confidence intervals with respect to △Ti,jk . Match scores are obtained from (a) COTS-1
and (b) COTS-2 matchers. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

Figure 2.8 Population-mean trends of genuine match scores and 95% confidence intervals with respect to AGEi,jk . Match scores are obtained from (a) COTS-1
and (b) COTS-2 matchers. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

57

Figure 2.9 Population-mean trends of genuine match scores and 95% confidence intervals with respect to Qi,jk . Match scores are obtained from (a) COTS-1 and
(b) COTS-2 matchers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

58

Figure 2.10 Population-mean trends of genuine match scores and 95% confidence intervals with respect to △Ti,jk , when the scores from ten fingers are fused.
Match scores are obtained from (a) COTS-1 and (b) COTS-2 matchers. . . .

62

Figure 2.11 Population-mean trends of genuine match scores and 95% confidence intervals with respect to AGEi,jk , when the scores from ten fingers are fused.
Match scores are obtained from (a) COTS-1 and (b) COTS-2 matchers. . . .

63

Figure 2.12 Parameter estimates of Model BT with genuine match scores provided
by COTS-1 matcher. The estimates for the population-mean parameters
(β00 , β10 ) and the parameters for each subject (ϕ0i , ϕ1i ) are represented as
a triangle and dots, respectively. The parameters associated with four outlier
subjects are marked as squares. . . . . . . . . . . . . . . . . . . . . . . . . .

64

Figure 2.13 A subject whose intercept in Model BT is very small due to the severe alteration of the fingerprint pattern (outlier case 1). (a) The observed responses
and fitting result of the subject, and (b) fingerprint impressions of the subject
at different ages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

66

Figure 2.14 A subject with high quality ridge pattern resulting in the large intercept
in Model BT (outlier case 2). (a) The observed responses and fitting result of
the subject, and (b) fingerprint impressions of the subject at different ages. .

67

Figure 2.15 A subject with steep negative slope (outlier case 3) resulting from a mislabeled fingerprint (the first impression). (a) The observed responses and fitting
result of the subject, and (b) fingerprint impressions of the subject at different
ages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

68

Figure 2.16 A subject with steep negative slope due to fingerprint impressions made
during his adolescence (outlier case 4). (a) The observed responses and fitting
result of the subject, and (b) fingerprint impressions of the subject at different
ages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

Figure 2.17 Probability of true acceptance with respect to time interval when match
scores from a single (right index) finger are used. (a) COTS-1 and (b) COTS-2. 71
xii

Figure 2.18 Probability of true acceptance with respect to time interval when match
scores from all ten fingers are fused by the sum rule. (a) COTS-1 and (b)
COTS-2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

72

Figure 3.1 Images containing fingerprint-like pattern. (a) Synthesized image obtained
by iterative contextual filtering [38], (b) altered fingerprint where the central
part of the fingerprint has been transplanted from a different friction ridge
skin, (c) synthesized fingerprint by SFinGe [38], and (d) latent fingerprint
from NIST SD27 [3]. The NFIQ value [124] and the fingerprint-ness score
(F ) of the orientation field are shown. NFIQ value of 1 indicates the highest
quality and NFIQ of 5 is the lowest quality. The fingerprint-ness score ranges
from 0 (the lowest) to 1 (the highest); if the proposed model cannot find a
feasible solution satisfying the constraints, there is no valid output from the
model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

78

Figure 3.2 A synthesized image with fingerprint-like ridge structure and its orientation field estimation. (a) Synthesized image obtained by iterative contextual
filtering [38], (b) orientation field extracted from the image in (a) using the
gradient-based method [34], and (c) orientation estimated by an approximation method, the polynomial model [66]. . . . . . . . . . . . . . . . . . . . .

84

Figure 3.3 Loop model from the rational polynomial function. (a) Orientation field
and (b) vector field with x-isocline (orange solid line) and y-isocline (blue
dotted line) with singular points (a core marked as a circle and a delta marked
as a triangle). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

Figure 3.4 Double-loop model from the rational polynomial function. (a) Orientation
field and (b) vector field with x-isocline (orange solid line) and y-isocline (blue
dotted line) with singular points (cores marked as circle and deltas marked as
triangle). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

91

Figure 3.5 Weight matrix c(x, y) used in Equation (3.28). (a) Input image, (b) the
map of |A| where A is the characteristic matrix in Equation (1.3), and (c)
the absolute value of (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95

Figure 3.6 Orientation field fit by the proposed model for (a) arch, (b) tented-arch,
(c) left-loop, (d) right-loop, (e) whorl, and (f) twin-loop type fingerprint. . .

97

Figure 3.7 Orientation field difference map. (a)–(d) Input fingerprint image, orientation field from the image, orientation field from the model, and the orientation
field difference map of the fingerprint image; (e)–(h) input non-fingerprint image, orientation field from the image, orientation field from the model, and
the orientation field difference map of the non-fingerprint image. . . . . . . .

98

Figure 3.8 Fingerprint images in NIST SD4 [2]. . . . . . . . . . . . . . . . . . . . .

99

Figure 3.9 Non-fingerprint images in the ImageNet dataset [48]. . . . . . . . . . . . 100
xiii

Figure 3.10 ROC curve. The average performance (red line) in the 10-fold cross validation is shown; the minimum and maximum performances (blue bars) over
the 10 folds are also indicated. . . . . . . . . . . . . . . . . . . . . . . . . . . 101
Figure 3.11 True positive examples. (a) and (e) Valid and good quality fingerprint
images, (b) and (f) orientation field from the image, (c) and (g) modeled
orientation field, and (d) and (h) orientation field difference map. . . . . . . 102
Figure 3.12 True negative examples. (a) and (e) Non-fingerprint image, (b) and (f)
orientation field from the image, (c) and (g) modeled orientation field, and
(d) and (h) orientation field difference map. . . . . . . . . . . . . . . . . . . 103
Figure 3.13 False positive examples. (a) and (e) Fingerprint images, (b) and (f) orientation field from the image, (c) and (g) modeled orientation field, and (d)
and (h) orientation field difference map. The model estimates the fingerprint
image in (a) as a loop fingerprint although it is indeed a double-loop fingerprint. The orientation difference map for the fingerprint image in (e) shows
high response in the noisy region; the estimated orientation field from the
model shows fingerprint-like behavior even in the noisy region. . . . . . . . . 104
Figure 3.14 False negative examples. (a) and (e) Non-fingerprint image, (b) and (f)
orientation field from the image, (c) and (g) modeled orientation field, and
(d) and (h) orientation field difference map. Both images have textured background which provides a smooth orientation field. . . . . . . . . . . . . . . . 105
Figure 4.1 Manual markup of ROI and singular points. (a) No singularities presented
in the image, (b) two real singular points, and (c) two real cores and two virtual
deltas. The ROI is outlined by green boundary. . . . . . . . . . . . . . . . . 109
Figure 4.2 Orientation elements extracted from a latent using STFT. (a) Latent
(NIST SD27, G027) and (b) orientation elements. . . . . . . . . . . . . . . . 110
Figure 4.3 Orientation element computation. (a) A local image block, (b) magnitude
spectrum of (a), (c) a set of directional filters, (d) energy of filtered responses
by each directional filter, and (e) two orientation elements in this local block
that correspond to the two local maxima in (d). . . . . . . . . . . . . . . . . 111
Figure 4.4 Orientation field model combining singular orientation field and residual
orientation field. (a) Fingerprint (NIST SD4, F0004), (b) orientation field
extracted from (a), (c) singular component of the orientation field, (d) residual component of the orientation field, (e) modeled residual orientation field
using the 4th order polynomial model, and (f) reconstructed orientation field,
ˆ y) = θs (x, y) + θˆr (x, y). . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
θ(x,
Figure 4.5 Orientation element grouping. (a) Fingerprint (NIST SD27, G017), (b)
residual orientation elements, and (c) five orientation element groups (each
shown in a different color). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
xiv

Figure 4.6 One iteration of hypothesis generation procedure for the latent in Figure
4.5(a). An orientation group is added to S at each step from (1) to (6) (newly
added groups are marked as red and existing groups in S are marked green in
the left-hand side image of each pair); a hypothesis is built at every update
in S and checked to see if all groups in S are consistent with the hypothesis
(red blocks in the right-hand side image in each pair indicate consistency in
S with the hypothesis). The final hypothesis M is obtained at the end of
the iteration when no more groups can be added to S. Then, M in (6) is
evaluated by checking the existence of singularity (see Figure 4.7). . . . . . . 117
Figure 4.7 Accepted hypothesis. (a) Accepted hypothesized residual orientation field
and (b) reconstructed orientation field using (a). Red blocks in (a) and (b)
indicate the consensus set. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Figure 4.8 Rejected hypothesis. (a) Rejected hypothesized residual orientation field
with singularities (red circle for core and yellow triangle for delta) and (b)
reconstructed orientation field using (a). . . . . . . . . . . . . . . . . . . . . 118
Figure 4.9 CMC curves showing the performance improvement due to latent enhancement. (a) All latents in NIST SD27, (b) good quality latents, (c) bad quality
latents, and (d) ugly quality latents.. . . . . . . . . . . . . . . . . . . . . . . 122
Figure 4.10 Successful examples where the proposed latent enhancement algorithm
improves the latent matching performance. Left: latent image, Center: estimated orientation field, and Right: binarized enhanced image. Match score of
the latent with the mated rolled print and its retrieval rank from a database
of 27,258 rolled prints are shown as: {score, rank} before enhancement →
{score, rank} after enhancement. . . . . . . . . . . . . . . . . . . . . . . . . 124
Figure 4.11 Failure case (G029). Due to the failure in orientation field estimation, the
latent-to-rolled match score drops from 23 (before enhancement) to 3 (after
enhancement), and the retrieval rank for the true mate increases from 12 to
15,801. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Figure 5.1 Inked impressions before and after fingerprint alteration (a) of Gus Winkler
[45] (pattern type is altered from twin-loop to left-loop), and (b) of Jose
Izquierdo [134] (altered by switching two parts of a ‘Z’ shaped cut on the
fingertip). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Figure 5.2 Flow chart for detecting and matching altered fingerprints. . . . . . . . . 130
Figure 5.3 Distribution of the number of altered fingerprints in tenprint cards in our
database. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Figure 5.4 Mated pre/post altered tenprint cards from a subject. (a) Pre-altered
fingerprints and (b) post-altered fingerprints. . . . . . . . . . . . . . . . . . . 133
xv

Figure 5.5 Match score distributions of pre/post alteration pairs according to type
and genuine and impostor pairs in NIST SD4. . . . . . . . . . . . . . . . . . 134
Figure 5.6 Examples where fingerprint alteration severely degrades the matching
score with the pre-altered mates. (a) Mutilation over a large area and (b)
ridge transformation. These altered fingerprints have a match score of 0 with
their true mates. All squares indicate minutiae extracted from the image
and squares filled with red color represent matched minutiae between the
pre/post altered fingerprints. The left-hand side image in each pair shows the
pre-altered fingerprint, and the right-hand side image shows the post-altered
fingerprint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Figure 5.7 Examples where the pre/post altered fingerprint mates are correctly
matched despite fingerprint alteration. (a) Alteration with a small damaged
area in the fingerprint and no ridge distortion and (b) sufficient number of
minutiae in the unaltered area even with severe fingerprint alteration. Only
a subset of the corresponding minutiae are connected with dotted lines for
visibility. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Figure 5.8 Fingerprint obliteration. Examples of (a) scar and (b) mutilation. . . . . 137
Figure 5.9 Fingerprint distortion. Examples of (a) transplantation within a finger by
‘Z’ cut and (b) transplantation from other friction ridge skin, e.g., from palm. 138
Figure 5.10 Fingerprint imitation. Left: pre-altered fingerprint, and Right: its postaltered fingerprint mate. (a) Removal of a portion of skin and (b) exquisite
transplantation from other friction ridge skin on the body. . . . . . . . . . . 139
Figure 5.11 Histograms of NFIQ values for 27,000 natural fingerprints in NIST SD14
and 4,433 altered fingerprints in our altered fingerprint database according to
the type of alteration. Recall that NFIQ = 1 indicates the highest quality. . 140
Figure 5.12 Flow chart of the altered fingerprint detection algorithm. . . . . . . . . . 143
Figure 5.13 Orientation field discontinuity. Column 1: fingerprint image; Column 2:
orientation field extracted from the image, θ(x, y); Column 3: orientation field
ˆ y); and Column 4: error map,
approximated by the polynomial model, θ(x,
ε(x, y). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
Figure 5.14 Minutiae density map. Column 1: Natural fingerprint (NIST SD14,
F0001826); Column 2: distorted fingerprint with dense minutiae along scars;
Column 3: obliterated fingerprint with dense minutiae distribution in the
altered region; Column 4: obliterated fingerprint with dense minutiae distribution over the entire altered region due to ridge-like pattern formed by
alteration. Note that the minutiae density maps have been scaled to the same
grayscale range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
xvi

Figure 5.15 ROC curves of the proposed algorithm and NFIQ criterion in detecting
altered fingerprints. (a) The ROC curves of the three approaches in the proposed algorithm and the NFIQ algorithm and (b) the ROC curves of the
proposed fusion algorithm and the NFIQ algorithm for each type of altered
fingerprints. The ROC curve of NFIQ criterion is shown as a set of points
(only one point is visible in the range of false positive rate plotted here) because its output can only take one of the five quality levels. . . . . . . . . . . 151
Figure 5.16 True positive detection cases by (a) orientation field discontinuity, (b)
minutiae distribution, (c) and (d) fusion of both approaches. . . . . . . . . . 152
Figure 5.17 False negative examples of the proposed algorithm. Minutiae and orientation field discontinuities of each example are shown. (a) Fingerprint with
small altered area and (b) imitated fingerprint. Note that NFIQ also fails to
detect these two altered fingerprints. . . . . . . . . . . . . . . . . . . . . . . 153
Figure 5.18 False positive examples of the proposed algorithm. Poor quality ridge
patterns: (a) NIST SD14, F0010811; and possibly altered fingerprints: (b)
F0019979, (c) F0002962, and (d) F0018103. . . . . . . . . . . . . . . . . . . 153
Figure 5.19 ROC curves of the proposed algorithm (including three approaches) and
NFIQ criterion for detecting altered fingerprints at subject level. . . . . . . . 154
Figure 5.20 True positive example of detection at subject level by the proposed algorithm. Although one of the altered fingerprints was not detected, this subject
is still detected as having altered fingerprints with high confidence since the
other nine fingerprints (boxed fingerprints) are correctly detected as altered.
None of the ten fingerprints is detected as altered using the NFIQ criterion. . 155
Figure 5.21 True negative example at subject level identified by the proposed algorithm
(NIST SD14, F0000121–F0000130). This subject can pass our alteration detector since the nine fingerprints are determined to be natural fingerprints by
the proposed algorithm. However, the NFIQ criterion raises a false alarm for
this subject since six of the fingerprints have the NFIQ value of 5. . . . . . . 155
Figure 5.22 Transformation of a skin patch in ‘Z’-cut fingerprint. (a) Points on a
boundary (X) including a vertex (ˆ
x) and a new position of the vertex (ˆ
x∗ ),
(b) rigid transformation of X (Xr ), (c) scaling of X (Xs ), and (d) weighted
sum of Xr and Xs (X∗ ). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
Figure 5.23 Restoration process. (a) Altered fingerprint image, (b) markups along the
edges of each skin patch, (c) normalization of the boundaries, (d) swapping of
two skin patches, (e) restored fingerprint, and (f) pre-altered fingerprint of (a). 160
Figure 5.24 Complete minutiae set automatically extracted by the matcher (red
squares) and minutiae in the valid fingerprint region (red-filled squares). (a)
No valid minutiae, (b) very few minutiae in the valid region, and (c) abundant
minutiae present in the valid region. . . . . . . . . . . . . . . . . . . . . . . . 161
xvii

Figure 5.25 Matching performance of altered fingerprints. (a) Rejection criterion (i.e.,
the number of valid minutiae in the minutiae set) versus rank-1 and rank-100
identification rate, and (b) CMC curves at the fingerprint rejection threshold
of 20 minutiae in the valid fingerprint region. . . . . . . . . . . . . . . . . . . 162
Figure 5.26 Example where the altered fingerprint matching is successful with all the
minutiae extracted by the matcher. The pre-altered mate is retrieved at rank
1 from the database with 27,382 fingerprints. . . . . . . . . . . . . . . . . . . 163
Figure 5.27 Example where removing spurious minutiae in the invalid region improves
the matching performance. (a) Matching with the complete minutiae set in
the altered fingerprint (match score is 9, and the pre-altered mate is retrieved
at rank 10,093), and (b) matching with the refined minutiae set by removing
spurious minutiae in the altered region (match score is 29, and the mate is
retrieved at rank 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Figure 5.28 Example where restoration of the ‘Z’-cut fingerprint improves the matching
performance. (a) Matching result of the altered fingerprint with its pre-altered
mate (match score is 5 and retrieval rank is 12,525), and (b) matching result
of the restored image with the mate (match score is now 51 and retrieval rank
is 1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
Figure 5.29 CMC curves for ‘Z’-cut fingerprints at the fingerprint rejection threshold of
20 minutiae in the valid region. While matching with the restored images alone
is still challenging, the rank-level fusion of the altered fingerprint matching
and the restored fingerprint matching significantly improves the matching
performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
Figure 5.30 Example where the altered fingerprints cannot be correctly matched with
their true mates using any refined minutiae sets. (a) Refined minutiae set
from the altered image and (b) refined minutiae set from its restored image.
Match scores for each pair in (a) and (b) are 3 and 9, respectively. Due to
the large amount of skin distortion, none of these methods are successful in
finding the correct mate within a practical size of the candidate list. . . . . . 166

xviii

Chapter 1
Introduction
Fingerprints have a long history of use as a means of reliably identifying individuals. Based
on the persistence and uniqueness of fingerprints, fingerprint recognition systems have become one of the most popular biometric systems used in many applications, including law
enforcement, border control, and forensics. In this chapter, we describe the fingerprint
representation at three levels which are widely used in fingerprint matching, and explain
two matching scenarios in fingerprint recognition: (i) exemplar fingerprint matching that
compares fingerprints obtained in tenprint cards and (ii) latent fingerprint matching that
searches latents found at crime scenes against exemplar fingerprint databases. We discuss
challenging contemporary issues in fingerprint recognition, including latent matching and
fingerprint obfuscation, and present the contributions of this dissertation that address these
issues.

1.1

Friction Ridge Pattern for Human Identification

Friction ridge skin is located only on particular parts of human body: the palms of the
hands and the soles of the feet. Although their biological function is presumably to increase
frictional force between an object and the hand or the foot to grab things firmly or walk on
the ground easily, another usage of the friction ridge skin was discovered thousands of years
1

Figure 1.1: The FBI’s tenprint card (from NIST SD29 [1]).

ago: human identification based on the patterns of the friction ridges. The historical records
of human identification by friction ridge patterns can be found in Babylon (1955–1913 BC)
and Ancient China (AD 600–700), where fingerprints were used to seal contracts and legal
documents [69]. However, scientific study of fingerprints as a tool of human identification
emerged only in the late 19th century [51, 60, 72].
The first reported case where fingerprints were officially accepted as an evidence to convict
a suspect involved a murder case in Argentina in 1893; bloody fingerprints on the door made
the mother confess to the murder of her two children [69]. After the Scotland Yard started to
include fingerprints on the anthropometric identification cards which recorded measurements
of various physical attributes of the criminals around 1900 [44], use of fingerprints spread
rapidly worldwide to identify habitual criminals. In the United States, the Federal Bureau of
Investigation (FBI) set up its fingerprint identification division in 1924, and their fingerprint
2

database initially contained about 810,000 tenprint cards [52]. Figure 1.1 shows an example
of the FBI’s tenprint card. With the increasing number of records in the database, it was
not feasible to do manual matching of fingerprints. Research in the design and development
of Automated Fingerprint Identification Systems (AFIS) was initiated by the FBI in 1970’s.
State and local law enforcement agencies took the lead from the FBI and started to operate
their own AFIS; the system installed in Minneapolis-St. Paul, Minnesota, in 1978 was one
of the first AFIS in the United States [95]. The FBI’s Integrated AFIS (IAFIS) currently
holds the tenprint records of over 75 million apprehended criminals and 39 million civilian
government job applicants as of November 2013; the average response time for tenprint
rapsheet requests is 1 minute and 9 seconds (97% of requests are completed within 15 seconds)
[7].

1.1.1

Friction Ridge Pattern: Fingerprints and Palmprints

It is widely accepted that the formation of friction ridge skin is related to the skin layer,
called volar pads [84]. The volar pads start to form at the 7th week of gestation, and the size
and shape of the embryo’s volar pads affect the fingerprint pattern; the area where volar pads
are located tends to create loop or whorl patterns while the area without volar pads tends
to have straight ridges. Primary ridges are developed after the volar pads disappear around
the 10th week of gestation until the 19th week, and the ridge structures developed during
this period do not change further and are established for life. Then, secondary ridges where
sweat pores do not exist (also called incipient ridges in fingerprint representation) start to
appear until the 24th week of fetal development. The volar pads also play a critical role
in the formation of friction ridge skin on the palm; four pads are present in the interdigital
regions (below the four digits from index finger to little finger) and one pad each is present
in the hypothenar and thenar region [46].
3

(a)

(b)

(c)

Figure 1.2: A. E. H. Herschel’s fingerprints [73] at (a) age 7, (b) age 17, and (c) age 40. The
pairwise match scores (i.e., similarity between a pair of fingerprints) from a state-of-the-art
fingerprint matcher for these three fingerprints are: (a) vs. (b) 6,217; (a) vs. (c) 5,032; (b)
vs. (c) 5,997; the maximum impostor score of (a) against 10,000 fingerprints in NIST SD4 [2]
is 3,325 and that of (b) is 2,935.

1.1.2

Premises of Fingerprints for Human Identification

Fingerprints are believed to be persistent during the lifetime of an individual. Figure 1.2
shows three fingerprint impressions captured by Herschel of his son’s finger at different
ages (age 7, 17, and 40) [73]. The pairwise match scores from a state-of-the-art fingerprint
matcher indicate that these genuine pairs (i.e., fingerprint impressions from the same finger)
have much higher similarity in fingerprint feature correspondences than the impostor pairs
(i.e., fingerprints from different fingers). This supports the general belief that there is no
significant change in fingerprint pattern of an individual over time.
Individual fingerprints are also known to be unique; even identical twins who share the
same DNA information have different fingerprints. In [81], the experimental results with
fingerprints collected from 94 pairs of identical twins showed that, even though the type of
fingerprint pattern is highly correlated between identical twins (see Figure 1.3; fingerprints
of the identical twins have the same pattern type, i.e., right-loop), the fingerprint recognition
system is able to distinguish them as different individuals based on the ridge details.
4

(a)

(b)

(c)

Figure 1.3: Fingerprints from the index fingers of identical twins [81]. (a) The first impression
of the index finger of a twin, (b) the second impression of the same finger of the twin, and
(c) an impression of the index finger of her sibling. The match score of (a) and (b), which is
a genuine match, is 487 from the matcher used in [81] while the match score of (a) and (c),
which is a twin-impostor match, is only 24.

1.1.3

Applications of Fingerprint Recognition

Fingerprint recognition is widely used in various applications ranging from law enforcement
and international border control to personal laptop access. Almost all law enforcement agencies worldwide routinely collect fingerprints of apprehended criminals to track their criminal
history [7]. To enhance border security in the United States, the US-VISIT program [8]
acquires fingerprints of visa applicants to identify high profile criminals on a watch list and
detect possible visa fraud. India’s UIDAI project was initiated to issue a unique 12-digit
identification number to each resident. Given the large population in India (approximately
1.2 billion), an identification number for an individual is associated with his biometric information (i.e., ten fingerprints and two irises) to ensure that each resident has only one
identification number [9].
Fingerprint recognition systems are now pervasive in our daily life. Disney Parks, for
example, captures fingerprints of visitors when they initially enter the park to link the ticket
to the ticket holder’s fingerprint. Fingerprint verification is performed whenever the same
5

ticket is presented for reuse to prevent fraudulent use of the ticket (e.g., sharing of a ticket
by multiple individuals). Many automated teller machines (ATMs) in Brazil use fingerprint
recognition as a replacement for personal identification numbers (PINs) [28]. Also, several
laptop computer models are equipped with fingerprint sensors and authenticate users based
on their fingerprints [29].

1.2

Fingerprint Representation

A fingerprint pattern consists of intervening ridges and valleys spaced almost equidistantly
(about 9 pixels in 500ppi fingerprint images of adults). Fingerprints are typically described
by features at three levels (see Figure 1.4): (i) Level-1 features: ridge flow and pattern type,
(ii) Level-2 features: ridge endings and bifurcations, and (iii) Level-3 features: fine ridge
details such as pores and incipient ridges [91].

1.2.1

Level-1 Features: Orientation Field and Pattern Type

1.2.1.1

Orientation Field

Orientation field1 of a fingerprint, θ(x, y), describes the tangential direction of the ridges at a
point (x, y), where 0 ≤ θ(x, y) < π. Since the orientation has π-ambiguity (i.e., two different
vectors, one directed at θ and the other directed at (θ + π), have the same orientation), the
orientation field is often converted to a vector field by doubling the angles.
A 2-dimensional vector field can be represented by the first-order ordinary differential
equations (ODE) as follows:

x˙ = f (x, y),
y˙ = g(x, y),
1

Orientation field is also called ridge flow.

6

(1.1)

(a)

(b)

(c)

(d)

Figure 1.4: Fingerprint features at three different levels of detail. (a) Rolled fingerprint
in NIST SD29 [1], (b) Level-1 features: orientation field and singular points (cores marked
as circles and deltas marked as triangles), (c) Level-2 features: minutiae, and (d) Level-3
features: incipient ridges.
where f (x, y) and g(x, y) are real-valued functions. Once f (x, y) and g(x, y) are known, the
orientation field can be uniquely determined as:

θ(x, y) =

1
tan−1
2

y˙
x˙

=

1
tan−1
2

g(x, y)
.
f (x, y)

(1.2)

The x-isocline in differential equations is the set of points where x˙ = 0; that is, the x7

isocline of the system in Equation (1.1) is the set of points where f (x, y) = 0 [75]. Similarly,
the y-isocline of the system is the set of points where y˙ = 0, that is, g(x, y) = 0. A singular
point2 occurs at a point where both x˙ = 0 and y˙ = 0; that is, the x-isocline and the y-isocline
intersect. In a fingerprint orientation field, the singular points correspond to core and delta
(see Figures 1.5(a) and (c)).
A way of determining the characteristics of a singular point of an ODE system is by a
linearization of the system. The local vector field can be approximated by a linear system
[120]:
x˙ = Ax + b,
where

(1.3)

 
 


 
x˙ 
x
a b 
e
x˙ =   , x =   , A = 
 , and b =   .
y˙
y
c d
f

The matrix A is called the characteristic matrix. The stability of the singularity at the
center of the local field is the same as that of the singularity at the origin of the linearized
field when the real parts of the eigenvalues of A are non-zero (see linearization theorem) [75].
Singularities in a vector field such as a source and a sink with |A| > 0, where |A| is the
determinant of A, correspond to a core in the fingerprint orientation field. On the other
hand, a saddle in a vector field which has |A| < 0 corresponds to a delta in the fingerprint
orientation field. Figure 1.5 shows the orientation fields of cores and deltas at different
orientations and the corresponding vector fields.
Another way of determining singular points is by using the Poincar´e index [83], which is
commonly used to detect singularities in a fingerprint. The Poincar´e index of an orientation
field along an arbitrary simple closed path γ is defined as:

I(γ) =

2

1
2π

d2θ(x, y),
(x,y)∈γ

In a vector field, a singular point is also called an equilibrium point or a critical point.

8

(1.4)

(a)

(b)

(c)

(d)
Figure 1.5: Orientation field and vector field around singular points. (a) Orientation fields of
cores with different orientations, (b) vector fields of the corresponding cores, (c) orientation
fields of deltas with different orientations, and (d) vector fields of the corresponding deltas.
A core in the orientation field corresponds to a source or a sink with |A| > 0 in the vector
field while a delta in the orientation field corresponds to a saddle in the vector field which
has |A| < 0.

where θ(x, y) is the orientation field. To determine if there is a singularity at a point P , the
simple closed path γ is generally set to the neighboring circular path surrounding the point
P . Then, the Poincar´e index always takes one of the following three integer values: I(γ) is
1 if P is a core, −1 if P is a delta, and 0 if P is in a smooth orientation field region.
9

(a)

(b)

(c)

(d)

(e)

(f)

Figure 1.6: Fingerprint pattern types. (a) Arch, (b) left-loop, (c) right-loop, (d) tented-arch,
(e) whorl, and (f) twin-loop. Core is marked as yellow circle, and delta is marked as red
triangle.

1.2.1.2

Pattern Types

The Henry classification of fingerprint patterns [71] is based on the number and the spatial
configuration of singular points in fingerprints, and almost all fingerprints3 fall into one of
the following three categories (see Figure 1.6): (i) no singularity (arch type), (ii) one core
and one delta (left-loop, right-loop, and tented-arch type), and (iii) two cores and two deltas
(whorl and twin-loop type). Note that a whorl can be viewed as consisting of two cores. The
fingerprints in category (iii) are collectively called double-loop type.
3

The statistics of fingerprint class or type distribution in a very large database containing more than 220
million fingerprints reported in [10] showed that almost all fingerprints belong to arch, loop or double-loop;
only 0.2% of fingerprints are classified as accidental whorl or scar/mutilation, and 0.15% of fingerprints are
determined as amputation/missing.

10

(a)

(b)

Figure 1.7: Minutia types in a fingerprint. (a) Ridge ending and (b) ridge bifurcation.

1.2.2

Level-2 Features: Minutiae

Minutia points are the most popular feature used in fingerprint matching. The two most
common types of minutiae found in a fingerprint are ridge ending (Figure 1.7(a)) and ridge
bifurcation (Figure 1.7(b)). The simplest way of representing a minutia is by using a 3-tuple
vector: (x, y, θ), where (x, y) is the position of the minutia and θ is its direction. Most fingerprint matching algorithms are based on measuring the similarity in global configurations
of two minutiae sets representing the two fingerprint images.

1.2.3

Level-3 Features: Pores, Dots, and Incipient Ridges

The fine ridge details in a fingerprint such as pores, dots, incipient ridges, etc. (see Figure
1.8) are defined as Level-3 features. They can be useful information to compare fingerprints
when the Level-1 and Level-2 features present in the fingerprints are not sufficient (often
the case with latent fingerprints found at crime scenes) to make a decision on a pair of
fingerprints: the two fingerprint impressions (i) come from the same finger or (ii) come from
two different fingers. The Level-3 features are easier to observe in high resolution images
(at least 1000 ppi as opposed to the typical resolution of 500 ppi used to collect fingerprint
images). Algorithms to extract Level-3 features are not only computationally expensive in
11

(a)

(b)

(c)

(d)

Figure 1.8: Level-3 features in a fingerprint. (a) Pores, (b) incipient ridges, (c) dots, and (d)
ridge edge protrusion.
general, but are also quite sensitive to image noise.

1.3

Fingerprint Matching

Fingerprint matching scenarios generally fall into one of the following two categories based on
the type of query fingerprint: (i) exemplar search and (ii) latent search. In exemplar search,
rolled or plain impression of a subject’s finger (Figures 1.9(a) and (b)) is searched against
the exemplar fingerprint database (typically consisting of rolled and plain impressions) by
using an AFIS. In law enforcement and border crossing applications, this generally involves
all ten fingerprints (i.e., tenprint search) to ensure the individual’s identity. In latent search,
a fingerprint captured at a crime scene is fed into the AFIS along with the manually marked
features; a latent examiner verifies the top N matching results (N varies according to the
importance of a crime; N is typically around 100) from an AFIS to confirm the identify of
the suspect.

1.3.1

Types of Fingerprints

1.3.1.1

Exemplar Fingerprints

Rolled and plain fingerprints, collectively called exemplar fingerprints, refer to the fingerprints obtained on a formatted tenprint card (see Figure 1.1; the first two rows contain rolled
12

(a)

(b)

(c)

Figure 1.9: Three types of impressions of the same finger. (a) Rolled fingerprint, (b) plain
fingerprint in NIST SD29 [1], and (c) latent fingerprint in NIST SD27 [3].

fingerprints of ten fingers and the last row contains plain fingerprints) in an attended mode
(i.e., typically in the presence of a law enforcement officer). Rolled fingerprints are obtained
by rolling a finger from one side to the other (“nail-to-nail”) in order to capture all the ridge
details of a finger (Figure 1.9(a)). Plain fingerprints, also called flat or slap fingerprints, are
acquired by pressing fingertips onto a flat surface of either a paper for inking methods or a
flatbed of a live-scan device (Figure 1.9(b)). To make sure that the indices of the fingerprints
in rolled impressions are correct, plain or slap impressions are made by capturing four fingers
of a hand (from index finger to little finger) together and then taking the thumb impression
separately (called 4-4-2 acquisition). Rolled fingerprints contain a large number of minutiae
(about 100), and a significant amount of skin distortion can be introduced during rolling of
the finger. Plain fingerprints, on the other hand, capture relatively small finger area with
a smaller number of minutiae (about 50), but have lower skin distortion. Both rolled and
plain fingerprints are typically acquired under the supervision of a human operator to ensure
that good quality impressions are collected. If the fingerprint image is determined to be of
poor quality, it is recaptured.
13

The matching performance of state-of-the-art AFIS for exemplar search has already
reached a highly satisfactory level in most fingerprint recognition applications. The Fingerprint Vendor Technology Evaluation (FpVTE) in 2003 [135] reported that the best performing commercial matcher achieved a 99.4% verification rate in searching plain fingerprints
against an exemplar database with 10,000 plain fingerprints.

1.3.1.2

Latent Fingerprints

Latent fingerprints (see Figure 1.9(c)) refer to the fingerprints lifted from the surface of
objects touched or handled by a person. Latents are an extremely important source of
evidence in crime scene investigation to identify and convict suspects. Unlike rolled and
plain fingerprints, latent fingerprints are often of poor quality: the latent fingerprints contain
partial ridge patterns of a finger, incomplete or missing ridge structures, smudged or blurred
ridges, mixture of ridge pattern and complex background noise or friction ridge structures
from other fingers, and large nonlinear skin distortion due to pressure variations (see Figure
1.10).
Matching a latent fingerprint against an exemplar fingerprint database is of utmost importance in forensics and law enforcement to apprehend suspects. However, the latent fingerprint
recognition is still a very challenging problem, particularly with respect to the following two
issues: (i) eliminate or minimize human intervention which is currently needed to process
latents and (ii) improve latent identification accuracy so that a large percentage of latents
can be identified by verifying a very short list of candidates from the exemplar database
(ideally the list contains only one candidate if there is a match). In contrast to the exemplar
matching that is fully automated except for very poor quality query prints, current practice in latent matching involves a large degree of human intervention in marking features
in the latents and comparing the latent to top N candidates retrieved by the AFIS from
the database. Furthermore, the ELFT-EFS (Evaluation of Latent Fingerprint Technologies:
Extended Feature Sets) in 2012 [78] showed that the state-of-the-art matching performance
14

(a)

(b)

(c)

(d)

Figure 1.10: Challenging latent fingerprint images in NIST SD27 [3]. (a) Partial area, (b)
unclear ridge structure, (c) overlapped with other fingerprints, and (d) complex background.

of latent fingerprints was 68.2% with a full feature set (i.e., latent image, minutiae, and
extended features such as Level-3 features and fingerprint skeleton) in searching 418 latents
against 100,000 tenprint exemplar database including both rolled and plain impressions.
15

1.3.2

Exemplar Fingerprint Matching

Exemplar fingerprint matching process consists of two phases: (i) enrollment and (ii) verification or identification [91]. In the enrollment phase, a user’s fingerprint is acquired and the
features extracted from the fingerprint images are stored as a template with the subject’s
ID and other demographic information. During the verification/identification phase, the
fingerprint of a subject is used to determine if he was previously enrolled in the system.

1.3.2.1

Quality Assessment

Fingerprint image quality is an important factor in the matching accuracy; features extracted
from poor quality fingerprint are likely to have many spurious or missing minutiae. Fingerprint image quality is influenced by intrinsic factors of the finger skin (i.e., skin condition such
as dryness or salience of the ridges) and extrinsic factors (i.e., sensitivity of the fingerprint
imaging sensor or positioning of the user’s finger on the sensor). AFIS for exemplar search
assess the fingerprint quality at the front end of the system, and ask users to provide another
impression of their fingerprints if the fingerprints are of poor quality in the enrollment phase.
In the recognition phase, the quality module rejects the poor quality fingerprints that are not
adequate for matching in the verification/identification phase instead of making erroneous
identification decisions.
Algorithms to assess fingerprint image quality mainly utilize the features to measure
local properties (i.e., clarity of ridge structure in a grayscale image) and global properties
(e.g., continuity of orientation field or energy concentration in the frequency domain over
the entire fingerprint region) [31]. NIST Fingerprint Image Quality (NFIQ) is one of the
de facto standards to determine fingerprint image quality, which gives one of five discrete
quality levels ranging from 1 (the highest quality) to 5 (the lowest quality). Figure 1.11
shows fingerprint images with three different NFIQ values.
16

(a)

(b)

(c)

Figure 1.11: Fingerprints of various quality levels: (a) NFIQ of 1, (b) NFIQ of 3, and (c)
NFIQ of 5.
1.3.2.2

Feature Extraction

During the enrollment phase, a template which contains a set of features such as orientation field, singular points, and minutiae from one or more fingerprint images of a finger is
created and stored in the system along with the images. To compensate the intra-class variations in the fingerprint images (e.g., each image can capture a different part of the finger,
or the quality of each impression can vary significantly due to the changes in acquisition
condition), either a template integrating multiple fingerprint images is created [82], or or
multiple prototype templates which represent the variations in a set of fingerprint images
are selected [127].

1.3.2.3

Verification and Identification

An exemplar fingerprint matching is conducted as either (i) verification or (ii) identification.
Verification is an one-to-one matching; when a user provides his fingerprint along with his
identity, the system retrieves the template corresponding to the identity and determines if
the two fingerprints match. On the other hand, in the identification scenario, a user provides
his fingerprint without claiming his identity, and the system searches his fingerprint against
all the fingerprints in the database (i.e., one-to-many matching) and determines if there is a
17

match or no match.
Two types of errors can be made in fingerprint recognition: (i) false acceptance and
(ii) false rejection. False acceptance refers to the case where the input fingerprint is falsely
matched to a fingerprint in the database which is not the mate of the input fingerprint.
False rejection is the case where the input fingerprint is not matched to its true mate in the
database. The performance of a fingerprint verification algorithm is usually measured by
a Receiver Operating Characteristic (ROC) curve which indicates the true acceptance rate
(TAR) with respect to the false acceptance rate (FAR).
A number of evaluations have been performed for fingerprint verification scenarios. The
NIST FpVTE 2003 determined that the best commercial AFIS had a TAR of 99.4% at FAR
of 0.01% in the medium-scale test with 10,000 plain fingerprints [135]. The best performing
algorithm in Fingerprint Verification Competition (FVC) achieved an average equal error
rate (EER)4 of 2.07% on the FVC 2004 datasets [39]. For the evaluation of fingerprint
identification performance, the FpVTE 2012 searching against the exemplar database with
millions of fingerprints has been conducted (but the results have not yet been released) [98].

1.3.3

Latent Fingerprint Matching

1.3.3.1

Acquisition

Latent fingerprints are lifted from the surface of objects through a variety of means ranging
from simply photographing the print to more complex dusting or chemical processing [87].
Unlike exemplar fingerprints which are obtained under a supervision of a well-trained operator, latent fingerprints are acquired from the residues of a fingermark such as sweat which
can be easily destructible in natural environments over time. This explains why the quality
of latent fingerprints is often poor and cannot be controlled.
4

The equal error rate (EER) refers to the error rate where FAR = FRR.

18

1.3.3.2

ACE-V Methodology

In matching latents to exemplar prints, latent fingerprint examiners are expected to follow
a methodology, called Analysis, Comparison, Evaluation, and Verification (ACE-V) [33]. In
the analysis phase, an examiner evaluates the ridge information contained in latent images.
If the latent is determined to have sufficient information for individualization or exclusion
(called “of value” latent; see the definitions described in the evaluation phase), the features in
the latent are manually marked by the examiner to search for their mates using an AFIS. In
the comparison phase, the examiner compares the “of value” latent with the candidate mates
retrieved from the exemplar database side-by-side and ascertains the similarity between the
latent and mated exemplar print pairs using feature markup in the latent. In the evaluation
phase, one of the following decisions is made about the latent in question: individualization,
exclusion, or inconclusive5 . Finally, in the verification phase, the decision made by the first
examiner is confirmed by having a second examiner analyze the results independently.

1.3.3.3

Performance Evaluation

Since manual comparisons between a latent and a set of candidate mates retrieved from
an exemplar database is involved in the comparison phase of the ACE-V methodology, the
performance of latent matching algorithms is commonly measured by plotting a Cumulative
Match Characteristic (CMC) curve. A CMC curve draws the cumulative rank-m identification rate (i.e., the percentage of the query latents whose mates are retrieved within rank m)
with respect to the rank m.
5
Individualization is the decision that a latent examiner makes on a pair consisting of a latent and an
exemplar print indicating that the pair originates from the same finger based on a sufficient agreement between the two ridge patterns. Exclusion, on the other hand, is the decision where an examiner concludes
that the pair did not originate from the same finger based on a sufficient disagreement between the two ridge
patterns. An inconclusive decision is made when an examiner cannot make a decision of either individualization or exclusion due to insufficient ridge details or small corresponding area between latent and exemplar
print [117].

19

1.4

Challenges in Fingerprint Recognition

Fingerprint recognition is regarded as one of the most reliable methods for human identification achieving a high level of matching accuracy [135] and throughput in the widespread
deployment of AFIS in large-scale operational applications [7–9]. However, there exist some
challenges in fingerprint recognition that need to be addressed: (i) demonstration of persistence and uniqueness of fingerprints to establish solid ground for fingerprint recognition, (ii)
“lights-out” latent fingerprint identification, and (iii) ensuring that AFIS cannot be compromised by various types of attacks by adversary.

1.4.1

Persistence and Uniqueness of Fingerprints

The persistence and uniqueness of fingerprints—two fundamental properties of fingerprints
enabling a high level of fingerprint recognition accuracy—have been presumed and accepted
as facts without the support of any scientific basis. In situations where fingerprints are
presented as forensic evidence in the courts of law, the linkage between a friction ridge
evidence and the suspect is required to be supported by scientific methodology with a known
error rate under the Daubert criteria [17].
Fingerprint uniqueness has been investigated based on statistical models of fingerprint
features. These models provide either (i) a probability of random correspondence (PRC)
[42, 105, 142] or (ii) a likelihood of a match in fingerprint comparison [101]. In [105], the
probability that a template fingerprint with m minutiae has q matched minutiae with a
query fingerprint with n minutiae was estimated under the restrictive assumptions that (i)
fingerprint minutiae are uniformly distributed, (ii) the location and direction of a minutia
are independent, and (iii) the correspondence of a minutiae pair is an independent event.
A more realistic minutiae model was developed in [142] based on a mixture model that
combines the distributions of minutiae location and direction; the PRC of two fingerprints
was approximated by a Poisson distribution. While the studies in [105, 142] focused only on
20

minutiae models, a model incorporating fingerprint type (arch, loop, and whorl) and pores
was also developed, which resulted in more realistic PRC values [42]. In a different approach
to the uniqueness problem, the likelihood ratio of the comparison between a latent and an
exemplar fingerprint was computed under the null hypothesis that the two impressions were
made by the same finger. The likelihood ratio indicates the reliability of the comparison
as forensic evidence [101]. That is, a small likelihood ratio value implies that the suspect
identification based on the fingerprint pairing may be misleading. This model used the
spatial configuration of minutiae, which is able to assess the latent-exemplar comparison
with a small number of minutiae and account for skin distortion.
Fingerprint persistence, on the other hand, still remains as anecdotal evidence. To our
knowledge, no large-scale studies on fingerprint persistence have been published. Perhaps,
this is due to the difficulty in collecting a large-scale longitudinal fingerprint database. Galton
[61] and Herschel [73] observed, from a set of genuine fingerprint pairs captured at two distinct
time instances with a large interval of several decades, that the fingerprint ridge structure
is stable over time. However, considering the current practice of fingerprint recognition that
is based on AFIS, permanence of fingerprint ridge structure is not of the utmost interest.
Instead, the temporal stability of fingerprint matching accuracy under variations in sensing
modality, feature representation, and matching algorithms needs to be demonstrated to
solidify the basis for fingerprint recognition.

1.4.2

“Lights-Out” Latent Identification

A “lights-out” fingerprint identification system refers to a system that requires only fingerprint images as input (query) and which returns a short list of exemplar prints as potential
mates [79]. While virtually all AFIS for exemplar matching operate in “lights-out” identification mode, matching latent fingerprints in “lights-out” mode is still very challenging. In
the 2012 ELFT-EFS [78], the best performing latent matcher achieved rank-1 identification
rate of 63.4% in “lights-out” identification mode.
21

In the current practice of matching latent fingerprints, a large degree of human intervention is needed to mark up the features in the latents, including minutiae and extended features and verify the mate from the candidate list retrieved from a large exemplar database.
Although the ACE-V methodology is widely accepted by the forensic community for latent print examination, the influence of human factors in the ACE-V procedure has raised
concerns about their reliability and consistency. A noteworthy case is the erroneous identification of Brandon Mayfield as a suspect in the Madrid train bombing incident based on
an incorrect match between Mayfield’s exemplar fingerprint and the latent print captured
at the bombing site [103, 104]. The National Research Council’s report on limitations and
recommendations of forensic science [100] pointed out two major shortcomings in the current
forensic science discipline: (i) “lack of mandatory and enforceable standards” that can be
globally referred to in crime labs and (ii) “unacceptable case backlogs in state and local crime
labs which likely make it difficult for laboratories to provide strong evidence for prosecutions
and avoid errors that could lead to imperfect justice”. Along with the efforts to understand
the human factors in latent fingerprint examination [99], standards and guidelines for latent
examiners’ practices have also been set up. As an example, the Science Working Group
on Friction Ridge Analysis, Study and Technology (SWGFAST) published standards which
define terminologies and establish the sufficiency level for decisions at each step of the ACEV methodology to alleviate subjectivity involved in feature markups and decision makings
among examiners [117].
Based on the guidelines in SWGFAST standard, latent examiners’ practices have been
evaluated from various aspects (e.g., reliability of decisions, degree of consensus and consistency of decisions) [74, 125, 126], mainly on two critical decisions that the examiners make
in ACE-V methodology: (i) latent value determination in the analysis phase and (ii) latent
individualization conclusion in the evaluation phase. This line of study indicates that a
significant amount of subjectivity and variation exist in the practices of the ACE-V methodology.
22

The advantages of “lights-out” latent identification mode include: (i) alleviating subjectivity in latent print examination and (ii) increasing throughput of latent print matching.
This will ease the burden on latent examiners, given their growing case workload. Hence,
important research topics in latent matching include: (i) pre-processing of latents such as
latent quality assessment, latent segmentation, and latent enhancement, and (ii) advanced
matching algorithm based on minutiae and extended features. The FBI’s Next Generation
Identification (NGI) program [11] also specifies the improved latent processing services as
one of the desirable tasks in advanced fingerprint identification technology.

1.4.3

Vulnerability of Automated Fingerprint Identification Systems

The widespread deployment of AFIS in law enforcement, international border crossing, and
access control to secure facilities has prompted some individuals to engage in extreme measures for the purpose of circumventing the AFIS: (i) fingerprint spoofing and (ii) fingerprint
obfuscation (or alteration). Fingerprint spoofing – the use of fake fingers made of glue, latex
or silicone – is a well publicized method to adopt another person’s identity. Figure 1.12 gives
examples of fake fingerprints. Figure 1.12(a) shows a gummy fingerprint from a mold made
by having a finger press down on the softened plastic and solidifying materials such as latex
or silicone in the mold. Figure 1.12(b) shows a dummy finger made of silicone with detailed
friction ridge pattern on the fingertip.
In order to detect attacks based on fake fingers, extensive research has been conducted
in the biometrics literature to measure the liveness of a finger that have resulted in: (i)
software solutions and (ii) hardware solutions. Software solutions utilize the conventional
fingerprint sensing device, but adopt a series of image frames of the fingerprint to observe
perspiration pattern [106] or skin distortion [32] of the finger. On the other hand, hardware
solutions involve additional sensing devices to measure electrical resistance [118] or spectral
characteristics [102] of the finger skin.
23

(a)

(b)

Figure 1.12: Fake fingerprints. (a) Gummy fingerprint: (Left) pressing a finger on the
softened plastic [19, 94], (Center) the mold generated from a finger [21], (Right) a gummy
fingerprint from the mold [4], and (b) dummy finger [5].

Unlike fake fingers, obfuscated or altered fingerprints6 are real fingers whose ridge structure has been severely changed by abrading, cutting, burning, or performing plastic surgery
on fingertips (see Figure 1.13). The purpose of fingerprint obfuscation is to conceal one’s
identity in order to evade AFIS. The problem of altered fingerprints has hitherto not been
studied and there are no reported techniques to identify them. Although a number of algorithms and methods to measure the fingerprint image quality and to detect fake fingerprints
have been proposed, none of them can be effectively used to detect altered fingerprints due to
the following reasons. (i) Not all the altered fingerprints are of poor quality (see Figures 5.9
and 5.10) and (ii) the altered fingerprints are indeed from live fingers, so the fake fingerprint
detectors which essentially measure the properties of the live fingers would not work.
To deal with the problem of attacks on AFIS by fingerprint obfuscation, the following
research problems need to be investigated: (i) analyzing altered fingerprints, (ii) detecting
altered fingerprints, and (iii) matching altered fingerprints to their pre-altered mates.

6

Fingerprint obfuscation and fingerprint alteration will be used interchangeably in this dissertation.

24

(a)

(b)

(c)

(d)

Figure 1.13: Photographs of altered fingerprints. (a) Transplanted friction ridge skin from
sole of the feet [6], (b) fingers that have been bitten [122], (c) fingers burnt by acid [67], and
(d) stitched fingers [23].

1.5

Dissertation Contributions

The contributions of this dissertation are: (i) longitudinal analysis of genuine fingerprint
match scores and identification decisions based on statistical model to demonstrate the persistence of fingerprint matching accuracy over time, (ii) global fingerprint orientation field
modeling, (iii) latent fingerprint enhancement, and (iv) detection and matching of altered
fingerprints.
• Objective of the longitudinal study of fingerprint recognition is to provide scientific
basis for the stability of fingerprint matching accuracy over time. In order to tackle this
problem, we first investigate how the time interval between two fingerprint impressions
25

obtained from the same finger at two different time instances accounts for the variation
in genuine match scores. Based on a longitudinal fingerprint database provided by the
Michigan State Police, we use a multilevel statistical model to infer the relationship
between time interval and genuine match score. In order to assess the impact of time
interval on genuine match scores, we compare it with other possible covariates including
subject’s age, gender, race, and fingerprint image quality. We find that (i) genuine
match score tends to decrease as time interval between two fingerprints increases, (ii)
although time interval and subject’s age have significant influence on genuine match
scores, fingerprint image quality is able to explain the variation in genuine match scores
the best, (iii) subject’s gender and race barely affect the fingerprint match scores, and
(iv) true acceptance rate tends to be stable even if the time interval between two
fingerprints in comparison increases.
• Global orientation field models are useful for estimating the orientation field in noisy
fingerprint images. The models are also useful in representing the unique characteristics
of fingerprint ridge flow patterns in a mathematical form. Global orientation field
models reported in the literature integrate the properties of local field around singular
points and arch-like global field. We develop a global orientation field model in the form
of ordinary differential equations which represent x-derivative and y-derivative with a
small number of polynomial terms and are constrained by the number of singular
points7 . The proposed model is used to determine if an arbitrary input image contains
a fingerprint pattern. This property can be used to (i) check the validity (e.g., deviation
from normal friction ridge pattern) of the input image to an AFIS, and (ii) investigate
the integrity of fingerprint images in an exemplar database.
• The manual markup of features in latent fingerprints is not only a tedious job for
latent examiners, but the markup features can also involve subjectivity (i.e., the feature
7

Almost all the fingerprints belong to one of the following categories based on the number of singular
points: (i) no singular point, (ii) one core and one delta, and (iii) two cores and two deltas.

26

sets marked by multiple examiners can be different). We propose a latent fingerprint
enhancement algorithm which requires minimal markup (only the region of interest
and singular points) to provide the enhanced latents to an AFIS that leads to more
robust and consistent minutiae extraction and matching. The key component of the
algorithm is the orientation field estimation in latents. For robust orientation field
estimation, we use (i) a global orientation field model which decomposes a singular
orientation field component with discontinuity around cores and deltas and a residual
orientation field component which is continuous over the entire fingerprint region, and
(ii) a randomized-RANSAC (Random Sample Consensus) algorithm to fit the model
to latents.
• Fingerprint obfuscation is a serious attack that can compromise the performance and
integrity of AFIS. However, unlike spoof fingerprints, fingerprint obfuscation has not
received adequate attention. We analyze the patterns found in the altered fingerprints
based on a large database of altered fingerprints provided by law enforcement agencies.
We develop an algorithm to detect altered fingerprints based on the abnormality in
orientation field and minutiae distribution that are observed in altered fingerprints.
In order to improve the matching accuracy of altered fingerprints to their pre-altered
mates, we propose an algorithm to restore the arrangement of local ridge patches, and
evaluate the performance of AFIS when the altered region in an input fingerprint is
restored or masked out.

27

Chapter 2
Longitudinal Study of Fingerprint
Recognition

2.1

Introduction

Friction ridge skin on fingers and palms has been purportedly known to be a physical characteristic of an individual that does not change over time (i.e., persistence or permanence of
friction ridge pattern) and can be used as a person’s “seal” or “signature” (i.e., uniqueness or
individuality of ridge pattern). Pioneering work of Herschel [73], Henry [71], Galton [61], and
Faulds [51] established the way for recognizing humans based on their fingerprints. Starting
with the first known case where the fingerprints found at the crime scene in Argentina in
1893 were officially accepted as an evidence to convict a suspect [69], friction ridge analysis
has become one of the most crucial methods in crime scene investigations worldwide. The
decision made in Frye v. United States in 1923 [16] is widely cited as the basis for the admissibility of forensic evidence, including friction ridge pattern; Frye standard states that a
scientific principle or discovery which has gained a general acceptance in the relevant field is
admissible in the courts.
In Daubert v. Merrell Dow Pharmaceuticals, Inc. in 1993 [17], however, the general
28

acceptance test of Frye was superseded by the Federal Rules of Evidence (FRE). The Daubert
ruling established a guideline for admitting forensic evidence which consists of the following
factors: (i) empirical testing, (ii) peer review and publication, (iii) the known or potential
error rate, (iv) standards controlling the operation, and (v) the Frye standard of general
acceptance. The Daubert standard provoked challenges to admissibility of friction ridge
evidence in the courts. Although all of about 40 such challenges resulted in a decision that
friction ridge analysis is acceptable as forensic evidence, the Daubert case highlighted a lack
of scientific basis of persistence and uniqueness that support the human identification by
friction ridge patterns and standards that can be universally referred to in friction ridge
analysis.
The Daubert ruling led to the development of standards and guidelines for friction ridge
analysis [117] and retraining of latent examiners [97], along with a body of research to
demonstrate the foundations of fingerprint identification, i.e., uniqueness and persistence of
friction ridge patterns. While a significant amount of effort has been made to study the
uniqueness of fingerprints by (i) estimating the probability of a random correspondence (i.e.,
two randomly selected fingerprints will be sufficiently similar to be claimed as genuine mates)
[42,105,142] or (ii) measuring the evidential value of latent fingerprint comparisons [101], no
systematic study on persistence of fingerprints has been reported.
Early studies on persistence of fingerprints focused on demonstrating the invariance of
ridge structure in the fingerprints with respect to time. As already shown in Figure 1.2,
Herschel collected three fingerprints of his son when he was 7, 17, and 40 years old, and
verified that all the ridge details in the three fingerprints did not change over time [73].
Galton collected 11 pairs of fingerprints from six different individuals at two different time
instances [61]. The time interval between a pair of fingerprints in Galton’s collection ranged
from 11 years to 31 years. The six subjects in his study were selected from different age
groups; the age at the second impression was as young as 15 years old and as old as 79
years old. Among the 389 minutiae pairs that were manually labeled by Galton, only a
29

(a)

(b)

Figure 2.1: Fingerprint pairs with minutiae correspondences labeled by Galton in his study
on fingerprint persistence [61]. (a) A pair of fingerprints with 13-year time interval showing
perfect minutiae correspondences, and (b) a pair of fingerprints from another finger of the
same subject with one minutia missing in the later age impression (denoted as ‘A’).
single minutia was missing in a fingerprint pair (see Figure 2.1). In addition to these case
studies, the temporal invariance of fingerprint patterns has been explained by the anatomical
structure of friction ridge skin; the ridge pattern formed in the inner (dermal) layer during
gestation remains unchanged with the protection of the outer (epidermal) layer [46].
Fingerprint recognition technology has made great strides since the Federal Bureau
of Investigation (FBI) initiated Automated Fingerprint Identification Systems (AFIS) in
1970’s [95]. Since then, there has been a phenomenal increase in both the size of the fingerprint databases held by various law enforcement agencies as well as the speed at which they
can be searched while maintaining high matching accuracy. Considering that the fingerprint
recognition today essentially involves AFIS searching large-scale databases, the objective of
research on fingerprint persistence should be to establish the temporal invariance of fingerprint recognition accuracy, rather than the permanency of the friction ridge pattern itself.
The 2009 National Research Council (NRC) report [100] pointed out that
“Uniqueness and persistence are necessary conditions for friction ridge identification to be feasible, but those conditions do not imply that anyone can reliably
30

discern whether or not two friction ridge impressions were made by the same
person. Uniqueness does not guarantee that prints from two different people are
always sufficiently different that they cannot be confused, or that two impressions
made by the same finger will also be sufficiently similar to be discerned as coming
from the same source.”
This means that the representation and extraction of invariant and discriminative features for
fingerprint identification may be deficient in a collection of fingerprint impressions captured
under various conditions. Furthermore, fingerprint comparison algorithms may be imperfect
to model the similarity among genuine fingerprints and the dissimilarity among impostor
fingerprints and separate the two groups [80].
Fingerprint recognition exhibits two types of comparison errors: (i) false rejection: falsely
determining two impressions from the same finger (a genuine fingerprint pair) as a nonmatch due to large intra-class variability, and (ii) false acceptance: falsely determining
two different fingerprint impressions from two distinct fingers (an impostor fingerprint pair)
as a match due to large inter-class similarity. The intra-class variability is observed due
to changes in intrinsic skin condition (e.g., finger skin dryness, distortion), and changes
in sensing method (inked or live-scan fingerprints) or sensing technology (known as the
interoperability problem [12]). On the other hand, the inter-class similarity can be observed
when the fingerprint impressions from two distinct fingers partially coincide. A notable
case of false recognition by friction ridge analysis in forensic investigation is the erroneous
identification of Brandon Mayfield as a suspect in the Madrid train bombing based on an
incorrect match between Mayfield’s exemplar fingerprint and the latent print captured at
the bombing site [103].
In the biometrics literature, a phenomenon called template aging has been reported,
which refers to the increase in the system error rate with respect to the time gap between
the query and the template (or reference) [92]. A study comparing groups of fingerprint pairs
with respect to time gap reported that the fingerprint comparisons with less than a 5-year
31

time gap show lower error rate than comparisons with a larger time gap [53]. Further, a
scheme to mitigate this template aging effect has been proposed by updating the templates
stored in the system with newly acquired data [127].
In order to determine the tendency of biometrics recognition accuracy with respect to
time interval between acquisitions of a biometric trait, we need to (i) collect longitudinal
biometrics data consisting of multiple acquisitions of a biometric trait from the sampled
population over a reasonably long period of time, and (ii) conduct an appropriate analysis,
considering the characteristics of the longitudinal data. If the longitudinal data is balanced
and time structured 1 , cross-sectional analysis can be readily applied to longitudinal data by
grouping the data according to cohort (for example, short-term and long-term comparison
groups) under the assumption of compound symmetry2 . In reality, however, it is often
not feasible to collect longitudinal biometrics data by following an identical measurement
schedule over a target sample satisfying the compound symmetry. To handle the unbalanced
and time-unstructured longitudinal data, several statistical models have been developed:
linear mixed-effects model [85], multilevel statistical model [62], hierarchical linear models
[112], and random coefficient regression [70]. Despite their different names and origins, these
models are essentially identical.
A number of published studies on template aging in major biometrics modalities (e.g., [53]
on fingerprint recognition, [56, 57] on iris recognition, and [86] on face recognition) made
incorrect use of cross-sectional analysis on unbalanced and time-unstructured longitudinal
data. On the other hand, the longitudinal study on iris recognition by the National Institute
of Standards and Technology (NIST) [64] correctly used a nonlinear mixed-effects model to
1
A longitudinal dataset is characterized by (i) the number of measurements per individual and (ii) the
time schedule used to make the measurements [121]. Balanced dataset means that every subject has the
same number of measurements. Time-structured dataset consists of the repeated measurements following an
identical time schedule across individuals. The sequence of measurements for each individual can be spaced
either regularly or irregularly.
2
The compound symmetry requires (i) homoscedasticity of variance: the variance of the measurements
at a time instance across all subjects is the same as that of the measurements at another time instance, and
(ii) constant covariance: the correlation between the measurements at the first and second time instances,
for example, is the same as that between the measurements at the first and third time instances, and so on.

32

show the relationship between genuine iris match scores and covariates such as time elapsed
after enrollment and the difference in iris dilation. Despite the use of an appropriate modeling
approach, the NIST study suffers from the following drawbacks: (i) the dataset used was
truncated in the sense that the iris match scores from falsely rejected genuine comparisons
were not included, and (ii) the validity of some of the assumptions in the mixed-effects model
(i.e., normality of residuals and random effects) was not verified. The truncated data is
problematic because the truncated portion of the data—erroneous identification decisions—
is the very target of the analysis to determine the tendency of error rate with respect to
time. Also, only if all the model assumptions are satisfied, the analysis and inferences from
the data can be accepted.
We demonstrate whether the fingerprint matching accuracy changes over time, namely
the time interval between two fingerprint impressions being compared. For this purpose, we
obtained a longitudinal database of fingerprints collected from 15,597 subjects booked by
the Michigan State Police over at least a 5-year time span. A multilevel statistical model
[62, 121] is used to understand temporal tendency of fingerprint recognition performance in
the longitudinal dataset which is unbalanced and time unstructured. More specifically, we
address the following two questions to statistically demonstrate the persistence of fingerprints
from the perspective of AFIS matching accuracy:
1. What is the trend of genuine match scores over time? It has been empirically noticed
that match scores of genuine fingerprint pairs with a large time gap tend to decrease,
possibly due to aging of finger skin and higher chance to have worn out or altered
fingerprints. To examine the relationship of time interval between two fingerprints
being compared with its genuine match score, a linear 2-level model with time interval
as a covariate is fit to the genuine match scores generated by commercial matchers.
Given the parameter estimates and confidence intervals, the null hypothesis “the slope
of the linear model is zero” is tested.
2. What is the trend of matching accuracy (or identification decisions) with respect to the
33

time interval between fingerprints? The ultimate question of interest is whether or
not the genuine match scores remain significantly higher than the decision threshold
in the presence of time lapse between impressions being compared. This problem
is formulated by making a binary identification decision on each genuine pair with
a predetermined decision threshold and fitting a linear 2-level model to the binary
decisions. The probability of true acceptance (i.e., a genuine fingerprint pair is correctly
determined as genuine), for a predetermined threshold, with respect to time interval is
estimated.
The rest of the chapter is organized as follows. Section 2.2 reviews the traditional and
recent approaches for longitudinal data analysis, and introduce the multilevel statistical
model used in this study. Section 2.3 explains the longitudinal fingerprint database analyzed
in this study and gives the overview of longitudinal analysis of the dataset with multilevel
model. In Section 2.4, the match scores of genuine fingerprint pairs are modeled by linear
2-level models with various covariates, including time interval, subject’s age, and fingerprint
image quality. The models with salient covariates are selected based on the evaluation
of goodness-of-fit. After the underlying model assumptions are validated, the tendency of
genuine match scores with respect to the selected covariates is investigated based on the
parameter estimates and their confidence intervals. In Section 2.5, a linear 2-level model is
fit to the binary decisions made on genuine fingerprint pairs by applying a decision threshold
to determine whether the true acceptance rate is stable over time. Finally, Section 2.6
summarizes the study and suggests future research directions.

2.2

Longitudinal Data Analysis

Longitudinal data refers to repeated measurements on a collection of individuals sampled
from a population over time. This is in contrast to cross-sectional data where a single measurement is made on each individual [62]. The approach for analyzing the longitudinal data
34

Subject 1
Subject 2
Subject 3
Subject 4
Subject 5

Measurement

Measurement

Young Subjects
Old Subjects

Age

Age

(a)

(b)

Figure 2.2: Cross-sectional analysis versus longitudinal analysis of balanced but timeunstructured longitudinal data (adapted from [49]). For this dataset (two measurements
for each of 5 subjects), (a) the cross-sectional analysis that discards subject labels on data
makes an inference that the measurement values tend to decrease with respect to subject’s
age, while (b) the longitudinal analysis interprets the data as the measurement values tend
to increase with respect to age.
differs according to the data characteristics. Early models for longitudinal data analysis were
derived from cross-sectional analysis, in particular analysis of variance (ANOVA) [113], assuming that (i) the longitudinal dataset is balanced and time structured (i.e., n repeated
measurements for each one of the N individuals following an identical measurement schedule), and (ii) the dataset satisfies the compound symmetry. Figure 2.2 shows a hypothetical
example that, if the dataset is unbalanced and/or time unstructured, the cross-sectional
analysis makes incorrect inference against the actual longitudinal behavior.
In this section, we will review the models based on ANOVA for longitudinal data analysis,
and then describe the details of multilevel statistical model which is used for our longitudinal
study of fingerprint recognition.

2.2.1

ANOVA-based Approach

ANOVA is widely used to compare multiple groups, where each group consists of crosssectional data. For example, consider an experiment to demonstrate the effectiveness of a
35

medicine for a disease. A simple experimental design would be to construct two groups of
test subjects: one group is treated by the medicine, while the other group, a control group,
is not treated by it. A popular null hypothesis tested in ANOVA is that the group means are
equal. By rejecting the null hypothesis, we can claim that the medicine makes a significant
difference in the treatment of the disease against the control group.
Although the traditional way of conducting ANOVA test is to use an F-statistic, a general
linear model (GLM) is preferred to describe ANOVA due to the conceptual and practical
advantages [116]. In the GLM framework, multiple concepts, such as regression, ANOVA,
and analysis of covariance (ANCOVA), can be easily linked, and one can develop a unified
methodology for statistical analysis under different circumstances. Also, the GLM makes it
easy to test the underlying assumptions for ANOVA and ANCOVA.
In the GLM framework, ANOVA model can be described as follows:

yij = µ + bi + εij , for i = 1, . . . , N, and j = 1, . . . , n,

(2.1)

where yij is the observed response (or measurement) for the j-th sample in group i, µ is the
grand mean for the entire population, bi is the random variable for group i, and the error εij
is normally distributed (εij ∼ N (0, σe2 )).
This model can be viewed as either a fixed-effects model or a random-effects model
according to the question of interest and the experimental design. If an investigator gives
different treatments to each of N groups and wants to determine if there is any significant
difference among treatments, for instance, the following null hypothesis can be tested: b1 =
b2 = · · · = bN = 0 (i.e., all N group means are the same). As the treatments applied to each
group are fixed, this is called a fixed-effects ANOVA. On the other hand, one can view the
treatment as a random variable sampled from a larger population of possible treatments.
Then the objective of statistical analysis will be to determine to what extent the treatments
account for the variance in the observed responses. This is called a random-effects ANOVA.
36

Under the assumptions, bi ∼ N (0, σb2 ) and yij ∼ N (µ, σb2 + σe2 ), the primary goals of randomeffects ANOVA include (i) testing the null hypothesis: σb2 = 0 (i.e., the variance in treatments
does not have any impact on the variance in the observed responses), or (ii) computing intraclass correlation coefficient (ICC) that is defined as:

ICC =

σb2
.
σb2 + σe2

(2.2)

In many situations, both fixed and random effects exist in the data, or it is difficult to
distinguish between them. A univariate repeated-measures ANOVA (also called rANOVA
or mixed-effects ANOVA) includes both fixed and random effects in the model [59]. In a
longitudinal dataset, the j-th measurement of subject i, yij , is made along with p explanatory
variables (xijk , k = 1, . . . , p; also referred to as covariates or predictors) observed at the time
of measurement. Then, a univariate repeated-measures ANOVA is described as:

yij = β1 xij1 + β2 xij2 + · · · + βp xijp + bi + εij ,
= xTij β + bi + εij , for i = 1, . . . , N, and j = 1, . . . , n,

(2.3)

where xij is a design vector consisting of the p explanatory variables, β is a regression
parameter vector, bi ∼ N (0, σb2 ), and εij ∼ N (0, σe2).

2.2.2

Multilevel Statistical Model

A multilevel model is primarily used to analyze hierarchically structured, nested, or clustered
data [62]. The model, for example, will be appropriate if one is interested in the factors that
affect the performance of students from multiple schools in a mathematics examination.
Consider N schools with school i having ni students. Let yij denote the test score of student
j in school i. The explanatory variables of the observed responses can be either (i) timevariant predictor (e.g., student’s age at the time of taking test) or (ii) time-invariant predictor
37

(e.g., student’s gender).
Longitudinal data can be viewed as hierarchically structured data in the following sense.
The first level (lower level) of the model consists of the repeated measurements taken from
each individual, and the level-1 model is regressed to the data of the individual and accounts
for the intra-subject changes. In the level-2 model (higher level), the population-averaged
tendency and deviations of individuals are modeled to account for the inter-subject changes.
The multilevel model is applicable for unbalanced and time-unstructured longitudinal data
and does not require compound symmetry.
A simple 2-level model with a single covariate can be represented by:

Level-1 Model: (Intra-subject change)

yij = ϕ0i + ϕ1i xij + εij ,
εij ∼ N (0, σe2),

Level-2 Model: (Inter-subject change)

(2.4)

ϕ0i = β00 + b0i ,
ϕ1i = β10 + b1i ,
 
  

2
b0i 
0  σ0 σ01 
  = N   , 
 .
b1i
0
σ10 σ12

(2.5)

In the level-1 model, the variables and parameters are defined as follows:
• yij is the j-th measurement (observed response) for subject i at the time instance xij ,
for i = 1, . . . , N, and j = 1, . . . , ni .
• ϕ0i is the true parameter representing the intercept of the linear model for subject i.
• ϕ1i is the true parameter representing the slope of the linear model for subject i.
• εij is the error in the j-th measurement of subject i from the model fit. The error is
assumed to be normally distributed with a zero mean and a variance of σε2 .
In the level-2 model, the true parameters, ϕ0i and ϕ1i , can be modeled by a mixture of fixed
and random effects.
38

• Parameters β00 and β10 are the fixed effects of the model, representing the grand means
of intercept and slope across all N subjects in the data, respectively.

• Parameters b0i and b1i are the random effects of the model, representing the deviations
of subject i’s intercept and slope from β00 and β10 , respectively. The random effects
are assumed to follow a Gaussian distribution.

Any covariates other than time instance can be introduced in the model. For instance, if
we are interested in whether or not gender (time-invariant predictor) is a factor that explains
differences in students’ performance in math exam, the level-2 model can be updated in the
following way:

ϕ0i = β00 + β01 GENDERi + b0i ,
ϕ1i = β10 + β11 GENDERi + b1i .

(2.6)

If the predictor of interest is time varying, it can be introduced in the level-1 model (for
example, the area of residency of the student at the time of taking exam):

yij = ϕ0i + ϕ1i xij + ϕ2i AREAij + εij .

(2.7)

Note that, depending on the nature of the covariate, the model parameter associated with
the covariate can have only fixed effects (i.e., ϕ2i = β20 ) or a mixture of fixed and random
effects (i.e., ϕ2i = β20 + b2i ).
The multilevel model is often represented in its composite form [121]. The composite
form of the 2-level model in Equation (2.4) is:

yij = ϕ0i + ϕ1i xij + εij
= [β00 + β10 xij ] + [b0i + b1i xij + εij ].
39

(2.8)

The first part of the composite model is called the structural component which contains
only the fixed effects of the model. The second part of the composite model is called the
stochastic component consisting of random effects [121]. The stochastic component shows
that the compound symmetry assumption is not required in the model. For example, the
term b1i xij indicates the heteroscedasticity of variance in the observed responses; the variance
can vary with respect to time instance xij for the j-th measurement of subject i. In addition,
the term b0i allows the residuals to be autocorrelated; that is, the residuals within a subject
can be linked across time. The composite form of the multilevel model shows that it is
equivalent to linear mixed-effects model.

Equation (2.8) can be also represented in a matrix form:

yij = (β00 + β10 xij ) + (b0i + b1i xij + εij )
 
 
β00 
b0i 
= 1 xij   + 1 xij   + εij
β10
b1i
= xTij β + zTij bi + εij .

(2.9)

Hence,
y = Xβ + Zb + ε,

(2.10)

where X is a design matrix for fixed effects, Z is a design matrix for random effects, β is
a fixed-effects coefficient vector, b is a random-effects coefficient vector, and ε is a residual
vector. Note that, although X and Z are the same in Equation (2.9), they can be different
in general when some of the covariates do not have random effects (thus, the components of
the design vector in Z are a subset of those in X).
40

2.2.2.1

Parameter Estimation Method

The maximum likelihood (ML) and generalized least-squares (GLS)3 estimations are widely
used to obtain parameters in the multilevel model [121]. The estimation based on ML
requires that the residuals be normally distributed; in this case, GLS estimates are the same
as ML estimates. The normality assumption is useful since, if the sample size is large,
ML estimates are (i) asymptotically unbiased (converging to true population parameters),
(ii) asymptotically normally distributed, and (iii) asymptotically efficient (smaller standard
errors than those derived by other methods).
Under the normality assumption (ε ∼ N (0,Ω)), the estimate for parameter β in Equation
(2.10) using GLS is given by [62]:
βˆ = (XT Ω−1 X)−1 XT Ω−1 y.

(2.11)

As the true error covariance Ω is unknown, the GLS estimate is obtained by a two-stage
approach:

1. Initialize β, and estimate Ω using the residuals from the model with the initial parameter value. The initial parameter value can be the OLS estimate of the composite
model.

2. Refit the composite model using GLS with the estimated Ω, and then find β.

The above two-stage scheme can be repeated to obtain a better fit by replacing the initial
estimate of parameter value in step 1 with the updated parameter value in step 2. This is
called an iterative GLS.
3

Note that ordinary least-squares (OLS) estimation cannot be used to estimate the parameters in the
multilevel model since the OLS assumes that the error terms are uncorrelated (recall that the multilevel
model allows them to be autocorrelated). Although the estimates of fixed-effects parameters using OLS can
be very close to the GLS results, the standard errors tend to be underestimated. This can result in incorrect
inferences from data, or wrong conclusions made by the statistical hypothesis test.

41

2.3

Multilevel Model for Longitudinal Fingerprint
Data

We introduce the longitudinal fingerprint data used in the study and give an overview of
analyzing the dataset with multilevel models towards understanding the temporal tendency
of genuine match scores and true acceptance decisions.
The following notations are consistently used throughout the paper.
• N: Total number of subjects in the longitudinal fingerprint database.
• ni : Number of different tenprint acquisitions (cards or impressions) of subject i; i =
1, . . . , N.
• Ti,j : Time stamp of the j-th tenprint impression of subject i; i = 1, . . . , N, and
j = 1, . . . , ni .
• The tenprint impressions of each subject are ordered according to the time sequence;
a set of tenprints of subject i is labeled as follows: Fi = {Fi,1 , · · · , Fi,ni }, such that
Ti,1 < . . . < Ti,ni .
• yi,jk : Genuine match score between the j-th and k-th fingerprint impressions of subject
i.
• △Ti,jk : Time interval between fingerprint impressions j and k; △Ti,jk = Ti,k − Ti,j , for
j < k.
• AGEi,jk : Age of the subject i when his k-th tenprint impression was made, where
Ti,j < Ti,k .
• Qi,j : Quality value of fingerprint impression j of subject i. In this study, we use NIST
Fingerprint Image Quality (NFIQ) measure [124], which assigns one of the five discrete
values ranged from 1 (the highest quality) to 5 (the lowest quality), to define fingerprint
image quality.
42

June 2001

September 2007

July 2002

April 2003

March 2008

October 2008

Figure 2.3: Six different impressions of the right index finger of a subject in the longitudinal
fingerprint database.
• Qi,jk : The value corresponding to the lower of the j-th fingerprint and the k-the fingerprint qualities of subject i; according to the definition of NFIQ, Qi,jk = max(Qi,j , Qi,k ).
• bMALEi : A binary indicator for gender of subject i; 1 for male and 0 for female.
• bW HIT Ei : A binary indicator for race of subject i; 1 for whites, and otherwise 0.

2.3.1

Longitudinal Fingerprint Database

A longitudinal database of fingerprint impressions was collected from the records of repeat
offenders booked by the Michigan State Police. Figure 2.3 shows an example of six fingerprint
impressions of the right index finger of a subject in the database acquired between June 2001
and October 2008.
43

3500

Number of Subjects

3000
2500
2000
1500
1000
500
0

5

10
15
20
Number of Tenprint Cards Per Subject

25

(a)
3500

Number of Subjects

3000
2500
2000
1500
1000
500
0

5

6

7
8
9
10
Time Span (Years)

11

12

(b)
Figure 2.4: Statistics of the longitudinal fingerprint database used in this study. Histograms
of (a) the number of tenprint cards per subject, (b) time span of data collection for a subject,
(c) age at the first and last tenprint acquisitions, (d) gender, and (e) race.

44

Figure 2.4: (cont’d)
4000
Age at the first acquisition
Age at the last acquisition

Number of Subjects

3500
3000
2500
2000
1500
1000
500
0

10

20

30

40
50
Age (Year)

60

(c)

15000

Number of Subjects

13617

10000

5000
1980
0

Male

Female
Gender

(d)

45

70

80

Figure 2.4: (cont’d)

10000
9112

Number of Subjects

8000
6356
6000

4000

2000

0

100
White

Black

American Indian
Race

29
Asian

(e)

In constructing this database, we ensured that each subject had at least 5 tenprint
impressions over a minimum of 5-year time span. A total of 15,597 subjects were identified
whose fingerprint data met this requirement, and the fingerprints from these subjects were
used for the longitudinal analysis. A summary of the fingerprint database is as follows:
• Each of the 15,597 subjects has at least 5 tenprint impressions. The average number
of tenprint impressions per subject is 8, with the maximum of 26 cards for one of the
subjects. The histogram of the number of tenprint impressions per subject is shown
in Figure 2.4(a).
• The tenprint impressions of a subject have a minimum of 5-year time span (the time
difference between the first and the last fingerprint acquisitions of a subject); that is,
△Ti,1ni ≥ 5 years for i = 1, . . . , N. The average time span is 9 years, and the maximum
time span in the database is 12 years. The histogram of time span for longitudinal
46

tenprint acquisitions for subjects is shown in Figure 2.4(b).
• Any two consecutive tenprint impressions of a subject are obtained with at least 2month time gap; (Ti,j+1 − Ti,j ) ≥ 2 months.
• Along with tenprint images, the following demographic information is also available
for each subject:
– Gender: Male or female
– Race: White/Hispanic, Black, American Indian/Eskimo, or Asian/Pacific Islander
– Age at the time of tenprint acquisition: The youngest subject at the time of the
first impression is 8 years; the oldest subject at the time of the last impression is
78 years.
The statistics of the demographics of subjects in the database are given in Figures
2.4(c)–(e).
Two commercial off-the-shelf (COTS) matchers (denoted as COTS-1 and COTS-2) are
used to compute fingerprint match scores. For subject i with ni fingerprint impressions, we
conduct all pairwise comparisons; that is,

ni
2

genuine match scores are generated from each

matcher. This is because law enforcement agencies store all the tenprint records for every
booked subject and compare a query fingerprint to all the records in the database. The
genuine match scores from each COTS matcher are normalized such that they have a mean
of 0 and a standard deviation of 1; the normalized genuine match score y˜i,jk is obtained by:

y˜i,jk =

yi,jk − µ
,
σ

where µ and σ are the mean and standard deviation of {yi,jk }, respectively.
47

(2.12)

2.3.2

Overview

A fingerprint comparison essentially involves two fingerprint impressions to generate a single
match score. The match score is then used to determine whether or not the two impressions
are from the same finger; if the match score is greater than a predetermined threshold4 , a
binary identification decision of genuine match is made. Since the impostor score distributions are considered to be stable under various acquisition conditions and time lapse, the
decision threshold is typically fixed in advance of system deployment.
With multilevel modeling, this study targets at analyzing the following observed responses:
• Genuine match score of the j-th and k-th fingerprint impressions of subject i (yi,jk )
• Binary identification decision of yi,jk by applying a decision threshold (T h) as follows.

∗
yi,jk
=




1 if yi,jk > T h

(2.13)



0 otherwise.
The covariates investigated in the study include:

• △Ti,jk : Time interval between fingerprint impressions being compared
• AGEi,jk : Subject’s age at the latter fingerprint impression between two fingerprints
being compared
• Qi,jk : The lower quality value between two fingerprints being compared
• bMALEi : Subject’s gender
• bW HIT Ei : Subject’s race
4

The decision threshold is determined by considering the desired performance of the fingerprint recognition
system. Typically, the decision threshold is decided by looking at the impostor score distribution; for example,
the threshold is set for a prespecified false acceptance rate, say 0.01%.

48

2.4

Longitudinal Analysis of Genuine Fingerprint
Match Scores

We address the first question—what is the trend of genuine match scores over time?—by
demonstrating the presence of a functional relationship between the time interval of two
fingerprints being compared (△Ti,jk ) and the corresponding genuine match score that is
commonly observed in the dataset. If the genuine match score is indeed affected by the
time interval between two impressions, we want to understand how much of the variation
in genuine match scores can be explained by time interval alone. To accomplish this, we
quantify the impact of △Ti,jk on the change in genuine match scores using goodness-of-fit
of the model, and compare it to the impacts of other covariates, namely Qi,jk (a timeindependent covariate that is known to be closely related to genuine match score [65]),
AGEi,jk , bMALEi , and bW HIT Ei .
We analyze the data under two scenarios: (i) a single finger is used for recognition and
(ii) all ten fingers are used for recognition. For (i), we carry out the analysis on the right
index finger of the subjects that is typically chosen as the primary finger in the single-finger
based recognition. For (ii), we fuse the genuine match scores of all ten fingers by a sum rule,
and analyze the fused scores.

2.4.1

Modeling of Genuine Match Scores

The genuine match scores from each of the two COTS matchers are fit by linear 2-level
models with various covariates (see Table 2.1):

• Model A (unconditional mean model) without any covariate

• Model B with a single covariate at level 1: Model BT with △Ti,jk , Model BA with
AGEi,jk , and Model BQ with Qi,jk
49

Table 2.1: Models with different combinations of covariates.
Model
Model
Model
Model
Model
Model

A
BT
BA
BQ
CG

Level-1 Model
yi,jk = ϕ0i + εi,jk
yi,jk = ϕ0i + ϕ1i △Ti,jk + εi,jk
yi,jk = ϕ0i + ϕ1i AGEi,jk + εi,jk
yi,jk = ϕ0i + ϕ1i Qi,jk + εi,jk
yi,jk = ϕ0i + ϕ1i △Ti,jk + εi,jk

Model CR

yi,jk = ϕ0i + ϕ1i △Ti,jk + εi,jk

Model D

yi,jk = ϕ0i + ϕ1i △Ti,jk + ϕ2i AGEi,jk
+ϕ3i Qi,jk + εi,jk

Level-2 Model
ϕ0i = β00 + b0i
ϕ0i = β00 + b0i , ϕ1i = β10 + b1i
ϕ0i = β00 + b0i , ϕ1i = β10 + b1i
ϕ0i = β00 + b0i , ϕ1i = β10 + b1i
ϕ0i = β00 + β01 bMALEi + b0i ,
ϕ1i = β10 + β11 bMALEi + b1i
ϕ0i = β00 + β01 bW HIT Ei + b0i ,
ϕ1i = β10 + β11 bW HIT Ei + b1i
ϕ0i = β00 + b0i , ϕ1i = β10 + b1i ,
ϕ2i = β20 + b2i , ϕ3i = β30 + b3i

• Model C with an additional covariate at level 2 of Model BT : Model CG with bMALEi ,
and Model CR with bW HIT Ei
• Model D with △Ti,jk , AGEi,jk , and Qi,jk as level-1 covariates
The true parameters of the linear models (ϕri , r = 0, 1, 2, 3) for subject i have both fixed
(βr0 ) and random effects (bri ).
We first assess the goodness-of-fit of each model, and compare various models to determine which of the covariates better explains the variation in genuine match scores. The
models with covariates that are significantly influential in explaining genuine match scores
are further verified to determine whether they satisfy the model assumptions. This is followed by parameter and confidential interval estimation to test the null hypothesis: slope of
linear model is zero (i.e., β10 = 0 in Model B).

2.4.1.1

Assessment of Goodness-of-Fit

Goodness-of-fit of a model evaluates how well the model fits the data, and is also used
to compare multiple models. The following three well-known criteria are typically used to
measure the goodness-of-fit: (i) Deviance, (ii) Akaike Information Criterion (AIC), and (iii)
Bayesian Information Criterion (BIC).
50

• Deviance (D): Deviance can be used to compare the goodness-of-fit of nested models.
The nested property is easily determined by checking if one model becomes equivalent
to the other by setting the coefficients for some of the covariates to zero. For example,
Model A and Model BT are nested; Model A and Model BQ are nested; however, Model
BT and Model BQ are not nested. The deviance is defined as:

D = −2 log(L),

(2.14)

where L is the maximum value of the likelihood function for the model.
• AIC: AIC can be used for any model comparison tasks (models do not need to be
nested). AIC is defined as:
AIC = 2k − 2 log(L),

(2.15)

where k is the number of parameters in the model, and L is the maximum value of the
likelihood function for the model.
• BIC: Under the assumption that the data distribution is in the exponential family, BIC
is defined as:
BIC = k log(n) − 2 log(L),

(2.16)

where k is the number of parameters in the model, n is the number of data points,
and L is the maximum value of the likelihood function for the model. BIC also can be
used for comparisons of non-nested models.
AIC and BIC add a constant term to the deviance for the sake of comparing non-nested
models. The smaller the deviance (AIC or BIC), the better the model fit.
Table 2.2 shows the goodness-of-fit measures of the models in Table 2.1. The model
comparisons based on the goodness-of-fit lead to the following observations:
• A decrease in D is observed when each of Model B is compared to Model A. This
51

Table 2.2: Goodness-of-fit of the models shown in Table 2.1.
Model
Model
Model
Model
Model
Model
Model
Model

A
BT
BA
BQ
CG
CR
D

Deviance
1,114,948
1,099,980
1,100,979
1,028,899
1,099,969
1,099,817
1,003,908

COTS-1
AIC
1,114,954
1,099,992
1,100,991
1,028,911
1,099,985
1,099,833
1,003,938

BIC
1,114,988
1,100,058
1,101,057
1,028,978
1,100,074
1,099,921
1,004,105

Deviance
1,142,532
1,115,191
1,120,911
1,060,037
1,115,117
1,114,378
1,019,412

COTS-2
AIC
1,142,538
1,115,203
1,120,923
1,060,049
1,115,133
1,114,394
1,019,442

BIC
1,142,571
1,115,269
1,120,990
1,060,115
1,115,222
1,114,483
1,019,608

means that each individual covariate used in Model B (△Ti,jk , AGEi,jk , and Qi,jk ) can
explain some of the variation in genuine match scores.
• Model BQ provides a better fit to the data than Model BT and Model BA . This implies
that fingerprint image quality is the best covariate to explain the variation in genuine
match scores among the three covariates used in Model B.
• Gender and race are not important covariates to explain changes in genuine match
scores since the deviance barely decreases from Model BT to Model CG or Model CR .
• Model D has the best fit to the genuine match scores, compared to the other models, as
it has the smallest goodness-of-fit value. In other words, including all three covariates
(△Ti,jk , AGEi,jk , and Qi,jk ) as covariates in the multilevel model better explains the
trend in genuine match scores compared to including a single covariate.

2.4.1.2

Validation of Model Assumptions

The multilevel model assumes that the residuals (εi,jk ) and random effects (bri ) follow normal
distributions. The inference made based on the model fitting is valid only if the underlying
assumptions of the multilevel model are satisfied. The normal probability plot is a way
to visually verify the normality of the data. If the normal probability plot is linear, one
can ascertain the data is from a normal distribution. Figures 2.5 and 2.6 show the normal
52

Probability

0.99
0.75
0.50
0.25
0.01

−4

−2
0
2
Standardized Residuals

4

(a)

0.99
Probability

Probability

0.99
0.75
0.50
0.25
0.01

0.75
0.50
0.25
0.01

−2
0
Standardized Residuals

2

−0.2

−0.1
0
0.1
Standardized Residuals

(b)

(c)

Figure 2.5: Normal probability plots of (a) residuals at level 1 (εi,jk ), (b) random-effects for
intercept at level 2 (b0i ), and (c) random-effects for slope at level 2 (b1i ) of Model BT fitting
the match scores obtained from COTS-1

probability plots of εi,jk , b0i , and b1i when Model BT is fit to the genuine match scores
obtained from COTS-1 and COTS-2 matchers, respectively.
While the residuals generally follow normal distributions, significant departures from
normality are observed at the tails for the scores output by both the matchers. A possible
cause of the non-normality at tails is that the scores from COTS fingerprint matchers are
typically censored, i.e., very low and high match scores are trimmed so that the output scores
53

Probability

0.99
0.75
0.50
0.25
0.01

0
5
10
15
Standardized Residuals

(a)

0.99
Probability

Probability

0.99
0.75
0.50
0.25
0.01

0.75
0.50
0.25
0.01

−1
0
1
2
3
Standardized Residuals

−0.2
−0.1
0
0.1
Standardized Residuals

(b)

(c)

Figure 2.6: Normal probability plots of (a) residuals at level 1 (εi,jk ), (b) random-effects for
intercept at level 2 (b0i ), and (c) random-effects for slope at level 2 (b1i ) of Model BT fitting
the match scores obtained from COTS-2.

are in a finite range. To resolve the issue of model assumption violation, a bootstrapping is
conducted to obtain reliable parameter estimates and establish empirical confidence intervals
for hypothesis test.
54

2.4.1.3

Parameter Estimation and Hypothesis Test

When the model assumptions are violated, the parameter estimates for fixed and random
effects tend to be reliable while the standard errors (consequently, the confidence intervals)
tend to be underestimated [90]. In this case, bootstrapping is a useful way to estimate
parameters and confidence intervals [88]. We perform a fully nonparametric bootstrap [62]
by repeating parameter estimation for bootstrap samples and then deriving the mean of
parameter estimates and percentile confidence intervals. To preserve the hierarchy in the
longitudinal data, a cluster bootstrap is used: for each bootstrap sample, N subjects with
replacement are resampled at level 1 and all the level-2 data belonging to those subjects are
included in the sample. We generate 1,000 bootstrap samples to establish 95% confidence
intervals.
Considering that all the three covariates (△Ti,jk , AGEi,jk , and Qi,jk ) were shown to
have impact on genuine match scores, we estimate the parameters and their 95% confidence
intervals in Models BT , BA , and BQ . The population-mean trends of genuine match scores
from two COTS matchers and 95% confidence intervals with respect to △Ti,jk (Figure 2.7),
AGEi,jk (Figure 2.8), and Qi,jk (Figure 2.9) are illustrated. Tables 2.3–2.5 summarize the
parameter estimates and 95% confidence intervals for fixed effects in Models BT , BA , and
BQ when a single finger is used for recognition.
The null hypothesis we want to test is: β10 = 0 in Model B (i.e., the slope of linear model
is zero). This null hypothesis is rejected for all three models, Models BT , BA , and BQ , at
the significance level of 0.05 since the 95% confidence interval for β10 does not contain zero.
Hence, the genuine match scores from both the matchers have negative correlation with the
above three covariates.
Model D incorporates all the three influential covariates into the model. Table 2.6 shows
the parameter estimates and 95% confidence intervals in Model D with two COTS matchers.
The fixed-effects parameter estimates for △Ti,jk (β10 ), AGEi,jk (β20 ), and Qi,jk (β30 ) remain
as negative in Model D. The estimated covariance matrix indicate the relationship (i) between
55

2

Bootstrap Mean
95% Confidence Interval

Match Score

1
0
−1
−2
−3
0

2

2

4
6
8
Time Interval [Year]
(a)

10

12

Bootstrap Mean
95% Confidence Interval

Match Score

1
0
−1
−2
−3
0

2

4
6
8
Time Interval [Year]
(b)

10

12

Figure 2.7: Population-mean trends of genuine match scores and 95% confidence intervals
with respect to △Ti,jk . Match scores are obtained from (a) COTS-1 and (b) COTS-2 matchers.

56

2

Bootstrap Mean
95% Confidence Interval

Match Score

1
0
−1
−2
−3
0

20

2

40
Age [Year]
(a)

60

80

Bootstrap Mean
95% Confidence Interval

Match Score

1
0
−1
−2
−3
0

20

40
Age [Year]
(b)

60

80

Figure 2.8: Population-mean trends of genuine match scores and 95% confidence intervals
with respect to AGEi,jk . Match scores are obtained from (a) COTS-1 and (b) COTS-2
matchers.

57

2

Bootstrap Mean
95% Confidence Interval

Match Score

1
0
−1
−2
−3
1

2

2

3
NFIQ
(a)

4

5

Bootstrap Mean
95% Confidence Interval

Match Score

1
0
−1
−2
−3
1

2

3
NFIQ
(b)

4

5

Figure 2.9: Population-mean trends of genuine match scores and 95% confidence intervals
with respect to Qi,jk . Match scores are obtained from (a) COTS-1 and (b) COTS-2 matchers.

58

Table 2.3: Parameter estimates and 95% confidence intervals in Model BT with bootstrapping
when a single finger is used for recognition.
Parameters
β00
Fixed Effects

Variance Components

β10
σε2
σ02
σ12
σ01

COTS-1
0.1496
(0.1406; 0.1590)
−0.0440
(−0.0450; −0.0430)
0.7057
0.5298
0.0034
−0.0134

COTS-2
0.2032
(0.1939; 0.2127)
−0.0616
(−0.0625; −0.0606)
0.7185
0.5744
0.0039
−0.0277

Table 2.4: Parameter estimates and 95% confidence intervals in Model BA with bootstrapping
when a single finger is used for recognition.
Parameters
β00
Fixed Effects

Variance Components

β10
σε2
σ02
σ12
σ01

COTS-1
0.5682
(0.5335; 0.6020)
−0.0175
(−0.0185; −0.0164)
0.6998
5.6003
0.0050
−0.1574

COTS-2
0.7447
(0.7072; 0.7843)
−0.0243
(−0.0254; −0.0231)
0.7120
7.5575
0.0066
−0.2136

Table 2.5: Parameter estimates and 95% confidence intervals in Model BQ with bootstrapping
when a single finger is used for recognition.
Parameters
β00
Fixed Effects

Variance Components

β10
σε2
σ02
σ12
σ01

COTS-1
0.7087
(0.6954; 0.7221)
−0.2750
(−0.2798; −0.2702)
0.6489
0.9096
0.1163
−0.2543

COTS-2
0.8456
(0.8316; 0.8595)
−0.3439
(−0.3489; −0.3385)
0.6738
0.9105
0.1027
−0.2473

△Ti,jk and Qi,jk (σ13 ), and (ii) between AGEi,jk and Qi,jk (σ23 ). Although the estimated
values for σ13 and σ23 are negative, the correlations are not strong. σ13 in Model D with
COTS-2 matcher cannot be said it is significantly different from 0 since the null hypothesis
σ13 = 0 is not rejected at the 0.05 significance level. Also, when we get correlation matrix
59

Table 2.6: Parameter estimates and 95% confidence intervals in Model D with bootstrapping
when a single finger is used for recognition.
Parameters
β00
β10
Fixed Effects

β20
β30

Variance Components

*

σε2
σ02
σ12
σ01
σ22
σ02
σ12
σ32
σ03
σ13
σ23

COTS-1
0.9137
(0.8765; 0.9471)
−0.0368
(−0.0378; −0.0358)
−0.0030
(−0.0042; −0.0019)
−0.2509
(−0.2558; −0.2463)
0.6033
6.6328
0.0041
0.0944
0.0068
−0.1941
−0.0036
0.1165
−0.2092
−0.0007
−0.0013

COTS-2
1.0353
(0.9947; 1.0750)
−0.0533
(−0.0543; −0.0522)
−0.0024
(−0.0036; −0.0011)
−0.3064
(−0.3112; −0.3015)
0.6127
7.8996
0.0040
0.0800
0.0082
−0.2335
−0.0033
0.1039
−0.1466
−0.0004*
−0.0030

The hypothesis test indicates that the null hypothesis the parameter is zero is
not rejected at the significance level of 0.05.

from the covariance matrix, the correlation coefficients for σ13 and σ23 are very close to 0.
For COTS-1 matcher, the correlation coefficients for σ13 and σ23 are −0.0324 and −0.0464,
respectively; for COTS-2 matcher, they are −0.0174 and −0.1035.
When all ten fingerprints of a subject are utilized for identification, the match scores
†
from the ten fingers can be fused by a sum rule; the fusion score yi,jk
is obtained by:

10
(m)

†
yi,jk
=

yi,jk ,

(2.17)

m=1

(m)

where yi,jk is the genuine match score of finger m of subject i.
Models BT and BA were also fit to the genuine match scores from all ten fingers fused
by a sum rule. Figures 2.10 and 2.11 show the population-mean trends and 95% confidence
60

Table 2.7: Parameter estimates and 95% confidence intervals in Model BT with bootstrapping
when the match scores from ten fingers are fused by a sum rule.
Parameters
β00
Fixed Effects

Variance Components

β10
σε2
σ02
σ12
σ01

COTS-1
0.1896
(0.1800; 0.1995)
−0.0603
(−0.0612; −0.0594)
0.6562
0.5986
0.0037
−0.0144

COTS-2
0.2258
(0.2159; 0.2360)
−0.0726
(−0.0736; −0.0717)
0.6615
0.6599
0.0040
−0.0304

Table 2.8: Parameter estimates and 95% confidence intervals in Model BA with bootstrapping
when the match scores from ten fingers are fused by a sum rule.
Parameters
β00
Fixed Effects

Variance Components
*

β10
σε2
σ02
σ12
σ01

COTS-1
0.5867
(0.5231; 0.6841)
−0.0185
(−0.0223; −0.0163)
0.6651
5.0636*
0.0046
−0.1409*

COTS-2
0.7537
(0.7056; 0.8996)
−0.0249
(−0.0295; −0.0235)
0.6602
8.6870
0.0074
−0.2423

The hypothesis test indicates that the null hypothesis the parameter is zero is
not rejected at the significance level of 0.05.

intervals, and Tables 2.7 and 2.8 show the parameter estimates and confidence intervals. We
observe a negative relationship between genuine match scores and the two covariates (△Ti,jk
and AGEi,jk ). The null hypothesis (β10 = 0 in Model B) is rejected for both of the models.
Note that Models BQ and D are not used in ten-finger fusion scenario since the covariate
corresponding to Qi,jk is difficult to define in this case.

2.4.1.4

Genuine Match Score Trends of Individual Subjects

The random effects (bri ) at level 2 in the multilevel model represent the deviation of subject i
from the population-mean trend (βri ). The parameter estimates of (ϕ0i , ϕ1i ) for each subject
in Model BT are shown in Figure 2.12 in addition to the population-mean trend (β00 , β11 ).
61

Bootstrap Mean
95% Confidence Interval

2

Match Score

1
0
−1
−2
−3
−4
0

2

4
6
8
Time Interval [Year]
(a)

10

12

Bootstrap Mean
95% Confidence Interval

2

Match Score

1
0
−1
−2
−3
−4
0

2

4
6
8
Time Interval [Year]
(b)

10

12

Figure 2.10: Population-mean trends of genuine match scores and 95% confidence intervals
with respect to △Ti,jk , when the scores from ten fingers are fused. Match scores are obtained
from (a) COTS-1 and (b) COTS-2 matchers.

62

Bootstrap Mean
95% Confidence Interval

2

Match Score

1
0
−1
−2
−3
−4
0

20

40
Age [Year]
(a)

60

80

Bootstrap Mean
95% Confidence Interval

2

Match Score

1
0
−1
−2
−3
−4
0

20

40
Age [Year]
(b)

60

80

Figure 2.11: Population-mean trends of genuine match scores and 95% confidence intervals
with respect to AGEi,jk , when the scores from ten fingers are fused. Match scores are
obtained from (a) COTS-1 and (b) COTS-2 matchers.

63

0.1
0.05

−0.05

10

1i

Slope (β +b )

0

−0.1
−0.15
−0.2
−0.25

Population−mean
Parameters
(β , β )
00

10

Outliers
−0.3
−4

−3

−2

−1
0
1
Intercept (β00+b0i)

2

3

Figure 2.12: Parameter estimates of Model BT with genuine match scores provided by COTS1 matcher. The estimates for the population-mean parameters (β00 , β10 ) and the parameters
for each subject (ϕ0i , ϕ1i ) are represented as a triangle and dots, respectively. The parameters
associated with four outlier subjects are marked as squares.
The parameter estimates associated with several outlying subjects who markedly deviate
from the population-mean trend are also indicated. Figures 2.13–2.16 show the individual
trends of the outlying subjects and their fingerprint impressions.
• Outlier case 1 (Figure 2.13): The estimated intercept of this subject is very small. The
subject consistently gives low genuine match scores since his fingerprints have been
severely scarred, resulting in poor fingerprint quality (the NFIQ values of the fingerprints are {4, 4, 5, 5, 4, 4}). This subject can be called a “goat” in the Doddington’s
biometric zoo nomenclature [50] which refers to the subjects that can easily lead to
false rejections.
• Outlier case 2 (Figure 2.14): The intercept of the fitted model for this subject is
rather large while the slope is negative. This subject consistently gives high genuine
match scores because his fingerprint impressions are of good quality (the NFIQ values
64

are {3, 1, 2, 1, 1, 3}). This subject can be viewed as a “sheep” in the Doddington’s
biometric zoo who tends to be successfully verified.

• Outlier case 3 (Figure 2.15): This subject shows a very sharp decrease in genuine
match scores as a function of time interval. In Figure 2.15(a), the genuine match scores
involving the first fingerprint impression are very low. This fingerprint impression is
indeed an impostor fingerprint (see Figure 2.15(b)) since it is of tented arch type
while the actual pattern of this finger is a right loop. This shows that the operational
fingerprint data can be mislabeled.

• Outlier case 4 (Figure 2.16): This subject also has a steep slope. It turns out that the
fingerprint impressions of this subject were collected during his adolescence (starting
at the age of 11 until the age of 21). It is known that an increase in the size of finger
during the adolescent period can cause false rejections in fingerprint matching when a
juvenile’s fingerprint impression is compared with his adult fingerprint impression [63].

2.5

Longitudinal Analysis of Fingerprint Matching Accuracy

The ultimate question of interest with regard to fingerprint persistence is as follows: what is
the trend of matching accuracy with respect to the time interval between fingerprints in the
comparison? This question is addressed by analyzing the binary identification decisions made
on genuine fingerprint pairs using the linear 2-level model. We introduce the multilevel model
for binary responses, and report the bootstrap results of parameter estimates and confidence
intervals.
65

2

Match Score

1
0
−1
−2
−3
0

2

4
6
8
Time Interval [Year]

10

12

(a) (ϕ0i , ϕ1i ) = (−3.2326, 0.0016)

Age 25

Age 31

Age 28

Age 32

Age 29

Age 33

(b)
Figure 2.13: A subject whose intercept in Model BT is very small due to the severe alteration
of the fingerprint pattern (outlier case 1). (a) The observed responses and fitting result of
the subject, and (b) fingerprint impressions of the subject at different ages.

66

2

Match Score

1
0
−1
−2
−3
0

2

4
6
8
Time Interval [Year]

10

12

(a) (ϕ0i , ϕ1i ) = (2.0281, −0.1167)

Age 34

Age 43

Age 40

Age 44

Age 42

Age 45

(b)
Figure 2.14: A subject with high quality ridge pattern resulting in the large intercept in
Model BT (outlier case 2). (a) The observed responses and fitting result of the subject, and
(b) fingerprint impressions of the subject at different ages.

67

2

Match Score

1
0
−1
−2
−3
0

2

4
6
8
Time Interval [Year]

10

12

(a) (ϕ0i , ϕ1i ) = (0.4353, −0.2695)

Age 18

Age 23

Age 21

Age 24

Age 22

Age 26

(b)
Figure 2.15: A subject with steep negative slope (outlier case 3) resulting from a mislabeled
fingerprint (the first impression). (a) The observed responses and fitting result of the subject,
and (b) fingerprint impressions of the subject at different ages.

68

2

Match Score

1
0
−1
−2
−3
0

2

4
6
8
Time Interval [Year]

10

12

(a) (ϕ0i , ϕ1i ) = (0.3443, −0.2491)

Age 11

Age 17

Age 13

Age 19

Age 15

Age 21

(b)
Figure 2.16: A subject with steep negative slope due to fingerprint impressions made during
his adolescence (outlier case 4). (a) The observed responses and fitting result of the subject,
and (b) fingerprint impressions of the subject at different ages.

69

2.5.1

Multilevel Model for Binary Responses

∗
A binary decision for each genuine fingerprint pair (yi,jk
) in the database was made by

applying a predetermined decision threshold as shown in Equation (2.13). We set the decision threshold corresponding to false acceptance rate of 0.01%, assuming that the impostor
distribution is stable over time.
The multilevel model cannot be directly fit to the binary responses since the model
assumptions (normality of residuals and random effects) will be obviously violated. Thus,
∗
a binary identification decision yi,jk
is modeled by a Bernoulli trial with the probability of

true acceptance πi,jk , and the expected πi,jk is modeled using a logit link function.

Level-1 Model: g(πi,jk ) = ϕ0i + ϕ1i △Ti,jk + εi,jk ,
∗
yi,jk
∼ Bin(1, πi,jk ),

Level-2 Model: ϕ0i = β00 + b0i ,
ϕ1i = β10 + b1i ,

(2.18)

where g(·) is a link function (for binary responses, g(·) is a logit function; g(πi,jk ) =
log

πi,jk
1−πi,jk

2.5.2

).

Trend of True Acceptance Rate over Time

The parameter estimates and 95% confidence intervals of the model in Equation (2.18) are
obtained by bootstrap. The population-mean trends of πi,jk are shown in Figure 2.17 when
a single finger is used for recognition, and in Figure 2.18 when the match scores from all ten
fingers are fused by a sum rule. Both results indicate that the probability of true acceptance
for genuine fingerprint pairs tends to remain very close at 1 even though the time interval
between two fingerprints in comparison increases up to 12 years (recall that the longitudinal
fingerprint data in this study has a maximum time span of 12 years). In other words,
the fingerprint pairs can be correctly determined as genuine regardless of the time interval
70

Probability of True Acceptance

1
0.8
0.6
0.4
0.2
Bootstrap Mean
95% Confidence Interval
0
0

2

4
6
8
Time Interval [Year]
(a)

10

12

Probability of True Acceptance

1
0.8
0.6
0.4
0.2
Bootstrap Mean
95% Confidence Interval
0
0

2

4
6
8
Time Interval [Year]
(b)

10

12

Figure 2.17: Probability of true acceptance with respect to time interval when match scores
from a single (right index) finger are used. (a) COTS-1 and (b) COTS-2.

71

Probability of True Acceptance

1
0.8
0.6
0.4
0.2
Bootstrap Mean
95% Confidence Interval
0
0

2

4
6
8
Time Interval [Year]
(a)

10

12

Probability of True Acceptance

1
0.8
0.6
0.4
0.2
Bootstrap Mean
95% Confidence Interval
0
0

2

4
6
8
Time Interval [Year]
(b)

10

12

Figure 2.18: Probability of true acceptance with respect to time interval when match scores
from all ten fingers are fused by the sum rule. (a) COTS-1 and (b) COTS-2.

72

(up to 12 years here) between the fingerprint impressions with high confidence. The 95%
confidence intervals become negligibly small when all ten fingerprints from a subject are used
in matching, compared to using a single finger.

2.6

Summary

Since ancient times, fingerprints have been recognized as persistent and unique to an individual. Early scientific studies on fingerprint recognition in the late 19th century claimed that
there is no significant change in the friction ridge structure over time by examining small sets
of genuine fingerprint pairs captured with large time interval. Although fingerprint recognition is now used to distinguish an extremely large number of individuals (for example,
India’s UIDAI [9] involving more than 1 billion people), the persistence of fingerprints can
only be claimed based on anecdotal evidence.
To understand the temporal behavior of fingerprint matching accuracy, multiple fingerprint records of 15,597 subjects booked by the Michigan State Police over a duration of 5–12
years were collected. The genuine match scores obtained by two COTS fingerprint matchers
have been analyzed by linear multilevel statistical models with various covariates, including
time interval between two fingerprints being compared. Our longitudinal study of fingerprint
recognition have led to the following conclusions:
• A formal test of hypothesis indicates that the genuine match scores tend to decrease
as the time interval between the two fingerprints being compared increases.
• The genuine match scores also tend to decrease as the subject’s age increases or when
the fingerprint image quality decreases.
• The goodness-of-fit measures of multilevel models with different covariates show that:
– Time interval, subject’s age, and fingerprint image quality best explain the variation in genuine match scores, while subject’s gender and race are not significant
73

covariates.
– Among the three covariates (time interval, subject’s age, and fingerprint image
quality), fingerprint image quality is the most influential covariate.
• There exist subjects in our database that do not conform to the population trend as
determined by model fit. These outlying subjects illustrate (i) the presence of individuals in the database used in the study that follow the nomenclature in the Doddington’s
biometric zoo, (ii) the degradation in genuine match scores when a juvenile fingerprint is compared to his adult fingerprint, and (iii) labeling errors in the operational
fingerprint database.
• Despite the downward trend in genuine match scores over time, the probability of
true acceptance, at a predetermined decision threshold, remains close to 1 even as the
time interval between fingerprints in comparison increases (up to 12 years which is
the maximum time span in our database). In other words, the fingerprint matching
accuracy tends to be stable over time under the assumption that the impostor match
scores are not affected by the time interval between fingerprints being compared.
• The inference made from fingerprint recognition results with single finger (right index
finger) applies to the inference from ten-finger fusion results.
• The results from two different COTS matchers used in the study coincide.
As future work, we plan to pursue the longitudinal study of fingerprint recognition in the
following ways:
• The match scores and identification decisions of impostor fingerprint pairs will be
analyzed by the multilevel model to determine whether the false acceptance rate is
stable over time.
• The interactions among covariates (time interval, subject’s age, and fingerprint image
quality) will be incorporated in the model.
74

• Given that we make all pairwise comparisons of the fingerprint impressions from each
subject, the correlation among the genuine match scores of a subject needs to be
reflected in the model.
• Nonliear multilevel models can be investigated and compared to the linear models.

75

Chapter 3
Fingerprint Orientation Field
Modeling

3.1

Introduction

Fingerprint patterns can be characterized by (i) ridge frequency, (ii) orientation field, and
(iii) minutiae distribution. Fingerprint ridges are spaced almost equidistantly; ridge period
is typically around 10 pixels in 500 ppi fingerprint images. Fingerprint orientation field has
distinct characteristics which can differentiate fingerprints from any other flow pattern: it
has a specific number of singular points, the configuration of singular points follows a certain
spatial distribution [40], and its global field is shaped like an arch. Minutiae distribution in a
fingerprint has a tendency to be dense around singular points since the ridge flow converges
or diverges around singular points while maintaining the ridge frequency [42].
To assess the quality of a fingerprint pattern, features based on local properties (i.e.,
clarity of ridge structure in a grayscale image) and global properties (e.g., continuity of
orientation field or energy concentration in the frequency domain over the entire fingerprint
region) have been utilized [31]. However, lack of global constraints that can specifically
distinguish a valid fingerprint pattern from any type of non-fingerprint images limits of the
76

ability of existing fingerprint quality measures to detect abnormalities in the images shown
in Figure 3.1. Figure 3.1(a) is a synthesized texture image based on the iterative contextual
filtering approach [38]; while it has a valid fingerprint ridge frequency, its orientation field
does not follow that of a fingerprint pattern. Figure 3.1(b) shows a fingerprint image whose
ridge structure in the central part of the finger has been transplanted from some other
friction ridge skin. Although the quality of local ridge structure in Figure 3.1(b) is good,
the orientation field shows discontinuity at the boundaries of the altered region. Figure
3.1(c) is a synthesized fingerprint image using the SFinGe (Synthetic Fingerprint Generator)
model [38]; while the ridge frequency and the orientation field of this fingerprint image appear
to be realistic, a large portion of the fingerprint area has ridges that flow parallel to each other
and hence contain no minutiae. Figure 3.1(d) is an example of a typical latent fingerprint
which is found at crime scenes. Although the quality of the latent print in this image is fairly
good, the background line structure with similar frequency value as the fingerprint pattern
makes it difficult to localize the fingerprint pattern in the image and extract features (e.g.,
orientation field and minutiae).
Fingerprint modeling has been developed to capture the unique characteristics of fingerprint patterns in orientation field and minutia. In the literature, fingerprint modeling
has been approached in terms of (i) stochastic modeling or (ii) deterministic modeling. In
stochastic modeling, properties of singularity distribution [40] and minutiae distribution [42],
for example, are modeled as parameterized probabilistic functions (e.g., Gaussian mixture
model) based on a large number of fingerprints. In orientation field modeling, learning
schemes based on a large set of fingerprints have been proposed; for instance, local orientation patches are learned as dictionaries to estimate orientation field in noisy or missing
regions of latent fingerprints [55]. In other approaches, the parameter space for the coefficients of the Fourier basis function is reduced by a set of fingerprints [130]. The stochastic
modeling inherently requires a large number of real fingerprints in order to establish the correct model. However, the size of the fingerprint database available for research is typically
77

(a) NFIQ = 1, (Model does not fit)

(b) NFIQ = 3, F = 0.74

(c) NFIQ = 2, F = 0.83

(d) NFIQ = 2, (Model does not fit)

Figure 3.1: Images containing fingerprint-like pattern. (a) Synthesized image obtained by
iterative contextual filtering [38], (b) altered fingerprint where the central part of the fingerprint has been transplanted from a different friction ridge skin, (c) synthesized fingerprint
by SFinGe [38], and (d) latent fingerprint from NIST SD27 [3]. The NFIQ value [124] and
the fingerprint-ness score (F ) of the orientation field are shown. NFIQ value of 1 indicates
the highest quality and NFIQ of 5 is the lowest quality. The fingerprint-ness score ranges
from 0 (the lowest) to 1 (the highest); if the proposed model cannot find a feasible solution
satisfying the constraints, there is no valid output from the model.
extremely small compared to the population size.
Deterministic models represent fingerprints in a mathematical form, and are often designed to provide fingerprint-like textured pattern as an output of model fitting. Deterministic modeling does not require fingerprint images for learning; instead, a set of functions
78

incorporating the unique characteristics of fingerprint patterns is designed. Generally, the
more constrained the model is to the fingerprint pattern, the less flexible it is to represent
the actual pattern in a given fingerprint.
Since the most salient characteristic of a fingerprint pattern that distinguishes it from any
other textured patterns is its orientation field, we propose a global orientation field model for
fingerprints that is based on constrained ordinary differential equations (ODE) [140]. First,
the rational polynomial model [119] which gives a nice topology of fingerprint ridge flow
with singular points is converted to the ODE form whose phase portrait is the same as the
orientation field from the rational polynomial function. It can be shown that the x-derivative
and y-derivative of the ODE system for double-loop fingerprints (the most complicated case)
are represented as the 4th order polynomial and the 3rd order polynomial, respectively, in
geometric forms. Second, a generalized ODE model is proposed, which consists of much
simpler polynomials and a smaller number of independent coefficients (i.e., 16 parameters in
the model and 1 parameter for rotation) compared to the polynomial model in [66] and the
constrained nonlinear phase portrait model in [89]1 . Third, the constraints on the number
of singular points (either 0, 2, or 4) based on the Hermite’s theorem are applied to reduce
the parameter space during optimization. Finally, the degree of similarity of a given image
to a fingerprint pattern, called fingerprint-ness, in terms of orientation field is measured by
computing the difference between the orientation field extracted from the given fingerprint
image and the orientation field fit by the proposed model.
This chapter is organized as follows. We survey on fingerprint orientation field models
that have been proposed in the literature in Section 3.2. Section 3.3 describes a proposed
global orientation field model which incorporates the distinctive characteristics of singular
point in fingerprints. Section 3.4 summarizes this chapter and indicates how the orientation
1

The numbers of coefficients in the polynomial model and the constrained nonlinear phase portrait model
are (n + 1)(n + 2) and (n + 1)(n + 2) − 3Ns , where n is the order of the polynomial and Ns is the number of
singular points detected in the image (see Table 3.1). In [66], n = 4 was used, which involves 30 coefficients;
in [89], n = 8 was used, which involves 90 − 3Ns coefficients. Note that Ns can be at most 4 in case of
double-loop type of fingerprints.

79

field models are used in this dissertation.

3.2

Fingerprint Orientation Field Models

Fingerprint orientation field can be represented in two ways: (i) a set of local orientations,
Θ = {θ(x, y)|(x, y) ∈ R}, where R is the region of interest (ROI) of the fingerprint image, or
(ii) a 2-dimensional function describing the global orientation field, θ(x, y) = f (x, y), where
f (x, y) is a real-valued function. Local orientations are extracted by finding the dominant
ridge direction in each local block. For good quality fingerprints, the local orientation field
extraction is sufficient to process the fingerprint images. On the other hand, global orientation field models are very useful to represent fingerprint ridge structure in noisy fingerprint
images or fingerprint images with missing parts. As the orientation field representation in
global models is much more compact (e.g., a coefficient vector) than the collection of local
orientations at each location, some researchers have used the global orientation field representation for fingerprint classification and indexing [130]. In addition, if the global model is
specifically designed to represent fingerprints, it can be used to synthesize realistic fingerprint images [38], simulate fingerprint pattern formation [84], and determine abnormality in
the given image as a fingerprint pattern (e.g., distinguish non-fingerprint patterns [140] or
detect altered fingerprints [139]).

3.2.1

Local Orientation Field Extraction

Ridge orientation in a local region is perpendicular to the gradient of the ridges. The gradient
vector of a fingerprint image I(x, y) is given by [34]:








∂I(x,y)
 ∂x 

Gx (x, y)

=
.
∂I(x,y
Gy (x, y)
)
∂y

(3.1)

The fingerprint orientation field is usually defined in local blocks instead of at each pixel
80

to make it robust to noise. The orientation in a block W can be computed by averaging the
doubled gradients [34]:
θ=

1
tan−1
2

Gxx − Gyy
2Gxy

,

(3.2)

where
G2x (x, y),

Gxx =
(x,y)∈W

G2y (x, y), and

Gyy =
(x,y)∈W

Gxy =

Gx (x, y)Gy (x, y).
(x,y)∈W

As the gradient-based orientation field estimation extracts a dominant orientation based
on the maximum magnitude of the averaged gradients in a local block, it is liable to extract
the orientations of structured noise rather than the fingerprint ridges if the local block
contains strong creases in the fingerprint or lines in the background. To overcome this
limitation, the orientation field extraction algorithm based on short-time Fourier transform
(STFT) [43] obtains multiple orientations characterized by both orientation and frequency
in a block. The Fourier transform of the fingerprint image in a local block can be represented
by F (r, θ). A set of dominant orientations with mated frequency corresponds to the local
maxima of the amplitude of F (r, θ), that is |F (r, θ)|. The averaged dominant orientation in a
local block also can be found by a probabilistic approximation. Considering the probability
density function p(r, θ) in Equation (3.3), the marginal density functions for frequency r and
orientation θ are defined in Equation (3.4). The expectation values for p(r) and p(θ) are the
average frequency and orientation in the block.

p(r, θ) =

|F (r, θ)|2
,
|F (r, θ)|2
r θ
81

(3.3)

Table 3.1: Global fingerprint orientation field models. Note that n is the order of the basis
function or polynomial and Ns is the number of singular points detected in the image. If the
model requires singular points as input, the number of singular points is not included in the
number of parameters to be estimated.
Model

# Parameters

Piecewise linear functions
[128]
Polynomials [66]
Fourier series [130]
Legendre polynomials [111]
Rational polynomial
function [119]
Constrained nonlinear
model [89]
Quadratic differentials [77]
Peripheral models [129]
Constrained nonlinear
model [140]
a

Singular
Points
Approximation Methods
10Ns
Estimated

Fingerprint-specific Features

Not utilized

(n + 1)(n + 2)
Estimated Not
2
2(2n + 1)
Estimated Not
(n + 1)(n + 2)
Estimated Not
Deterministic Mathematical Models
1
Required
Not
(n+1)(n+2)−3Ns

Estimated

5
2 for each modela
17

Required
Estimated
Not
required

utilized
utilized
utilized
utilized

Constraints on coefficients
from singular points
Arch-shaped global field
Arch-shaped global field
Number of singular points

The number of coefficients here is only for the peripheral models, and does not include parameters in
the Fourier expansion [130].

p(r) =

p(r, θ)dθ,
θ

p(θ) =

p(r, θ)dr.

(3.4)

r

3.2.2

Global Orientation Field Models

Global orientation field models for fingerprints have been developed primarily based on two
approaches: (i) approximation method and (ii) deterministic mathematical model (see Table
3.1).
82

3.2.2.1

Approximation Method

Approximation methods represent the global orientation field with a set of piecewise linear
functions [128], a set of polynomials [66], or a set of basis functions such as Fourier series [130]
or Legendre polynomials [111]. In Equation (1.1), x-derivative and y-derivative of ridge flow
are represented by functions f (x, y) and g(x, y), respectively. The basis functions used in
the approximation methods are as follows:
• Polynomial [66]:
n

k

akl xk−l y l ,

(3.5)

akl ei2π( K x+ L y) ,

(3.6)

f (x, y) =
k=0 l=0

• Fourier series [130]:
K−1 L−1

k

f (x, y) =

l

k=0 l=0

• Legendre polynomial [111]:
n

k

f (x, y) =

akl φkl (x, y)
k=0 l=0
n
k

=

akl φk−l (x)φl (y),

(3.7)

k=0 l=0

where
φk (x) =

1 dk
(x2 − 1)k ,
k
k
2 k! dx

akl is a coefficient for each term in the basis function, n is the order of the basis function or
polynomial, K and L are the width and height of a block. Note that g(x, y) for y-derivative
in each method is of the same form as f (x, y), but with different coefficients.
The approximation method with piecewise linear functions proposed in [128] is a variation
of the deterministic mathematical model with rational polynomial function [119]. From the
orientation field modeled by the rational polynomial function shown in Equation (3.12)2 , a
2

Equation (3.12) will appear in the next section

83

(a)

(b)

(c)

Figure 3.2: A synthesized image with fingerprint-like ridge structure and its orientation
field estimation. (a) Synthesized image obtained by iterative contextual filtering [38], (b)
orientation field extracted from the image in (a) using the gradient-based method [34], and
(c) orientation estimated by an approximation method, the polynomial model [66].

set of piecewise linear functions, {fk } and {gl }, is introduced to reflect the actual ridge flow
in the model:

θ(z) = θ∞ +

1
2

K

L

fk (arg(z − qk )) −
k=1

gl (arg(z − pl )) .

(3.8)

l=1

The parameter space for the coefficients of the basis functions is often reduced by training
the coefficient vectors on a large number of fingerprints. However, since the coefficient vectors
are not invariant to rotation and translation, the location and orientation of the fingerprint
pattern have to be determined first before projecting to the basis functions. In addition,
when high order basis functions are used to represent fingerprints with high curvature (e.g.,
fingerprints with singular points), these models can fit well to virtually any flow pattern.
Figure 3.2(c) shows the orientation field estimated by the polynomial model [66] with the
4th order polynomial for x-derivative and the 3rd order polynomial for y-derivative of an
image with fingerprint-like ridge structure shown in Figure 3.2(a). The coefficients are found
by the following objective function:
84

ˆ y)],
sin2 [θ(x, y) − θ(x,

min

(3.9)

(x,y)∈R

where θ(x, y) is the orientation field extracted from the image by the gradient-based method,
ˆ y) is the orientation field approximated by the polynomial model, and R is the ROI where
θ(x,
the ridge structure is present. Since the polynomial model is not constrained for fingerprint
patterns, it also fits well to the non-fingerprint patterns and results in an orientation field
which is not likely to be found in fingerprints as an output of the model fitting.

3.2.2.2

Deterministic Mathematical Models

Deterministic mathematical models, on the other hand, incorporate the unique characteristics of fingerprint orientation field such as local field around singular points [77, 89, 119] and
global field shaped like an arch [77, 129]. Sherlock et al. [119] proposed a rational polynomial function which gives topological behavior of the global fingerprint ridge flow induced
by singular points. The rational polynomial function is defined as:

Q(z) =

(z − q1 )(z − q2 ) · · · (z − qK )
,
(z − p1 )(z − p2 ) · · · (z − pL )

(3.10)

where z = x + iy, {qk }1≤k≤K and {pl }1≤l≤L are zeros and poles, respectively, in the complex
domain. Given this, the orientation field from Q(z) is obtained by:

θ(z) =

1
arg ei2θ∞ · Q(z) ,
2

(3.11)

where θ∞ is the orientation of the finger. Since the Poincar´e indices are +1 at zeros and −1
at poles, cores and deltas in fingerprints correspond to zeros and poles in Equation (3.10),
respectively. Equation (3.11) can be equivalently represented by:
1
θ(z) = θ∞ +
2

K

L

arg(z − qk ) −
k=1

arg(z − pl ) .
l=1

85

(3.12)

As the model in [119] requires only the location and type of the singularities, it does not
reflect the actual ridge flow of the fingerprint. Also, in Sherlock et al.’s approach [119], there
is no model for arch type of fingerprints, which does not contain any singular points.
Li et al. [89] proposed a constrained nonlinear phase portrait model which represents the
x-derivative and y-derivative of the doubled orientation field with nth order polynomials as
shown in Equation (3.5). Then, a set of constraints on the coefficients of the polynomials
is derived from the local orientation field behavior around singular points. That is, the
local orientation field with a singular point at (xo , yo ) in the Cartesian coordinates can be
represented by a polynomial system in the following way:
n

k

akl (x − xo )k−l (y − yo )l = a∗00 + a∗10 x + a∗11 y + f˜(x, y),

x˙ =
k=0 l=0
n
k

bkl (x − xo )k−l (y − yo)l = b∗00 + b∗10 x + b∗11 y + g˜(x, y),

y˙ =

(3.13)

k=0 l=0

where f˜(x, y) and g˜(x, y) are the functions containing the second order or higher polynomial
terms. Since the linearization of the system preserves the local behavior around the singular
point, the following approximation can be established:

a∗00 = 0, a∗10 = a, a∗11 = b,
b∗00 = 0, b∗10 = c, b∗11 = d,

(3.14)

where a, b, c, and d are the elements of the characteristic matrix A in Equation (1.3).
In this model, the global orientation field is reconstructed by combining the orientation
field computed from the image with the trained orientation field from a set of fingerprint
images according to the coherence3 of the local block; for example, if a local block has low
coherence due to existence of singularity or noise, the orientation field from training data
3

Coherence is a measure of consistency of orientations in a local region; coherence of 1 occurs when all
the orientations point in the same direction while coherence of 0 occurs when the orientations point in all
different directions so that the sum in the vector field cancels out.

86

has more weight than the orientation field extracted from the image for the block.
Huckemann et al. [77] proposed a model based on quadratic differentials that describes
local fields around singular points (core, delta, and whorl), and global field simulating archshaped field. The local field around a singular point can be represented by Qlocal (z)dz 2 > 0,
where z = x + iy and dz 2 = z˙ 2 which is the quadratic differential; the rational function
Qlocal (z) for each singularity is as follows:

Qlocal (z) =





z





for a delta

1

z






− 1

z2

In general,
Qlocal (z) =

for a core
for a whorl.

(z − Rq1 )(z − Rq2 )
,
(z − Rp1 )(z − Rp2 )

(3.15)

where Rpj and Rqj , for j = 1, 2, are the locations of cores and deltas, respectively. If the
fingerprint is a loop type (i.e., one core and one delta), the model has p2 = q2 ; in case of a
whorl, p1 = p2 .
The global field which resembles arch-like flow is modeled by locating virtual poles at
±R:
(k)

Qglobal (z) =

(z 2

1
,
− R2 )2k

(3.16)

where k is the number of poles at each +R and −R that determines the curvature of the
global field. The orientation field integrating local and global field is given by:
¯ local (z)Q(k) (z),
Q(z) = Qlocal (z)Q
global

(3.17)

¯ local (z) is the complex conjugate of Qlocal (z) to ensure that the quadratic differentials
where Q
are positive.
The orientation field can be represented by the solution curve of the quadratic differen87

tials, Q(z)dz 2 > 0:
θ(z) =

z,

dz 2
|dz|2

: Q(z) = 0 or ∞ .

(3.18)

The coordinates of the fingerprint (translation, rotation, scale, and aspect ratio of the
axes) are estimated during the model fitting, while the singular points are required as input
to determine the local orientation field.
Wang et al. [129] proposed two peripheral models: a modified cosine function used in [37]
and a fluid model which describes the 2-dimensional flow of a uniform stream toward a
cylinder.
Most deterministic mathematical models require information about singular points (location and type). The rational polynomial model [119] and the quadratic differential model [77]
assume that actual location and type of the singular points are given. The constrained nonlinear phase portrait model [89] estimates the singular points by computing the Poincar´e
index [34] of the orientation field obtained from image gradient. However, the singular point
information is not typically available as a prior knowledge in practice and is extracted automatically from the image. Accurate detection of singular points is still a challenging problem,
especially in noisy fingerprints. If the information about singular points is not correct or
otherwise not available, the deterministic mathematical models give poor estimates of the
orientation field.

3.3

Global Orientation Field Modeling

We propose a global orientation field model for fingerprints that is based on constrained
ordinary differential equations (ODE) [140]. First, the rational polynomial model [119]
which gives a nice topology of fingerprint ridge flow with singular points is converted to
the ODE form whose phase portrait is the same as the orientation field from the rational
polynomial function. It can be shown that the x-derivative and y-derivative of the ODE
system for double-loop fingerprints (the most complicated case) are represented as the 4th
88

order polynomial and the 3rd order polynomial, respectively, in geometric forms. Second,
a generalized ODE model is proposed, which consists of much simpler polynomials and a
smaller number of independent coefficients (i.e., 16 parameters in the model and 1 parameter
for rotation) compared to the polynomial model in [66] and the constrained nonlinear phase
portrait model in [89]4 . Third, the constraints on the number of singular points (either 0,
2, or 4) based on the Hermite’s theorem are applied to reduce the parameter space during
optimization. Finally, the degree of similarity of a given image to a fingerprint pattern,
called fingerprint-ness, in terms of orientation field is measured by computing the difference
between the orientation field extracted from the given fingerprint image and the orientation
field fit by the proposed model.

3.3.1

From Rational Polynomial Function to Ordinary Differential
Equations

Sherlock et al. [119] proposed a fingerprint orientation field model with rational polynomial
function which is given in Equation (3.10). The rational polynomial function can be converted to differential equations whose phase portrait is equivalent to the vector field from
the rational polynomial function. For a loop type of fingerprint with a core at zc = xc + iyc
and a delta at zd = xd + iyd , the rational polynomial function is given by:

QLoop (z) =

z − zc
ac eiφc
ac i(φc −φd )
=
=
e
,
z − zd
ad eiφd
ad

(3.19)

where ac = [(x − xc )2 + (y − yc )2 ]1/2 , ad = [(x − xd )2 + (y − yd )2 ]1/2 , φc = tan−1
φd = tan−1

y−yd
x−xd

y−yc
x−xc

, and

.

For simplicity, denote u =

uy
ux

=

y−yc
x−xc

and v =

4

vy
vx

=

y−yd
.
x−xd

Then, the phase part in

The numbers of coefficients in the polynomial model and the constrained nonlinear phase portrait model
are (n + 1)(n + 2) and (n + 1)(n + 2) − 3Ns , where n is the order of the polynomial and Ns is the number of
singular points detected in the image (see Table 3.1). In [66], n = 4 was used, which involves 30 coefficients;
in [89], n = 8 was used, which involves 90 − 3Ns coefficients. Note that Ns can be at most 4 in case of
double-loop type of fingerprints.

89

Equation (3.19) can be written as:

φc − φd = tan−1 u − tan−1 v
= tan−1
= tan−1

u−v
1 + uv
uy vx − ux vy
ux vx + uy vy

Considering that the set of points where φc − φd =

.

(2k+1)π
,
2

(3.20)

k is an integer, corresponds

to the x-isocline, the x-isocline of the vector field for a loop is: ux vx + uy vy = 0, which is
equal to:
(x − xo )2 + (y − yo)2 − ro2 = 0,

(3.21)

where
xo =

xc + xd
yc + yd
(xc − xd )2 + (yc − yd )2
, yo =
, and ro2 =
.
2
2
4

The x-isocline for the loop type of fingerprint corresponds to a circle.
Similarly, the set of points where φc − φd = kπ, k is an integer, corresponds to y-isocline
where uy vx − ux vy = 0 in Equation (3.20). Thus, the y-isocline of the vector field for a loop
is:
ax + by + c = 0,

(3.22)

where a = −yc + yd , b = xc − xd , and c = yc xd − xc yd . The y-isocline for the loop type of
fingerprint is a line. Figure 3.3 illustrates the orientation field of a loop model obtained from
the rational polynomial function and its vector field with x-isocline and y-isocline.
For double-loop type fingerprints, the rational polynomial function with two cores at
zcj = xcj + iycj and two deltas at zdj = xdj + iydj for j = 1, 2 is as follows:

QDoubleLoop (z) =

(z − zc1 )(z − zc2 )
.
(z − zd1 )(z − zd2 )

(3.23)

The x-isocline and y-isocline for double-loop fingerprints also can be represented in geo90

(a)

(b)

Figure 3.3: Loop model from the rational polynomial function. (a) Orientation field and (b)
vector field with x-isocline (orange solid line) and y-isocline (blue dotted line) with singular
points (a core marked as a circle and a delta marked as a triangle).

(a)

(b)

Figure 3.4: Double-loop model from the rational polynomial function. (a) Orientation field
and (b) vector field with x-isocline (orange solid line) and y-isocline (blue dotted line) with
singular points (cores marked as circle and deltas marked as triangle).

metric form. Denote uj =

ujy
ujx

=

y−ycj
x−xcj

and vj =

vjy
vjx

=

y−ydj
,
x−xdj

j = 1, 2, for cores and deltas,

respectively. Then, the x-isocline corresponds to the curve of (u1x u2x − u1y u2y )(v1x v2x −
91

v1y v2y ) + (u1y u2x + u1x u2y )(v1y v2x + v1x v2y ) = 0, which is equal to:
(x2 + y 2){(x − xo )2 + (y − yo )2 − ro2 } + (Ax2 + Bxy − Ay 2 + Cx + Dy + E) = 0,

xo =

(3.24)

α1 + α2
β1 + β2 2 (α1 + α2 )2 + (β1 + β2 )2
, yo =
, ro =
− (α1 α2 + β1 β2 ),
2
2
4
A = γˆ1 + γˆ2 , B = 2(γ1 + γ2 ),

C = −α1 γˆ2 − α2 γˆ1 − β1 γ2 − β2 γ1 , D = −α1 γ2 − α2 γ1 + β1 γˆ2 + β2 γˆ1 , E = γ1 γ2 + γˆ1 γˆ2 ,
where
α1 = xc1 + xc2 , α2 = xd1 + xd2 , β1 = yc1 + yc2, β2 = yd1 + yd2 ,
γ1 = xc1 yc2 + xc2 yc1, γ2 = xd1 yd2 + xd2 yd1 , γˆ1 = xc1 xc2 − yc1 yc2, and γˆ2 = xd1 xd2 − yd1 yd2 .
The y-isocline for double-loop occurs when (u1y u2x + u1x u2y )(v1x v2x − v1y v2y ) − (u1x u2x −
u1y u2y )(v1y v2x + v1x v2y ) = 0, which is equal to:
(x2 + y 2 )(ax + by + c) + (Ax2 + Bxy − Ay 2 + Cx + Dy + E) = 0,

(3.25)

a = −β1 + β2 , b = α1 + α2 , c = −α1 β2 + α2 β1 ,
A = γ1 − γ2 , B = −2(ˆ
γ1 − γˆ2 ), C = α1 γ2 − α2 γ1 − β1 γˆ2 + β2 γˆ1 ,
D = −α1 γˆ2 + α2 γˆ1 − β1 γ2 + β2 γ1 , E = γ1 γˆ2 − γ2 γˆ1 .
The x-isocline and y-isocline for double-loop fingerprints also consist of geometric forms:
line, circle, and hyperbola. Figure 3.4 shows the double-loop model from the rational polynomial function with x-isocline and y-isocline in the vector field.
92

3.3.2

Generalized Orientation Field Model

Based on the rational polynomial function converted into the ODE form, a generalized
fingerprint orientation field model is derived from the double-loop model, which is the most
complicated case. The generalized model is shown in Equation (3.26): f (x, y) is the 4th order
polynomial with a reduced number of polynomial terms and the coefficients of the 3rd order
polynomial terms are correlated; g(x, y) is the 3rd order polynomial with full polynomial
terms, but the coefficients of the 3rd order polynomial terms are correlated. Thus, there are
8 coefficients each for f (x, y) and g(x, y).

x˙ = f (x, y)
= x4 + 2x2 y 2 + y 4 + ax3 + bx2 y + axy 2 + by 3 + Ax2 + Bxy + Cy 2 + Dx + Ey + F,
y˙ = g(x, y)
= a′ x3 + b′ x2 y + a′ xy 2 + b′ y 3 + A′ x2 + B ′ xy + C ′ y 2 + D ′ x + E ′ y + F ′ .

3.3.2.1

(3.26)

Constraints on Singularity

As a global constraint which characterizes a fingerprint pattern, the number of singular
points in the modeled orientation field needs to be restricted to 0, 2, or 4. Considering
that the singular points occur when x-isocline and y-isocline intersect, we want to find a
constraint on the number of real roots of the following polynomial system:



f (x, y) = 0



g(x, y) = 0.

According to Hermite’s theorem, the constraint which specifies the number of real roots
of a polynomial system can be found as follows [109]:

1. Find the Gr¨obner bases [30] of the polynomial system, G.
93

2. Construct a set of monomials that are not multiples of the leading terms of the polynomials in G, M = {m1 , m2 , . . . , mP }.
3. Compute normal forms5 of each monomial in M multiplied by x and y; that is, for
each monomial mp in M, the normal forms of xmp and ymp are computed.
4. Construct coefficient matrices, Px and Py , where the (i, j)-th entry of Px is the coefficient of the term mi in the normal form of xmj (similarly, the (i, j)-th entry of Py is
the coefficient of the term mi in the normal form of ymj ).
5. Construct a trace matrix T1 which is defined as follows:




 T r(m1 m1 ) · · · T r(m1 mP ) 


..
..
,
T1 = 
.
.




T r(mP m1 ) · · · T r(mP mP )
k +kj

where T r(mi mj ) is the trace of a matrix Pxi

l +lj

Pyi

(3.27)

when mi = xki y li and mj = xkj y lj .

6. Hermite’s Theorem The signature of T1 is equal to the number of real roots of the
polynomial system [108]; the signature of a real symmetric matrix is the difference
between the numbers of positive and negative eigenvalues.
3.3.2.2

Parameter Estimation

A foreground mask, R, consists of the local blocks with sufficient dynamic range in image
intensity [132]. The orientation field in R is computed by image gradients [34]. To ensure
that the modeled orientation field accurately reflects the high curvature ridge structure,
the absolute value of |A|, where A is the characteristic matrix, in Equation (1.3) from
linearization6 is used in parameter estimation. Figure 3.5 shows the map of |A| for a given
5

Given the Gr¨obner bases G of a polynomial system, the normal form of any polynomial is a polynomial
which does not contain any term that is divisible by the leading terms of the polynomials in G after a finite
number of reductions.
6
Recall that the characteristic matrix in the linearized differential equations retains the local properties
of the original differential equations.

94

(a)

(b)

(c)

Figure 3.5: Weight matrix c(x, y) used in Equation (3.28). (a) Input image, (b) the map of
|A| where A is the characteristic matrix in Equation (1.3), and (c) the absolute value of (b).

image and the map of the absolute value of |A|.

The objective function for parameter estimation is:
ˆ y)] · [ω + (1 − ω)c(x, y)]
sin2 [θ(x, y) − θ(x,

min
(x,y)∈R

subject to the signature of T1 as 0, 2, or 4,

(3.28)

ˆ y) is the modeled orienwhere θ(x, y) is the orientation field extracted from the image, θ(x,
tation field, ω is a constant (ω = 0.2 is used), c(x, y) is the map of the absolute value of |A|,
and T1 is the trace matrix in Equation (3.27).

While the origin of the coordinates is set to the center of the image (translation parameters are not needed), the rotation parameter needs to be estimated. The modeled orientation
field with rotation angle r is obtained as follows:
R2 g(R−1 x)
R2 f (R−1 x)

1
ˆ
θ(x)
= tan−1
2
95

,

(3.29)

where

 


x
 cos r sin r 
x =   , and R = 
.
y
− sin r cos r

(3.30)

In total, 17 parameters, including a rotation parameter, are estimated for the model
fitting. For the initial parameter estimation, the objective function in Equation (3.28) is
used without applying the constraints. Then the parameters are estimated by applying one
of the three constraints for the number of intersections (0, 2, and 4) at each time. Only the
estimated parameters which do not violate the constraint are considered as valid. Figure 3.6
shows the orientation field estimated by the proposed model for various types of fingerprints.

3.3.3

Defining Fingerprint Pattern: Fingerprint-ness

One of the most interesting applications of the global fingerprint orientation field model is
to determine if a given image (e.g., an input to AFIS or an image in an exemplar database)
contains a valid fingerprint pattern. If a valid fingerprint image given as input is of good
quality, a global orientation field model specifically designed to represent fingerprint patterns
is expected to fit well to the orientation field of the input image. If the input image is a
poor quality fingerprint which does not provide reliable orientation field as input to the
model or the input is not a fingerprint image, the orientation field obtained from the model
is expected to show a large difference from the orientation field of the image. Figure 3.7
shows an example of a good quality fingerprint image and its orientation field difference map
(i.e., difference of image orientation field and modeled orientation field) and an example of
a non-fingerprint image and its orientation field difference map.
As a measure of similarity of a given image to fingerprint pattern (i.e., fingerprint-ness) in
terms of orientation field, the gray-level co-occurrence matrix (GLCM) [68] is computed from
the orientation difference map. A 5-dimensional feature vector consists of contrast, energy,
and homogeneity of the GLCM, and the mean and standard deviation of the orientation
difference map in the foreground region R. Prior to applying the proposed model to the
96

(a)

(b)

(c)

(d)

(e)

(f)

Figure 3.6: Orientation field fit by the proposed model for (a) arch, (b) tented-arch, (c)
left-loop, (d) right-loop, (e) whorl, and (f) twin-loop type fingerprint.

97

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 3.7: Orientation field difference map. (a)–(d) Input fingerprint image, orientation
field from the image, orientation field from the model, and the orientation field difference
map of the fingerprint image; (e)–(h) input non-fingerprint image, orientation field from
the image, orientation field from the model, and the orientation field difference map of the
non-fingerprint image.
orientation field of a given image, the image is rejected if R takes less than 30% of the
entire image area. If the model does not find any feasible solution satisfying any of the three
constraints on the number of singular points, the image is also rejected. For example, nonfingerprint images such as Figure 3.1(a) cannot be fit by the model satisfying the required
number of singular points. Even for fingerprint images, if heavy structured noise is present
in the image (e.g., the latent fingerprint image shown in Figure 3.1(d)), the model cannot
find a good fit to the orientation field of the image.

3.3.4

Experimental Results

The proposed fingerprint orientation field model is evaluated as a detector of a valid fingerprint pattern in a given image. As a fingerprint database, 2,000 images of the first impressions
98

Figure 3.8: Fingerprint images in NIST SD4 [2].

in NIST SD4 [2] are used. As a non-fingerprint database, 2,000 images are drawn from the
ImageNet dataset [48]; 100 object classes in the ImageNet dataset are randomly selected
with 20 images per class. Figures 3.8 and 3.9 show the images used in the experiments.
The fingerprint images are set as a positive class while the non-fingerprint images are set
as a negative class for a 2-class classification experiment. The 5-dimensional feature vector
extracted from the orientation field difference map is used to determine if a given image is
a valid fingerprint or not. The SVM with radial basis function [41] is used as a classifier
and the performance is evaluated by 10-fold cross validation. Figure 3.10 shows the ROC
curve with the average performance of the cross validation; the minimum and maximum
performances are also indicated. Figures 3.11 and 3.12 show the images that are successfully
classified based on the orientation field of the images.
Figure 3.13 shows false positive cases. If the model fit is wrong (Figure 3.13(a) is a double99

Figure 3.9: Non-fingerprint images in the ImageNet dataset [48].

loop fingerprint, but the model fits to a loop fingerprint), a high response in the orientation
field difference map is observed. On the other hand, if the orientation field extracted from
the image is noisy due to the poor quality of the fingerprint ridges (e.g., Figure 3.13(b)), the
orientation field difference can also be high. However, the modeled orientation field for the
partially noisy image in Figure 3.13(b) is still able to detect a fingerprint-like flow pattern.
Figure 3.14 shows false negative examples where the images contain large areas of textured
pattern with a smooth orientation field.
100

True Positive Rate (%)

100

95

90

85

80

75
0.5

1

10
False Positive Rate (%)

100

Figure 3.10: ROC curve. The average performance (red line) in the 10-fold cross validation
is shown; the minimum and maximum performances (blue bars) over the 10 folds are also
indicated.

3.4

Summary

Global fingerprint orientation field model is ideal for capturing unique characteristics of fingerprint patterns. It will assist in distinguishing fingerprints from any other texture pattern,
representing the fingerprint orientation field in a compact form, and estimating the orientation field from noisy or partially missing fingerprints. There are two approaches to model the
fingerprint orientation field: (i) approximation methods and (ii) deterministic mathematical
models. In approximation methods, the global orientation field is represented by a set of
basis functions, and the coefficient vectors are sometimes used as an index of the fingerprint.
Deterministic mathematical models, on the other hand, are designed to specifically represent
fingerprint ridge flow and incorporate unique characteristics of fingerprint orientation field
into the model.
The global orientation field models published in the literature are highly dependent on
101

(a) F = 1.0

(b)

(c)

(d)

(e) F = 0.99

(f)

(g)

(h)

Figure 3.11: True positive examples. (a) and (e) Valid and good quality fingerprint images,
(b) and (f) orientation field from the image, (c) and (g) modeled orientation field, and (d)
and (h) orientation field difference map.
singular point information; if incorrect information about singularities is given or if the
singular points are missing, the models are likely to fail to fit to the image. We propose
an ODE representation of the global orientation field derived from the rational polynomial
model and a set of constraints for the number of singular points in fingerprint is applied
to estimate coefficients of the model. The proposed model is used to detect abnormality in
the orientation field of a given image as a fingerprint and then classify it as a fingerprint or
non-fingerprint pattern.
Global orientation field models also have been used in this dissertation for (i) latent
fingerprint enhancement (for robust orientation field estimation in latents) in Chapter 4 and
(ii) altered fingerprint detection (for abnormality measure in orientation field) in Chapter 5.
Future work on global orientation field modeling and fingerprint-ness measure includes:

1. Improve the global orientation field model by incorporating fingerprint-specific features
102

(a) F = 0

(b)

(c)

(d)

(e) F = 0

(f)

(g)

(h)

Figure 3.12: True negative examples. (a) and (e) Non-fingerprint image, (b) and (f) orientation field from the image, (c) and (g) modeled orientation field, and (d) and (h) orientation
field difference map.
such as the configuration of singular points and arch-shaped global field.
2. Include features from ridge frequency and minutiae distribution into the definition of
fingerprint-ness.

103

(a) F = 0.43

(b)

(c)

(d)

(e) F = 0.59

(f)

(g)

(h)

Figure 3.13: False positive examples. (a) and (e) Fingerprint images, (b) and (f) orientation
field from the image, (c) and (g) modeled orientation field, and (d) and (h) orientation field
difference map. The model estimates the fingerprint image in (a) as a loop fingerprint
although it is indeed a double-loop fingerprint. The orientation difference map for the
fingerprint image in (e) shows high response in the noisy region; the estimated orientation
field from the model shows fingerprint-like behavior even in the noisy region.

104

(a) F = 0.85

(b)

(c)

(d)

(e) F = 0.83

(f)

(g)

(h)

Figure 3.14: False negative examples. (a) and (e) Non-fingerprint image, (b) and (f) orientation field from the image, (c) and (g) modeled orientation field, and (d) and (h) orientation
field difference map. Both images have textured background which provides a smooth orientation field.

105

Chapter 4
Latent Fingerprint Enhancement

4.1

Introduction

The success of AFIS in forensics and law enforcement applications is based on the availability of large legacy databases of rolled and plain prints of the ten fingers of all apprehended
criminals. The size of these background databases is huge and is constantly increasing; for
example, as of November 2012, the FBI’s IAFIS fingerprint database contained the tenprints
of about 73 million criminals. While the “lights-out” mode of operation for exemplar matching is a reality, a “lights-out” identification mode for latent search is still a research topic of
high priority. One of the major goals of the FBI’s NGI program [11] is to develop a latent
matching system that will accept a latent image as input and return a short list of exemplar
candidates from the database with no human intervention [79]. In a recent NIST report highlighting the results of ELFT-EFS [78], the best performing latent matcher achieved rank-1
identification rate of 63.4% in searching 418 latents against a 100,000 tenprint exemplar
database when only latent images are given as input. As a comparison, the best performing matcher in verifying plain fingerprints against 10,000 plain fingerprints showed a true
acceptance rate of 99.4% at a false acceptance rate of 0.01% in the 2003 FpVTE [135].
The primary focus in developing automated latent identification algorithms is to reduce
106

the human (latent examiners) intervention to as little as possible while preserving the matching accuracy that can be achieved with full manual markup. Automatic fingerprint feature
extractors designed for rolled/plain prints do not give acceptable results on latents since
many true minutiae are likely to be missed due to low ridge clarity and many spurious
minutiae are likely to be extracted due to background noise.
We propose a semi-automatic latent fingerprint enhancement algorithm [137, 138] which
requires minimal markup, namely ROI and singular points. Note that, in the proposed
approach, a latent examiner is not required to mark minutiae or ridges, which demands
significant effort. The objectives of the latent fingerprint image enhancement are to: (i)
improve automatic feature extraction and matching performance of latent fingerprints, and
(ii) provide visually enhanced images to latent examiners to enhance their ability to mark
fingerprint features.
Estimating the orientation field of a latent fingerprint is a crucial stage in the latent
enhancement algorithm. The significance of the proposed orientation field estimation algorithm in latents are: (i) extracting all dominant ridge orientations in a block, called orientation elements, considering the presence of background noise in the image, (ii) adopting
randomized-RANSAC (R-RANSAC) algorithm [93], which is powerful in fitting a model to
the dataset containing outliers, and (iii) using a global orientation field model to find the
best hypotheses generated from the R-RANSAC algorithm. Once the orientation field is estimated, the quality of fingerprint ridges can be improved by Gabor filtering which enhances
the local ridge clarity along the ridge orientation and suppresses noise in other directions.
The proposed latent fingerprint enhancement algorithm consists of the following four
steps:
1. Manual markup of ROI and singular points.
2. Orientation element computation using the short-time Fourier transform (STFT) [43].
3. Orientation field estimation using R-RANSAC.
107

4. Fingerprint enhancement using Gabor filters [76].

4.2

Manual Markups of Latents

We assume that the following information is manually marked by latent examiners: (i)
fingerprint region in the latent image, or the ROI, and (ii) singular points. ROI is a closed
region that is bounded at the outermost trim of the latent. Figure 4.1 shows the boundary
of ROI in the latent images. Only the features extracted in the ROI are regarded as valid.
Singularities observed in almost all the fingerprints fall into one of the following categories:
(i) no singularity (i.e., arch type of fingerprints), (ii) one core and one delta (i.e., loop and
tented-arch type), and (iii) two cores and two deltas (i.e., whorl and twin-loop type). Note
that not all singular points may be observed in a given fingerprint image; for example, plain
impression tends to capture only the central area of a finger. Based on this observation,
latent examiners are expected to mark singular points using the following convention:
• If the latent does not contain any singularity, no singular points are marked (see Figure 4.1(a)). Even though the latent fingerprint may in fact come from a finger with
singularity, the latent will be treated as plain arch, the simplest fingerprint pattern.
• If the latent contains singular points, cores and deltas should be marked in pairs. For
example, the latent fingerprint in Figure 4.1(b) has one core and one delta in the ROI.
These singular points are called real singular points since they are present in the ROI.
On the other hand, when the numbers of core and delta are not equal, the missing
singular points are marked with the examiner’s best guess. These are called virtual
singular points since they are not observable in the ROI. For example, the latent in
Figure 4.1(c) contains only two real cores, and the two virtual deltas are also marked
with the examiner’s best guess.

108

(a)

(b)

(c)

Figure 4.1: Manual markup of ROI and singular points. (a) No singularities presented in
the image, (b) two real singular points, and (c) two real cores and two virtual deltas. The
ROI is outlined by green boundary.

4.3

Orientation Field Estimation

In this stage, we use a three-level approach to estimate the orientation field of a latent: (i)
the orientation elements are computed in each block in the ROI, (ii) the orientation elements
in a neighborhood are merged into an orientation group whose elements are compatible with
each other, and (iii) a robust estimate of the global orientation field is obtained by a set
of orientation groups. The following sections describe the orientation field model and the
details of the orientation field estimation algorithm.

4.3.1

Orientation Element Computation

Fingerprint ridges in a local image block generally contain only one dominant orientation
if the fingerprint image is of good quality. However, in latent fingerprints, multiple orientations may appear in a block due to the structured background noise such as lines (see
Figure 4.2(a)). A popular approach to compute multiple dominant orientations (orientation
elements) in a block is based on the STFT [43], which detects the local maxima in the mag109

(a)

(b)

Figure 4.2: Orientation elements extracted from a latent using STFT. (a) Latent (NIST
SD27, G027) and (b) orientation elements.
nitude spectrum of the local image. As the local maximum corresponding to the fingerprint
ridges can be easily confused with the local maxima corresponding to the structured noise,
we determine the true ridge orientation in the next stage. Figure 4.2(b) shows the extracted
orientation elements in each block in the ROI of the latent image in Figure 4.2(a).
For each local block of 16 × 16 pixels in the ROI, the orientation elements are computed
as follows:
1. Compute the STFT of a local image block (see Figures 4.3(a) and (b)).
2. Multiply the magnitude spectrum of the image with a set of directional filters (Figure
4.3(c)) in Fourier domain; each directional filter is constructed by multiplying a binary
mask (1 for θ ∈

π
L

i−

1
2

, Lπ i +

1
2

, i = 0, 1, . . . , L − 1; 0, otherwise) and a band-

pass filter whose frequency range includes possible fingerprint ridge frequencies. L = 8
is selected.
3. Sum the energy from each filtered response (Figure 4.3(d)).
110

(b)

(c)

Energy

(a)

2
4
6
8
Directional Filter Index
(d)

(e)

Figure 4.3: Orientation element computation. (a) A local image block, (b) magnitude spectrum of (a), (c) a set of directional filters, (d) energy of filtered responses by each directional
filter, and (e) two orientation elements in this local block that correspond to the two local
maxima in (d).

4. Find peaks (local maxima) in the one-dimensional energy plot. Orientation corresponding to the peak from the i-th directional filter is

π
i
L

+

π
2

mod π.

Figure 4.3(e) shows two orientation elements extracted from the image block in Figure 4.3(a).

4.3.2

Orientation Field Model

Orientation field, θ(x, y), of a fingerprint can be decomposed into two components:

θ(x, y) = [θs (x, y) + θr (x, y)] mod π,
111

(4.1)

where θs (x, y) represents the singular orientation field and θr (x, y) represents the residual
orientation field.
Singular orientation field, θs (x, y), describes the abstract ridge flow determined by only
the singular points where the fingerprint orientation field changes abruptly. The singular
orientation field is obtained based on the rational polynomial function [119]:

θs (z) =

1
(z − q1 )(z − q2 ) · · · (z − qK )
arg ei2θ∞
2
(z − p1 )(z − p2 ) · · · (z − pL )

mod π,

(4.2)

where z = x+iy, {qk } and {pl } are the positions of cores and deltas, and θ∞ is the orientation
of the finger.
Residual orientation field, θr (x, y), represents natural changes in ridge flow of a fingerprint
that are not influenced by the singularities; it is continuous everywhere. A set of polynomials
can represent the x-derivative and y-derivative of the doubled residual orientation field as
follows [66]:
n

k

x˙ r = fn (x, y) =

akl xk−l y l ,

(4.3)

bkl xk−l y l ,

(4.4)

k=0 l=0
n

k

y˙ r = gn (x, y) =
k=0 l=0

where {akl } and {bkl } are the polynomial coefficients for fn (x, y) and gn (x, y), respectively.
The order of the polynomials is set as 4 (i.e., n = 4).
Figure 4.4 shows an example where the orientation field model is applied to a fingerprint.

4.3.3

Orientation Element Grouping

Neighboring orientation elements which are compatible with each other are grouped in order
to facilitate the subsequent global orientation field estimation. Based on that the residual
orientation field is continuous, the compatibility of the orientation elements is defined in the
(i)

residual orientation field, and a unique label is assigned to each group. Let θr (x, y) be the
i-th residual orientation element in a block at (x, y), and L(i) (x, y) be the label assigned to
112

(a)

(b) θ(x, y)

(c) θs (x, y)

(d) θr (x, y)

(e) θˆr (x, y)

ˆ y)
(f) θ(x,

Figure 4.4: Orientation field model combining singular orientation field and residual orientation field. (a) Fingerprint (NIST SD4, F0004), (b) orientation field extracted from (a),
(c) singular component of the orientation field, (d) residual component of the orientation
field, (e) modeled residual orientation field using the 4th order polynomial model, and (f)
ˆ y) = θs (x, y) + θˆr (x, y).
reconstructed orientation field, θ(x,

this orientation element. Note that the number of orientation elements in a block varies
from 1 to L. Initially, L(i) (x, y) = 0 for all i in a block at (x, y). Orientation element
grouping starts from the elements which are the only dominant orientation in a block; they
(i)

become seed points. For a seed point θr (x, y), an orientation element in a neighboring block
(j)

θr (x′ , y ′) is deemed as a candidate to belong to the same group as this seed point if the
following three conditions are satisfied:
113

(a)

(b)

(c)

Figure 4.5: Orientation element grouping. (a) Fingerprint (NIST SD27, G017), (b) residual
orientation elements, and (c) five orientation element groups (each shown in a different color).
(i) L(j) (x′ , y ′) = 0: no label is yet assigned to this neighboring orientation element;
(ii) The distance between two blocks is within 5 blocks; and
(i)

(j)

(iii) |θr (x, y) − θr (x′ , y ′ )| < π/2L: the orientation difference is less than a threshold.
The candidates which are 4-connected to the seed point (i.e., a 4-connected path can be
found among the set of candidate blocks) are assigned the same label as the seed point. Once
all the seed points are grouped, the orientation elements which are the only one unlabeled
element in a block become new seed points. This procedure is repeated until every orientation
element has been assigned a label. Figure 4.5 shows five of the orientation element groups
in a latent fingerprint.

4.3.4

Hypotheses Generation

Given a set of orientation element groups as the input, hypotheses for the residual orientation
field are built based on the R-RANSAC algorithm [93]. RANSAC algorithms produce a
number of hypotheses during iterations, and an iteration generally consists of three basic
114

steps: (i) select a set of initial data points randomly, (ii) build a hypothesis, and (iii) evaluate
the hypothesis. A set of data points that are consistent with a given hypothesis is called the
consensus set. The differences between R-RANSAC [93] and the basic RANSAC [58] are: (i)
the number of initial data points selected in R-RANSAC is more than the minimum number
of points required to build a hypothesis, and (ii) the hypothesis evaluation against all data
points is conducted only if all initial data points are consistent with the hypothesis.
Let G be the set of all orientation elements and N be the total number of the orientation
groups. An orientation group is randomly selected from G based on the following probability
density function (pdf) which is constructed from the area of each group. The probability for
random selection, pi , of the i-th group with area Ai is defined as:

pi =

Ai
.
N
j=1 Aj

(4.5)

Orientation elements in the selected group are added to a set S; the size of S increases
monotonically during an iteration. Initially, non-overlapping orientation groups are selected
randomly according to the pdf of the size of groups until the size of S is greater than
the minimum number of data points (m) to build a hypothesis; m is 15 for the 4th order
polynomial.
Once the size of S is greater than m, a hypothesis is built using all orientation elements
in the current S. The hypothesized model refers to the coefficients of the polynomials, {akl }
and {bkl }, in Equations (4.3) and (4.4), which are obtained using the least-squares estimation
by minimizing
(i)

|fn (x, y) − cos 2θr(i) (x, y)|2,

(4.6)

(i)

|gn (x, y) − sin 2θr(i) (x, y)|2 .

(4.7)

θr (x,y)∈S

θr (x,y)∈S

If all orientation elements in S are within some error tolerance of the hypothesis (which
is set to π/L), the consensus set S ∗ is determined by testing the hypothesis against all
orientation elements in G and this hypothesis is recorded if the size of the S ∗ is the largest in
115

this iteration. The current iteration continues by adding a new non-overlapping orientation
group to S. Figure 4.6 shows the procedure of hypothesis generation for one iteration.
Suppose not all orientation elements in S are consistent with the hypothesis. Then, one
of the following two actions is taken: (i) if the inconsistent group is the most recently added
one, remove this group from S, add a new group to S, and continue the current iteration; (ii)
otherwise, terminate the iteration and evaluate the best hypothesis at this iteration. Action
(ii) is also taken when no more non-overlapping orientation groups can be added to S.
The best hypothesis at each iteration is verified by checking if the hypothesized residual orientation field includes any singularity in the ROI. Singularities are found using the
Poincar´e index [83]. The hypothesis is accepted if there is no singularity present in the ROI.
Figure 4.7 shows an accepted hypothesis, and the reconstructed orientation field combining
the hypothesized residual orientation field with singular orientation field represents the true
ridge flow well. If the hypothesized residual orientation field contains any singularity, it is
rejected (see Figure 4.8).
The algorithm terminates when the number of iterations exceeds (i) a predetermined
maximum number of trials, or (ii) the minimum number of trials k satisfying [58]

k≥

log(1 − pf )
,
log(1 − εm )

(4.8)

where pf is the desired probability of having at least one S that all the orientation groups
in S are from the target latent fingerprint and ε is the true fraction of orientation elements
from the latent in G. Since ε is typically unknown, it is updated with the size of the best
consensus set during the iterations.
Once the top-10 best candidate hypotheses for the orientation field are found, the latent
fingerprint is enhanced using Gabor filters [76], which is described in the following section.
The orientations of the Gabor filters are tuned to each orientation field hypothesis and their
frequencies are set to a fixed value (1/8 ridges per pixel). All ten enhanced latents are input
116

((1))

((2))

((3))

((4))

((5))

((6))

Figure 4.6: One iteration of hypothesis generation procedure for the latent in Figure 4.5(a).
An orientation group is added to S at each step from (1) to (6) (newly added groups are
marked as red and existing groups in S are marked green in the left-hand side image of each
pair); a hypothesis is built at every update in S and checked to see if all groups in S are
consistent with the hypothesis (red blocks in the right-hand side image in each pair indicate
consistency in S with the hypothesis). The final hypothesis M is obtained at the end of the
iteration when no more groups can be added to S. Then, M in (6) is evaluated by checking
the existence of singularity (see Figure 4.7).

117

(a)

(b)

Figure 4.7: Accepted hypothesis. (a) Accepted hypothesized residual orientation field and
(b) reconstructed orientation field using (a). Red blocks in (a) and (b) indicate the consensus
set.

(a)

(b)

Figure 4.8: Rejected hypothesis. (a) Rejected hypothesized residual orientation field with
singularities (red circle for core and yellow triangle for delta) and (b) reconstructed orientation field using (a).

118

to the fingerprint matcher. Then, the ten match scores output by the matcher are fused by
the max rule [115].

4.4

Fingerprint Enhancement

Fingerprint ridges in a local region can be enhanced by applying a set of Gabor filters [76].
Gabor filter is widely used to select local structure with specific orientation and frequency,
and the Gabor function is given by:

h(x, y; θ, f ) = exp −

1
2

x2θ yθ2
+ 2
δx2
δy

cos(2πf xθ ),

(4.9)

  
 
xθ   cos θ sin θ x
 =
 ,
yθ
− sin θ cos θ
y

where θ is the orientation of the Gabor filter, f is the frequency of the filter, and δx and δy
are standard deviations which determine the envelope of the Gabor filter.

4.5
4.5.1

Experimental Results
Database

The experiments are conducted on the public domain latent fingerprint database, NIST
SD27 [3], which contains 258 latent fingerprints and their corresponding rolled fingerprints.
Each latent image in this database was assigned one of three (subjective) quality levels good, bad, and ugly - by latent fingerprint examiners. The numbers of latents belonging to
the “good”, “bad”, and “ugly” category are 88, 85, and 85, respectively. To make the latent
matching problem more realistic and challenging, the background database was enlarged to
27,258 fingerprints by including 27,000 rolled prints in NIST SD14 [10].
119

Algorithm. Hypotheses Generation for Orientation Field Estimation
m: Minimum number of blocks to build a hypothesis.
G: The set of orientation elements in all groups.
S: A set of orientation elements in selected groups (initially, S is empty).
pi for i = 1, . . . , N : A pdf for random selection of orientation groups.
N : A total number of orientation groups.
I. Hypothesis
1. Initialize S: Non-overlapping groups are selected randomly based on the given p such
that the total number of orientation elements in S is greater than m.
2. Build a hypothesis M : {akl } and {bkl } are estimated by the least-squares estimation
using S.
3. If all orientation elements in S are consistent with the M , go to step 4. If the inconsistent
orientation elements are only from the most recently added group, discard this group from
S and go to step 5. Otherwise, go to step 6.
4. Find the consensus set S ∗ : S ∗ is determined by a subset of G which are within some error
tolerance of the regularized residual orientation field from M . If |S ∗ | > |Sbest |, update
Sbest and Mbest with S and M . Go to step 5.
5. Add a group to S which is selected randomly in G and that does not overlap with any
orientation elements in S and go back to step 2. If there are no more groups to be added,
go to step 6.
6. Accept/reject the hypothesis: Check if the regularized residual orientation field from the
hypothesis Mbest contains any singularity [34]. If singularity exists in the ROI, reject the
hypothesis. Otherwise, proceed to evaluation stage.
II. Evaluation
The accepted hypotheses are ranked in a descending order according to the size of the
∗ .
consensus set Sbest
Go back to I.
III. Output
Top-10 best hypotheses are retrieved from the accepted hypotheses.

120

4.5.2

Performance Evaluation

The accuracy of the proposed latent fingerprint enhancement algorithm is evaluated by
measuring the latent matching performance before and after enhancement using a commercial
matcher, Neurotechnology VeriFinger SDK 4.2 [13]. The CMC curves of four types of the
input to the fingerprint matcher are shown in Figure 4.9. These inputs are: (i) enhanced
latent by manually marked orientation field; (ii) enhanced latent by the estimated orientation
field using the R-RANSAC algorithm [138]; (iii) enhanced latent by the estimated orientation
field using the least-squares method [137]; and (iv) latent image with no enhancement.
Note that the performance of using a manually marked orientation field provides the
upper bound. As shown in Figure 4.9(a), the automatic matching performance is significantly
improved when the enhanced images are used as input to the matcher. Furthermore, the
proposed algorithm based on R-RANSAC performs better than the least-squares estimation.
The CMC curves are also shown separately according to the quality of the latents. For
good quality latents, the proposed algorithm achieves performance close to the upper bound
(manually marked orientation field; see Figure 4.9(b)). For bad and ugly quality latents,
while the proposed algorithm performs much better compared to the least-squares estimation
method or the no enhancement case (see Figures 4.9(c) and (d)), there is a significant gap
in performance between the proposed algorithm and the upper bound. This shows that the
automatic orientation field estimation in poor quality latents is still a challenging problem.
Figure 4.10 shows three successful examples in each quality category where the proposed
enhancement algorithm improved the match score of the latent with the mated rolled fingerprint. In these three cases, the mated rolled print can be retrieved at a high rank from
the exemplar database containing 27,258 images. Figure 4.11 shows a failure case where the
failure in orientation field estimation leads to a lower genuine match score after enhancement
compared to no enhancement.
121

Rank−m Identification Rate (%)

80
70
60

Latent enhanced with marked OF
Latent enhanced with estimated OF, RANSAC
Latent enhanced with estimated OF, LS
No enhancement

50
40
30
20
10
0

5

10
Rank (m)

15

20

(a)

Rank−m Identification Rate (%)

70
60
50
40
30
20
10
0

Latent enhanced with marked OF
Latent enhanced with estimated OF, RANSAC
Latent enhanced with estimated OF, LS
No enhancement
5

10
Rank (m)

15

20

(b)
Figure 4.9: CMC curves showing the performance improvement due to latent enhancement.
(a) All latents in NIST SD27, (b) good quality latents, (c) bad quality latents, and (d) ugly
quality latents..

122

Figure 4.9: (cont’d)

Rank−m Identification Rate (%)

80
70
60

Latent enhanced with marked OF
Latent enhanced with estimated OF, RANSAC
Latent enhanced with estimated OF, LS
No enhancement

50
40
30
20
10
0

5

10
Rank (m)

15

20

(c)

Rank−m Identification Rate (%)

60
50

Latent enhanced with marked OF
Latent enhanced with estimated OF, RANSAC
Latent enhanced with estimated OF, LS
No enhancement

40
30
20
10
0

5

10
Rank (m)

(d)

123

15

20

(a) Good quality latent (G019): {4,5277}→{54,1}

(b) Bad quality latent (B142): {3,1253}→{34,1}

(c) Ugly quality latent (U282): {0,27258}→{24,1}
Figure 4.10: Successful examples where the proposed latent enhancement algorithm improves
the latent matching performance. Left: latent image, Center: estimated orientation field,
and Right: binarized enhanced image. Match score of the latent with the mated rolled print
and its retrieval rank from a database of 27,258 rolled prints are shown as: {score, rank}
before enhancement → {score, rank} after enhancement.

124

Figure 4.11: Failure case (G029). Due to the failure in orientation field estimation, the
latent-to-rolled match score drops from 23 (before enhancement) to 3 (after enhancement),
and the retrieval rank for the true mate increases from 12 to 15,801.

4.6

Summary

Latent fingerprints found at crime scenes provide crucial evidence to law enforcement agencies. The latents are typically searched against a large fingerprint database which is the
collection of rolled/plain fingerprints of previously apprehended criminals. Due to the generally poor quality of latents, latent examiners perform manual feature markup and visual
comparison between the latent and the candidate fingerprints from the database. A “lightsout” mode for latent identification is desired to reduce the burden on latent examiners and
to introduce a level of consistency in fingerprint matching, particularly in searching evergrowing exemplar fingerprint databases.
We have proposed a latent fingerprint enhancement algorithm that requires minimal
markup (i.e., ROI and singular points) to improve the automatic latent matching accuracy.
The orientation field of the latents is estimated by the R-RANSAC algorithm, which is effectively used to find a correct orientation field in the noisy and partial latent fingerprints. The
estimated orientation field is used to enhance ridge structures by Gabor filtering. The proposed algorithm significantly improves the matching performance of a commercial matcher
when the enhanced latents are fed into the matcher.
We propose to extend our work on latent enhancement as follows:
125

• Improve the performance of the orientation field estimation algorithm for bad and ugly
quality latents in NIST SD27.
• Reduce the human markup even further; ideally, the input of the algorithm should
only be the latent image.
• Assess the quality of the latents automatically. The reliability of the features extracted
from the latents can be adjusted according to the quality in order to automatically
determine the degree of human intervention for feature markup and improve the overall
matching accuracy.

126

Chapter 5
Fingerprint Obfuscation

5.1

Introduction

Fingerprint obfuscation refers to the deliberate alteration of the fingerprint pattern [45] using
techniques varying from abrading, cutting, and burning fingers to performing plastic surgery
(see Figure 1.13). The use of altered fingerprints to mask one’s identity constitutes a serious
“attack” against a border control biometric system since it defeats the very purpose for
which the system was deployed in the first place, i.e., to identify individuals in a watch list.
The problem involving altered fingerprints falls under a broader category of attacks known
as biometric obfuscation. Obfuscation can be defined as a purposeful attempt by an individual to mask his identity, so that it cannot be recognized by a biometric system, by altering
the biometric trait prior to its acquisition by the system. Examples include mutilating the
ridges of one’s fingerprint by using abrasive material, perturbing the texture of the iris by
wearing theatrical lenses, or altering facial attributes such as nose and lips via surgical procedures. In this study, we will concern ourselves with the problem of fingerprint obfuscation for
the following reasons: (i) fingerprint-based biometric systems are much more widespread for
large-scale identification than any other biometric modality; (ii) it is relatively easy to alter
one’s fingerprints using chemicals and abrasives compared to, say, one’s iris or face where a
127

(a)

(b)

Figure 5.1: Inked impressions before and after fingerprint alteration (a) of Gus Winkler [45]
(pattern type is altered from twin-loop to left-loop), and (b) of Jose Izquierdo [134] (altered
by switching two parts of a ‘Z’ shaped cut on the fingertip).

more elaborate surgical procedure may be necessary; and (iii) mutilated fingerprints are being routinely encountered by law enforcement and immigration officials in several countries,
thereby underscoring the urgency of finding a solution to this problem.
Fingerprint alteration has a long history. As early as 1933, Gus Winkler, a murderer and
bank robber, was found to have altered the fingerprints of his left hand except for the thumb
by slashing and tearing the flesh of the fingers [45]. Further, the pattern type of one of his
fingers was altered from twin-loop to left-loop (see Figure 5.1(a)).
In more recent cases, a man using the name Alexander Guzman, arrested by Florida
officials in 1995 for possessing a false passport, was found to have obfuscated fingerprints
(see Figure 5.1(b)). After a two-week search based on manually reconstructing the damaged
fingerprints and searching the FBI database containing 71 million records, the reconstructed
fingerprints of Alexander Guzman were linked to the fingerprints of Jose Izquierdo who was
an absconding drug criminal [134]. In this particular case, the mutilation process consisted
of three steps: (i) making a ‘Z’ shaped cut on the fingertip, (ii) lifting and switching two
triangular skin patches, and (iii) stitching them together. In September 2005, a drug dealer
named Marc George was apprehended because his limping gait as a result of surgery involving
transplantation of friction ridge skin taken from the sole of his feet caught the attention of
border officials (see Figure 1.13(a)) [14].
128

Table 5.1: High Profile Cases of Fingerprint Alteration
Case

Year

Gus Winkler [45]

1933

John Dillinger [14]

1934

Robert J. Philipps [14]

1941

Jose Izquierdo [134]

1997

Marc George [14]

2005

A man arrested for
vehicle theft [122]
Mateo Cruz-Cruz [67]

2007

Alteration
Description
Type
Criminal Cases
Imitation
Pattern type was changed from twin-loop to
left-loop (Figure 5.1(a)).
Obliteration Fingerprints were mutilated by applying
acid.
Obliteration Skin from the chest was transplanted to the
fingertips.
Distortion
A fingerprint with strange pattern was
formed by ‘Z’ cut (Figure 5.1(b)).
Imitation
Friction ridge skin from sole of the feet was
implanted to the fingertips (Figure 1.13(a)).
Obliteration Fingers were bitten (Figure 1.13(b)).

2007

Obliteration

Gerald Perez [107]

2008

A woman crossing U.S. border [67]
Asylum seekers to EU [20,
24]
A woman attempting to
evade the Japanese
border control system [25]
Three people charged in
Boston with conspiring to
mutilate fingerprints [27]

2007
2008

Fingerprints were blackened as a result of
applying acid (Figure 1.13(c)).
Obliteration Fingertips
with
thick
stitches
(Figure 1.13(d)).
Non-criminal Cases
Obliteration A surgery was performed on fingertips to
generate strange fingerprint pattern.
Obliteration Fingertips were abraded and burned.

2009

Imitation

2010

Obliteration

Friction ridge skins from thumbs and index
fingers were swapped between left and right
hands.
A physician, a broker, and a patient were
involved in a scheme to mutilate or surgically remove the fingerprints to conceal illegal aliens from detection.

It is not just criminals who have been found to alter their fingerprints. In December
2009, a woman successfully evaded the Japanese immigration AFIS by surgically swapping
fingerprints of her left and right hands [25]. Although she was originally arrested for faking
a marriage license, scars on her hands made the border police suspicious.
Fingerprint alteration has even been performed at a much larger scale involving a group
of individuals. It has been reported that hundreds of asylum seekers had cut, abraded,
and burned their fingertips to prevent identification [20, 24] by EURODAC [22], a European
Union-wide fingerprint system for identifying asylum seekers. Table 5.1 lists reported cases
129

Restoration
‘Z’
‘Z’-cut
Fingerprint

Altered Fingerprint Altered
Detection
(Altered or Natural)

Classificati
Classification
(‘Z’-cut
cut or Not)
N

Not ‘Z’-cut

Matching

Mated Print
Or No Mate

Figure 5.2: Flow chart for detecting and matching altered fingerprints.

of fingerprint alteration.
Although the number of publicly disclosed cases of altered fingerprints is not very large,
it is extremely difficult to estimate the actual number of individuals who have successfully
evaded identification by fingerprint systems as a result of fingerprint alteration. Almost
all the persons that have been identified so far to have altered their fingerprints were not
detected by AFIS, but by some other means such as improper documents [25] or by a product
of the surgery (e.g., limping gait) [14].
With the growing use of AFIS in law enforcement and border control, it is expected that
there will be more instances where altered fingerprints will be encountered by the authorities. Therefore, it is necessary that AFIS should have the capability to determine the true
identity of individuals with altered fingerprints. To tackle the problem of fingerprint alteration, new algorithms for detecting and matching altered fingerprints are urgently needed.
An overview of the procedure to deal with altered fingerprints is presented in Figure 5.2.
Fingerprints submitted to AFIS need to pass through an altered fingerprint detector at the
front end of the AFIS. Abnormality in orientation field and minutiae distribution in altered
fingerprints provides indications of possible alterations [54, 139]. Once the altered fingerprints are detected, the suspect is sent to a secondary inspection in order to verify (i) that
the unusual fingerprint pattern is indeed due to alteration, and (ii) whether these altered
fingerprints could still be matched to the suspect’s pre-altered fingerprints if present in the
databases [141].
130

Percentage of tenprint cards (%)

60
50
40
30
20
10
0

1 2 3 4 5 6 7 8 9 10
Number of altered fingerprints in a card

Figure 5.3: Distribution of the number of altered fingerprints in tenprint cards in our
database.
This chapter is organized as follows. In Section 5.2, the impact of the fingerprint obfuscation on the matching performance is investigated and three different categories of altered
fingerprints and their potential counter-measures are described. The proposed approach for
detecting altered fingerprints is presented in Section 5.3. Section 5.4 describes an approach
to improve the performance of matching altered fingerprints to their pre-altered mates by
masking out the altered region and restoring ‘Z’-cut cases. Finally, Section 5.5 proposes
future directions for research on this topic.

5.2

Analysis of Altered Fingerprints

Based on a database of altered fingerprints made available to us by law enforcement agencies,
we (i) determine the impact of fingerprint alteration on the matching performance, (ii)
categorize altered fingerprints into three types1 : obliteration, distortion, and imitation, and
1

While the categorization is exclusive, there is ambiguity in some altered fingerprints.

131

(iii) assess the utility of a well-known fingerprint quality measure for altered fingerprint
detection.

5.2.1

Altered Fingerprint Database

The database contains 4,433 altered fingerprints from 535 tenprint cards of 270 subjects. We
summarize some of the characteristics of this database below.
• Not all the ten fingers in a tenprint card may have been altered. The distribution of
the number of altered fingers in a tenprint card is shown in Figure 5.3; in 57% of the
tenprint cards, all ten fingerprints were altered; 85% of the tenprint cards have more
than five of the ten fingerprints altered.
• The number of tenprint cards for a subject varies from 1 to 16; a total of 87 subjects
out of the 270 subjects have multiple tenprint cards due to multiple arrests.
• For subjects with multiple tenprint cards, there exist 1,335 pairs of pre-altered (natural)
and post-altered fingerprints. Figure 5.4 shows an example of pre-altered and postaltered tenprint cards of a subject.

5.2.2

Vulnerability of Fingerprint Identification Systems

Fingerprint alteration is a serious threat to AFIS, since it revokes one of the fundamental
premise that fingerprint is persistent during one’s lifetime. To understand the vulnerability
of AFIS to fingerprint alteration, we used a commercial matcher, VeriFinger SDK 4.2 [13],
to match 1,335 altered fingerprints to their mated pre-altered fingerprints. To establish a
baseline, NIST SD4 database [2], which consists of 2,000 fingers with two impressions per
finger, was used to obtain genuine and impostor match score distributions using the matcher2 .
2

Note that while the analysis is based on a specific fingerprint matcher, the results of fingerprint alteration
are likely to affect all commercial matchers in a similar manner. VeriFinger, like other state-of-the-art
fingerprint matchers, utilizes ridge pattern for matching, which is what the culprits are trying to change
through fingerprint alteration.

132

(a)

(b)
Figure 5.4: Mated pre/post altered tenprint cards from a subject. (a) Pre-altered fingerprints
and (b) post-altered fingerprints.
Figure 5.5 shows the score distributions for pre/post altered fingerprint pair matches
according to type of alteration and genuine and impostor matches in NIST SD4. The key
observations based on these matching results are:

1. The match score distributions of pre/post altered fingerprint pairs for all alteration
133

100
Genuine Match
Impostor Match
Obliterated Fingerprint Match
Distorted Fingerprint Match
Imitated Fingerprint Match

Percentage (%)

80
60
40
20
0
0

50

100
150
Match Score

200

250

Figure 5.5: Match score distributions of pre/post alteration pairs according to type and
genuine and impostor pairs in NIST SD4.
types follow the impostor score distribution.

2. Heavy tails in pre/post altered match score distributions indicate that fingerprint alteration, as observed in our database, is not always successful in evading AFIS.

3. At a threshold of 41, which corresponds to 0% false acceptance rate on NIST SD4, 83%
of the pre/post altered fingerprint pairs have genuine match scores below the threshold.
This means that an AFIS is unable to link most of the altered fingerprints to their true
mates.

Figure 5.6 shows examples where altering a fingerprint leads to failure in matching it
to its true mate. The process of fingerprint mutilation destroys the ridge structure itself so
that minutiae extraction is not possible in the altered region (Figure 5.6(a)). A severe ridge
distortion such as ridge structure transformation (Figure 5.6(b)) or ridge deformation due
to scars alters the spatial distribution of the minutiae.
134

(a)

(b)

Figure 5.6: Examples where fingerprint alteration severely degrades the matching score with
the pre-altered mates. (a) Mutilation over a large area and (b) ridge transformation. These
altered fingerprints have a match score of 0 with their true mates. All squares indicate minutiae extracted from the image and squares filled with red color represent matched minutiae
between the pre/post altered fingerprints. The left-hand side image in each pair shows the
pre-altered fingerprint, and the right-hand side image shows the post-altered fingerprint.

(a) Match score = 233

(b) Match score = 173

Figure 5.7: Examples where the pre/post altered fingerprint mates are correctly matched
despite fingerprint alteration. (a) Alteration with a small damaged area in the fingerprint
and no ridge distortion and (b) sufficient number of minutiae in the unaltered area even with
severe fingerprint alteration. Only a subset of the corresponding minutiae are connected with
dotted lines for visibility.

There is no guarantee that fingerprint alteration will always be successful in evading an
AFIS (see Figure 5.7). As long as there are a sufficient number of minutiae that can be
extracted in the unaltered area, pre/post fingerprint mates can be successfully matched by
AFIS.
135

Table 5.2: Exclusive Categorization of the Altered Fingerprints into Three Types

Type
Number of Images

5.2.3

Obliteration
Scar Mutilation
1,457
2,480

Distortion
Z-cut Transplantation
297
148

Imitation
51

Types of Altered Fingerprints

We classify altered fingerprints into three categories (i.e., obliteration, distortion, and imitation) based on the change in ridge pattern due to alteration. This categorization will assist
us in three ways: (i) getting a better understanding of the nature of alterations that can
be encountered, (ii) detecting altered fingerprints by modeling types of alteration, and (iii)
developing methods for altered fingerprint restoration and matching.
Table 5.2 shows the exclusive categorization of 4,433 altered fingerprints in our database.
Note that this classification is not based on the method of alteration which is not known to
us. Our classification is subjective and is based on our examination of the ridge patterns in
a large number of altered fingerprint images in the database.

5.2.3.1

Obliteration

Friction ridge patterns on fingertips can be obliterated by abrading [36], cutting [45], burning
[18, 20, 24], applying strong chemicals (Figure 1.13(c)), and transplanting smooth skin [14].
Further, factors such as skin disease (such as leprosy [131]) and side effects of a cancer
drug [136] can also obliterate fingerprints. Friction ridge structure is barely visible within the
obliterated region. According to Table 5.2, obliteration appears to be the most popular form
of fingerprint alteration. This may be because obliteration which completely destroys ridge
structures is much simpler to perform than distortion/imitation which requires a surgical
procedure. Furthermore, detecting distorted or imitated fingerprints is much more difficult
for human examiners than obliterated fingerprints.
Obliterated fingerprints can evade fingerprint quality control software, depending on the
136

(a)

(b)

Figure 5.8: Fingerprint obliteration. Examples of (a) scar and (b) mutilation.
area of the damage. If the affected finger area is small, the existing fingerprint quality
assessment softwares may fail to detect it as an altered fingerprint (the fingerprint in Figure
5.8(a) has an acceptable NFIQ value of 3), but AFIS is likely to successfully match the
damaged fingerprint to the original mated fingerprint (Figure 5.7(a)). But, if the altered
area is sufficiently large, fingerprint quality control software can easily detect the damage.
For example, the obliterated fingerprint in Figure 5.8(b) has the lowest NFIQ value of 5.
To identify individuals with severely obliterated fingerprints, it may be necessary to treat
these fingerprints as latent images, perform an AFIS search using manually marked features,
and adopt an appropriate fusion scheme for tenprint search [96]. In rare cases, even if the
finger surface is completely damaged, the dermal papillary surface, which contains the same
pattern as the epidermal pattern, may be used for identification [110].

5.2.3.2

Distortion

Friction ridge patterns on fingertips can be turned into unnatural ridge patterns as a result
of obfuscation [23, 26, 134]. This can happen, for example by removing portions of skin from
a fingertip and either grafting them back in different positions (Figure 5.9(a)) or replacing
them with friction ridge skin on the palm or sole (Figure 5.9(b)). Distorted fingerprints have
unusual ridge patterns which are not found in natural fingerprints. These abnormalities
include abnormal spatial distribution of singular points or abrupt changes in orientation
137

(a)

(b)

Figure 5.9: Fingerprint distortion. Examples of (a) transplantation within a finger by ‘Z’
cut and (b) transplantation from other friction ridge skin, e.g., from palm.

field along the scars. Note that an orientation field discontinuity in natural fingerprints is
usually observed only at singular points.
Distorted fingerprints can also successfully pass the fingerprint quality test since their
local ridge structures remain similar to natural fingerprints; it is their global ridge pattern
that is abnormal. For instance, a distorted fingerprint as a result of swapping skin patches
within the same finger (e.g. Figure 5.9(a)) retains the same ridge property (e.g. ridge
frequency and width) over the entire fingerprint area. Figure 5.9(a) is indeed assigned the
highest quality level, NFIQ of 1. Similarly, the altered fingerprint in Figure 5.9(b) is assigned
the second highest quality level, NFIQ = 2.
Fingerprints altered by ‘Z’ cut are of special interest since they retain their original ridge
structure, enabling a reconstruction of the original fingerprint pattern before alteration.
Therefore, it is imperative to upgrade current fingerprint quality control software to detect
the distorted fingerprints. Once detected, the following operations may be performed to
assist the AFIS: (i) identify unaltered regions of the fingerprint and manually mark the
features (i.e., the minutiae) in these regions and (ii) reconstruct the original fingerprint as
in the ‘Z’ cut case [134].
138

(a)

(b)

Figure 5.10: Fingerprint imitation. Left: pre-altered fingerprint, and Right: its post-altered
fingerprint mate. (a) Removal of a portion of skin and (b) exquisite transplantation from
other friction ridge skin on the body.
5.2.3.3

Imitation

Friction ridge patterns on fingertips can still preserve fingerprint-like pattern after an elaborate procedure of fingerprint alteration: (i) a portion of skin is removed and the remaining
skin is pulled and stitched together (Figure 5.10(a)), (ii) friction ridge skin from other parts
of the body is used to fill the removed part of the fingertip to reconcile with the remaining
ridge structure (Figure 5.10(b)), or (iii) transplantation of the entire fingertip. As reported
in [25], simply swapping the skin on fingertips between the left and right hands successfully
evaded an AFIS.
Imitated fingerprints can not only successfully pass the fingerprint quality assessment
software, they can also confound human examiners. Figure 5.10 shows pre-altered and
post-altered fingerprint mates. The altered fingerprint in Figure 5.10(a) has a very smooth
orientation field over the entire fingerprint area (which looks like an arch type fingerprint)
and the only evidence of possible alteration is a thin scar. This fingerprint has the highest
NFIQ value of 1. However, its pre-altered mate is indeed of right-loop type, and the match
score between this pair of fingerprints is only 19, much below the threshold (a score of 41)
on match score corresponding to 0% FAR of the matcher. The altered fingerprint in Figure
5.10(b) was generated by an exquisite surgical procedure to have very natural ridge flow
even along the surgical scars. This fingerprint also has the highest NFIQ value of 1 with a
139

Percentage (%)

40

Natural
Obliterated
Distorted
Imitated

30

20

10

0

1

2

3
NFIQ

4

5

Figure 5.11: Histograms of NFIQ values for 27,000 natural fingerprints in NIST SD14 and
4,433 altered fingerprints in our altered fingerprint database according to the type of alteration. Recall that NFIQ = 1 indicates the highest quality.

match score between pre/post altered fingerprint pair of only 28.
To match altered fingerprints in Figure 5.10, matching algorithms that are robust to
distortion and inconsistency in the fingerprint flow pattern need to be developed. In the
case where fingerprints from different fingers are swapped, fingerprint matching without
using finger position information (i.e., left thumb is allowed to match to right index finger)
may help in determining the true identity at the expense of significantly higher matching
time.

5.2.4

Effectiveness of Fingerprint Quality Assessment Algorithm

To determine the effectiveness of the commonly used fingerprint quality control softwares in
detecting altered fingerprints, quality levels of altered fingerprints and natural fingerprints
were estimated using the NFIQ software [124], which is the de facto standard of fingerprint
quality. To construct a natural fingerprint database, we used the 27,000 fingerprints in NIST
140

SD14 [10]. From the histograms of NFIQ values for altered and natural fingerprints shown
in Figure 5.11, we can observe that:
1. A significant portion of altered fingerprints have the lowest quality level of 5 while only
a small percentage of natural fingerprints have this lowest quality level. In particular,
the obliterated fingerprints have the largest portion at the NFIQ level of 5. By contrast,
the distorted and imitated fingerprints have relatively small portion at the level of 5.
2. A large number of altered fingerprints have good quality; about 7% of altered fingerprints have the highest quality level of 1 in total, and a significant portion of distorted
and imitated fingerprints has the highest quality level.
3. If the NFIQ value of 5 is used as a criterion for detecting altered fingerprints, it will lead
to a true positive (an altered fingerprint is correctly classified as an altered fingerprint)
rate of 31.6% at a false positive (a natural fingerprint is misclassified as an altered
fingerprint) rate of 2.1%.

5.3

Detection of Altered Fingerprints

Developing an automatic solution to detect altered fingerprints is the first step in countering
the threats due to fingerprint alteration. Fingerprint quality assessment routines used in
most fingerprint identification systems, such as the open source NFIQ software [124], may
be useful in detecting altered fingerprints if the corresponding images are indeed of poor
quality. But, as mentioned earlier, not all altered fingerprint images have poor quality
(see Figures 5.9 and 5.10). Since existing fingerprint quality assessment algorithms [31] are
designed to examine if an image contains sufficient information (say, minutiae) for matching,
they have limited capability in determining if an image is a natural fingerprint or an altered
fingerprint. For example, while the synthesized ridge pattern in Figure 3.2(a) is not likely to
appear on fingertips, it is declared to be of the best quality according to the NFIQ measure
(i.e., NFIQ of 1).
141

Given that the altered fingerprints are likely to be encountered in large-scale national
identification or border control systems, the automatic detector must satisfy the following
three requirements:
1. Given the large throughput requirement of these systems, the algorithm must be extremely fast. In other words, it should not increase the computational burden of the
matcher by any significant amount. State-of-the-art AFIS can process fingerprints at
the rate of about 1 million matches per second. This implies that the feature extraction
and decision rule used to automatically detect altered fingerprints must be efficient.
2. In operational scenarios, the number of individuals with altered fingerprints that will
be encountered by an AFIS will be very small. Keeping this in mind, the altered
fingerprint detection algorithm should operate at a very low false positive rate, say 1%
or lower. Since subjects that are suspected to have altered fingerprints will need to go
through a secondary inspection stage, it is desirable not to have many individuals to
be sent for secondary inspection.
3. The altered fingerprint detector should be easily integrated into any AFIS.
In the previous section, we showed that the NFIQ algorithm is not suitable for detecting
altered fingerprints, especially the distortion and imitation types. In fact, the distorted and
imitated fingerprints are very hard to detect for any fingerprint image quality assessment
algorithm that is based on local image quality alone. In this section, we consider the problem
of automatic detection of alterations based on properties of the ridge orientation field and
minutiae distribution [139]. The flow chart of the proposed alteration detector is given in
Figure 5.12.

5.3.1

Abnormality in Orientation Field

Good quality fingerprints have a smooth orientation field except near the singular points.
Based on this fact, many orientation field models have been developed by combining the
142

Orientation Field Level
Orientation
Orientation
Field
Field
Estimation Discontinuity
Fingerprint
Minutiae
Extraction

Minutiae
Density Map

Feature
Level
Fusion

SVM
Classification

Altered
Or Not

Minutiae Level
Figure 5.12: Flow chart of the altered fingerprint detection algorithm.
global orientation field model for the continuous flow field of the fingerprint with the local
orientation field model around the singular points [66, 77, 129]. The global orientation field
model represents either arch type fingerprints, which do not have any singularity, or the
overall ridge orientation field except singularity in fingerprints. If the global orientation field
model alone is used for orientation field approximation, the difference between the observed
orientation field and the model will ideally be non-zero only around the singular points. On
the other hand, for obfuscated fingerprints, the model fitting error is observed in the altered
region as well. Thus, we use the difference between the observed orientation field extracted
from the fingerprint image and the orientation field approximated by the model as a feature
vector for classifying a fingerprint as natural fingerprint or altered one. The main steps of
the proposed algorithm to detect altered fingerprints at orientation field level are described
below:
1. Normalization: An input fingerprint image is normalized to 512×480 pixels by cropping
a rectangular region of the fingerprint, which is located at the center of the fingerprint
and aligned along the longitudinal direction of the finger, using the NIST Biometric
Image Software (NBIS) [132]. This step ensures that the features extracted in the
subsequent steps are invariant with respect to translation and rotation of the finger.
2. Orientation field extraction: The orientation field of the fingerprint, θ(x, y), is com143

puted using the gradient-based method [34]. The initial orientation field is smoothed
by a 16×16 averaging filter, followed by averaging the orientations in 8×8 pixel blocks.
Foreground mask is obtained by measuring the dynamic range of gray values of the fingerprint image in local blocks and morphological process for filling holes and removing
isolated blocks is performed.
3. Orientation field approximation: The orientation field θ(x, y) is approximated by a
ˆ y).
polynomial model [66] to obtain θ(x,
4. Feature extraction: The error map, ε(x, y), is computed as the absolute difference
ˆ y) and used to construct the feature vector.
between θ(x, y) and θ(x,
More details of steps 3 and 4 are given below.

5.3.1.1

Orientation Field Approximation

To represent the global orientation field, a set of polynomials is used, which is not only
computationally efficient, but also provides a good approximation in orientation field modeling. Let θ(x, y) denote the orientation field. Then, the x-derivative and y-derivative of the
doubled orientation at (x, y) can be represented by polynomials of order n:
n

k

x˙ = fn (x, y) =

akl xk−l y l ,

(5.1)

bkl xk−l y l ,

(5.2)

k=0 l=0

n

k

y˙ = gn (x, y) =
k=0 l=0

where {akl } and {bkl } are the polynomial coefficients for fn (x, y) and gn (x, y), respectively.
As the order of the polynomials increases, the model becomes more flexible in representing
abrupt changes in the orientation field. When the order of the polynomial model is too low,
the orientation field approximated by the model is quite different from the true orientation
field. However, the order of the polynomial model does not need to be very high; polynomial
144

models with 6 or higher order do not make significant difference in the fitting results. Thus,
we select the order of the polynomial model as 6 (i.e., n = 6).
Using the orientation field θ(x, y) obtained in step 2 (orientation field extraction), the
polynomial coefficients akl and bkl can be estimated by the least-squares method. For simplicity, we represent Equations (5.1) and (5.2) in matrix form:
fn (x, y) = xT a,

gn (x, y) = xT b,

(5.3)

where x = [1 x y x2 xy y 2 · · · xn · · · y n ]T , and a and b are the corresponding coefficient
vectors. The problem of estimating a and b can be formulated as:
ˆ = arg min gn − Xb 2 ,
ˆ = arg min fn − Xa 2 , b
a
a

where

(5.4)

b











T
 x1




 gn (x1 , y1 ) 
 fn (x1 , y1 ) 
 




 xT 
 gn (x2 , y2 ) 
 fn (x2 , y2 ) 
 2




,
and
X
=
,
g
=
fn = 
 . 



..
..
 . 

 n 

.
.
 . 




 




xTN
gn (xN , yN )
fn (xN , yN )

from N observations of θ(x, y), where (x, y) ∈ R and R = {(x, y): (x, y) in foreground}.
ˆ y), is obtained
Finally, the orientation field approximated by the polynomial model, θ(x,
by:
ˆ y) = 1 tan−1
θ(x,
2

gˆn (x, y)
fˆn (x, y)

,

(5.5)

ˆ
ˆ and gˆn (x, y) = xT b.
where fˆn (x, y) = xT a

5.3.1.2

Feature Extraction

While the low order polynomial model can adequately represent smooth (global) changes in
the orientation field, it cannot accurately model the abrupt changes in the orientation field
145

(a) Natural fingerprint (NIST SD14, F0000001)

(b) Scarred fingerprint

(c) Mutilated fingerprint

(d) Distorted fingerprint by ‘Z’ cut

(e) Distorted fingerprint by transplantation from other friction ridge skin
Figure 5.13: Orientation field discontinuity. Column 1: fingerprint image; Column 2: orientation field extracted from the image, θ(x, y); Column 3: orientation field approximated by
ˆ y); and Column 4: error map, ε(x, y).
the polynomial model, θ(x,

146

in local areas, e.g., around cores and deltas in natural fingerprints. One of the observed
characteristics of altered fingerprints is that their ridge flow can be discontinuous in nonsingular regions as well, such as severely scarred areas (Figure 5.8(a)), mutilated areas (Figure
5.8(b)), and distorted ridge areas (Figures 5.9(a) and (b)). The difference between the
observed orientation field and the modeled orientation field indicates the locations and the
amount of abrupt changes in the ridge flow.
We define the error map ε(x, y) as:
ˆ y)|, π − |θ(x, y) − θ(x,
ˆ y)|)/(π/2).
ε(x, y) = min (|θ(x, y) − θ(x,

(5.6)

Figure 5.13 shows the error maps of a natural fingerprint and four different altered fingerprints. The size of the error map is 60×60 blocks after removing two columns from each side
of the error map.
The feature vector extracted from the error map consists of histograms of local spatial
regions [47]. The error map is divided into 3×3 cells, where each cell is of size 20×20 blocks.
A histogram of the error map in each cell is computed in 21 bins in the range [0, 1], and the
histograms from all the 9 cells result in a 189-dimensional feature vector.

5.3.2

Abnormality in Minutiae Distribution

A minutia in the fingerprint indicates ridge characteristics such as ridge ending or ridge bifurcation. Almost all fingerprint recognition systems use minutiae for matching. In addition
to the abnormality observed in the orientation field, we also noted that minutiae distribution
of altered fingerprints often differs from that of natural fingerprints.
Based on the minutiae extracted from a fingerprint by the open source minutiae extractor in NBIS, a minutiae density map is constructed by using the Parzen-window method
with uniform kernel function.

Let Sm be the set of minutiae of the fingerprint, i.e.,

Sm = {x|x = (x, y) is the position of minutia}. Then, the minutiae density map from Sm
147

(a) Fingerprint image

(b) Minutiae extracted from the image

(c) Minutiae density map
Figure 5.14: Minutiae density map. Column 1: Natural fingerprint (NIST SD14, F0001826);
Column 2: distorted fingerprint with dense minutiae along scars; Column 3: obliterated
fingerprint with dense minutiae distribution in the altered region; Column 4: obliterated
fingerprint with dense minutiae distribution over the entire altered region due to ridge-like
pattern formed by alteration. Note that the minutiae density maps have been scaled to the
same grayscale range.
is computed as follows:

1. Initial estimation: Initial minutiae density map, Md (x), is obtained by

Kr (x − xo ),

Md (x) =

(5.7)

xo ∈Sm

where Kr (x − xo ) is a uniform kernel function centered at xo with radius r (r is set to
40 pixels).
148

2. Low-pass filtering: Md (x, y) is smoothed by a Gaussian filter of size 30×30 pixels with
a standard deviation of 10 pixels.

3. Normalization: Md (x, y) is transformed to lie in the interval [0, 1] by


 Md (x, y)/T
Md (x, y) =

 1

if Md (x, y) ≤ T

(5.8)

otherwise,

where T is a predetermined threshold.

Figure 5.14 shows the minutiae density maps of a natural fingerprint and three altered
fingerprints. In the natural fingerprint, minutiae are well spread and distributed almost
uniformly. In the altered fingerprints, on the other hand, the distributions of minutiae are
quite different: (i) many spurious minutiae are extracted along scars and in the obliterated
region due to ridge discontinuity, and (ii) an excessive number of minutiae appear when a
new ridge-like pattern is formed after alteration. These examples demonstrate that minutiae
distribution can be useful for detecting altered fingerprints.
A feature vector from the minutiae density map is also constructed by local histograms
in 3×3 cells. Then, the feature vectors from the orientation field discontinuity map and the
minutiae density map are combined by concatenating local histograms in each cell, and fed
into a support vector machine (SVM) for classification.

5.3.3

Experimental Results

The proposed algorithm was evaluated at two levels: finger level (one finger) and subject
level (all ten fingers). At the finger level, we evaluate the performance of distinguishing
between natural and altered fingerprints. At the subject level, we evaluate the performance
of distinguishing between subjects with natural fingerprints and those with altered fingerprints. Since most AFIS used in law enforcement, national identification, and border control
149

applications process all ten of a person’s fingerprints, the subject-level performance utilizes
this domain-specific information for detecting individuals with altered fingerprints.

5.3.3.1

Finger-Level Evaluation

The altered fingerprint database available to us contains 4,433 fingerprints from 535 tenprint
cards. For the non-altered fingerprint database, we use 27,000 fingerprints from the 2,700
tenprint cards in the NIST SD14 [10]. This database contains two impressions for each
finger, called file and search; the file impression is used in our experiments.
LIBSVM [41] with radial basis kernel function is used for classification with 10-fold crossvalidation. The scores output by LIBSVM are linearly scaled to the range [0, 1]. The
normalized score is used as a measure of the deviation from natural fingerprint pattern, and
denoted as F . When F of an input image is smaller than a predetermined threshold value,
the system raises an alarm to indicate that the image is a possible altered fingerprint. If
this image is indeed an altered fingerprint, it is deemed to be a true positive; otherwise, it is
deemed to be a false positive. Similarly, true negative indicates that a natural fingerprint is
correctly classified as natural and false negative indicates that an altered fingerprint is not
detected as altered.
The ROC curves of the proposed approach and NFIQ software for detecting altered
fingerprints are given in Figure 5.15. At the false positive rate of 2.1%, where natural
fingerprints in NIST SD14 with the NFIQ value of 5 are determined as altered fingerprints,
the proposed algorithm attains a 70.2% true positive rate while the true positive rate of
the NFIQ is only 31.6%. Figure 5.15(a) shows the ROC curves for the three approaches
for detecting altered fingerprints (orientation field discontinuity, minutiae distribution, and
their feature-level fusion) and the NFIQ algorithm. Figure 5.15(b) shows the ROC curves
of the proposed fusion algorithm and the NFIQ algorithm according to alteration type.
Both obliterated and distorted fingerprints can be detected by the proposed algorithm at
similar accuracy while NFIQ can only identify obliterated cases. On the other hand, imitated
150

True Positive Rate (%)

100
80

Fusion
OF Discontinuity
Minutiae Distribution
NFIQ = 5

60
40
20
0
0.1

0.2 0.3 0.5
1
False Positive Rate (%)

2

3

2

3

(a)

True Positive Rate (%)

100
80

Obliteration
Distortion
Imitation

60
40
20
0
0.1

0.2 0.3 0.5
1
False Positive Rate (%)
(b)

Figure 5.15: ROC curves of the proposed algorithm and NFIQ criterion in detecting altered
fingerprints. (a) The ROC curves of the three approaches in the proposed algorithm and the
NFIQ algorithm and (b) the ROC curves of the proposed fusion algorithm and the NFIQ
algorithm for each type of altered fingerprints. The ROC curve of NFIQ criterion is shown
as a set of points (only one point is visible in the range of false positive rate plotted here)
because its output can only take one of the five quality levels.

151

Table 5.3: NFIQ Distribution for False Positive Cases at the False Positive Rate of 1% by
the Proposed Algorithm
NFIQ Value
Number of Images

1
2

2
1

3
39

4
145

5
83

(a) F = 0.56, NFIQ=1 (b) F = 0.42, NFIQ=4 (c) F = 0.36, NFIQ=1 (d) F = 0.48, NFIQ=1
Figure 5.16: True positive detection cases by (a) orientation field discontinuity, (b) minutiae
distribution, (c) and (d) fusion of both approaches.
fingerprints are challenging for both algorithms.
At the false positive rate of 1% (which means 270 fingerprints among the 27,000 in NIST
SD14 would be misclassified as altered fingerprints), the threshold value for F is 0.60. Figure
5.16 shows examples of successfully detected alterations using the proposed algorithm even
though the NFIQ measure assigns acceptable quality level to these images.
Not all the altered fingerprints can be detected by the proposed algorithm. If the altered
area is too small (Figure 5.17(a)), the evidence of alteration is difficult to detect. In the
imitation case, the ridge structure is very natural even at the boundary of the altered region;
the orientation field is continuous and there is insignificant abnormality in minutiae density
along scars (Figure 5.17(b)).
The main reasons for false positive cases are: (i) poor image quality, leading to incorrect
fingerprint feature extraction (see Figure 5.18(a)) and (ii) ground truth error; some of the
fingerprints in NIST SD14 may possibly have been altered (see Figures 5.18(b), (c), and (d))!
Table 5.3 shows the NFIQ distribution of the false positive examples found by the proposed
algorithm at the false positive rate of 1%. Most of the false positive images have NFIQ of
4 or 5. Note that it is acceptable to raise alarms on poor quality fingerprints since (i) poor
152

(a) F = 0.92, NFIQ = 1

(b) F = 0.86, NFIQ = 1

Figure 5.17: False negative examples of the proposed algorithm. Minutiae and orientation
field discontinuities of each example are shown. (a) Fingerprint with small altered area and
(b) imitated fingerprint. Note that NFIQ also fails to detect these two altered fingerprints.

(a) F = 0.33, NFIQ=5 (b) F = 0.57, NFIQ=1 (c) F = 0.58, NFIQ=2 (d) F = 0.52, NFIQ=3
Figure 5.18: False positive examples of the proposed algorithm. Poor quality ridge patterns:
(a) NIST SD14, F0010811; and possibly altered fingerprints: (b) F0019979, (c) F0002962,
and (d) F0018103.
quality images need to be manually checked and (ii) criminals may purposely present poor
quality fingerprints to the fingerprint system to evade identification [133]. All three false
positive cases with NFIQ = 1 or 2 appear to have been altered (two of them are shown in
Figures 5.18(b) and (c)).
5.3.3.2

Subject-Level Evaluation

In our altered fingerprint database, we observed that when a person resorts to fingerprint
alteration, he tries to alter as many fingers as possible (Figure 5.3). This makes sense since
large-scale AFIS applications typically use a fusion of match scores from all ten fingerprints
for identification. So, altering just one or two fingerprints is not likely to change the identification decision. Based on this observation, we use the following decision-level fusion rule to
153

True Positive Rate (%)

100
80
60
40
20
0
0.1

Fusion
OF Discontinuity
Minutiae Distribution
NFIQ = 5
0.2 0.3 0.5
1
2
3
False Positive Rate (%)

Figure 5.19: ROC curves of the proposed algorithm (including three approaches) and NFIQ
criterion for detecting altered fingerprints at subject level.
perform the subject-level detection for altered fingerprints. When six or more fingerprints
are detected as altered, the subject is claimed to have altered fingerprints. Subjects with
fewer than six altered fingerprints are not considered as a threat to the AFIS since even five
(out of ten) natural fingerprints are generally sufficient for reliable identification.
For the subject-level evaluation, 453 tenprint cards with more than five altered fingerprints and 2,700 tenprint cards in NIST SD14 are used. Figure 5.19 shows the ROC curves
of the proposed algorithm (including three approaches) as well as the NFIQ criterion for detecting subjects with altered fingerprints. At a false positive rate of 0.3%, where the NFIQ
criterion determines subjects with six or more fingerprints of NFIQ = 5 in NIST SD14 as
persons who altered their fingerprints, the proposed algorithm attains a true positive rate of
66.4% while the NFIQ criterion obtains a 26.5% true positive rate.
Figure 5.20 shows an example of a tenprint card where the subject-level decision is
successful. Even though one altered finger is not correctly detected due to the smoothness of
the orientation field and the absence of abnormality in minutiae distribution in the altered
region, our subject-level fusion algorithm still flags this person because as many as nine
154

NFIQ = 3

NFIQ = 4

NFIQ = 2

NFIQ = 4

NFIQ = 4

NFIQ = 2

NFIQ = 4

NFIQ = 4

NFIQ = 4

NFIQ = 4

Figure 5.20: True positive example of detection at subject level by the proposed algorithm.
Although one of the altered fingerprints was not detected, this subject is still detected as
having altered fingerprints with high confidence since the other nine fingerprints (boxed
fingerprints) are correctly detected as altered. None of the ten fingerprints is detected as
altered using the NFIQ criterion.
NFIQ = 3

NFIQ = 4

NFIQ = 3

NFIQ = 5

NFIQ = 5

NFIQ = 4

NFIQ = 5

NFIQ = 5

NFIQ = 5

NFIQ = 5

Figure 5.21: True negative example
(NIST SD14, F0000121–F0000130).
the nine fingerprints are determined
However, the NFIQ criterion raises a
have the NFIQ value of 5.

at subject level identified by the proposed algorithm
This subject can pass our alteration detector since
to be natural fingerprints by the proposed algorithm.
false alarm for this subject since six of the fingerprints

fingers are determined to be altered.
Fusion of multiple fingerprints also helps to reduce the false positive for a person who
either did not alter his fingerprints or simply has one or two fingerprints that appear to have
been altered due to accidents or occupational reasons. Figure 5.21 shows one such example.
155

In this case, however, the NFIQ criterion will falsely raise an alarm for this subject since six
of the ten fingerprints are assigned the NFIQ value of 5.
We also have access to a small altered fingerprint database (254 images) from another
government agency. This database has larger variance in terms of image format such as
compression method, image resolution, and image type (single finger impressions, slap impressions, and tenprint cards). As a result, we report the detection performance on this
database separately. We trained an SVM using all the 4,433 images in our first altered fingerprint database and tested on this second small database. The same NFIQ criterion was
also used as a comparison. At the false positive rate of 2.1%, the proposed algorithm shows
a 33.1% true positive rate compared to 9.4% for the NFIQ criterion.

5.4

Matching of Altered Fingerprints

Fingerprint alteration does not always fulfill its intended purpose, namely masking one’s
identity, for the following reasons. (i) Permanent modification or removal of friction ridge
pattern often fails since the ridge details in the epidermis layer reappear on the surface of the
skin after a few months [46]. (ii) Although the local fingerprint information in the altered
region is lost, the true identity can still be established based on ridge details in the unaltered
area. In 1941, Roscoe Pitts, a habitual criminal, had plastic surgery performed to remove
the skin of his fingertips and replace it with skin grafts from his chest [14]. After he was
arrested by the police, his true identity was revealed as Robert Philipps by comparing the
second joints of his fingers with the original fingerprint card.
There is also a reported case where altered fingerprints were submitted as a query to AFIS.
In 1995, a man named Alexander Guzman was arrested by Florida officials for possessing
a false passport. His fingerprints were found to have been altered by a ‘Z’ shaped cut on
the fingertips: two triangular skin patches from the ‘Z’ cut were lifted, switched, and then
stitched back (see Figure 5.1(b)). Through a manual restoration of his altered fingerprints
156

and a search against the FBI database, the restored fingerprints of Alexander Guzman were
linked to the fingerprints of Jose Izquierdo, an absconding drug criminal [134].
Altered fingerprint matching is a challenging problem due to the following reasons: (i)
friction ridge structure can be severely damaged by abrading, cutting, burning, or applying
strong chemicals on fingertips, resulting in a number of unreliable minutiae (Figure 5.8); (ii)
even if the ridge structure is well defined in local regions, orientation field can be highly
unusual during the procedure of switching skin patches in cases of ‘Z’-cut prints (Figure
5.9(a)); and (iii) minutiae in a well-defined ridge area may not belong to the fingerprint of
interest if a portion of skin on the fingertip was transplanted from other parts of the body
(e.g., palm or sole) (Figure 5.9(b)).
The matching phase can be divided into two parts: (i) altered fingerprint restoration
and (ii) altered fingerprint matching. Among altered fingerprint types, ‘Z’-cut cases are of
special interest since the original ridge structure of the finger is still retained in the finger,
but in different positions. Once the ‘Z’-cut prints are detected, the ridge structure in the
triangular patches can be restored by reversing the transposing procedure. The restored ‘Z’cut fingerprint and all other altered fingerprints are submitted to a special matcher which is
robust to a large amount of skin distortion and utilizes local minutiae information.
We investigate the feasibility of a state-of-the-art commercial fingerprint matcher to link
altered fingerprints to their pre-altered mates [141] by (i) refining the minutiae that are
automatically extracted by the matcher and (ii) restoring the altered region in the ‘Z’ shaped
cut by swapping two triangular skin patches with each other.

5.4.1

Restoration of Altered Fingerprints

Minutiae distribution in altered fingerprints is significantly affected by severe skin distortion
introduced during the process of alteration. Restoration of altered fingerprints attempts to
relocate the minutiae to their original positions by undoing the alteration process, so that
skin distortion can be relaxed. However, this is a very challenging problem because (i) each
157

x1

x
ˆ
xc

X

x
ˆ

x
ˆ

x
ˆ

Xr

Xs

X∗

xn
x
ˆ∗

(a)

x
ˆ∗

(b)

x
ˆ∗

(c)

x
ˆ∗

(d)

Figure 5.22: Transformation of a skin patch in ‘Z’-cut fingerprint. (a) Points on a boundary
(X) including a vertex (ˆ
x) and a new position of the vertex (ˆ
x∗ ), (b) rigid transformation of
X (Xr ), (c) scaling of X (Xs ), and (d) weighted sum of Xr and Xs (X∗ ).
application of ‘Z’-cut alteration leads to a different outcome in ridge pattern, and (ii) the
alteration process often discards a portion of the fingerprint.
The following procedure is proposed to restore ‘Z’-cut fingerprints:
1. Mark the edges of each skin patch along the scars and determine a vertex of each
patch, x
ˆ in Figure 5.22(a), and its new position, x
ˆ∗ in Figure 5.22(a), to define the
rigid transformation of the skin patch (Figure 5.23(b)). One edge of the triangular
region is opened and connected to the rest of the fingerprint.
2. Normalize each skin patch to make the boundaries of skin patches flat (Figure 5.23(c)).
3. Swap the two skin patches based on the thin-plate spline (TPS) model [35] (Figure
5.23(d)).
Normalizing and switching a skin patch follow a nonrigid transformation due to skin
elasticity. The skin distortion is modeled by TPS for smooth transition of skin. The boundary
of a skin patch is represented by a set of control points, X; two ending points of the boundary
are denoted as x1 and xn , and one of the points in X is selected as a vertex, x
ˆ (see Figure
5.22(a)). Correspondences in the TPS model are built by combining rigid transformation
for rotation and translation with nonlinear scaling along two edges while preserving the
158

following constraints: (i) the vertex point, x
ˆ, is mapped to a new vertex position, x
ˆ∗ ; and
(ii) the opened edge to the unaltered region stays in the same position.
The first constraint gives rigid transformation parameters (i.e., rotation matrix R and
translation vector t in Equation (5.9)). For each point x in X, the rigid transformation is
applied as follows:
xr = R(x − xc ) + xc + t,

(5.9)

where R is the rotation matrix with angle θ,

θ = tan−1

yˆ∗
xˆ∗

− tan−1

yˆ
,
xˆ

(5.10)

x
ˆ = (ˆ
x, yˆ)T , x
ˆ∗ = (ˆ
x∗ , yˆ∗)T , xc is the center of the rotation defined by the center of two
boundary ending points (x1 and xn ), and t is the translation parameter to relocate the
rotated patch to meet the new vertex, t = x
ˆ∗ − x
ˆr .
Projection of the control points in X onto the new edges determined by x1 x
ˆ∗ and xn x
ˆ∗
gives the scaling factor in smooth transition. For a point x in X,

xs = s(x · e)e,

(5.11)

where s is a scaling parameter defined as the ratio of x1 x
ˆ to x1 x
ˆ∗ for the control points
between x1 and x
ˆ or the ratio of xn x
ˆ to xn x
ˆ∗ for the control points between xn and x
ˆ, and
e is the unit vector directing from an ending point to the new vertex.
These two transformations are combined by their weighted sum:

x∗ = w(|x − x
ˆ|)xr + (1 − w(|x − x
ˆ|))xs ,

(5.12)

where w(r) is a weight function with respect to the distance from the vertex and defined as

w(r) =

1
,
1 + e−ar

159

(5.13)

(a)

(b)

(c)

(d)

(e)

(f)

Figure 5.23: Restoration process. (a) Altered fingerprint image, (b) markups along the edges
of each skin patch, (c) normalization of the boundaries, (d) swapping of two skin patches,
(e) restored fingerprint, and (f) pre-altered fingerprint of (a).
where parameter a determines the slope of the sigmoid function that adjusts the transition
rate between Xr and Xs along an edge.
Now, the TPS deformation model is specified by the correspondences between X and
X∗ , in addition to the constraint that the open edge of a skin patch stays the same. Figure
5.23 shows the restoration procedure of a ‘Z’-cut fingerprint and its pre-altered mate for
comparison.

5.4.2

Matching of Altered Fingerprints

The number of valid minutiae can vary a lot according to the area of valid fingerprint region
(i.e., the fingerprint region is unaltered and located in the ROI). The altered fingerprints in
Figures 5.24(a) and 5.24(b) have very few minutiae that can be useful in matching. In this
160

(a)

(b)

(c)

Figure 5.24: Complete minutiae set automatically extracted by the matcher (red squares)
and minutiae in the valid fingerprint region (red-filled squares). (a) No valid minutiae, (b)
very few minutiae in the valid region, and (c) abundant minutiae present in the valid region.
case, fingerprint matching based on minutiae may not be successful in finding corresponding
mates in the database. On the other hand, fingerprints with large valid area contain a
number of valid minutiae (see Figure 5.24(c)).
Three minutiae sets are evaluated: (i) all the minutiae extracted from the altered fingerprints, (ii) a subset of minutiae obtained from the altered fingerprints by removing spurious
minutiae in the invalid fingerprint region, and (iii) a subset of minutiae obtained from the
restored fingerprint image by removing spurious minutiae in the invalid fingerprint region.
Note that all the minutiae in altered fingerprints are automatically extracted by the matcher,
and then spurious minutiae in the invalid region are masked out.
Matching performance of altered fingerprints is evaluated by the CMC curves. We view
altered fingerprint matching in the same spirit as latent fingerprint matching in the sense
that these are high profile cases where a forensic examiner needs to examine the top N candidates retrieved from the background database. As a fingerprint matcher, Neurotechnology
VeriFinger SDK 6.3 [13] is used to extract minutiae and match fingerprints. The altered
fingerprint database consists of 1,332 pre/post-altered fingerprint pairs from 382 unique fingers; among them, 200 pairs are of ‘Z’-cut type. If multiple pre-altered impressions of a
finger exist, the best quality fingerprint image assessed by NFIQ software [124] is selected as
161

90

Identifiction Rate (%)

85
80
75
70
65
Refined minutiae set: Rank−100
Refined minutiae set: Rank−1
Complete minutiae set: Rank−100
Complete minutiae set: Rank−1

60
55
0

10
20
30
40
Rejection Criterion: Number of Minutiae

50

(a)

Rank−m Identification Rate (%)

85

80

75

70

65

60

Rank−level fusion
Removal of spurious minutiae in invalid region
Complete minutiae set in altered fingerprint

20

40
60
Rank (m)

80

100

(b)
Figure 5.25: Matching performance of altered fingerprints. (a) Rejection criterion (i.e., the
number of valid minutiae in the minutiae set) versus rank-1 and rank-100 identification
rate, and (b) CMC curves at the fingerprint rejection threshold of 20 minutiae in the valid
fingerprint region.

162

Figure 5.26: Example where the altered fingerprint matching is successful with all the minutiae extracted by the matcher. The pre-altered mate is retrieved at rank 1 from the database
with 27,382 fingerprints.
an exemplar fingerprint. To enlarge the exemplar database size, 27,000 fingerprints in NIST
SD14 were added.
A query fingerprint is rejected if the total number of minutiae in the valid fingerprint
region is smaller than a threshold. Figure 5.25(a) shows the rank-1 and rank-100 identification rate with respect to the threshold for fingerprint rejection. The minutiae sets refined
by removing spurious minutiae in the invalid fingerprint region significantly improve the
matching performance compared to the minutiae sets containing all the minutiae from the
altered fingerprints. At the threshold of 20 (i.e., minutiae sets with fewer than 20 minutiae
in the valid region are rejected), the CMC curves for the complete minutiae set from the
altered fingerprints, the refined minutiae set obtained by discarding minutiae in the invalid
region, and their rank-level fusion are shown in Figure 5.25(b). The highest rank method is
used for rank-level fusion.
Fingerprint alteration is not always successful in lowering the genuine match scores.
Furthermore, the severity of the alteration does not predict degradation in matching performance. Figure 5.26 shows an example where the fingerprint alteration appears to be severe
due to the skin transplantation over a large area. However, it can be successfully matched
to its pre-altered mate; the match score with its true mate is sufficiently high to be correctly
163

(a)

(b)

Figure 5.27: Example where removing spurious minutiae in the invalid region improves
the matching performance. (a) Matching with the complete minutiae set in the altered
fingerprint (match score is 9, and the pre-altered mate is retrieved at rank 10,093), and (b)
matching with the refined minutiae set by removing spurious minutiae in the altered region
(match score is 29, and the mate is retrieved at rank 1).

(a)

(b)

Figure 5.28: Example where restoration of the ‘Z’-cut fingerprint improves the matching
performance. (a) Matching result of the altered fingerprint with its pre-altered mate (match
score is 5 and retrieval rank is 12,525), and (b) matching result of the restored image with
the mate (match score is now 51 and retrieval rank is 1).
identified at the top rank.
Removal of spurious minutiae in the altered region can improve the matching performance (see Figure 5.27). In most altered fingerprint matching, it is observed that minutiae
pairing results are globally inconsistent due to a number of spurious minutiae from scars
and mutilated regions. By removing spurious minutiae, the matcher is able to find more
164

Rank−m Identification Rate (%)

95

90

85
Rank−level fusion
Refined minutiae set in restored fingerprint
Complete minutiae set in altered fingerprint

80

20

40
60
Rank (m)

80

100

Figure 5.29: CMC curves for ‘Z’-cut fingerprints at the fingerprint rejection threshold of 20
minutiae in the valid region. While matching with the restored images alone is still challenging, the rank-level fusion of the altered fingerprint matching and the restored fingerprint
matching significantly improves the matching performance.

consistent mates in minutiae pairings, which results in a higher genuine match score.
For ‘Z’-cut prints, the restoration of the distorted skin patches is helpful to improve the
matching performance. Figure 5.28 shows an example where ridge structures of two local
patches are successfully relocated. The restored image of the altered fingerprint shows much
better consistency in minutiae pairing. Further, a significantly larger number of minutiae
contribute to correct matchings. The CMC curves in Figure 5.29 show that the rank-level fusion of the minutiae from an altered fingerprint and the minutiae from its restored fingerprint
helps to improve the overall matching performance.
Altered fingerprint matching fails mainly due to: (i) insufficient number of minutiae in
the unaltered region which leads to rejection from minutiae-based matching, and (ii) a large
amount of skin distortion that changes the structure of the neighboring minutiae (Figure
5.30).
165

(a)

(b)

Figure 5.30: Example where the altered fingerprints cannot be correctly matched with their
true mates using any refined minutiae sets. (a) Refined minutiae set from the altered image
and (b) refined minutiae set from its restored image. Match scores for each pair in (a) and
(b) are 3 and 9, respectively. Due to the large amount of skin distortion, none of these
methods are successful in finding the correct mate within a practical size of the candidate
list.

5.5

Summary

The success of AFIS and their extensive deployment all over the world have prompted some
individuals to take extreme measures to evade identification by altering their fingerprints.
The problem of fingerprint alteration or obfuscation is very different from that of fingerprint
spoofing, where an individual uses a fake fingerprint in order to adopt the identity of another individual. While the problem of spoofing has received substantial attention in the
literature, the problem of obfuscation has not been addressed in the biometric literature,
in spite of numerous documented cases of fingerprint alteration for the purpose of avoiding
identification. Large-scale fingerprint identification systems are facing a growing threat due
to fingerprint alteration since, compared to other biometric modalities (e.g., face and iris),
it is relatively easier to obfuscate or alter fingerprints.
We have introduced the problem of fingerprint alteration and conducted a quantitative analysis of the threat of altered fingerprints to a commercial fingerprint matcher. We
also evaluated the capability of a well-known fingerprint image quality assessment software,
NFIQ, for detecting altered fingerprints. Since the NFIQ has limited capability in distin166

guishing altered fingerprints from natural fingerprints, we developed an algorithm to automatically detect altered fingerprints based on the characteristics of the fingerprint orientation
field and minutiae distribution. The proposed algorithm based on the features extracted from
the orientation field and minutiae satisfies the three essential requirements for an alteration
detection algorithm: (i) fast operational time, (ii) high true positive rate at low false positive rate, and (iii) easy integration into any AFIS. The proposed algorithm and the NFIQ
criterion were tested on a large public domain fingerprint database (NIST SD14) as natural
fingerprints and altered fingerprint databases provided by law enforcement agencies. At a
false positive rate of 0.3%, the proposed algorithm can correctly detect 66.4% of the subjects
with altered fingerprints, while 26.5% of such subjects are detected by the NFIQ algorithm.
Once altered fingerprints are detected, the subject will be sent to a secondary inspection for further investigation and for matching his altered fingerprints against an exemplar
database. We show that some of the altered fingerprints still have sufficient ridge information to be identified even though the severity of the alteration performed to the fingerprint
appears to be large. Given an exemplar fingerprint database consisting of 27,000 images from
NIST SD14 and 382 images from a pre-altered mated fingerprint set, 86% of 1,332 altered fingerprints find their true mates within rank 100 by simply removing spurious minutiae in the
invalid fingerprint region, while the minutiae sets including all the minutiae extracted from
the altered fingerprint achieve a 77% identification rate at rank 100. In addition, restoration of ‘Z’-cut fingerprints can boost the matching performance significantly by fusing the
minutiae sets from the altered fingerprints and their restored versions at rank level.
This study can be further extended along the following directions:
1. Reconstruct altered fingerprints. For some types of altered fingerprints where the ridge
patterns are damaged locally or the ridge structure is still present on the finger but
possibly at a different location, reconstruction is indeed possible.
2. Match altered fingerprints to their pre-altered mates. A matcher specialized for altered
fingerprints can be developed to link them to pre-altered mates in the database, which
167

is robust to skin distortion and that maximally uses local ridge structure in the valid
fingerprint region.
3. Use multi-biometrics [115] to combat the growing threat of individuals evading AFIS.
Federal agencies in the United States have adopted or are planning to adopt multibiometrics in their identity management systems (FBI’s NGI [11] and DoD’s Automated Biometric Identification System (ABIS) [15]). However, other biometric traits
can also be altered successfully. It has been reported that plastic surgery can significantly degrade the performance of face recognition systems [123] and that cataract
surgery can reduce the accuracy of iris recognition systems [114]. To effectively deal
with the problem of evading identification by altering biometric traits, a systematic
study of possible alteration approaches for each major biometric trait is needed.

168

Chapter 6
Conclusions and Future Research
6.1

Conclusions

Friction ridge skin on fingers and palms has been purportedly known to be a unique physical
characteristic of an individual that does not change over time and can be used as a person’s
“seal” or “signature” since ancient times. With the high and growing demand for reliable
person recognition in modern era, fingerprint recognition has become one of the most successful solutions that achieves high recognition accuracy, ease of use, and high throughput.
Fingerprints are now routinely collected not only from apprehended criminals, but also for
the purpose of border crossing, entrance to amusement parks, and accessing laptops and
mobile phones. Fingerprint recognition technology enables authorities to find suspect(s)
involved in a crime and check the background of government job applicants.
Despite the widespread use and success of fingerprint recognition technology, there remain
certain limitations and concerns about fingerprint recognition. This dissertation has made
an attempt to address some of these challenging issues. A summary of our contributions is
listed below.
1. Persistence of fingerprints Although fingerprint pattern is supposedly known to be
permanent during one’s life time and unique to an individual, no statistical study to
169

demonstrate the stability of fingerprint recognition accuracy over time has been reported. Based on a longitudinal fingerprint database collected from repeat offenders
by a law enforcement agency, we have analyzed the genuine match scores obtained
by two state-of-the-art fingerprint matchers. Our analysis based on multilevel statistical models demonstrated the impact of time interval between two fingerprints being
matched on the corresponding genuine match score. While the genuine match score
tends to decrease with increase in the time interval between two different impressions
of the same finger and the subject’s age, our analysis showed that fingerprint quality
is a better predictor (covariate) of the variation in genuine match scores. Furthermore,
an analysis of the binary identification decisions on genuine fingerprint pairs showed
that true acceptance rates of fingerprint matchers tend to be stable even as the time
interval between two fingerprints being compared increases.

2. Fingerprint modeling Fingerprint orientation field models are useful in distinguishing
fingerprints from any other textured pattern, representing the fingerprint orientation
field in a compact form, and estimating the orientation field from noisy or partially
missing fingerprints. We have developed a global orientation field model that captures
the distinctive characteristics of fingerprint ridge flow pattern, namely the number and
type of singular points. The model has been evaluated by testing its capability to filter
out non-fingerprint images in a fingerprint database.

3. Latent fingerprint enhancement The high accuracy of fingerprint recognition is conditioned on the high quality of fingerprint images being compared. However, latent fingerprints, unintentionally left on the surface of an object, often have very poor quality
possibly with severe distortion. NIST evaluations of state-of-the-art latent fingerprint
matchers show a large gap between exemplar fingerprint matching and latent fingerprint matching performances. The latent fingerprint enhancement algorithm that we
have developed not only improves the matching accuracy, but also facilitates manual
170

markup by latent examiners.
4. Fingerprint obfuscation The widespread deployment of AFIS, especially at border
crossings, has prompted some individuals with prior criminal record to purposely alter
or change their fingerprint pattern in order to conceal their true identity. In order to
identify such individuals, it is necessary to develop a method that detects “abnormal”
fingerprint patterns. We have developed a simple and computationally efficient algorithm for this task. An input fingerprint is suspected to have been altered if (i) its
orientation field does not fit well the fingerprint orientation field model, and (ii) its
minutiae distribution deviates from the empirical distribution of normal fingerprints.
Furthermore, we have developed methods to restore and match altered fingerprints in
order to reveal the person’s true identity from the unaltered ridge pattern remained
after fingerprint alteration.

6.2

Future Research

Fingerprint recognition research presented here can be further advanced as follows:
• A statistical analysis of impostor match scores needs to be conducted to determine the
temporal tendency of the impostor match scores and the false acceptance rate of the
fingerprint matchers.
• Fingerprint orientation field modeling should be extended by integrating arch-like
global orientation field in the model and designing a convex objective function for
fast model fitting.
• Latent fingerprint enhancement algorithm can be further improved by utilizing a
fingerprint-specific model in the orientation field estimation.
• Restoration and matching algorithms for altered fingerprints that can handle severe
distortion need to be developed.
171

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