Detection and Rectification of Distorted Fingerprints

Detection and Rectification
of Distorted Fingerprints
Xuanbin Si, Student Member, IEEE, Jianjiang Feng, Member, IEEE,
Jie Zhou, Senior Member, IEEE, and Yuxuan Luo
Abstract—Elastic distortion of fingerprints is one of the major causes for false non-match. While this problem affects all fingerprint
recognition applications, it is especially dangerous in negative recognition applications, such as watchlist and deduplication
applications. In such applications, malicious users may purposely distort their fingerprints to evade identification. In this paper, we
proposed novel algorithms to detect and rectify skin distortion based on a single fingerprint image. Distortion detection is viewed as a
two-class classification problem, for which the registered ridge orientation map and period map of a fingerprint are used as the feature
vector and a SVM classifier is trained to perform the classification task. Distortion rectification (or equivalently distortion field estimation)
is viewed as a regression problem, where the input is a distorted fingerprint and the output is the distortion field. To solve this problem, a
database (called reference database) of various distorted reference fingerprints and corresponding distortion fields is built in the offline
stage, and then in the online stage, the nearest neighbor of the input fingerprint is found in the reference database and the
corresponding distortion field is used to transform the input fingerprint into a normal one. Promising results have been obtained on three
databases containing many distorted fingerprints, namely FVC2004 DB1, Tsinghua Distorted Fingerprint database, and the NIST SD27
latent fingerprint database.
Index Terms—Fingerprint, distortion, registration, nearest neighbor regression, PCA
Ç
1 INTRODUCTION
ALTHOUGH automatic fingerprint recognition technolo-
gies have rapidly advanced during the last forty years,
there still exists several challenging research problems, for
example, recognizing low quality fingerprints [2]. Finger-
print matcher is very sensitive to image quality as observed
in the FVC2006 [3], where the matching accuracy of the
same algorithm varies significantly among different data-
sets due to variation in image quality. The difference
between the accuracies of plain, rolled and latent fingerprint
matching is even larger as observed in technology evalua-
tions conducted by the NIST [4].
The consequence of low quality fingerprints depends on
the type of the fingerprint recognition system. A fingerprint
recognition system can be classified as either a positive or
negative system. In a positive recognition system, such as
physical access control systems, the user is supposed to be
cooperative and wishes to be identified. In a negative recog-
nition system, such as identifying persons in watchlists and
detecting multiple enrollment under different names, the
user of interest (e.g., criminals) is supposed to be uncooper-
ative and does not wish to be identified. In a positive recog-
nition system, low quality will lead to false reject of
legitimate users and thus bring inconvenience. The conse-
quence of low quality for a negative recognition system,
however, is much more serious, since malicious users may
purposely reduce fingerprint quality to prevent fingerprint
system from finding the true identity [6]. In fact, law
enforcement officials have encountered a number of cases
where criminals attempted to avoid identification by dam-
aging or surgically altering their fingerprints [7].
Hence it is especially important for negative fingerprint
recognition systems to detect low quality fingerprints and
improve their quality so that the fingerprint system is not
compromised by malicious users. Degradation of finger-
print quality can be photometric or geometrical. Photomet-
ric degradation can be caused by non-ideal skin conditions,
dirty sensor surface, and complex image background (espe-
cially in latent fingerprints). Geometrical degradation is
mainly caused by skin distortion. Photometric degradation
has been widely studied and a number of quality evaluation
algorithms [8], [9], [10] and enhancement algorithms [11],
[12], [13], [14], [15] have been proposed. On the contrary,
geometrical degradation due to skin distortion has not yet
received sufficient attention, despite of the importance of
this problem. This is the problem this paper attempts to
address. Note that, for a negative fingerprint recognition
system, its security level is as weak as the weakest point.
Thus it is urgent to develop distorted fingerprint (DF) detec-
tion and rectification algorithms to fill the hole.
Elastic distortion is introduced due to the inherent flexi-
bility of fingertips, contact-based fingerprint acquisition
procedure, and a purposely lateral force or torque, etc. Skin
distortion increases the intra-class variations (difference
among fingerprints from the same finger) and thus leads to
false non-matches due to limited capability of existing fin-
gerprint matchers in recognizing severely distorted finger-
prints. In Fig. 1, the left two are normal fingerprints, while
The authors are with the Department of Automation, Tsinghua University,
Beijing 100084, China. E-mail: {sixb13, luoyx12}@mails.tsinghua.edu.cn,
{jfeng, jzhou}@tsinghua.edu.cn.
Manuscript received 25 Jan. 2014; revised 2 July 2014; accepted 28 July 2014;
date of current version 13 Feb. 2015.
Recommended for acceptance by D. Maltoni.
For information on obtaining reprints of this article, please send e-mail to:
reprints@ieee.org, and reference the Digital Object Identifier below.
Digital Object Identifier no. 10.1109/TPAMI.2014.2345403
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 37, NO. 3, MARCH 2015 555
0162-8828 ß 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

the right one contains severe distortion. According to Veri-
Finger 6.2 SDK [5], the match score between the left two is
much higher than the match score between the right two.
This huge difference is due to distortion rather than over-
lapping area. While it is possible to make the matching algo-
rithms tolerate large skin distortion, this will lead to more
false matches and slow down matching speed.
In this paper, novel algorithms are proposed to deal
with the fingerprint distortion problem. See Fig. 2 for the
flowchart of the proposed system. Given an input finger-
print, distortion detection is performed first. If it is deter-
mined to be distorted, distortion rectification is performed
to transform the input fingerprint into a normal one. A dis-
torted fingerprint is analogous to a face with expression,
which affects the matching accuracy of face recognition
systems. Rectifying a distorted fingerprint into a normal
fingerprint is analogous to transforming a face with
expression into a neutral face, which can improve face
recognition performance.
In this paper, distortion detection is viewed as a two-
class classification problem, for which the registered
ridge orientation map and period map of a fingerprint
are used as the feature vector and a SVM classifier is
trained to perform the classification task. Distortion recti-
fication (or equivalently distortion field estimation) is
viewed as a regression problem, where the input is a dis-
torted fingerprint and the output is the distortion field.
To solve this problem, a database of various distorted ref-
erence fingerprints and corresponding distortion fields is
built in the offline stage, and then in the online stage,
the nearest neighbor of the input fingerprint is found in
the database of distorted reference fingerprints and the
corresponding distortion field is used to rectify the input
fingerprint. An important property of the proposed
system is that it does not require any changes to existing
fingerprint sensors and fingerprint acquisition proce-
dures. Such property is important for convenient incorpo-
ration into existing fingerprint recognition systems.
The proposed system has been evaluated on three data-
bases, FVC2004 DB1 whose images are markedly affected
by distortion, Tsinghua distorted fingerprint database
which contains 320 distorted fingerprint video files, and
NIST SD27 latent fingerprint database. Experimental results
demonstrate that the proposed algorithms can improve the
matching accuracy of distorted fingerprints evidently.
The remainder of this paper is organized as follows. In
Section 2, we review the related work. In Section 3, we
explain how to detect distorted fingerprints. In Section 4,
we present the distorted fingerprint rectification algorithm
in details. In Section 5, we give the experiment results. In
Section 6, we summarize the paper and discuss the future
research directions.
2 RELATED WORK
Due to the vital importance of recognizing distorted finger-
prints, researchers have proposed a number of methods
which can be coarsely classified into four categories.
2.1 Distortion Detection Based on Special Hardware
It is desirable to automatically detect distortion during
fingerprint acquisition so that severely distorted finger-
prints can be rejected. Several researchers have proposed
to detect improper force using specially designed hard-
ware [16], [17], [18]. Bolle et al. [16] proposed to detect
excessive force and torque exerted by using a force sen-
sor. They showed that controlled fingerprint acquisition
leads to improved matching performance [17]. Fujii [18]
proposed to detect distortion by detecting deformation of
a transparent film attached to the sensor surface. Dorai
et al. [19] proposed to detect distortion by analyzing the
motion in video of fingerprint.
However, the above methods have the following limita-
tions: (i) they require special force sensors or fingerprint
sensors with video capturing capability; (ii) they cannot
detect distorted fingerprint images in existing fingerprint
databases; and (iii) they cannot detect fingerprints distorted
before pressing on the sensor.
2.2 Distortion-Tolerant Matching
The most popular way to handle distortion is to make the
fingerprint matcher tolerant to distortion [20], [21], [22],
[23], [24], [25]. In other words, they deal with distortion on a
case by case basis, i.e., for every pair of fingerprints to be
Fig. 2. Flowchart of the proposed distortion detection and rectification system.
Fig. 1. Three impressions of the same finger from FVC2004 DB1. The left
two are normal fingerprints, while the right one contains severe distortion.
The match score between the left two according to VeriFinger 6.2 SDK
[5], is much higher than the match score between the right two. This huge
difference is due to distortion rather than overlapping area. As shown by
red and green rectangles, the overlapping area is similar in two cases.
556 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 37, NO. 3, MARCH 2015

compared. For the most widely used minutiae-based finger-
print matching method, the following three types of strate-
gies have been adopted to handle distortion: (i) assume a
global rigid transformation and use a tolerant box of fixed
size [20] or adaptive size [21] to compensate for distortion;
(ii) explicitly model the spatial transformation by thin plate
spline (TPS) model [22]; and (iii) enforce constraint on dis-
tortion locally [24]. Various methods for handling distortion
during matching have also been used in image-based
matcher [23] or skeleton-based matcher [25].
However, allowing larger distortion in matching will
inevitably result in higher false match rate. For example, if
we increased the bounding zone around a minutia, many
non-mated minutiae will have a chance to get paired. In
addition, allowing larger distortion in matching will also
slow down the matching speed.
2.3 Distortion Rectification Based on
Finger-Specific Statistics
Ross et al. [26], [27] learn the deformation pattern from a set
of training images of the same finger and transform the tem-
plate with the average deformation. They show this leads to
higher minutiae matching accuracy.
But this method has the following limitations: (i) acquir-
ing multiple images of the same finger is inconvenient in
some applications and existing fingerprint databases gener-
ally contain only one image per finger; and (ii) even if multi-
ple images per finger are available, it is not necessarily
sufficient to cover various skin distortions.
2.4 Distortion Rectification Based on General
Statistics
Senior and Bolle [28] developed an interesting method to
remove the distortion before matching stage. This method
is based on an assumption that the ridges in a fingerprint
are constantly spaced. So they deal with distortion by
normalizing ridge density in the whole fingerprint into a
fixed value. Since they did not have a distortion detection
algorithm, they apply the distortion rectification algo-
rithm to every fingerprint.
Compared to the other methods reviewed above, Senior
and Bolle method has the following advantages: (i) it does
not require specialized hardware; (ii) it can handle a single
input fingerprint image; and (iii) it does not require a set of
training images of the same finger.
However, ridge density is neither fixed within a finger
nor fixed across fingers. In fact, several researchers have
reported improved matching accuracy due to incorporating
ridge density information into minutiae matchers [29], [30].
Simply normalizing ridge density of all fingerprints will
lose discriminating information in fingerprints and may
improve impostor match scores. Furthermore, without any
constraint on validity of orientation map, this method may
generate fingerprints with fixed ridge period but strange
orientation map. Compare to the first limitation, the second
limitation is even more harmful, since it will reduces genu-
ine match scores. These limitations were not found in [28]
since the algorithm was tested only on a small database con-
sisting of six fingers and finger rotation was not considered.
Our method shares the advantages of Senior and Bolle
method over other methods, meanwhile overcomes some of
its limitations. Our method is based on statistics learnt from
real distorted fingerprints, rather than on the impractical
assumption of uniform ridge period made in [28]. Distortion
due to finger rotation can be handled by our method. In fact,
the proposed method is able to deal with various types of
distortion as long as such distortion type is contained in the
training set. In addition, extensive experiments have been
conducted to validate the proposed method. The current
work is a significant update of our preliminary study in [1],
which detects distortion based on simple hand-crafted fea-
tures and has no rectification functionality.
3 FINGERPRINT DISTORTION DETECTION
Fingerprint distortion detection can be viewed as a two-
class classification problem. We used the registered ridge
orientation map and period map as the feature vector,
which is classified by a SVM classifier. The distortion detec-
tion flowchart is shown in Fig. 3.
Fig. 3. Flowchart of fingerprint distortion detection. Oi represents ridge orientation at the ith sampling grid of registered orientation map, while Pj rep-
resents ridge period at the jth sampling grid of registered period map. l1 and l2 represent the number of sampling points in registered orientation map
and registered period map, respectively.
SI ET AL.: DETECTION AND RECTIFICATION OF DISTORTED FINGERPRINTS 557

3.1 Fingerprint Registration
In order to extract meaningful feature vector, fingerprints
have to be registered in a fixed coordinate system. For this
task, we propose a multi-reference based fingerprint regis-
tration approach. In the following, we describe how the ref-
erence fingerprints are prepared in the offline stage, and
how to register an input fingerprint in the online stage.
3.1.1 Reference Fingerprints
In order to learn statistics of realist fingerprint distortion,
we collected a distorted fingerprint database called Tsing-
hua distorted fingerprint database. A FTIR fingerprint scan-
ner with video capture functionality was used for data
collection. Each participant is asked to press a finger on the
scanner in a normal way, and then distort the finger by
applying a lateral force or a torque and gradually increase
the force.
A total of 320 videos (with a frame rate of 10 FPS) were
obtained from 185 different fingers. Each finger produces
1$10 videos and each video contains only one of ten differ-
ent distortion types as shown in Fig. 4. In every video, the
first frame is the normal fingerprint, and the last frame con-
tains largest distortion. The duration of each video is
around 10 seconds. For training and testing purpose, the
collected database is divided into two parts with
ntrain ¼ 200 videos used as training data and ntest ¼ 120 vid-
eos used as testing data. In each video, only the first frame
(normal fingerprint) and the last frame (distorted finger-
print) are used for training and testing. Note that all finger-
prints have a resolution of 500 ppi.
We use 500 fingerprints as reference fingerprints which
consist of 100 normal fingerprints from FVC2002 DB1_A,
200 pairs of normal and distorted fingerprints from the
training set of Tsinghua DF database. Note that there are no
common fingerprints between training and testing data. A
large number of references are used in order to properly
register fingerprints of various pattern types, while dis-
torted fingerprints are also used as references in order that
new distorted fingerprints can be properly registered.
A reference fingerprint is registered based on its finger
center and direction. For fingerprints whose core points
can be correctly detected by a Poincare index based algo-
rithm [31], the upper core point is used as the finger cen-
ter. For arch fingerprints and those fingerprints whose
upper core points are not correctly detected, we manu-
ally estimate the center point. Finger direction is defined
to be vertical to finger joint and was manually marked
for all reference fingerprints. Since the reference finger-
prints were registered in the offline stage, manual inter-
vention is acceptable. Fig. 5 shows the finger center and
direction for two reference fingerprints.
3.1.2 Online Fingerprint Registration
In the online stage, given an input fingerprint, we perform
the registration w.r.t. registered reference fingerprints.
Level 1 features (orientation map, singular points, period
map) are extracted using traditional algorithms [11], [31].
According to whether the upper core point is detected or
not, the registration approach can be classified into two
cases.
If the upper core point is not detected, we do a full search
to find the pose information, namely solve the following
optimization formula:
arg max
x;y;a;i
kOrientDiffðROROiðx; y; aÞ; OOÞ utk0; (1)
where x and y denote the translation parameters, a denotes
the rotation parameter, i denotes the corresponding refer-
ence fingerprint ID, OO is the orientation map of the input
fingerprint, ROROi denotes the orientation map of the ith refer-
ence fingerprint, function OrientDiffðÞ computes the differ-
ence of two orientation maps at each location, k Á k0 counts
the number of nonzero elements, and ut is the threshold,
which is empirically set as 10 degrees. Note that the ridge
orientation map is defined on blocks of 16 Â 16 pixels.
Fig. 4. Examples of 10 distortion types in Tsinghua DF database. The blue arrows represent the directions of force or torque, and red grids represent
the distortion grids which are calculated from matched minutiae between the normal fingerprint and the distorted fingerprint.
Fig. 5. The center (indicated by red circle) and direction (indicated by red
arrow) of two fingerprints.

If the upper core point is detected in the input finger-
print, we align the upper core point to the center point of
reference fingerprints. Namely, ðx; yÞ is known. We find the
optimal rotation parameter for Eq. (1).
Finally, we register the ridge orientation map and period
map of the input fingerprint to the fixed coordinate system
by using the obtained pose information. The flowchart in
Fig. 3 shows an example of registration.
3.2 Feature Vector Extraction
We extract a feature vector by sampling registered orienta-
tion map and period map. The sampling grid is shown in
Fig. 3, where finger center is also marked. Note that the two
sampling grids are different. The sampling grid of period
map covers the whole fingerprint, while the sampling grid
of orientation map covers only the top part of the finger-
print. This is because the orientation maps below finger cen-
ter are very diverse even within normal fingerprints. See
Fig. 6 for examples. So they are not good features for distin-
guish distorted fingerprints from normal fingerprints.
The feature vector is defined as ½sinð2OOÞ cosð2OOÞPPŠ, where
OO denotes the orientation vector on sampling grids, and PP
denotes the period vector on sampling grids. Feature value
at sampling points outside fingerprint region is set as 0.
3.3 Classification
The 500 reference fingerprints that we mentioned in Section
3.1, were used as training samples. Distorted fingerprints
are viewed as positive samples while normal fingerprints
are viewed as negative samples. LibSVM [32] was used to
train a Support Vector Classifier with quadratic polynomial
kernel. All parameters used in LibSVM are default ones.
Specifically, SVM type is C-SVC, g in kernel function is 1=L
(L is the length of feature vector), and coef0 in kernel
function is 0.
4 DISTORTED FINGERPRINT RECTIFICATION
A distorted fingerprint can be thought of being generated
by applying an unknown distortion field dd to the normal fin-
gerprint, which is also unknown. If we can estimate the dis-
tortion field dd from the given distorted fingerprint, we can
easily rectify it into the normal fingerprint by applying the
inverse of dd. So we need to address a regression problem,
which is quite difficult because of the high dimensionality
of the distortion field (even if we use a block-wise distortion
field). In this paper, a nearest neighbor regression approach
is used for this task.
The proposed distorted fingerprint rectification algo-
rithm consists of an offline stage and an online stage. In the
offline stage, a database of distorted reference fingerprints
is generated by transforming several normal reference fin-
gerprints with various distortion fields sampled from the
statistical model of distortion fields. In the online stage,
given a distorted input fingerprint (which is detected by the
algorithm described in Section 3), we retrieval its nearest
neighbor in the distorted reference fingerprint database and
then use the inverse of the corresponding distortion field to
rectify the distorted input fingerprint. The distorted finger-
print rectification flowchart is shown in Fig. 7.
In the first two sections, we describe the two steps of the
offline stage: statistical modeling of distortion fields and
generation of distorted reference fingerprint database. In
Section 4.3, we explain how to estimate the distortion field
of an input fingerprint by nearest neighbor search.
4.1 Statistical Modeling of Distortion Fields
In order to learn statistical fingerprint distortion model,
we need to know the distortion fields (or deformation
fields) between paired fingerprints (the first frame and
the last frame of each video) in the training set. The dis-
tortion field between a pair of fingerprints can be esti-
mated based on the corresponding minutiae of the two
fingerprints. Unfortunately, due to the severe distortion
between paired fingerprints, existing minutiae matchers
cannot find corresponding minutiae reliably. Thus, we
extract minutiae in the first frame using VeriFinger and
perform minutiae tracking in each video. Since the rela-
tive motion between adjacent frames is small, reliable
minutiae correspondences between the first frame and
the last frame can be found by this method.
Given the matching minutiae of a pair of fingerprints, we
estimate the transformation using thin plate spline model
[33]. We define a regular sampling grid on the normal finger-
print and compute the corresponding grid (called distortion
grid) on the distorted fingerprint using the TPS model. Fig. 4
shows the distortion grids on 10 distorted fingerprints.
Let xxN
i and xxD
i denote the coordinate vectors of sam-
pling grids of the ith pair of normal fingerprint and dis-
tortion fingerprint. The distortion field of the ith pair of
fingerprints is given by
ddi ¼ xxD
i À xxN
i : (2)
Given a set of distortion fields fddi; i ¼ 1; . . . ; ntraing, we
use PCA to get a statistical distortion model that captures
the statistical variations of the training distortion fields
[34], [35], [36]. Since all normal fingerprints are registered
using the method in Section 3.1, the distortion fields of all
training fingerprints can be viewed as feature vectors.
From all ntrain distortion field samples, a mean distortion
field, dd ¼
Pntrain
i¼1 ddi=ntrain, is first computed, and then a dif-
ference vector ddi À dd for each ddi is calculated to construct
an overall difference matrix D:
D ¼ ððdd1 À ddÞ; . . . ; ðddntrain
À ddÞÞ: (3)
From this overall difference matrix, we can compute a
covariance matrix
Fig. 6. Orientation maps of three patterns: (a) loop, (b) whorl, and (c)
arch. A fingerprint is separated into two regions by the green separating
lines crossing the center points. The orientation maps above the lines
are similar, while orientation maps below the lines are very different.

CovðDÞ ¼
1
ntrain
DDTT
: (4)
Next, we calculate the eigenvectors feeig and eigenvalues
fig (sorted in decreasing order) of this covariance matrix.
The eigenvalues reflect the energy distribution of the train-
ing distortion fields among eigenvectors, and the eigenvec-
tors with the largest eigenvalues generally cover the
majority of the energy within the training distortion fields.
Therefore, a small number of eigenvectors, serving as basis
functions, can well capture the distribution of training dis-
tortion fields. By using this distortion model, a new distor-
tion field dd can be approximated as
dd % dd þ
Xt
i¼1
ci
ffiffiffiffiffi
i
p
eei; (5)
where fcig are the coefficients on the respective eigenvec-
tors, and t is the number of selected eigenvectors. Fig. 8
shows the first two principal components as distortion grids.
4.2 Generation of Distorted Reference
Fingerprint Database
To generate the database of distorted reference fingerprints,
we use nref ¼ 100 normal fingerprints from FVC2002
DB1_A which are same to what we described in Section 3.1.
Note that, these fingerprints have been registered following
the procedure described in Section 3.1.
The distortion fields are generated by uniformly sam-
pling the subspace spanned by the first two principle com-
ponents. For each basis, 11 points are uniformly sampled in
the interval [À2,2]. See Fig. 9 for an example of generating
distortion fields and applying such distortion fields to a ref-
erence fingerprint to generate corresponding distorted fin-
gerprints. In Fig. 9, for visualization purpose, only one
reference fingerprint (the fingerprint located at the origin of
the coordinate system) is used to generate the database of
distorted reference fingerprints, and for each basis, five
points are sampled. In practice, multiple reference finger-
prints are used to achieve better performance. Also note
Fig. 8. First two principal components of distortion fields from the training
set of Tsinghua DF database.
Fig. 7. Flowchart of distorted fingerprint rectification.

that instead of storing the fingerprint image, we store the
ridge orientation map and period map of each fingerprint in
the reference database.
4.3 Distortion Field Estimation by Nearest
Neighbor Search
Distortion field estimation is equal to finding the nearest
neighbor among all distorted reference fingerprints as
shown in Fig. 9. The similarity is measured based on level 1
features of fingerprint, namely ridge orientation map and
period map. We conjecture that distortion detection and rec-
tification of human experts also relies on these features
instead of minutiae. The similarity computation method is
different depending on whether the upper core point can be
detected in the input fingerprint.
If the upper core point is detected, we translate the input
fingerprint by aligning the upper core point to center point.
Then we do a full search of u in the interval ½À30
; 30
Š for
the maximum similarity. For a specific u, the similarity
between two fingerprints is computed as follows:
s ¼
sO
1 þ sO
2
m
À
wO
1 sO
1 þ wO
2 sO
2
Á
þ
sP
1 þ sP
2
m
À
wP
1 sP
1 þ wP
2 sP
2
Á
; (6)
where m denotes the number of blocks in the overlapping
area, sO
1 and sO
2 denote the number of blocks with similar
orientation above and below the center point, sP
1 and sP
2
denote the number of blocks with similar period above and
below the center point, and the four weights wO
1 , wO
2 , wP
1 ,
wP
2 , are empirically set as 1, 0.5, 1, 1.5, respectively. The
Fig. 9. Estimating the distortion field of an input fingerprint is equal to searching its nearest neighbor in the database of distorted reference finger-
prints. Here, for visualization purpose, only one reference fingerprint (the fingerprint located at the origin of the coordinate system) is used to gener-
ate the database of distorted reference fingerprints. In practice, multiple reference fingerprints are used to achieve better performance.

thresholds for similar orientation and similar period are
empirically set 10 degrees and 1 pixel, respectively.
If no upper core point is detected, we use generalized
Hough transform algorithm [37], [38] to compute the sim-
ilarity between two fingerprints, which is more efficient
than computing Eq. (6) for all possible translation and
rotation parameters.
5 EXPERIMENT
In this section, we first evaluate the proposed distortion
detection algorithm. Then, we evaluate the proposed distor-
tion rectification algorithm by performing matching experi-
ments on three databases. Finally, we discuss the impact of
the number of reference fingerprints on distorted finger-
print rectification. Table 1 provides a summary of the data-
bases used in this study.
5.1 Performance of Distortion Detection
We view distortion detection as a two-class classification
problem. Distorted fingerprints are viewed as positive sam-
ples and normal fingerprints as negative samples. If a dis-
torted fingerprint is classified as a positive sample, a true
positive occurs. If a normal fingerprint is classified as a posi-
tive sample, a false positive occurs. By changing the deci-
sion threshold, we can obtain the receiver operating
characteristic (ROC) curve. Fig. 10 shows the ROC curves of
the proposed algorithm and our previous algorithm [1] on
FVC2004 DB1 and the test set of Tsinghua DF database. The
test set of Tsinghua DF database contains 120 pairs of dis-
torted and normal fingerprints. FVC2004 DB1 contains
TABLE 1
Fingerprint Databases Used in This Study1
Database Description Purpose
FVC2002 DB1_A 100 normal fingerprints reference fingerprints
FVC2004 DB1 880 fingerprints algorithm evaluation
FVC2006 DB2_A 1,680 fingerprints scaled to 500 ppi algorithm evaluation
Tinghua DF 320 fingerprint videos training and algorithm evaluation
NIST SD27 258 pairs of latent rolled fingerprints algorithm evaluation
NIST SD14 27,000 fingerprints background database
1
All fingerprints have a resolution of 500 ppi.
Fig. 10. The Detection ROC curves of our previous algorithm [1] and current algorithm on the (a) FVC2004 DB1 and (b) Tsinghua DF database.
Fig. 11. Three distorted examples. Our previous algorithm [1] fails to
detect their distortion, while the current algorithm can detect their distor-
tion correctly. The red transformation grids estimated by the proposed
algorithm are overlaid on them. The blue numbers show the matching
scores without/with rectification. It shows the importance of detecting
them as distorted fingerprints. First two examples come from FVC2004
DB1, while the last one comes from Tsinghua DF database.
Fig. 12. An example of false negative due to slight distortion. (a) Gallery
fingerprint, (b) query fingerprint, and (c) query fingerprint rectified by the
proposed rectification algorithm. Although this query fingerprint is not
detected as a distorted fingerprint, due to its slight distortion, it can still
be successfully matched with the gallery fingerprint by VeriFinger (the
matching score is as high as 305). If we apply the rectification algorithm
to the query fingerprint, its matching score with the gallery fingerprint is
further improved to 512.

791 normal fingerprints and 89 distorted fingerprints, which
are found by visually examining the images. As we can see
from this figure, the current algorithm performs much bet-
ter. Three distorted examples in Fig. 11 further demonstrate
the superior detection performance of current algorithm
over our previous algorithm.
Although most fingerprints can be correctly classified,
there are some false negatives and false positives. False neg-
atives are mainly because the distortion is slight.
Fortunately, we found that this is not a severe problem since
fingerprint matchers can successfully match slightly dis-
torted fingerprints. Such an example is given in Fig. 12. As
the query fingerprint contains slight distortion, the pro-
posed detection algorithm fails to detect it as distorted one,
but the matching score between the query fingerprint and
the galley fingerprint is 305, a very high matching score
according to VeriFinger. If this query fingerprint is rectified
by the proposed rectification algorithm, the matching score
can be further improved to 512.
False positives are mainly due to low image quality,
small finger area, or non-frontal pose of finger. In such
cases, there is no sufficient information for correctly align-
ing and classifying the fingerprint. Such an example is
Fig. 13. An example of false positive due to low quality and small area.
(a) Gallery fingerprint, (b) query fingerprint, and (c) query fingerprint rec-
tified by the proposed rectification algorithm. The matching scores are
overlaid on the images.
TABLE 2
Statistics of Detection Error
Database False negatives (#Error/#Total) False positives (#Error/#Total)
Slight distortion Low quality Small area Non-frontal pose
FVC 2004 DB1 9/89 26/791 16/791 6/791
Tsinghua DF 7/120 5/120 0/120 8/120
Fig. 14. The ROC curves of three fingerprint matching experiments on each of the following four databases: (a) FVC2004 DB1, (b) distorted subset of
FVC2004 DB1, (c) Tsinghua DF database, and (d) FVC2006 DB2_A. The input images to VeriFinger in three matching experiments are original fin-
gerprints (no rectification is performed), fingerprints rectified by Senior and Bolle approach [28], and fingerprints rectified by the proposed approach,
respectively.

shown in Fig. 13. Applying rectification to normal finger-
prints may reduce matching scores.
We have examined all detection errors on FVC 2004 DB1
and Tsinghua DF database and have categorized the rea-
sons into four types. The results are shown in Table 2. Note
that this classification is not exclusive and one example
might be attributed to multiple reasons (such as both low
quality and small area).
5.2 Performance of Distortion Rectification
The final purpose of rectifying distorted fingerprints is to
improve matching performance. To quantitatively evaluate
the contribution of the proposed rectification algorithm to
the matching accuracy, we conducted three matching
experiments on each of the following four databases:
FVC2004 DB1, distorted subset of FVC2004 DB1, Tsinghua
DF database, and FVC2006 DB2_A. VeriFinger 6.2 SDK was
used as the fingerprint matcher. The input images to Veri-
Finger in the three experiments are original fingerprints,
rectified fingerprints by Senior and Bolle approach, and rec-
tified fingerprints by the proposed algorithms, respectively.
No impostor matches were conducted because the matching
score of VeriFinger is linked to the false accept rate (FAR).
FVC2006 DB2_A was used to examine whether distortion
rectification may have negative impact on matching
accuracy in situations where distorted fingerprints are
absent or scarce. The distorted subset of FVC2004 DB1 con-
sists of 89 distorted fingerprints and mated normal finger-
prints. It was separately tested in order to clearly evaluate
the contribution of distortion rectification to matching dis-
torted fingerprints alone.
The ROC curves on the four databases are shown in
Fig. 14. From Fig. 14, we can clearly see that:
1) On all the four databases, Senior and Bolle algorithm
actually reduces the matching accuracy;
2) On the databases containing many distorted finger-
prints (FVC2004 DB1 and Tsinghua DF database),
the proposed algorithm significantly improves the
matching accuracy;
3) On the database without severely distorted finger-
prints (FVC2006 DB2_A), the proposed algorithm
has no negative impact.
Five examples from FVC2004 DB1 and Tsinghua DF
database are given in Fig. 15 to compare the rectified results
and matching performance of the three cases (no rectifica-
tion, rectified by Senior and Bolle approach, and rectified by
the proposed approach).
In order to further evaluate the proposed rectification
algorithm, we conducted a matching experiment on NIST
Fig. 15. Genuine match scores of original query fingerprints and query fingerprints rectified by two different approaches for five examples (left three
from FVC2004 DB1, right two from Tsinghua DF database). The red transformation grids estimated by the proposed approach are overlaid on the
original query fingerprints to visualize the distortion. We can see that the distortion between query fingerprints and gallery fingerprints is greatly
reduced by the proposed approach, leading to higher matching scores.

SD27 latent database which contains some distorted latent
fingerprints. VeriFinger was used as the fingerprint matcher.
The cumulative match characteristic (CMC) curve is com-
monly used to report latent matching accuracy. To make the
experiment more realistic, we use all 27,000 file fingerprints
in the NIST SD14 database as the background database. Due
to the complex background of latent fingerprints, the ridge
orientation map and period map extracted from the original
image are not reliable. So we use the features extracted from
the enhanced fingerprints by the algorithm in [15] instead.
Because of the small area of many latents, the distortion
detection result is not reliable. Thus we apply the recti-
fication algorithm to all latent fingerprints. Then we use
a max rule to fuse the two matching scores: one from
original fingerprint and the other from rectified fingerprint.
The CMC curves on NIST SD27 shown in Fig. 16 correspond
to the following three cases: no rectification, latent finger-
prints rectified by Senior and Bolle approach, and latent
Fig. 16. The CMC curves of three matching experiments on NIST SD27:
Original latent fingerprints (no rectification), latent fingerprints rectified
by Senior and Bolle approach [28], and latent fingerprints rectified by the
proposed approach.
Fig. 17. Genuine match scores and ranks of original latent fingerprints and latent fingerprints rectified by two different approaches for five examples
from NIST SD27. The red transformation grids estimated by the proposed approach are overlaid on the original latent fingerprints to visualize the dis-
tortion. The proposed approach significantly improves the rank of corresponding rolled fingerprints.
Fig. 18. Two examples of unsuccessful rectification due to non-frontal
pose and low image quality. (a) Query fingerprint with non-frontal pose,
and (b) and (a) rectified by the proposed algorithm; (c) query fingerprint
in NIST SD27 with low image quality, and (d) and (c) rectified by the pro-
posed algorithm. The matching scores with corresponding gallery finger-
prints are overlaid.

fingerprints rectified by the proposed approach. From
Fig. 16, we can see that both rectification algorithms can
improve the recognition rate and the proposed algorithm
performs better. Senior and Bolle approach also helps
improve matching accuracy here because of the max fusion
rule. Five examples from NIST SD27 are given in Fig. 17 to
compare the rectified results by two algorithms.
Although the genuine match scores of most distorted fin-
gerprints are improved after rectification, there are some
examples whose matching scores dropped after rectifica-
tion. Unsuccessful rectification can be classified into two
categories: (1) a normal fingerprint is incorrectly detected as
a distorted one and then undergoes the rectification process,
and (2) the rectification for a distorted fingerprint is incor-
rect. False positive of distortion detection is discussed in
Section 5.1. The main causes for unsuccessfully rectified dis-
torted fingerprints are non-frontal pose of finger, low image
quality and small area. In these cases, there is no sufficient
information for correctly estimating the distortion field.
Such two examples are given in Fig. 18.
We have examined all the matching pairs with reduced
scores on the distorted subset of FVC 2004 DB1 and Tsing-
hua DF database and has categorized the cause of error. The
results are shown in Table 3. For a matching pair, if the nor-
mal fingerprint is a false positive, the cause is set as false
positive; otherwise, the distorted one is analyzed and the
cause is set as low image quality, small finger area, and/or
non-frontal pose of finger.
5.3 Impact of the Number of Reference Fingerprints
The number of reference fingerprints used in distortion rec-
tification is an important parameter. Fig. 19 shows the
impact of the number of reference fingerprints on matching
accuracy on FVC2004 DB1. As we can see from this figure, a
larger number of reference fingerprints lead to higher
matching accuracy. But a larger number of reference finger-
prints also mean longer process time. In the experiments
described in Section 5.2, we use 100 reference fingerprints to
generate 12,100 distorted reference fingerprints. The aver-
age times of the proposed distortion detection and rectifica-
tion algorithm on a PC with 2.50 GHz CPU are reported in
Table 4. The percentages of fingerprints with/without cen-
ter point are also reported in Table 4.
6 CONCLUSION
False non-match rates of fingerprint matchers are very high
in the case of severely distorted fingerprints. This generates
a security hole in automatic fingerprint recognition systems
which can be utilized by criminals and terrorists. For this
reason, it is necessary to develop a fingerprint distortion
detection and rectification algorithms to fill the hole.
This paper described a novel distorted fingerprint detec-
tion and rectification algorithm. For distortion detection, the
registered ridge orientation map and period map of a fin-
gerprint are used as the feature vector and a SVM classifier
is trained to classify the input fingerprint as distorted or
normal. For distortion rectification (or equivalently distor-
tion field estimation), a nearest neighbor regression
approach is used to predict the distortion field from the
input distorted fingerprint and then the inverse of the dis-
tortion field is used to transform the distorted fingerprint
into a normal one. The experimental results on FVC2004
DB1, Tsinghua DF database, and NIST SD27 database
showed that the proposed algorithm can improve recogni-
tion rate of distorted fingerprints evidently.
TABLE 3
Statistics of Rectification Error
Database Normal fingerprints (#Error/#Total) Distorted fingerprints (#Error/#Total)
False positive Low quality Small area Non-frontal pose
Distorted subset of FVC 2004 DB1 0/89 7/89 5/89 0/89
Tsinghua DF 10/120 4/120 0/120 5/120
Fig. 19. The impact of the number of reference fingerprints on matching
accuracy on the whole FVC2004 DB1.
TABLE 4
Speed of the Proposed Distortion Detection and Rectification Algorithms
Algorithm FVC2004 DB1 Tsinghua DF NIST SD27
Time (sec) Percentage Time (sec) Percentage Time (sec) Percentage
Detection with center point 1.2 89.43% 1.4 96.25% - -
Detection without center point 15.3 10.57% 16.8 3.75% - -
Rectification with center point 63.9 86.07% 64.6 97.62% 65.3 75.97%
Rectification without center point 67.1 13.93% 66.3 2.38% 67.5 24.03%

A major limitation of the current approach is efficiency.
Both detection and rectification steps can be significantly
speeded up if a robust and accurate fingerprint registration
algorithm can be developed. Another limitation is that the
current approach does not support rolled fingerprints. It is
difficult to collect many rolled fingerprints with various dis-
tortion types and meanwhile obtain accurate distortion
fields for learning statistical distortion model. It is our ongo-
ing work to address the above limitations.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science
Foundation of China under Grants 61225008, 61373074, and
61020106004, the National Basic Research Program of China
under Grant 2014CB349304, the Ministry of Education of
China under Grant 20120002110033, and the Tsinghua Uni-
versity Initiative Scientific Research Program.
REFERENCES
[1] X. Si, J. Feng, and J. Zhou, “Detecting fingerprint distortion from a
single image,” in Proc. IEEE Int. Workshop Inf. Forensics Security,
2012, pp. 1–6.
[2] D. Maltoni, D. Maio, A. K. Jain, and S. Prabhakar, Handbook of Fin-
gerprint Recognition, 2nd ed. Berlin, Germany: Springer-Verlag,
2009.
[3] FVC2006: The fourth international fingerprint verification competi-
tion. (2006). [Online]. Available: http://bias.csr.unibo.it/fvc2006/
[4] V. N. Dvornychenko, and M. D. Garris, “Summary of NIST latent
fingerprint testing workshop,” Nat. Inst. Standards Technol., Gai-
thersburg, MD, USA, Tech. Rep. NISTIR 7377, Nov. 2006.
[5] Neurotechnology Inc., VeriFinger. (2009). [Online]. Available:
http://www.neurotechnology.com
[6] L. M. Wein and M. Baveja, “Using fingerprint image quality to
improve the identification performance of the U.S. visitor and
immigrant status indicator technology program,” Proc. Nat. Acad.
Sci. USA, vol. 102, no. 21, pp. 7772–7775, 2005.
[7] S. Yoon, J. Feng, and A. K. Jain, “Altered fingerprints: Analysis
and detection,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 34,
no. 3, pp. 451–464, Mar. 2012.
[8] E. Tabassi, C. Wilson, and C. Watson, “Fingerprint image qual-
ity,” Nat. Inst. Standards Technol., Gaithersburg, MD, USA, Tech.
Rep. NISTIR 7151, Aug. 2004.
[9] F. Alonso-Fernandez, J. Fierrez-Aguilar, J. Ortega-Garcia, J. Gon-
zalez-Rodriguez, H. Fronthaler, K. Kollreider, and J. Big€un, “A
comparative study of fingerprint image-quality estimation meth-
ods,” IEEE Trans. Inf. Forensics Security, vol. 2, no. 4, pp. 734–743,
Dec. 2007.
[10] J. Fierrez-Aguilar, Y. Chen, J. Ortega-Garcia, and A. K. Jain,
“Incorporating image quality in multi-algorithm fingerprint ver-
ification,” in Proc. Int. Conf. Biometrics, 2006, pp. 213–220.
[11] L. Hong, Y. Wan, and A. K. Jain, “Fingerprint image enhance-
ment: Algorithm and performance evaluation,” IEEE Trans. Pat-
tern Anal. Mach. Intell., vol. 20, no. 8, pp. 777–789, Aug. 1998.
[12] S. Chikkerur, A. N. Cartwright, and V. Govindaraju, “Fingerprint
enhancement using STFT analysis,” Pattern Recognit., vol. 40,
no. 1, pp. 198–211, 2007.
[13] F. Turroni, R. Cappelli, and D. Maltoni, “Fingerprint enhancement
using contextual iterative filtering,” in Proc. Int. Conf. Biometrics,
2012, pp. 152–157.
[14] J. Feng, J. Zhou, and A. K. Jain, “Orientation field estimation for
latent fingerprint enhancement,” IEEE Trans. Pattern Anal. Mach.
Intell., vol. 35, no. 4, pp. 925–940, Apr. 2013.
[15] X. Yang, J. Feng, and J. Zhou, “Localized dictionaries based orien-
tation field estimation for latent fingerprints,” IEEE Trans. Pattern
Anal. Mach. Intell., vol. 36, no. 5, pp. 955–969, May 2014.
[16] R. M. Bolle, R. S. Germain, R. L. Garwin, J. L. Levine, S. U. Pan-
kanti, N. K. Ratha, and M. A. Schappert, “System and method for
distortion control in live-scan inkless fingerprint images,” U.S.
Patent No. 6 064 753, May 16, 2000.
[17] N. Ratha and R. Bolle, “Effect of controlled image acquisition on
fingerprint matching,” in Int. Conf. Pattern Recognit., 1998, vol. 2,
pp. 1659–1661.
[18] Y. Fujii, “Detection of fingerprint distortion by deformation of
elastic film or displacement of transparent board,” U.S. Patent
No. 7 660 447, Feb. 9, 2010.
[19] C. Dorai, N. K. Ratha, and R. M. Bolle, “Dynamic behavior analy-
sis in compressed fingerprint videos,” IEEE Trans. Circuits Syst.
Video Technol., vol. 14, no. 1, pp. 58–73, Jan. 2004.
[20] N. K. Ratha, K. Karu, S. Chen, and A. K. Jain, “A real-time match-
ing system for large fingerprint databases,” IEEE Trans. Pattern
Anal. Mach. Intell., vol. 18, no. 8, pp. 799–813, Aug. 1996.
[21] X. Chen, J. Tian, and X. Yang, “A new algorithm for distorted fin-
gerprints matching based on normalized fuzzy similarity meas-
ure,” IEEE Trans. Image Process., vol. 15, no. 3, pp. 767–776, Mar.
2006.
[22] A. M. Bazen, and S. H. Gerez, “Fingerprint matching by thin-plate
spline modelling of elastic deformations,” Pattern Recognit.,
vol. 36, no. 8, pp. 1859–1867, Aug. 2003.
[23] L. R. Thebaud, “Systems and methods with identity verification
by comparison and interpretation of skin patterns such as finger-
prints,” U.S. Patent No. 5 909 501, Jun. 1, 1999.
[24] Z. M. Kovacs-Vajna, “A fingerprint verification system based on
triangular matching and dynamic time warping,” IEEE Trans. Pat-
tern Anal. Mach. Intell., vol. 22, no. 11, pp. 1266–1276, Nov. 2000.
[25] J. Feng, Z. Ouyang, and A. Cai, “Fingerprint matching using
ridges,” Pattern Recognit., vol. 39, no. 11, pp. 2131–2140, 2006.
[26] A. Ross, S. C. Dass, and A. K. Jain, “A deformable model for fin-
gerprint matching,” Pattern Recognit., vol. 38, no. 1, pp. 95–103,
2005.
[27] A. Ross, S. C. Dass, and A. K. Jain, “Fingerprint warping using
ridge curve correspondences,” IEEE Trans. Pattern Anal. Mach.
Intell., vol. 28, no. 1, pp. 19–30, Jan. 2006.
[28] A. Senior, and R. Bolle, “Improved fingerprint matching by distor-
tion removal,” IEICE Trans. Inf. Syst., vol. 84, no. 7, pp. 825–831,
Jul. 2001.
[29] D. Wan, and J. Zhou, “Fingerprint recognition using model-based
density map,” IEEE Trans. Image Process., vol. 15, no. 6, pp. 1690–
1696, Jun. 2006.
[30] J. Feng, “Combining minutiae descriptors for fingerprint
matching,” Pattern Recognit., vol. 41, no. 1, pp. 342–352, 2008.
[31] A. M. Bazen, and S. H. Gerez, “Systematic methods for the com-
putation of the directional fields and singular points of finger-
prints,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 24, no. 7,
pp. 905–919, Jul. 2002.
[32] C.-C. Chang, and C.-J. Lin, “LIBSVB: A Library for support vector
machines,” ACM Trans. Intell. Syst. Technol., vol. 2, pp. 27:1–27:27,
2011.
[33] F. L. Bookstein, “Principal warps: Thin plate splines and the
decomposition of deformations,” IEEE Trans. Pattern Anal. Mach.
Intell., vol. 11, no. 6, pp. 567–585, Jun. 1989.
[34] S. Novikov and O. Ushmaev, “Principal deformations of finger-
prints,” in Audio and Video Based Biometric Person Authentication.
Berlin, Germany: Springer-Verlag, 2005, pp. 250–259.
[35] D. Rueckert, A. F. Frangi, and J. A. Schnabel, “Automatic con-
struction of 3-D statistical deformation models of the brain using
nonrigid registration,” IEEE Trans. Med. Imag., vol. 22, no. 8,
pp. 1014–1025, Aug. 2003.
[36] S. Tang, Y. Fan, G. Wu, M. Kim, and D. Shen, “RABBIT: Rapid
alignment of brains by building intermediate templates,” Neuro-
image, vol. 47, no. 4, pp. 1277–1287, 2009.
[37] D. H. Ballard, “Generalizing the Hough transform to detect arbi-
trary shapes,” Pattern Recognit., vol. 13, no. 2, pp. 111–122, 1981.
[38] J. Dai, J. Feng, and J. Zhou, “Robust and efficient ridge-based
palmprint matching,” IEEE Trans. Pattern Anal. Mach. Intell.,
vol. 34, no. 8, pp. 1618–1632, Aug. 2012.

Xuanbin Si received the BS degree from the
Department of Automation, Tsinghua University,
Beijing, China, in 2010. Since 2010, he has been
working toward the PhD degree in the Depart-
ment of Automation, Tsinghua University. His
research interests include fingerprint recognition,
palmprint recognition, and computer vision. He is
a student member of the IEEE.
Jianjiang Feng (M’10) received the BS and PhD
degrees from the School of Telecommunication
Engineering, Beijing University of Posts and Tele-
communications, China, in 2000 and 2007,
respectively. He is currently an associate profes-
sor in the Department of Automation at Tsinghua
University, Beijing. From 2008 to 2009, he was a
postdoctoral researcher in the PRIP Lab at Michi-
gan State University. He is an associate editor of
Image and Vision Computing. His research inter-
ests include fingerprint recognition and computer
vision. He is a member of the IEEE.
Jie Zhou (M’01-SM’04) received the BS and MS
degrees both from the Department of Mathemat-
ics, Nankai University, Tianjin, China, in 1990
and 1992, respectively, and the PhD degree from
the Institute of Pattern Recognition and Artificial
Intelligence, Huazhong University of Science and
Technology (HUST), Wuhan, China, in 1995.
From then to 1997, he served as a postdoctoral
fellow in the Department of Automation, Tsinghua
University, Beijing, China. Since 2003, he has
been a full professor in the Department of Auto-
mation, Tsinghua University. His research interests include computer
vision, pattern recognition, and image processing. In recent years, he
has authored more than 100 papers in peer-reviewed journals and con-
ferences. Among them, more than 30 papers have been published in top
journals and conferences such as the IEEE Transactions on Pattern
Analysis and Machine Intelligence, IEEE Transactions on Image Proc-
essing, and CVPR. He is an associate editor for the International Journal
of Robotics and Automation, Acta Automatica, and two other journals.
He received the National Outstanding Youth Foundation of China Award.
He is a senior member of IEEE.
Yuxuan Luo received the BS degree from Tsing-
hua University, Beijing, China, in 2012. He is cur-
rently working toward the MS degree in the
Department of Automation, Tsinghua University.
His research interests include pattern recogni-
tion, computer vision, and machine learning.
For more information on this or any other computing topic,
please visit our Digital Library at www.computer.org/publications/dlib.

Detection and Rectification of Distorted Fingerprints

More Related Content

What's hot (20)

Similar to Detection and Rectification of Distorted Fingerprints (20)

Recently uploaded (20)

Detection and Rectification of Distorted Fingerprints