Fingerprint Verification Based on Statistical Analysis
Mohammed S. Khalil, Dzulkifli Muhammad
Department of Computer Graphics and Multimedia
Universiti Teknologi Malaysia
Muhammad Khurram Khan1, Khaled Alghathbar1,2
1 Center of Excellence in Information Assurance (CoEIA)
King Saud University, Saudi Arabia
2 Information Systems Department, College of Computer &
Information Sciences, King Saud University, Saudi Arabia
email@example.com , firstname.lastname@example.org
Abstract— In this paper, we have statistically analyzed biometric-
fingerprint images for personal identification. A sub-image of 129
x 129 was extracted from the original image and transformed
into a co-occurrence matrix. Four different type of relative
position distances were used to generate the matrices. The results
have been analyzed by the Program for Rate Estimation and
Statistical Summaries (PRESS). The efficiency of the proposed
method has been demonstrated by the experimental results and
that the further the distances of the relative position the lower the
error equal rate.
Keywords-component; Fingerprint; Reliability; Statistical
descriptor; Biometrics; Fingerprint verification; Co-occurrence
Nowadays the need for identifying the human being is
increasing, biometric fingerprints are probably the most widely
used personal identification tool, as they have been used for
many centuries due to their individuality, uniqueness and
reliability. The international biometric group  in their
biometrics market and industry report 2009-2014 indicate that
fingerprint remains the leading on non automatic fingerprint
identification systems (AFIS). Due to the range of
environments in which fingerprint can be deployed, its years of
development, and the strong companies involved in the
technology's manufacture and development, fingerprint
revenues are projected to grow from $198 million in 2003 to
$1.493 billion in 2008. Fingerprint revenues are expected to
comprise approximately 32% of the entire biometric market.
The individuality of fingerprints lies in the high degree of
difficulty in terms of forgery, along with the fact that
fingerprints are unique to each person. In fact, fingerprints
provide an outstanding source of entropy which makes them an
excellent candidate for security applications. Users cannot pass
their fingerprint characteristics to others as easily as they do
with their cards or passwords [2, 3]. The pattern of the valleys
and ridges on human fingertips forms the fingerprint image.
Analyzing this pattern at different levels reveals different types
of global and local features. A global feature normally provides
a special pattern of ridges and valleys including singularities or
Singular Point (SP). However, the important points of the
singularities are core and delta. While the core is usually
defined as a point on the inner most ridges, the delta is known
as the center point where three different flows meet. The SP
provides important information used for fingerprint
classification [4-6], fingerprint matching [7, 8] and fingerprint
alignment [9, 10]. The local feature known as minutiae is
considered important for fingerprint matching.
There are three main methods to extract and match
fingerprint features are: minutiae-based, correlation-based, and
hybrid . Minutiae-based techniques attempt to align two
sets of minutiae points from two fingerprints and count the
total number of matched minutia [12, 13]. Performance of
minutiae-based techniques, however, relies on the accurate
detection of minutiae points as well as the use of sophisticated
matching techniques to compare two minutiae fields that
undergo non-rigid transformations. In the correlation-based
approach, global patterns of ridges and furrows are compared
to determine whether two fingerprints are aligned [14, 15].
Performance of correlation-based techniques is affected by
non-linear distortions and noise present in the image. Finally,
in hybrid methods, local orientation and frequency, ridge
shape, and texture information are used to extract fingerprint
features [7, 16-18]. Meanwhile, the robustness of hybrid
methods is affected by the difficulty of detecting all minutiae.
In addition, the computational requirements are very high.
Recently, Arivazhagan et al.  proposed a fingerprint
verification method using Gabor wavelets and co-occurrence
matrices to obtain a fingercode. Yazdi et al.  also used the
co-occurrence matrices to classify the fingerprint image.
This paper proposes a new method to verify an enhanced
fingerprint image using four statistical descriptors to
characterize a co-occurrence matrix. The steps in this method
includes: enhancing the fingerprint image, detecting the
reference point, making the reference point as the center of the
fingerprint image, extracting a sub-image of 129×129 from the
center point, rotating the sub-image orientation to zero and
finally, analyzing the oriented sub-image texture in order to
extract the feature set. Comparatively, this method has an
advantage over previous methods as it incorporates two
additional techniques; detecting the reference point by using
the fingerprint image orientation reliability and analyzing the
fingerprint image texture based on statistical analysis of the co-
The paper is organized as follows: Section II describes the
proposed method. While sub-section II.A discusses the
fingerprint image enhancement algorithm using the short time
Fourier Transform analysis (STFT), sub-section II.B explains
the procedures for locating the reference point. Furthermore,
978-1-4244-6949-9/10/$26.00 ©2010 IEEE
sub-sections II.C and II.D accordingly address the extraction of
the reference point sub-image & orientation normalization as
well as the feature extraction. Experimental results and
conclusions are discussed in sections III and IV, respectively.
This section describes the proposed method and it is
organized into four main sub sections. Figure 1 shows the
proposed methodology diagram.
Figure 1. Proposed methodology for fingerprint verification
A. Fingerprint Image Enhancement
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of the current designations. High quality fingerprint image is
very important for fingerprint verification to function properly.
In real life, the quality of the fingerprint image is affected by
noise like smudgy area created by over-inked area, breaks in
ridges created by under-inked area, changing the positional
characteristics of fingerprint features due to skin resilient in
nature, dry skin lead to fragmented and low contrast ridges,
wounds may cause ridge discontinuities, and sweat on
fingerprints also leads to smudge marks and connects parallel
ridges. Figure 2 shows original fingerprint images; Figure 3
shows enhanced fingerprint images
Figure 2. Original fingerprint images
Figure 3. Enhanced fingerprint image
The short time Fourier Transform analysis (STFT)
proposed by [21, 22] is applied here for fingerprint image
enhancement, STFT analysis and the enhancement method can
be summarized as follows:
The fingerprint image is divided into overlapping
Stage I: STFT analysis
1. For each overlapping window B(x,y) in the image:
a. Remove the DC component of B, using B=B-
b. Multiply by spectral window w
c. Acquire the FFT of the window F=FFT(B)
d. Execute root filtering on F
e. Execute STFT analysis. The analysis outputs are
Ridge Orientation Image O(x,y), Energy Image
E(x,y), and Ridge Frequency Image F(x,y).
2. Smooth the orientation image O(x,y) using vector
averaging to yield a smooth orientation image O’(x,y),
and using the smooth orientation image O’(x,y) to
generate the coherence image C(x,y).
3. Generate region mask R(x,y) by thresholding the
energy image E(x,y).
Stage II: Enhancement
4. For each overlapping window B(x,y) in the image:
a. Generate the angular filter FA centered on the
orientation in the smooth orientation image
O(x,y) with a bandwidth inversely proportional to
coherence image C(x,y).
b. Generate the radial filter FR centered around the
ridge frequency image F(x,y).
c. Filter the window in the FFT domain,
d. Generate the enhanced window by the inverse
Fourier transform B’(x,y) = IFFT(F).
5. Reconstruct the enhanced image by composing
enhanced blocks B’(x,y).
B. Reference Point Detection
The fingerprint image is made up of pattern of ridges and
valleys; they are the replica of the human fingertips. The
fingerprint image represents a system of oriented texture and
has very rich structural information within the image. This
flow-like pattern forms an orientation field extracted from the
style of valleys and ridges. In the large part of fingerprint
topologies, the orientation field is quite smooth, while in some
areas, the orientation appears in a discontinuous manner. These
regions are called singularity or singular points, including core
and delta, are defined as the centers of those areas. In addition,
the reference point is defined here as the point with maximum
curvature on the convex ridge. The reliability of the orientation
filed describes the consistency of the local orientations in a
neighborhood along the dominant orientation is used to locate
the unique reference point constantly for all types of
fingerprints. The reliability can be also computed using the
coherence as proposed by  and . The implementation is
elaborated on in the following:
1. The orientation image is hardly ever computed at full-
resolution. Instead each non-overlapping block of size W
× W of the image is assigned a single orientation that
corresponds to the most apparent or dominant orientation
of the block. In this proposed method, W is set equal to
2. The horizontal and vertical gradients Gx(x, y) and Gy(x, y)
at each pixel (x,y) respectively are computed using simple
gradient operators such as a Sobel mask . The mask is
set to 3×3.
3. Compute the ridge orientation of each pixel (x,y) by
averaging the squared gradients within a W × W window
centered at [xi,yj] as follows :
4. Because of noise, corrupted ridge, valley structures, and
low gray value contrast, a low-pass filter can be used to
adjust the erroneous local ridge orientation. However, to
perform the low-pass filtering, the orientation image needs
to be converted into a continuous vector field as follows:
where Φx and Φy are the x and y components of the vector
field, respectively. With the resulting vector field, the Gaussian
low-pass filter can be applied as follows:
where W is a two-dimensional low-pass filter with unit
5. Since the singular point has the maximum curvature. It can
be located by measuring the strength of the peak using the
, 2/ )
),,( min_),( max_yxinertiaGGyx inerita
6. After the computation of the orientation field reliability,
the coordinate of the singular points is needed to be known
in terms of x and y values so the following operations are
applied to locate the exact coordinate.
a. The orientation field reliability image contains the
singular points and the rest of the information of the
original fingerprint image as figure 4 shows that. To
locate the candidate areas of the singular points a
threshold 0.5 > t > 0.1 is applied to the orientation
field reliability image from observation the values of
the reliability singular points area are around 0.5 and
b. The image produced by the threshed still has an
undesirable effect of noise and the size of the singular
point contour is more than one pixel. For these
reasons, the width of the structure is reduced to one
c. After applying thinning to the singular point contour,
now it can be reduced to a single point through
applying morphological opening and closing.
In Figure 4 the reference points can be seen clearly.
Figure 4. Reference points in fingerprint images
C. Extracting the Reference Point Sub-Image & Orientation
Fingerprint image does not come in same size. Different
acquisition for the same finger may result in different size or
location of fingerprint image. Since the area near the reference
point contains correct and efficient information about the
fingerprint. Making the reference point as the center, a sub
image of 129 × 129 is extracted from the original fingerprint
image. In addition, this will reduce the computation time and
the storage size. For fingerprint verification two images have to
be compared, for this, it is necessary that the images
themselves are aligned appropriately to ensure an overlap of
the common region in the two fingerprint images. This is done
by rotating the image to zero orientation at the reference point.
This process is performed in order to avoid the time-consuming
translation alignments of previous algorithms. Figure 5 shows
the extracted fingerprint sub-images and its rotation.
Figure 5. Rotated sub-image
D. Feature Extraction
The importance of texture for human visual system
provides information for recognition and interpretation used in
identifying objects or regions of interest in an image. Texture is
a region descriptor that provides a quantifying measure of the
property such as smoothness, coarseness and regularity. The
three main approaches to describe texture are statistical,
structural and spectral. Statistical techniques describe texture
by the statistical properties of the grey levels of the points
comprising a surface such as smooth coarse grains. In general,
these properties are computed from the statistical moments of
the intensity histogram or gray level co-occurrence matrix of an
image or region. To incorporate this type of information into
the texture-analysis process is to consider not only the
distribution of intensities, but also the relative positions of
pixels in an image. The use of co-occurrence matrix produces
this type of information. Structural techniques characterize
texture as being composed of simple “texture primitive”, that
are regularly arranged on a surface according to some rules.
These rules limit the number of possible arrangement of the
primitives. Spectral techniques are based on properties of the
Fourier spectrum and describe the directionality period of the
grey levels of a surface by identifying high-energy peaks in the
The Gray-level co-occurrence matrix (GLCM); it is a
statistical approach that can describe second-order statistics of
a texture image. A GLCM is basically a two-dimensional
histogram in which the (i, j)th element is the frequency that
event i co-occurs with event j. A co-occurrence matrix is
specified by the relative frequencies P(i, j , d, θ) in which two
pixels, separated by distance d, occur in a direction specified
by angle θ, one with gray level i and the other with gray level j.
A co-occurrence matrix is therefore a function of distance r,
angle θ and grayscales i and j .
A single GLCM might not be enough to describe the
textural features of an input fingerprint. For example, a single
horizontal spatial relationship might not be sensitive to texture
with a vertical orientation. For this reason, multiple GLCMs
are computed for values of θ at 0°, 45°, 90°, and 135°. And the
relative distance is one pixel. Based on each computed GLCM,
four features that can successfully characterize the statistical
behavior of a co-occurrence matrix are extracted. They are as
ij Pji Contrastii
y Homogeneit iv
Where mr, mc are means and σr, σc are the standard
deviations computed along the rows and columns respectively,
and Pij is the number of times that pixel occurred.
The proposed algorithm has been evaluated using the
fingerprint datasets Db1_a, Db2_a, Db3_a, and Db4_a from the
public databases of FVC2002 . Each dataset contains 800
fingerprint images from 100 different fingers with 8 images
from each finger; these images were captured using a low-cost
capacitive sensor, which results in many poor-quality images.
Four main experiments have been conducted based on the co-
occurrence relative distance pixels 1, 2, 3 and 4. For each
experiment, the four databases were divided into a training set
and testing set. Six out of eight fingerprints from each person
were chosen for training; the remaining two were set aside for
testing. Therefore, 600 patterns were used for training, and 200
for testing and this was repeated twice by selecting different
fingerprints for training and testing. The results for each
experiment were compound for each finger and analyzed by
the Program for Rate Estimation and Statistical Summaries
(PRESS) . Table I shows the average equal error rate
(EER) for experiment 1, 2, 3 and 4 is 0.45%, 0.37%, 0.34%
and 0.29% respectively. The results indicate clearly that
analyzing the fingerprint texture with moving distance from the
pixel of interest results on low equal error rate. It can be seen
that the difference between one position and four is 0.16.
Table I The average EER (%) for the FVC2002 datasets
Relative pixel 1 2 3 4
EER% 0.45 0.37 0.34 0.29
Figure 6 shows the average ROC graph for experiment 1, 2,
3 and 4.
Figure 6. Average ROC graph for data-sets with respect to the relative
The experimental analysis was performed in MATLAB
7.4.0 and run using a HP Compaq Intel core2 duo CPU E4400
with 2.00GHz and 1.96GB RAM.
This paper proposes a novel method to verify enhanced
fingerprint images using the co-occurrence matrices to
compute four statistical descriptors. In reality, the quality of the
fingerprint images is low, thus for this reason, the short time
Fourier Transform analysis is applied to enhance the images.
Given that the reference point is important for image
alignment; a new reliable method has been introduced, which
uses the fingerprint orientation reliability. The experimental
results were analyzed by the Program for Rate Estimation and
Statistical Summaries (PRESS). The experimental results have
demonstrated that the proposed algorithm exhibits encouraging
performance for verifying the enhanced fingerprint images.
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