Hindawi
International Journal of Mathematics and Mathematical Sciences
Volume 2021, Article ID 5545488, 12 pages
https://doi.org/10.1155/2021/5545488
Research Article
Implementationof aTransform-MinutiaeFusion-BasedModel for
Fingerprint Recognition
Justice Kwame Appati , Prince Kofi Nartey , Ebenezer Owusu ,
and Ismail Wafaa Denwar
Department of Computer Science, University of Ghana, Accra, Ghana
Correspondence should be addressed to Ebenezer Owusu; ebeowusu@ug.edu.gh
Received 27 January 2021; Revised 13 February 2021; Accepted 19 February 2021; Published 4 March 2021
Academic Editor: Chin-Chia Wu
Copyright © 2021 Justice Kwame Appati et al. +is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is
properly cited.
Biometrics consists of scientific methods of using a person’s unique physiological or behavioral traits for electronic identification
and verification.+e traits for biometric identification are fingerprint, voice, face, and palm print recognition. However, this study
considers fingerprint recognition for in-person identification since they are distinctive, reliable, and relatively easy to acquire.
Despite themany works done, the problem of accuracy still persists which perhaps can be attributed to the varying characteristic of
the acquisition devices. +is study seeks to improve the issue recognition accuracy with the proposal of the fusion of a two
transform and minutiae models. In this study, a transform-minutiae fusion-based model for fingerprint recognition is proposed.
+e first transform technique, thus wave atom transform, was used for data smoothing while the second transform, thus wavelet,
was used for feature extraction. +ese features were added to the minutiae features for person recognition. Evaluating the
proposed design on the FVC 2002 dataset showed a relatively better performance compared to existing methods with an accuracy
measure of 100% as to 96.67% and 98.55% of the existing methods.
1. Introduction +ere are several other biometric authentication
techniques. However, this research adopts the fingerprint
Biometrics deals with the technology used for electronic recognition technique as its area of discussion. +e reason
identification and verification of an individual based on for this choice is that fingerprints have recently been
behavioral and physiological characteristics they possess adopted extensively and successfully to aid in proof of
[1]. It focuses on scientific approaches for identifying identity because of their originality, durability through
these individuals uniquely based on these characteristics. history, peculiarity, public acceptance, and the minimal
+ese traits are known to be unique for every person. risk of personal invasion that characterize fingerprint
Some standard biometric identification methods are matching [4]. A fingerprint is the impression of patterns
fingerprint recognition, voice recognition, facial recog- from a finger’s surface [5]. Because fingerprint-based
nition, and signature dynamics. Biometric devices are authentication and identification are distinct for every
conventionally made of a biometric engine. A biometric person and are not significantly distorted with age, it is
engine is a program that operates together with the one of the most common biometric technologies. Aside
biometric systems’ hardware devices. Its purpose is to from being relatively inexpensive to implement, the main
administer biometric data during the capture, extraction, reasons why fingerprint recognition has become the most
and matching process stages [2]. Successful research into widely used biometric authentication approach, averaging
biometric technologies has significantly improved the more than 50 percent of all recognition systems currently
reliability and security of identification, authentication, in use, are factors such as the distinctiveness, reliability,
and verification standards [3]. and relative ease of acquisition [6]. Due to its numerous
2 International Journal of Mathematics and Mathematical Sciences
advantages, a considerable number of researchers’ at- Figure 1. +e technique is known to accurately demonstrate
tention has been drawn to the fingerprint identification both multiscale and multidirectional properties, given an
method in recent years [4]. One of the main benefits is that image data [4]. For a better appreciation of this transform
the legal community acknowledges its use for personal compared with other transforms, two indexes α and β are
identification. +is identification technique is effortless, introduced in the analysis of its scheme [11]. +e parameter
accurate, cheap, and relatively easy to identify [7]. α denotes a multiscale decomposition while β defines the
Moreover, this recognition approach is widely recog- localization of basic elements. From the figure shown, the
nized for its authentication precision and the likelihood that parametric value satisfying a wavelet transform is α � β � 1,
the same fingerprint occurring in two persons is minimal. the Gabor transform is α � β � 0, curvelets are α � 1 and
All said and done, there are other instances where the system β � 1/2, and ridgelets are α � 1 and β � 0. However, the
fails to recognize some fingerprints due to the possibility that wave atom transform demonstrates a trade-off between
the fingerprint reader may lose its sensitivity with time, or a multiscale and multidirectional spaces with α � β � 1/2
user’s fingerprint might be damaged [8]. +ese problems making it a choice that might be useful in this study as a
lend us to two main errors in recognition, thus Type-I and denoising technique.
Type-II errors. When a recognition system rejects an au-
thorized user, a Type-I error or false rejection is expected. In
contrast, the system may accept imposters, leading to an 2.1.2. Image Normalization. +e normalization of the fin-
unauthorized access granted resulting in a Type-II error or gerprint images was necessary in this study to adjust the in-
the occurrence of false acceptance [4]. +ese errors are the tensity of the values [12].Mathematically, the normalization is a
motivations to building a system that properly mitigates linear pixel-wise operator which helps lessen the gray-level
against these two types of errors. Fingerprint distinctiveness variations along the furrows and ridges which are features of
can be attained by analyzing minutiae points, ridge, and interest while achieving an invariant mean and variance. Be-
furrow patterns. Identifying minutiae and patterns are sides, the dataset for the study was captured with varying finger
imperative for recognizing fingerprints because no two pressures and sensor noise effects to exhibit a real industrial
fingerprints are the same [9]. scenario and these effects require normalization to reduce their
Extensive research works on fingerprint recognition sys- prevalence. In its implementation, a window of size w × w is
tems have been carried out, and several approaches and used to enhance the computational time. Given an image
techniques have been proposed, yet the issue of recognition img(i, j), with an estimated Mean Mi and Variance Vi, the
accuracy still exists in fingerprint recognition [4]. Further normalized image N(i, j) can be defined as
research is still ongoing to resolve the accuracy problem,mostly 􏽱����������������⎧⎪ 2
due to mismatch or misclassification of extracted fingerprint ⎨ M0 + V0( img(i, j) − Mi􏼁 , if img(i, j)>M,
N(i, j) � 􏽱����������������
features. +erefore, the features to be extracted for recognition ⎪⎩ 2
must be acceptable to improve accuracy. +e subsequent M0 − V0( img(i, j) − Mi􏼁 , otherwise.
sections of the paper are organized as follows. +e method- (1)
ology is introduced in Section 2. Section 3 discusses experi-
mentation. Section 4 extensively discusses the results recorded. Once the fingerprint image is normalized, the orienta-
Lastly, the work is concluded in Section 5. tion of the ridges and furrows are estimated as outlined in
Section 2.1.3.
2. Research Design
2.1.3. Ridge Orientation Estimation. In order to detect
+is section discusses the fingerprint image preprocessing points of singularity from a given fingerprint image, ridge
and how these fingerprint characteristics are extracted to aid orientations are estimated [13]. +e ridges and furrows
in person recognition. possess unique patterns of flow exhibiting several orienta-
tions that ranges from 0 to 180 degrees denoted by θ(i, j).
2.1. Fingerprint Image Preprocessing. +e preprocessing of Instead of defining a single pixel, the image map is localized
the fingerprint images is imperative in building a successful with a block operator as outlined as follows:
recognition or authentication system. +is section discusses (a) +e input image is divided into nonoverlapping
the various stages of smoothing fingerprint images to help w × w block sizes.
extract relevant features for accurate recognition. +e wave
atom denoising technique was leveraged on for this study for (b) +e image gradients δx and δy for each pixel in the
image smoothing. Image normalization, ridge orientation, block are computed. +is image gradient map can be
and estimation are further performed as outlining the estimated using operators such as Canny and Sobel
subsequent subsections. and among others. Equation (2) is an example of the
Sobel gradient operator:
− 1 0 1 − 1 2 − 1
2.1.1. Wave Atom Transform Technique for Smoothing. ⎢⎢⎡⎢ ⎤⎥⎥ ⎡⎢⎢ ⎤⎥⎥
In numerical analysis and processing of images, a wave atom G ⎢⎢x � ⎢⎢⎣ − 2 0 2
⎥ ⎢
⎥⎥⎥⎥⎦ and Gy � ⎢
⎢
⎣⎢⎢ 0 0 0 ⎥
⎥
⎦⎥
⎥
⎥. (2)
transform is a new technique used for performing multiscale − 1 0 0 1 2 1
transforms proposed by Demanet and Ying [10], as shown in
International Journal of Mathematics and Mathematical Sciences 3
β 2.2. Feature Extraction. +is section describes in detail the
characteristics of fingerprints and how they are extracted for
Wavelets
1 person identification. Broadly features of a fingerprint image
can be grouped into two: global and local.+e global fingerprint
features include delta and core points also known as singular
points, as well as the ridge orientation and spacing [14].
1/2 CurveletsWave atoms 2.2.1. Fingerprint Characterization. According to Maltoni
et al. [15] in their book “Handbook of Fingerprint Rec-
ognition,” there are three basic fingerprint ridge patterns:
0 1/2 1 α the arch, loop, and whorl.
Gabor Ridgelets /e Arch. With this pattern, as depicted in Figure 2, the
Figure 1: Various transforms (α, β) as wave packet families [10]. finger’s ridges emerge from one edge, curve up in the
midsection forming an arc, and then end on the opposite
(c) +e computation of the local field orientation is then edge without rotating centrally. +e arch pattern can be
estimated using classified into four main types [4], that is, plain, radial, ulnar,
and tented arch.
i+(w/2) i+(w/2)
Vx � 􏽘 􏽘 2δx(u, v)δy(u, v), (3) /e Loop. With this pattern, as shown in Figure 3, the ridges
u�i− (w/2) v�i− (w/2) emerge from one edge of the finger, make a curve, and then
/2 /2 end back at the same edge where the ridges initially emerged.i+(w ) i+(w )
2 2
V � 􏽘 􏽘 δ (u, v)δ (u, v). (4) Loops are classified into four types [4]: plain, central pocket,y x y
u�i− (w/2) v�i− (w/2) lateral pocket, and twinned loop patterns.
From these two equations, the orientation field is /e Whorl. With this pattern, as shown in Figure 4, ridges
estimated with are circularly formed in the finger’s midsection. Delta point
1 V
θ y
(i, j)
(i, j) � . (5) formations in these patterns classify them into four types [4]:
2 Vx(i, j) accidental whorl, double-pocket loop whorl, central pocket
(d) At this point, it is expected that some level of noise loop whorl, and plain whorl patterns.
will be introduced leading a point of discontinuity in
the orientation field. +is effect could be minimized 2.2.2. Fingerprint Keypoints. On the other hand, minutiae
or softened using a low-pass filter; however, this points are local characteristics on a fingerprint that exist
process requires that the orientation field be trans- either as a ridge ending or a bifurcation [1]. In brief, the ridge
formed into a continuous vector field as shown in the ending is the termination point of ridges on the fingerprint
following equations: while a ridge bifurcation is a point on the fingerprint where
∅x(i, j) � cos cos (2θ(i, j)), (6) one ridge splits into two different ridges. In general, the
minutiae characteristics of fingerprint as enlisted in +e
∅y(i, j) � sin sin(2θ(i, j)). (7) Guardia Civil Database (GCDB) in Spain, is as shown in
(e) +e low-pass filter can then be applied to the re- Figure 5.
sultant output of equations (6) and (7) as expressed Labels of the minutiae characteristics in Figure 5 are
in tabulated in Table 1.
(h/2) (h/2)
∅′x � 􏽘 􏽘 G(u, v).∅x(i − uw, j − vw), (8)
/2 2.2.3. Minutiae Extraction with Sequential Binarization.u�−(h ) v�−(h/2)
In theory, a sequential approach to binarization is easy and
(h/2) (h/2) effective for extraction of features from the point of view of
∅′ � 􏽘 􏽘 G(u, v).∅ (i − uw, j − vw). (9) design and processing. In general, the following three stepsy y
u�−(h/2) v�−(h/2) consist of a sequential binarization procedure: binarization,
thinning, and minutiae extraction [16].
(f ) Finally, the smoothened orientation field can be
obtained with Binarization.+e original grayscale image is converted into a
θ ′ binary image which presents the image as a 2D gray-level1 1 y(i, j)θ(i, j) � tan− . (10) intensity function f(x, y) with values ranging from 0 to
2 θ ′x(i, j) L − 1, where L denotes all individual gray-levels. Let n denote
the total number of pixels in an image and ni be the number
+is orientation field is now used to identify the fin- of pixels with gray-level i, and the probability that gray-level
gerprint core point which is a keypoint feature. i may occur is defined as
4 International Journal of Mathematics and Mathematical Sciences
n
pi �
i. (11)
n
+e fingerprint image gray-level is averaged with
L− 1
μT � 􏽘 ipi. (12)
i�0
After averaging, the fingerprint image pixels are
classified into two distinct groups: C1 � {0, 1, . . . , t} and
C2 � {t + 1, t + 2, . . . , L − 1} with t as the threshold value.
+e objects of interest in the foreground and background
of a given image correspond to the C1 and C2, respectively.
Equations (13) and (14) are the respective probabilities:
t
ω1(t) � 􏽘 pi, (13)
i�0
Figure 2: +e arch. L− 1
andω2(t) � 􏽘 pi. (14)
i�t+1
+e average gray-level values for C1 and C2 are calcu-
lated, respectively, with the following equations:
t
ip
μ i1(t) � 􏽘 , (15)
0 ω (t)i� 1
L− 1 ip
and μ i2(t) � 􏽘 . (16)ω
i�t+1 2(t)
/inning. After the binarization process is complete, the
thinning process is engaged to reduce the ridge line
thickness to one pixel. +is operation is imperative to allow
for simplification of the resultant image for accurate ex-
traction of features. +e thinning process firstly divides the
image into two separate maps in a checkered arrangement.
In the initial subiteration, pixel p is deleted from the first
Figure 3: +e loop. image map if the G1, G2, and G3 conditions are met while
pixel p is deleted from the second image map if the G1, G2,
and G4 conditions are all met in the final subiteration. +e
condition is defined as follows.
Condition G1 is presented in equation (17) with its
variables defined in equation (18):
XH(p) � 1, (17)
where
4
XH(p) � 􏽘 bi ,
i�1
1, if x2i− 1 � 0 andx2i � 1 orx2i+1 � 1,
bi � 􏼨 0, otherwise.
(18)
+e values x1, x2, . . . , x8 are the 8 neighbors of p, be-
ginning with the east neighbors and counted in an anti-
Figure 4: +e whorl. clockwise manner.
International Journal of Mathematics and Mathematical Sciences 5
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
Figure 5: +e Guardia Civil database minutiae characteristics [7].
Table 1: Labeling of minutiae characteristics. Minutiae Extraction. +is process involves determining
No. Name whether or not pixels belong to distinct ridges and, in whichcase, whether the ridges are ending points or bifurcations,
1 Ridge ending
2 Bifurcation thereby acquiring a candidate minutiae group. +e x and y
3 Deviation coordinates are recorded for every detected minutia as well
4 Bridge as the orientation and the corresponding ridge feature. +e
5 Fragment extraction of minutiae is performed using the crossing
6 Interruption numbermethod which is one of themost popular techniques
7 Enclosure for this kind of task [17]. +e method uses a 3× 3 window to
8 Point check the local neighborhoods of each ridge pixel p in the
9 Ridge crossing image. By definition, the crossing number of p is half the
10 Transversal sum of the differences between adjacent pixel pairs that form
11 Circle the 8-neighborhood of p, as given in
12 Delta
13 Assemble 8
14 M-structure 􏼌 􏼌CN � 0.5 􏼌􏽘 􏼌􏼌P 􏼌􏼌
15 Return i
− Pi+1􏼌, (24)
i�1
where Pi denotes the pixel’s value (one or zero) in a 3× 3
Condition G is shown in equation (19) as neighborhood of P, as shown in Figure 6.2 +e crossing number and its corresponding character-
2 ≤min􏼈n (p), n (p)􏼉≤ 3, (19) istic are listed in Table 2.1 2 In summary, the following is the algorithm for finding
minutiae:
where
Input: fingerprint image
4 Output: ridge endings and bifurcations
n1(p) � 􏽘 x2k− 1 ∨x2k, (20)
1 Step 1: binarize input fingerprint image.k�
Step 2: apply thinning to the image.
4
n (p) � 􏽘 x ∧x . (21) Step 3: analyze the thinned fingerprint image and detect2 2k 2k+1
k�1 the minutiae by using the 8-neighborhood pixels to
compute for each block of the ridge bifurcations and
Condition G3 is shown in equation (22) as ridge endings.
Step 4: store the detected minutiae in a file.
( x2∨x3∨x8􏼁∧x1 � 0. (22) Step 5: end.
Condition G is shown in equation (23) as Once the minutiae point coefficients are extracted, the4 wavelet coefficient extraction process is performed next.
( x6∨x7∨x4􏼁∧x5 � 0. (23)
At the end of the thinning process, some pixels 2.2.4. Wavelet Transform Technique. In computing the
considered as spur pixel, h-connected pixel, and isolated wavelet transform (DWT) for the fingerprint images, low-
pixels emerge, which are cleaned up. Finally, a bridge pass and high-pass filters are used to convolve the smoothed
operator is applied to the resultant image to maintain an images. A downsampling procedure is applied by columns
optimal skeleton appropriate for minutiae extraction. on the images obtained. Here, all indexed columns are
6 International Journal of Mathematics and Mathematical Sciences
Table 2: Crossing number characteristics. +e db9 wavelet transform is applied to the fingerprint
CN Characteristics images to extract these coefficients for the recognition of the
fingerprint. Once both minutiae and db9 wavelet coefficients
0 Isolated point
1 End point are extracted for each image, the corresponding features are
2 Continuing point merged with concatenation operator to form a single matrix.
3 Bifurcation point +e resultant matrix is partitioned into the training and
4 Crossing point testing dataset using 75 : 25 criteria.
2.3. Classification Techniques
P4 P3 P2
2.3.1. Support Vector Machine (SVM). +is study looks at a
P5 P P1 multiclass classification problem and used amulticlass SVM for
this purpose. +e classifier utilizes K(K − 1)/2 binary SVM
P P P models using the one-versus-one coding design, with K being6 7 8
the number of different class labels. +e SVM algorithm is
Figure 6: A 3 3 mask. mainly used for locating a hyperplane that precisely groups the×
associated feature points into classes in anN-dimensional space
withN features [21]. Sets of data points that occur on either side
chosen, after which high-pass and low-pass filters are used to of a hyperplane can be banded together into separate classes.
convolve the images again with rows downsampling pro- However, the number of features available determines the
cedure. Consequentially, four subband images of half the dimension of the hyperplane. For instance, if there are 2 input
size of original images are obtained. +ese generated sub- features, the dimension of the hyperplane produced becomes a
band images hold the approximation (A), vertical (V), line as depicted in Figure 7. If input features are 3, then a two-
horizontal (H), and diagonal (D) information of the fin- dimensional hyperplane will be produced as depicted in Fig-
gerprint image. Amongst the four subband images, the ure 8. +erefore, it becomes quite challenging to determine
approximation coefficients hold significant information of when the number of features goes beyond the value of 3.
the fingerprint image. Due to this, it is a primary choice for To distinguish between the two data point classes, there are
our feature selection. +e Daubechies 9 (db9) wavelet is several possible choices of hyperplanes to be selected. +e ob-
considered in this study as it generates similar results jective is to determine a plane with the largest margin, such as
compared to complex Gabor wavelets [18]. It also extracts the most significant distance between each class’s data points.
more appropriate features from an image relative to simpler +e margin distance is maximized to provide some room to
wavelets such as Haar. Finally, it takes less time to retrieve classify future data points with more surety. +e feature points
results than other complex wavelet techniques [19]. A closest to the hyperplane that affects its direction and location
general expression for the wavelet transform is shown in are called support vectors. With the support vectors obtained,
∞ the classifier margin is maximized, as shown in Figure 9.
∗
F(a, b) � 􏽚 f(x)ψ(a,b)(x)dx, (25)
− ∞
where∗ represents the complex conjugate while the function 2.4. Performance Evaluation. +is study’s main objective is
ψ is any function satisfying some well-defined properties to improve fingerprint recognition accuracy, such as other
[20]. Several types of wavelets exist and can be classified biometric authentication systems; in this proposed model,
based on the orthogonality property. +is property helps an input fingerprint image is compared to the database
develop the discrete wavelet transform while the continuous templates. A classification process helps to accept or reject
wavelet transforms can be generated using the non- the user. To achieve this, the metrics used to measure this
orthogonal wavelets. +e two transform types are charac- model’s performance are precision, recall, and recognition
terized by the following properties [20]: accuracy, as stated in equations (26) to (28), respectively.+e
(1) With discrete wavelet transforms, a data vector of the precision defines what numbers of positive predictions were
same size as the input is returned. Typically, a large positive. Recall on the other hand defines the number of all
number of data in this vector are almost zero. +e positive samples that were correctly predicted as positive by
main reason is that the input signal is decomposed the classifier. Recall can also be referred to as true positive
into a group of functions or wavelets equilateral to its rate (TPR). From the equations listed, TP denotes true
scaling and translations. Hence, this signal decom- positive, FP denotes false positive, and FN denotes false
position returns an equal or lower number of the negative:
wavelet coefficient spectrum as the number of signal TP + FN
data points. accuracy � , (26)TP + FP + TN + FN
(2) However, continuous wavelet transforms return
arrays that are a single dimension larger than their TPprecision � , (27)
input data. TP + FP
International Journal of Mathematics and Mathematical Sciences 7
x2 x2
Optimal hyperplane
Maximum
margin
x1 x1
(a) (b)
Figure 7: Possible hyperplanes (left) and optimal hyperplane (right).
A hyperplane in R2 is a line A hyperplane in R3 is a line
7
7
6
6
5 5
4
4
3
3 2
1
2
0
10
1
5
0 3 4 5
6 7
0 2
0 1 2 3 4 5 6 7 0 1
(a) (b)
Figure 8: Hyperplanes in 2D (left) and 3D (right).
TP (PolyU HRF), among others, are databases available online
recall � . (28)
TP + TN for evaluation purposes upon request. For a fair compar-
ison with existing studies, this study uses the FVC2002 for
its model evaluation. +e selected dataset generally comes
3. Results and Discussion in four forms thus as follows: DB1, DB2, DB3, and DB4.
Each dataset has 880 grayscale fingerprints in all, made up
+is section of the study reports data acquisition, infor- of 110 fingers with 8 impressions each. Each dataset is
mation, and analysis of the acquired fingerprint dataset. +e divided into two sets, A and B with the following naming
computational experience and results obtained from the convention: DB1_A and DB1_B, DB2_A and DB2_B, in
evaluation are comparatively discussed. that order. Set A contains fingerprints labeled 1 to 100 (800
impressions in total), and Set B contains those labeled 101
to 110 (80 impressions in total) for each. +is study used all
3.1. Dataset Availability and Information. +e National the FVC2002 Set B (DB1_B, DB2_B, DB3_B, and DB4_B)
Institute of Standards and Technology (NIST), the Fin- images resulting in 320 impressions in total for evaluation.
gerprint Verification Competition (FVC), and the Hong +e DB1_B images were obtained from an optical sensor,
Kong Polytechnic University High-Resolution Fingerprint “TouchView II” by Identix, which gave an image size of
8 International Journal of Mathematics and Mathematical Sciences
Small margin Large margin
Support vectors
Figure 9: Support vectors.
388× 374 (142 Kpixels) with 500 dpi each. Likewise, the +is operation is repeated four times successively on the
DB2_B images were obtained from an optical sensor approximation coefficient. At the fourth level of the de-
“FX2000” by Biometrika, which also gave an image size of composition process, a set of forty-seven Daubechies 9
296× 560 (162 Kpixels) with 569 dpi each. +e DB3_B coefficient was extracted. +ese coefficients which represent
images were captured with a capacitive sensor “100 SC” by the characteristic features of a given fingerprint are extracted
Precise Biometrics, and image sizes are 300× 300 (88 from the approximation subbands.+e resultant features are
Kpixels) with 500 dpi each. Finally, the DB4_B images were appended to the extracted minutiae in Section 3.2.3.
obtained from a synthetic fingerprint generator, “SFinGe
v2.51,” which had an image size of 288× 384 (108 Kpixels)
with about 500 dpi each. All these variations introduce 3.2.3. Minutiae Extraction. +e core point, ridge endings,
some level of difficulty when it comes to their analysis. and bifurcations on the fingerprints were detected, while
Figure 10 depicts the 8 fingerprint impressions from the removing spurious minutiae. +is is done by binarizing the
finger of individual 101 in the DB1_B database. fingerprint image, thinning the binarized image, and
detecting the minutiae. +e input image and its corre-
sponding binarized image are shown in Figure 14.
3.2.Analysis of Results of ProposedApproach. As an overview In Figure 15, we have the thinned image (left) created
of the proposed method, the wave atom denoising is per- from the binarized image and an overlay of the minutiae
formed on all fingerprint images of the selected dataset, from (right) on the thinned image after removing all spurious
which both wavelet coefficients and minutiae are extracted minutiae. +e red spots represent ridge endings, the pink
and saved. +e extracted minutiae and wavelet coefficients and blue spots represent bifurcations, and the green spot
are concatenated to form a single feature matrix for the represents the core point.
purpose of classification. Pictorially, Figure 11 gives the +e numeric features of the corresponding minutiae
schematic view of the proposed pipeline. points for each fingerprint are extracted and stored. A
sample feature vector representing the first three impres-
sions of finger 101 is shown in Table 3.
3.2.1. Fingerprint Denoising. Each grayscale fingerprint
image is denoised and smoothed using wave atom trans-
form. Firstly, a right circular shift process is applied to the 3.2.4. Numerical Evaluation of Proposed Approach. +e
input fingerprint image, after which the forward 2D wave metrics precision, recall, and recognition accuracy are
atom transform is applied. +e resultant output of the computed separately for all four datasets evaluated using the
process is the wave atom coefficients. Hard thresholding is proposed approach. Evaluation of the four FVC2002 Set B
applied to these coefficients to remove noisy signals and the datasets was performed separately mainly for comparison
inverse 2D wave atom transform is then applied afterward. with previous works. A summary of the results from the
Lastly, a left circular shift is applied to the output to complete experimentation is shown in Table 4. Moreover, Table 5
the image denoising process.+e denoised fingerprint image shows the model’s performance on each of the two features
is then reorganized from the final set of coefficients as shown when experimented separately.
in Figure 12.
3.3. Comparative Analysis. +e proposed method is com-
3.2.2. Discrete Wavelet Transform Coefficients. Each pared with previous works from other studies that experi-
denoised fingerprint image is decomposed into the four mented on the same datasets used for evaluation, thus the
subbands resulting in Figure 13. FVC2002 DB1_B dataset.
International Journal of Mathematics and Mathematical Sciences 9
101_1.tif 101_2.tif 101_3.tif 101_4.tif
101_5.tif 101_6.tif 101_7.tif 101_8.tif
Figure 10: +e 8 impressions from finger 101.
Minutiae
coefficients
extraction
Fingerprint Wave atom Merge Train and test
image smoothing coefficients partitioning
DWT
coefficient SVM
extraction classification
Figure 11: Design pipeline.
Figure 12: Input image (left) and smoothened image using wave atom transform (right).
10 International Journal of Mathematics and Mathematical Sciences
Approximation Horizontal Vertical Diagonal
Figure 13: Details of DWT fingerprint image decomposition.
Figure 14: Input fingerprint image (left) and binarized image (right).
Figure 15: +inned image (left) and display of minutiae (right).
International Journal of Mathematics and Mathematical Sciences 11
Table 3: Feature vector representation of the first three impressions of fingers 101.
Finger ID x coordinate y coordinate Crossing number Angle
101_1.tif 90.4696 120.3922 1.729448 1.978024
101_2.tif 120.80335 108.6511 2.059126 1.979613
101_3.tif 101.3366 104.6962 1.973153 1.884723
Table 4: Performance of various datasets.
Dataset Precision Recall Recognition accuracy (%)
DB1_B (TouchView II optical sensor) 1.00 1.00 100
DB2_B (FX2000 optical sensor) 0.95 0.95 95
DB3_B (100 SC capacitive sensor) 1.00 1.00 100
DB4_B (SFinGe v2.51 synthetic FP generator) 0.95 0.95 95
Table 5: Performance of separate features (minutiae and DWT).
Dataset Minutiae only (%) DWT only (%)
DB1_B (TouchView II optical sensor) 50 95
DB2_B (FX2000 optical sensor) 70 80
DB3_B (100 SC capacitive sensor) 40 95
DB4_B (SFinGe v2.51 synthetic FP generator) 65 40
Table 6: A comparative analysis of experimental results using the FVC 2002 DB1_B dataset.
Method by Database Features Recognition accuracy (%)
Sang et al. [22] DB1_B Minutiae + invariant moment 96.67
Ali et al. [23] DB1_B Minutiae 98.55
Proposed approach DB1_B Minutiae + db9 wavelet 100.00
As observed in Table 6, this study’s proposed ap- features. From the experimentation, it was realized that the
proach performs considerably better than the named prediction accuracy rises significantly when more features
authors’ previous works. +e proposed model in general (columns) are added during the feature selection stage of the
performs significantly well when tested on the other three model; hence, the smaller the number of features selected, the
datasets of FVC2002–DB2_B, DB3_B, and DB4_B with a lower the prediction accuracy. +is may account for the lower
recognition accuracy of 95%, 100%, and 95%, scores produced for the minutiae features, which are only 6 for
respectively. each finger impression, compared to 47 features for DWT
producing better results.
4. Discussion
5. Conclusion
It is observed from Table 4 that each of the four datasets was
obtained from different sensors. However, the proposed model +is study proposed and presented a transform-minutiae fu-
performed relatively well, with 100% accuracy for DB1_B and sion-based model to improve the accuracy of fingerprint rec-
DB3_B. On the contrary, the model wrongly predicted one out ognition. +e wave atom denoising approach was proposed to
of 20 test data in the other two datasets, which yielded 95% initially remove noise from fingerprint images for better feature
accuracy. However, upon further experimentation on the detection and extraction. In the proposed method, both mi-
extracted features as disjoint sets to ascertain the proposed nutiae and wavelet transform coefficients (db9 wavelet) are
model’s performance, DWT features yielded a near accurate extracted and used for recognition. +e datasets used for
score of 95% on DB1_B. Nonetheless, on testing the model on evaluation were from all the FVC 2002 Set B databases (DB1_B,
minutiae features only, a prediction accuracy of 50% was DB2_B, DB3_B, and DB4_B) consisting of 320 fingerprint
recorded which is considerably poor. +e results from DB2_B images in total.+e proposed method proved to perform better
also show relatively good prediction accuracies of 80% and 70% with a recognition accuracy of 100% as compared with previous
for DWT features and minutiae features, respectively. For studies using the DB2_B dataset.
DB3_B, the model’s performance was poor with the minutiae
features with an accuracy score of 40% but performed better on Data Availability
the DWT features yielding 95% accuracy. +e performance for
DB4_B in contrast to the initial datasets yielded a higher +e data employed to support this study’s experimentation
percentage accuracy for the minutiae features, with 65% can be obtained from FVC2002 (http://bias.csr.unibo.it/
compared to a relatively low accuracy of 40% for the DWT fvc2002/).
12 International Journal of Mathematics and Mathematical Sciences
Conflicts of Interest fingerprint feature extraction methods on multiple impres-
sion dataset,” British Journal of Mathematics & Computer
+e authors declare that there are no conflicts of interest Science, vol. 5, no. 3, pp. 383–396, 2015.
regarding the publication of this paper. [17] S. Shi, J. Cui, X.-L. Zhang, Y. Liu, J.-L. Gao, and Y.-J. Wang,
“Fingerprint recognition strategies based on a fuzzy com-
mitment for cloud-assisted IoT: a minutiae-based sector
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