Fingerprint Feature Extraction & Matchingshodhganga.inflibnet.ac.in/bitstream/10603/9044/7/07... ·...

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Fingerprint Feature Extraction & Matching

As discussed previously (Section 2.1.1.2) mainly two types,

fingerprint recognition systems namely Minutiae based matching &

Correlation based matching are found in literature. A feature

extractor finds the ridge endings and ridge bifurcations from the

input fingerprint images. If ridges can be perfectly located in an

input fingerprint image, then minutiae extraction is just a trivial

task of extracting singular points in a thinned ridge map. In

practice, however, it is not always possible to obtain a perfect ridge

map.

Table 3.7

Fingerprint Samples Taken from Same User and Corresponding ROI

User Fingerprint 1 Fingerprint 2 Fingerprint 3 Fingerprint 4

1

Fingerprint

ROI

2

Fingerprint

ROI

The performance of currently available minutiae-extraction

algorithms depends heavily on the quality of input fingerprint

images. Due to a number of factors (aberrant formations of

81

(a)

(b)

Fig. 3.25. Enrollment of Fingerprint (a) Fingerprint Preprocessing & ROI

Extraction (b) Training Samples used for Enrolling Fingerprint in

Database

epidermal ridges of fingerprints, postnatal marks, occupational

marks, problems with acquisition devices, etc.); fingerprint images

may not always have well-defined ridge structures. Reliable

minutiae-extraction algorithms should not assume perfect ridge

structures and should degrade gracefully with the quality of

fingerprint images. We are focusing on correlation based

fingerprints which are robust but less accurate; this accuracy can be

increased by combining with another trait in a multimodal biometric

system. We extract spectral features of a fingerprint based on 2D

Image transforms and wavelets.

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For feature extraction we are using following variants,

1. Kekre’s Wavelets based Feature Extraction.

2. Partitioned Complex Walsh Plane in Transform Domain. We

use Cal, Sal function plot in complex Walsh plane

3. Partitioned Complex Planes of Kekre’s Transform, Hartley

Transform, Discrete Cosine Transform, Kekre’s Wavelets. The

above mentioned approach is extended to generate Even and

Odd function plot of listed transforms.

We preprocess the fingerprint as discussed above and detect the

Registration Point (Core point or High Curvature point). This point is

used to select the Consistent Region of interest. User can place

fingerprint in varying position hence we take multiple samples to

select the ROI using method discussed above. This is shown in

Table 3.7; the fingerprints are captured from two different users.

3.1.2 Fingerprint Recognition using Kekre’s Wavelets

In the previous sections we have seen the fingerprint acquisition,

preprocessing steps in the design of automatic fingerprint

recognition systems. We have a fingerprint Region of Interest (ROI)

of dimensions 144*144 pixels after above mentioned operations.

This dimension is chosen because this was the maximum size of the

square fitting inside the fingerprints without violating the boundary

of the fingerprint images. This ROI is then used for feature

extraction. A typical fingerprint with above mentioned preprocessing

steps is shown in Fig. 3.25. The core region is also shown. This

region of interest is further used for enrolling fingerprints and

feature extraction. From each user we are selecting five samples

which will be used for training & testing of the algorithms discussed

here. In this section we will discuss texture feature extraction from

fingerprint. Fingerprint contains ridges and furrows, and their

organization is unique for each finger. This information is captured

by texture based features. We are using a new family of orthogonal

wavelets called as Kekre’s wavelets. For generation of Kekre’s

wavelets we need basis function as in case of other families, this

basis functions are generated from Kekre’s Transform matrix [214].

The generation of Kekre’s wavelet along with its properties is

discussed in detail in the next section. Advantage of Kekre’s wavelet

is that they can be generated by any number dimension (e.g.

144x144) using basis as Kekre’s transform. As we have ROI of 144*

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144 pixels we can generate Kekre’s wavelet of this order without

scaling it to either 128x128 or 256x256 pixels.

3.1.2.1 Kekre’s Wavelets

Kekre’s wavelets are orthogonal family of wavelets. For

generation of Kekre’s wavelets we need basis function as in case of

other families, this basis functions are generated from Kekre’s

Transform matrix.

A. Kekre’s Transform [214]

Let us generate the Kekre’s Matrix [K] for size mxm where m can

be any integer not necessarily the power of 2 as required for many

other conventional transforms. This matrix has all 1’s on the main

diagonal and upper triangle of the matrix. The sub-diagonal just

below the main diagonal has the value (-m+i) where ‘m’ is the

order of matrix and ‘i’ is the column number. Rests of the elements

of lower triangle below the sub diagonal are all zeros. The general

form of Kekre’s matrix [K] can be written as

1 1 1 ….

1 1

-N+1 1 1 …

.

1 1

0 -N+2 1 …

.

1 1

.

.

.

.

.

.

.

.

.

…

.

.

.

.

.

.

.

0 0 0 ….

1 1

0 0 0 ….

-N+(N-1) 1

The formula for generating the element Kxy of Kekre’s transform

matrix is,

Kxy= (3.31)

The properties of Kekre’s Transform are as follows:

1) The Kekre’s transform is real and orthogonal transform.

[K]T [K]=[µ] (3.32)

K NxN =

1 ; x ≤ y

-N + (x-1) ; x= y + 1

0 ; x > y + 1

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Where [k]T is transpose of [K] and [µ] is a diagonal matrix

and its elements are given by

µ11 = m

µii = (m-i+1)(m-i+2) (3.33)

2) It has a fast algorithm as it contains m(m+1)/2 number of

ones and (m-1)(m-2)/2 number of zeros leaving only (m-1)

integer multiplications and only (m-1)(m/2) additions for

transforming a column vector of dimension mx1. For a normal

matrix transformation we require m2 multiplications and m

(m-1) additions.

3) The transform of a vector f is given by

F = [K] f (3.34)

And inverse is given by

f = [K]T [µ]-1 F (3.35)

K11 K12 K13 … K1 (N-1) K1N

K21 K22

K23 … K2 (N-1) K2N

K31 K32

K33 … K3 (N-1) K3N

.

.

.

.

.

.

… .

.

.

.

KN1 KN2

KN3 … KN (N-1) KNN

Fig. 3.26. Kekre’s Transform (KT) matrix of size NxN

4) All entries in Kekre’s Transform Matrix are integers and hence no

floating point operations are required.

B. Kekre’s Wavelets [215]

Kekre’s Wavelet transform is derived from Kekre’s transform.

From NxN Kekre’s transform matrix, we can generate Kekre’s

Wavelet transform matrices of size (2N)x(2N), (3N)x(3N),……, up to

maximum (N2)x(N2). For example, from 5x5 Kekre’s transform

matrix, we can generate Kekre’s Wavelet transform matrices of size

10x10, 15x15, 20x20 and 25x25. In general MxM Kekre’s Wavelet

transform matrix can be generated from NxN Kekre’s transform

matrix, such that M = N * P where P is any integer between 2 and N

that is, 2 ≤ P ≤ N. Consider the Kekre’s transform matrix of size

NxN shown in Fig. 3.26. MxM Kekre’s Wavelet transform matrix

generated from NxN Kekre’s transform matrix is shown in Fig 3.26.

K NxN =

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First ‘N’ number of rows of Kekre’s Wavelet transform matrix is

generated by repeating every column of Kekre’s transform matrix P

times. To generate remaining (M-N) rows, extract last (P-1) rows

and last P columns from Kekre’s transform matrix and store

extracted elements in to temporary matrix say T of size (P-1) x P .

Fig. 3.27 shows extracted elements of Kekre’s transform matrix

stored in T.

K(N-P+2) (N-P+1)

K(N-P+2) (N-P+2) … K(N-P+2) N

K(N-P+3) (N-P+1) K(N-P+3) (N-P+2)

….. K(N-P+3)N

.

.

.

.

….

….

.

.

KN(N-P+1)

KN(N-P+2) ….. KNN

Fig. 3.27.Temporary Matrix T of size (P-1) x P

Values of matrix T can be computed as,

T(x, y) = K( N-P+(x+1), N-P+ y) ; 1≤ x≤ (P-1) , 1≤ y≤ P (3.36)

First row of T is used to generate (N+1) to 2N rows of Kekre’s

Wavelet transform matrix. Second row of T is used to generate

(2N+1) to 3N rows of Kekre’s Wavelet transform matrix, Like wise

last row of T is used to generate ((P-1) N + 1) to PN rows [236].

We have used Kekre’s Wavelet Transform Matrices of Size 128,

64, 32 Generated from Kekre’s Transform Matrix of Size 64, 32, 16

respectively. We calculate Wavelet energy feature for the fingerprint

image using these wavelet matrices.

Properties of Kekre’s Wavelet Transform:

1. Orthogonal- The transform matrix K is said to be orthogonal

if the following condition is satisfied.

[K][K]T = [D], Where D is a diagonal matrix.

Kekre’s Wavelet Transform matrix satisfies this property

and hence it is orthogonal. The diagonal matrix value of

Kekre’s transform matrix of size NxN can be computed as

(3.37)

T =

86

2. Asymmetric- As the Kekre’s transform is upper triangular

matrix, it is asymmetric.

3. Non Involutional - An involutionary function is a function

that is its own inverse. So involution transform is a

transform which is inverse transform of itself. Kekre’s

transform is non-involution transform.

4. Transform on Vector -The Kekre’s Wavelet transform on a

column vector f is given by

F = [KW] f (3.38)

And inverse is given by

f = [KW]T [D]-1 F (3.39)

5. Transform on 2D Matrix- Kekre’s Wavelet transform on 2D

matrix f is given by

[F] = [KW] [f] [KW]T (3.40)

Obtaining Inverse:

Calculate Diagonal matrix D as,

[D] = [KW][KW]T (3.41)

D1 0 0 0 0 0

0 D2 0 0 0 0

0 0 D3 0 0 0

0 0 0 … 0 0

0 0 0 0 … 0

0 0 0 0 0 DN

Inverse is calculated as

[f] = [KW]T [ Fij / Dij ] [KW] (3.42)

Where Dij = Di * Dj ; 1≤ i ≤ N and 1≤ j ≤ N

Next an example of Kekre’s wavelet transform is given,

Fig. 3.34 shows the Kekre’s Wavelet transform matrix of size 15 x

15 generated from the Kekre’s transform matrix of size 5 x 5. Here

We have M =15, N =5 and P =M/N=3

1 1 1 1 1

-4 1 1 1 1

0 -3 1 1 1

0 0 -2 1 1

0 0 0 -1 1

D =

K5X5 =

87

As shown in Fig. 3.28, all the columns of Kekere’s transform matrix

are repeated P=3 times to generate first N=5 number of rows of

Kekre’s Wavelet transform matrix. To generate remaining (M-N) =

10 rows, extract last (P-1) = 2 rows and last P=3 columns from

Kekre’s transform matrix and store these elements into temporary

matrix T. The temporary matrix T is as follows .

-2 1 1

0 -1 1

The first row of T [-2 1 1 ] is used to generate next 5-10 rows of

KW transform matrix as shown above. Second row of T [0 -1 1] is

used to generate last 11-15 rows of KW transform matrix.

Fig. 3.28. 15x15 Kekre’s Wavelet Transform Matrix Generated from 5x5

Kekre’s Transform Matrix

3.1.2.2 Feature Vector Extraction

With the development of wavelet theory, Wavelet Analysis has

been valued highly in various domains of research. It is a powerful

tool of multi-resolution analysis. Here we construct wavelet energy

feature (WEF) by the high frequency to describe the fingerprint

images texture and use it to describe the ridges & principle lines.

We take the Kekre’s Wavelet (KW) Transform of the selected

fingerprint ROI. The wavelets will capture localized spectral

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

-4 -4 -4 1 1 1 1 1 1 1 1 1 1 1 1

0 0 0 -3 -3 -3 1 1 1 1 1 1 1 1 1

0 0 0 0 0 0 -2 -2 -2 1 1 1 1 1 1

0 0 0 0 0 0 0 0 0 -1 -1 -1 1 1 1

-2 1 1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 -2 1 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 -2 1 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 -2 1 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 -2 1 1

0 -1 1 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 -1 1 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 -1 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 -1 1 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 -1 1

5th column of

KT repeated P

=3 times

1st

column of

KT repeated P

=3 times

2ndt column of

KT repeated P

=3 times

3ndt column of

KT repeated P

=3 times

4th column of

KT repeated P

=3 times

KW15X15 =

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information from the ROI. We have the ROI of Size 144 X 144

Pixels. At each level Mth order KW matrix (of MXM Size) is generated

by M/2 order Kekre’s Transform Matrix (N=M/2, P=2). The wavelet

energy in horizontal, vertical and diagonal directions at the i-level

can be, respectively, defined as:

2

1 1

( ( , ))M N

h

i i

x y

E H x y (3.43)

2

1 1

( ( , ))M N

v

i i

x y

E V x y (3.44)

2

1 1

( ( , ))M N

d

i i

x y

E D x y (3.45)

(256x256)

(128x128)

(128x128)

LL LH

(128x128)

(128x128)

HL HH

(a) (b)

Fig. 3.29. Wavelet Decomposition of Selected ROI of Fingerprint Image

(a) Selected ROI (b) Kekre’s Wavelet First level Components

These energies reflect the strength of the images’ details in different

direction at the i-level decomposition. Hence the feature vector

1,2,3,...,( , , )h v d

i i i i kE E E where K is the total number of wavelet

decomposition level, can describe the global details feature of

fingerprint texture. One such decomposition is shown in Fig. 3.29.

Using above mentioned vector, the features extracted from the

whole ROI don’t preserve the information concerning the spatial

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location of different details of ridges and principle lines, so its ability

to describe fingerprint uniqueness is weak. In order to deal with this

problem, we divide the detail images into S×S non-overlap blocks

equally, and then compute the energy of each block. Then, the

energies of all blocks are used to construct a vector. This is shown

in Fig. 3.30. Finally the vector is normalized by the total energy. We

are also normalizing this vector each level and Component wise

also. These normalized vectors are named as wavelet energy

feature.

WEF has a strong ability to distinguish fingerprints. According to

these figures, WEFs of the same fingerprints are very similar while

those of different fingerprint are quite dissimilar. This is helpful for

fingerprint recognition.

Fig. 3.30. Dividing Wavelet Components into 4x4 Non-Overlapping Blocks

Only Horizontal, Vertical and Diagonal Components are divided into 4x4

blocks. Each component gives 16 values and per level we get 48 values of

wavelet energy

Each component is divided into 4x4 (SxS) non-overlapping blocks;

hence for a single component (LH, HL or HH) we have 16 wavelet

energy values. In a single decomposition we have 3 components

(LH, HL & HH) hence we get total 48 components. We normalize the

feature vector by dividing energy of components at each level by

the sum of all the components energy at that level. We have such 5

levels (J) of decompositions hence we have total 3xSxSxJ i.e. 240

(3*4*4*5) values in the wavelet energy feature vector. We call this

feature vector as Kekre’s Wavelet Energy Feature Vector (KWEFV).

KWEFV = {WE0, WE1, ….., WEn) n=3xSxSxJ. (3.46)

90

(a)

(b)

Fig. 3.31. Kekre’s Wavelet Energy Feature Vector Plot (a) Normalized by

Total Energy (b) Normalized by Level-wise Energy

(a)

(b)

Fig. 3.32. Kekre’s Wavelet Energy Distribution for Each Component (a)

Energy of Each Component (b) Energy of Each Level

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For the fingerprint shown in Fig. 3.29 the plot of Wavelet Energy

Coefficients (KWEFV) are shown in Fig. 3.31. The coefficients are

normalized in two different ways. In one method we use total

energy to divide all coefficients, the plot is shown in Fig. 3.31 (a)

and in other method the sum of coefficient of each level

(LH+HL+HH) is used for normalization, the plot is shown in Fig 3.31

(b). We have total 15 Components (3*J), We also find total energy

of each component for analysis. The component energy is

normalized by total energy at the level. The distribution is a coarser

estimate of spectral content. This is shown in Fig. 3.32.

3.1.2.3 Relative Wavelet Entropy

We are using two metrics for analyzing similarity between two

energy distributions (Kekre’s Wavelet Energy Feature Vector). We

are using Wavelet Energy Entropy [216] as one of the similarity

measure & other is the Euclidian distance between two sequences.

We have normalized the wavelet energy feature vector hence this

can be treated as a probability distribution.

Let us now suppose that we have two different probability

distributions {pi} and {qj}, with ∑j pj = ∑j qj =1. Here consider

them as wavelet energy distributions. We define Relative Wavelet

Entropy as,

0

( | ) lnn

j

wt j

j j

pS p q p

q (3.47)

Which give degree of similarity between two probability distributions

with respect to each other. The RWE is a positive real number and it

vanishes when j jp q . Fig. 3.33 presents three different relative

wavelet energy (Probability) distribution levels (j=1,2,..,5). It is

clear from the figure that distributions A and B are quite similar,

and present broad band spectra. In contrast, distribution C sows a

clear dominance of the resolution level j=-2. According to this

description, for the total WE the following relation can be expected:

SWT(A) ≈ SWT(B) > SWT(C). We can see that SWT(B|A) ≈0 and

SWT(C|A)>>0. When Corresponding numerical values for the

distribution are used, a very good match with previous relation is

obtained. We are using this metric for matching the Wavelet Energy

Distribution per level as well as for full sequence of wavelet energy

coefficients.

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(a) (b)

(c)

Fig. 3.33. Relative Wavelet Energy (Probability) Distribution for Wavelet

Resolution Levels (j=1,…..,5). Distribution A,{pj}={0.06, 0.10, 0.30,

0.34, 0.20}; B,{pj}={0.03, 0.10, 0.12, 0.33, 0.37}; C,{pj}={0.03, 0.11,

0.11, 0.70, 0.05}. The WE values for these distributions are

SWT(A)=1.440, SWT(B)=1.37, SWT(C)=0.994. Taking Distribution A as

reference, SWT(B|A)=0.015 and SWT(C|A)=0.220

3.1.2.4 Results

We are using scanned fingerprint from 57 different persons

captured using FS88 fingerprint scanner. For each person 5 samples

were taken for training & testing. Imposter fingerprints were

selected from other person’s samples. We have extracted Wavelet

Energy Feature Vectors using Kekre’s Wavelets and Haar Wavelets

(Modified). As discussed earlier the feature vector is normalized per

level. Fig. 3.25 & Fig. 3.26 shows some of these feature vectors. We

are representing the fingerprint by its feature vector (KWEFV). We

analyze similarity in three modes.

The feature vector is normalized level wise i.e. for all 48

components (16 LH, 16 HL, 16 HH) and then we can evaluate

the Relative Wavelet Energy Entropy for this normalized

0

0.1

0.2

0.3

0.4

1 2 3 4 5

A

Wavelet Resolution Level

Re

lati

ve E

ner

gy

0

0.1

0.2

0.3

0.4

1 2 3 4 5

B

Re

lati

ve E

ner

gy


0

0.2

0.4

0.6

0.8

1 2 3 4 5

C


Re

lati

ve E

ner

gy

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feature vector, final matching is given by summation of all

levels relative entropy.

Euclidian Distance (ED) between two KWEFV sequences (Seq.

X & Seq. Y).

2

, ,

0

( )n

x i y i

i

ED KWEFV KWEFV (3.48)

RWEE (Relative Wavelet Energy Entropy) for two normalized

KWEFV directly. We take full wavelet energy coefficient

sequence and normalize it by total energy. This distribution is

then used for finding full sequence relative entropy.

We have performed total 672 tests in parallel for intra class

matching i.e. genuine fingerprint testing and 5330 tests for inter

class matching i.e. cross matching and imposter testing. Euclidian

distance and relative energy entropy for each test is calculated. We

have divided the test results in two classes as Genuine Tests

Distance and Forgery Tests Distance (Imposter distance). The range

of distance values against the participation in specific class is shown

in Fig. 3.34. We can see that two peaks for two test classes. For

genuine fingerprints the relative distance lies in the range of 10 to

65 and that for imposter fingerprint lies in the range of 45 to 110.

Fig. 3.34. Relative Probability for Matching Distance of Genuine and

Forgery Tests

Two clear classes can be seen, with threshold distance as 55. This can be

used for designing classifier

0

5

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bab

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P-GEN

P-Forge

Distance

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We are using simple Euclidian Distance based K-nearest

neighborhood classifier (K-NN). Evaluation metrics such as False

Acceptance Rate (FAR), False Rejection Rate (FRR), True

Acceptance Rate (TAR) and True Rejection Rate (TRR) are

evaluated. They are specified as follows,

Total Number Imposter Fingerprints Accepted as Genuine

Total Number of Forgery Tests PerformedFAR

(3.49)

Total Number Genuine Fingerprints Rejected as Imposter

Total Number of Genuine Matching Tests PerformedFRR

(3.50)

Total Number Genuine Fingerprints Accepted

Total Number of Genuine Matching Tests PerformedTAR

(3.51)

Total Number Imposter Fingerprints Rejected

Total Number of Forgery Tests PerformedTRR

(3.52)

A. Relative Energy Entropy of Full Sequence of Wavelet Energy

We evaluate the Relative Energy Entropy for two KWEFV Full

Sequence.

Fig. 3.35. Test Results for Relative Entropy of Full Sequence of Energy

Feature Vector FAR-FRR Plot

(RKEEF : Relative Kekre’s Energy Entropy Full Sequence)

Higher the value lesser the matching and for matching

fingerprints the RWEE value is low. We plot the FAR-FRR curve for

accuracy calculations. We can see that from Fig. 3.35 the Equal

Error Rate (EER) i.e. the rate at which FAR and FRR both are

0

10

20

30

40

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10

15

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51

10

FRR

FAR

RKEEF FAR vs FRR Plot

% R

ate

Distance Threshold

EER = 22%

PI= 78%

95

minimum is at 22%, We are evaluating relative Energy Entropy

(REE) between two wavelet energy sequences; one such sequence

is shown in Fig. 3.31 (b). The EER for FAR-FRR analysis should be

low (ideally zero). We define Performance Index (PI) of a biometric

system based on this as follows,

PI=100-EER (3.53)

To indicate the performance of the systems hereafter

Performance Index (PI), Equal Error Rates (EER) of FAR-FRR Plot

and Correct Classification Ratio (CCR) are used. Correct

classification ratio is defined previously. This convention is followed

throughout the thesis.

B. Relative Energy Entropy of Energy Sequence Normalized

Levelwise

Here we have calculated the Euclidian Distance between two

KWEFV sequences. The sequence is normalized for each level. This

mode of matching gives maximum accuracy. Performance Index

(PI) of this system is 86% and 14% EER for FAR-FRR, which is

shown below.

Fig. 3.36. Test Results for Relative Entropy for Level wise Normalized

Sequence FAR-FRR Plot

C. Euclidian Distance of KWEFV Normalized Level Wise

Here we have calculated the Euclidian Distance between two KWEFV

sequences. The analysis is shown in Fig. 3.37.

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0FRR

FAR

RKEEF FAR vs FRR Plot

Distance Threshold

% R

ate

PI= 86%

EER = 14%

96

Fig. 3.37. Test Results for Euclidian Distance Between Wavelet Energy

Sequences ( FAR-FRR Plot)

The sequence is normalized for each level, i.e. by total energy of

each level. This mode of matching gives maximum accuracy. It has

PI of 89% and 11% EER for FAR-FRR.

D. Fusion of Relative Entropy & Euclidian Distance based Metrics

Here we have fused the score of Relative Entropy and Euclidian

Distance based distance. We have used linear fusion of score where

the final score Df is given by fusion of Relative Entropy ER & El

(Levelwise Entropy) and Normalized KWEFV distance DWN.

Df = W1*ER + W2*El+ W3*DWN (3.54)

Where W1, W2 & W3 are fusion weights, W1=0.001, W2= 10, W3=10.

These weights are empirically decided so that their contribution

towards final distance is equal; this is also called as score

normalization.

For Kekre’s wavelet based feature vector the observed Range

for ER is (1890- 3940), for El the range is (0.805 – 1.564) and that

of Dwn is (0.2950-0.5245), after weighting this range becomes

(1.890- 3.940), (8.05 – 15.64) & (2.950-5.245) respectively. Fusion

of these scores gives the Performance Index of 90% and EER as

10%.

The similar feature vectors are extracted using Haar wavelets

also and performance of both the wavelets is compared.

Comparison of above mentioned techniques and given in Fig. 3.38.

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FRR

FAR

RWEEL FAR vs FRR Plot

Distance Threshold

% R

ate

EER= 11%

PI= 89%

97

Fig. 3.38. Comparison of Kekre’s & Haar Wavelet Based Fingerprint

Matching Techniques

We can see that Euclidian distance based feature vector

classification method has highest Performance Index. The

performance of Level wise entropy is next best. The fusion

performed here is acting like weighted average. We can conclude

that Euclidian distance based classifier works best for the wavelet

energy based fingerprint matching. Besides this Kekre’s Wavelet

based feature vector gives higher PI for fusion.

Table 3.8

Summary of Fingerprint Matching Tests

Sr. Type of Wavelet Accuracy (%) - CCR

1 Kekre’s Wavelets 84.40

2 Haar Wavelets 81.15

Finally we have performed total 520 tests for intra class matching &

5330 tests for inter class matching for both Kekre’s & Haar

Wavelets. The total accuracy (CCR) is for Kekre’s wavelets based

fingerprint recognition system is 84.40% and that of Haar wavelet is

81.15%; we have used simple Euclidian distance based K-NN

classifier with three training samples per person. This is an example

of multi-algorithmic biometric fusion. Performance of Kekre’s

Wavelet is better and they give higher PI & CCR. Next we discuss

use of Walsh, Hartley, Kekre’s Transform, DCT & Kekre’s Wavelets

for fingerprint recognition.

KWEFV RWEEL RKEEF Fusion

PI-Kekre 89 86 78 90

CCR-Kekre 86.22 81.52 72.04 84.4

PI-Haar 89 84 75 88

CCR-Haar 85.87 79.21 70.25 81.15

0102030405060708090

100

% R

ate

Comparison of PI & EER (FAR-FRR) for Wavelet Energy Based Fingerprint Matching Techniques

98

3.1.3. Fingerprint Recognition using Partitioned Complex

Walsh Plane in Transform Domain

Here we discuss a method which deals with fingerprint

identification in the transform domain is considered. The one-step

Walsh transform i.e. either the row or the column transforms of the

fingerprint is subjected to partitioning to generate the feature

vector. This process is based on Cal & Sal Functions of Walsh

Transform, next we discuss the Walsh transform & it’s Cal, Sal

functions.

3.1.3.1 Walsh Functions [217]

Walsh functions are a set of orthogonal functions which can be

used to represent any discrete-time signal. The Walsh functions (W0

- W7) as shown in the Fig.3.39 are generated from square wave

functions of different sequency.

Fig. 3.39. First Eight Walsh Functions

The even functions (C0 - C3) are called Cal functions and the

odd functions (S1-S4) are called Sal functions. The basic square

wave functions are S1, S2 and S4. C0 is DC component and the

remaining functions are generated from the basic square waves by

EX-OR operation (equivalent to multiplication). This operation

generates only the difference sequency functions (as opposed to the

case of sinusoidal signals where both difference and sum

frequencies are generated) e.g. C1 = S1 ⊕ S2, here S1 and S2

being odd function, their EX-OR operation results in an even

function (C1). Similarly EX-OR operation of an even and odd

function generates an odd function e.g. S3 = S4 ⊕ C1, which can

further be simplified to S3 = S4 ⊕ S2 ⊕ S1, showing that all

99

functions are generated from the basic square waves S1, S2 and

S4.

Walsh functions can be ordered in a number of ways.

The sequency ‘k’ of a Walsh function is defined as half the number

of zero crossings in one cycle of the time base. Walsh functions with

non-identical sequencies are orthogonal, as are the functions W(n,

2k) and W(n, 2k+1). The product of two Walsh functions is also a

Walsh function. Harmuth in [217] designates the even Walsh

functions Cal(k) and the odd Walsh functions Sal(k)[218],

Cal (n, k) = W(n, 2k) (3.55)

Sal (n, k) = W(n, 2k+1) (3.56)

where ‘k’ is the sequency.

The Walsh transform matrix (W) is then generated by sampling

these Walsh functions at the middle of the smallest time interval.

The matrix, as in Eqn. (3.57) is obtained, which can be directly used

to generate the transform coefficients of a discrete signal both of 1-

D and 2-D as shown in Eqn. 3.55 and Eqn. 3.56 respectively,

(3.57)

F1D=W.f (3.58)

F2D=W.f.WT (3.59)

The interpretation of Walsh transform of a 2-D signal can be

understood by Fig. 3.46, where first the row transform is calculated

and then the column transform. The final output has DC component

in the top left corner and the sequency components increase

leftwards and downwards.

In the current approach, we are first generating the

intermediate transform, i.e. the row transform (or column

transform) of a fingerprint image as shown in Fig. 3.40., which have

DC component as its first row (or column) and higher sequency

components (Sal and Cal) as the following rows (or columns).

100

Fig. 3.40. Transform of a 2D Function

(a) (b)

Fig. 3.41. a) Row Transform and b) Column Transform of a Fingerprint

3.1.3.2 Complex Walsh Plane [219] & Feature Vector

Generation

The Cal and the Sal components of the same sequency are

grouped together and are considered to be in the four quadrants of

2-D complex coordinate plane as listed in Fig.3.41. This complex

plane is now partitioned into different numbers of blocks.

Fig. 3.42. Complex Walsh Plane

101

The complex plane consisting of same-sequency (Sal, Cal)

components is now partitioned 256 square blocks as shown in

Fig.3.43. For each block a feature vector is generated which is the

mean value of all the transform coefficients in that block, as well as

the number of points i.e. the density is also considered. Such a

complex Walsh plane & its partitioning is shown in Fig. 3.43.

(a) (b)

Fig. 3.43. Complex Walsh Plane (a) Partitioned Cal+jSal Function Plot of

Row Transform (b) Partitioned Cal+jSal Function Plot for Column

Transform

This value is unique for each fingerprint as the sequency

distribution of each fingerprint is unique in different blocks. As

compared to all or those transform coefficients which contain major

part of signal energy feature vectors generated using partitioning

are much less in number and hence the reduction in processing time

and complexity. The blocks generated are square shaped and the

mean values of the transform coefficients in each block are

calculated as in Eqn. 3.60, where Mk is the mean and N is the

number of coefficients in a block, which form the features. The DC

component, separate means of the Sal and Cal component and the

last sequency component together form the feature vector, and

hence the number of features is 2S+2, where S is the number of

blocks.

1

1 n

k i

i

M WN

(3.60)

The features obtained from the test image are compared with

those obtained from the stored fingerprint in the database and the

102

results matched. The Euclidian distances between the feature

vectors of the test image and the database images are calculated.

The minimum distance gives the best match.

3.1.3.3 Fingerprint Feature Vector Extraction

As discussed above the intermediate Walsh transform is used to

generate the complex Walsh plane, this plane is then partitioned

into 256 blocks (16x16). In each block the mean is calculated as

well as DC component and the last sequency component is together

treated as feature vector.

(a) (b)

(c) (d)

Fig. 3.44. Partitioned Complex Walsh Plane of Fingerprint

(a) Row Transform Function Plot for Full Fingerprint

(b) Column Transform Complex Function Plot for Full Fingerprint

(c) Row Transform Complex Function Plot for Core Point ROI

(d) Column Transform Complex Function Plot for Core Point ROI

103

In the previous sections methods for fingerprint segmentation as

well as core point detection are discussed. The current method is

tested on the segmented fingerprint as the detected core area. The

fingerprint matching is performed in two modes

1. Full Segmented fingerprint is considered for feature vector

generation

2. First the core point (or registration point) on the fingerprint is

located. A region of interest of m*m pixels is segmented and

considered for feature extraction. Both the plots are shown in

Fig. 3.44.

The Optical fingerprint scanner Futronics FS88 is used for live

fingerprint capture, this device gives image of size 320*480 pixels

at 500dpi. This image is preprocessed and segmented to remove

the background as well as noise. Then the core point is detected

from the fingerprint. The Region of Interest (ROI) of size 144*144

pixels is the segmented from the preprocessed fingerprint. Finally,

full segmented fingerprint as well as the core point ROI is available

for feature extraction. This procedure is shown below,

The segmented fingerprint as shown in Fig. 3.11 and Core

Point ROI as shown in Table 3.7 are then subjected to the

intermediate transform generation. The complex Cal + jSal function

plots are generated by intermediate Row & Column Walsh

transform. As discussed previously the complex Walsh plane is

partitioned. The complex Walsh plane plots for full finger as well as

core point ROI is shown in Fig. 3.44. As discussed earlier each plot

gives 2S+2 coefficients, we have 256 blocks in each plot, hence one

plot gives 514 (256*2 +2) coefficients. For each type of input i.e.

segmented fingerprint and core point ROI we have two plots, one

for row and one for column transform hence we have 1028 (514 *2)

coefficients for each type of fingerprint input. Finally we have 1028

coefficients in the feature vector of segmented fingerprint and

another 1028 for core point ROI. Similar Feature vector is

generated for Density of the points in complex Walsh Plane for each

fingerprint input. This feature vectors are used for enrollment and

matching of the fingerprints.

3.1.3.4 Results

To test the matching algorithm, 285 samples collected from 57

persons (5 samples per person) have been used. The experiment

was conducted on two different modes; one is on Full Segmented

104

Fingerprint and another is on Fingerprint Core point ROI. Total 2421

different tests are performed. Equal Error Rate (EER) is evaluated

and PI (Performance Index) is calculated. While testing the DC &

Sequency components and its effect on matching is also evaluated.

For each type of fingerprint input the feature vector is generated in

following variations

1. Row transform mean feature vector (Row TRF).

2. Column transform mean feature vector (Col TRF).

3. Row density feature vector (Row Density).

4. Column density feature vector (Col Density).

5. Fusion of above mention feature vectors with DC & Sequency

components (Fusion).

The fusion is performed by score normalization. The

normalization is performed by weighting the distance by specific

coefficient decided empirically to give proper weightage to each

feature vector. These feature vectors are extracted for full

fingerprint as well core point area of fingerprint. From each user five

samples are taken out of that two samples are used for testing and

remaining samples are used for training.

(a) (b)

Fig. 3.45. FAR-FRR Analysis for Walsh Cal-Sal based fused Feature

Vectors (a) Plot for Fingerprint Core point ROI Feature Vector (b) Plot for

Full Segmented Fingerprint Feature Vector

For classification Euclidian distance based K-NN classifier is used.

This algorithm is tested on a machine running Windows XP SP3,

with AMD Athlon 64FX Processor running at 1880 MHz and 1.5 GB

of RAM. The FAR-FRR plot for Fused Feature vector matching for full

0102030405060708090

100

40 80 120 160 200 240 280 320 360

% R

ate

Fingerprint Core Point Feature Vector Fusion FAR-FRR

FRR

FAR

Threshold

EER= 05% PI = 95%

0102030405060708090

100

60 100 140 180 220 260 300

% R

ate

Full Finger Feature Vector Fusion FAR-FRR

FRR

FAR

Threshold

EER= 19% PI=91%

105

finger and core point area are shown in Fig. 3.45. The plot shows

that EER for core point ROI based feature vector is high (EER= 5%)

for FAR-FRR Analysis, this shows high accuracy as compared to

feature vector of full segmented finger (EER =19%). This is mainly

because the core point ROI is more consistent and has less

variations due to change in finger placement, pressure applied,

dryness of finger etc. The results are summarized in Fig. 3.46 for

all the feature vectors variations.

Fig. 3.46. Performance Comparison for Feature Vector Variants of

Partitioned Walsh Cal-Sal Function Fingerprint Matching.

Score Fusion based Matching Gives Higher Performance Index; this is

Indicated by Bars in Red Colour. (TRF: Transform, FV: Feature Vector)

It is clearly seen that the core point based feature vectors give

higher accuracy. As compared to the density based feature vector

the coefficient mean based feature vector give higher accuracy. The

Fusion of Row & Column Transform mean & Density with DC &

Sequency coefficient gives 95% PI for core point based feature

vector and that of full segmented fingerprint’s feature vector gives

81% PI. The individual Row & column transform mean based

feature vectors have 85% & 88% PI for core point ROI based

feature vector, this shows that due to fusion of feature vector with

DC & Sequency component the performance has improved. Similar

improvement can be seen with full fingerprint’s feature vectors.

In the next section we continue this feature extraction

mechanism for Even and Odd functions (similar to Cal & Sal function

of Intermediate Walsh transform) of intermediate transforms of

Hartley Transform, Kekre’s Transform, DCT & Kekre’s Wavelets.

RowTRF-CorePoint

ColTRF-CorePoint

Row-Density-CorePoint

Col-Density-CorePoint

Fusion-CorePoint

FV

RowTRF-Full

Finger

ColTRF-Full

Finger

Row-Density

-FullFinger

Col-Density

-FullFinger

Fusion- Full

FingerFV

PI 85 88 80 82 95 80 70 66 69 81

0102030405060708090

100

% P

I

Partitioned Walsh Cal Sal Function Based Fingerprint Matching Performance Comparison of PI

106

3.1.4. Fingerprint Matching using Partitioned Complex Plane

in Transform Domain of Hartley Transform, Discrete Cosine

Transform, Kekre’s Transform and Kekre’s Wavelets

The feature vector extraction mechanism discussed earlier is

extended here for other transforms. The complex plane is generated

by Cal & Sal function of Intermediate Walsh transform as shown in

Fig. 3.43; in case of other transforms Cal and Sal functions

analogous part is Even & Odd functions. The even and odd function

are used to generate complex transform plane by plotting complex

pair (Even+jOdd), then the above discussed feature vectors are

extracted for fingerprint matching. We discuss the results one by

one for the listed transforms.

3.1.4.1 Fingerprint Matching using Partitioned Hartley Plane

in Transform Domain

A discrete Hartley transform (DHT) is a Fourier-related transform

of discrete, periodic data similar to the discrete Fourier transform

(DFT), with analogous applications in signal processing and related

fields. Its main distinction from the DFT is that it transforms real

inputs to real outputs, with no intrinsic involvement of complex

numbers. Just as the DFT is the discrete analogue of the continuous

Fourier transform, the DHT is the discrete analogue of the

continuous Hartley transform, introduced by R. V. L. Hartley in 1942

[220].

The real valued Hartley transform [221] is an alternative to the

more familiar complex valued Fourier transform [222], [223].

Because any two dimensional intensity distributions has only real

values, the Fast Hartley transform technique is an alternative to the

Fast Fourier transform for transforming and inverse transforming

images.

The Hartley transform has the advantage of having the same

formula for forward and inverse transform (it is involutionary) and

tends to require less memory space since complex numbers are not

used, and a separate inversion program is not required. Regardless

of speed, the Hartley transform approach is worthy of consideration

for image processing applications due to its theoretical elegance,

symmetry of the inversion formula, and the economy of memory

utilization. In the case of two-dimensional real image data, the

discrete Hartley transform H (u, v) is defined as

107

1 1

0 0

1( , ) ( , ) [2 ( )]

( )

M N

x y

ux vyH u v f x y cas

MN M N (3.61)

The kernel [2 ( )]ux vy

casM N

is not separable into products of

factors, unlike exp[ 2 ( )]ux vy

iM N

.

(a) (b)

(c) (d)

Fig. 3.47. Partitioned Complex Hartley Plane of Fingerprint





Since the One dimensional FHT has space advantage over the

one dimensional FFT for real numbered data, a method by Bracewell

[224] which is directly analogous to the two-dimensional FFT can be

108

used for the two dimensional fast Hartley transform. It takes the

one dimensional Hartley transform of the rows one by one, and then

transform the columns using the expression. Same approach is

implemented here. The intermediate Hartley transform is generated

by taking transform of rows first and then the even and odd rows of

this transforms are used for generating the coefficients for

(Even+jOdd) complex plane plot. These functions are similar to Cal

& Sal functions as used to generate the (Cal+jSal) complex plane.

The complex plane for Hartley transform is shown in Fig. 3.47. Plots

for (Even+jOdd) function points of full finger as well as core point

ROIs are shown. The feature vector as discussed earlier are

extracted from them and used for matching in exactly same way as

discussed for Walsh transform. The performance comparison of the

feature vectors is shown below.


Partitioned Hartley Even-Odd Function Fingerprint Matching.

Score Fusion based Matching Gives Higher Performance this is Indicated

by Bars in Red Colour. (TRF: Transform, FV: Feature Vector)

The core point based feature vectors give higher accuracy as

they have higher PI (Performance Index), we can see that first five

columns (belonging to fingerprint core point ROI based feature

vectors) have high EER as compared to last five columns for TAR-

TRR analysis. The fusion of row & column transform mean & Density

with DC & Sequency coefficient gives 94% PI for core point based

feature vector and that of full segmented fingerprint’s feature vector

gives 84% PI. The individual Row & column transform mean based

feature vectors have 88% & 89% PI for core point ROI based

RowTRF-CorePoint

ColTRF-CorePoint



Fusion-CorePoint

FV

RowTRF-Full

Finger

ColTRF-Full

Finger

Row-Density

-FullFinger

Col-Density

-FullFinger

Fusion- Full

FingerFV

PI 88 89 82 80 94 83 77 70 71 84

0102030405060708090

100

% P

I

Partitioned Hartley Even Odd Function Based Fingerprint Matching Performance Comparison of PI

109

feature vector, this shows that due to fusion of feature vector with

DC & Sequency component the performance has improved. Similar

improvement is seen with full fingerprint’s feature vectors as shown

in Fig. 3.48. Next we discuss Discrete Cosine Transform (DCT)

based feature vectors.

3.1.4.2 Fingerprint Matching using Partitioned DCT Plane in

Transform Domain

(a) (b)

(c) (d)

Fig. 3.49. Partitioned Complex DCT Plane of Fingerprint





110


Partitioned DCT Even-Odd Function Fingerprint Matching.



The discrete cosine transform (DCT) represents an image as a

sum of sinusoids of varying magnitudes and frequencies. The DCT

function for 2-dimensional image is given by Eqn. 3.62 & 3.63.

1 1 (2 1) (2 1)

B2 20 0

mnC CpqM N m p n p

A os osM Nm n

p q (3.62)

1 If 0

2 If 1 1

p pM

p MM

1 If 0

2 If 1 1

q qN

q NN

(3.63)

Where Bpq are called the DCT coefficients of A which can be an

image data A(m, n). The DCT decomposes a signal into its

elementary frequency components. When applied to an MXN

image/matrix, the 2D-DCT compresses all the energy information of

the image and concentrates it in a few coefficients located in the

upper-left corner of the resulting real-valued MXN DCT frequency

matrix [225]. First the DCT kernel of desired size is generated and

then it is used for generating intermediate transform matrix of the

input fingerprint image. The intermediate transforms are generated

as discussed for Walsh & Hartley transform to generate the complex

plane in transform domain using Even and Odd functions of the

RowTRF-CorePoint

ColTRF-CorePoint



Fusion-CorePoint

FV

RowTRF-Full

Finger

ColTRF-Full

Finger

Row-Density

-FullFinger

Col-Density

-FullFinger

Fusion -Full

FingerFV

PI 80 75 71 75 79 75 67 66 63 70

0

10

20

30

40

50

60

70

80

90%

PI

Partitioned DCT Even Odd Function Based Fingerprint Matching Performance Comparison of PI

111

intermediate transform. The even and odd functions are used to

plot (Even + jOdd) points in complex plane and then the feature

vector variants are extracted as discussed earlier. The complex

plane for DCT is shown in Fig 3.49. This plane is partitioned and

mean and density based feature vectors are extracted. The

matching results for these feature vectors are summarized in Fig.

3.50. The fusion of even and odd functions and their mean as well

as density with DC & Sequency component gives highest PI of 79%

for fingerprint core point ROI. The feature vector generated for full

fingerprint however have low PI of 70%.

(a) (b)

(c) (d)

Fig. 3.51. Partitioned Complex Kekre’s Transform Plane of Fingerprint





112

3.1.4.3 Fingerprint Matching using Partitioned Kekre’s Plane

in Transform Domain

The Kekre’s transform is discussed in detail in section 3.1.2.1.

The Kekre’s transform matrix is generated as discussed and then

the intermediate row and column transform of the fingerprint input

image is taken to extract the even and odd function points and

these points are plotted in complex plane. The partitioned complex

plane of Kekre’s transform even and odd function point are shown

in Fig. 3.51.

The Performance comparison of feature vectors extracted from

this is given in Fig.3.52. Here the Column Transform mean based

feature vector of fingerprint core point ROI gives best performance

of (PI=84% for Core TRF-Core Point Feature Vector). Fusion of

feature vectors has lower performance (PI=83% for Fusion-Core

point FV). For full fingerprint fusion of feature vectors gives PI of

81%, much higher than individual feature vectors EER. In the next

section we discuss the Kekre’s wavelets based feature vectors

performance.


Partitioned Kekre’s Transform Even-Odd Function Fingerprint Matching.



RowTRF-CorePoint

ColTRF-CorePoint



Fusion-CorePoint

FV

RowTRF-Full

Finger

ColTRF-Full

Finger

Row-Density

-FullFinger

Col-Density

-FullFinger

Fusion -Full

FingerFV

PI 76 84 80 81 83 64 72 68 69 81

0

10

20

30

40

50

60

70

80

90

% P

I

Partitioned Kekre's Transform Even Odd Function Based Fingerprint Matching Performance Comparison of PI

113

3.1.4.4 Fingerprint Matching using Partitioned Kekre’s

Wavelet’s Plane in Transform Domain

(a) (b)

(c) (d)

Fig. 3.53. Partitioned Complex Kekre’s Wavelet Plane of Fingerprint





The Kekre’s Wavelets are new family of wavelet, discussed in

section 3.1.2.1. Here the wavelets are used in a novel way to

extract the intermediate row & column wavelet transform. The

wavelet matrix is generated form Kekre’s transform matrix with

proper selection of M,N & P Parameters (p=M/N, takes as P=2 for

current feature vector generation using Kekre’s wavelets). The

wavelet matrix is used for taking intermediate column & row

transform. The even and odd functions of the intermediate

transform are used to plot (Even + jOdd) points in complex plane.

114

Here the wavelets are used for extracting the complex plane based

features in transform domain rather than the texture features of the

fingerprints. The complex plane plots are shown in Fig. 3.53. The

feature vectors are generated as discussed previously and the

fingerprint matching analysis is shown in Fig. 3.54.


Partitioned Kekre’s Wavelets Even-Odd Function Fingerprint Matching.


by Bar in Red Colours. (TRF: Transform, FV: Feature Vector)

Maximum PI is given by fusion of mean & density feature

vectors with DC & Sequency components , it is equal to 88% for

fingerprint core point ROI. The same for full fingerprint feature

vector gives 75% PI. It is seen that the performance of fingerprint

core point ROI based feature vector is higher as compared to full

fingerprint.

Next we compare the performance of all the techniques based on

partitioning of complex plane. Table 3.9 (a) & (b) and Fig. 3.55 give

comparison of Correct Classification Rates (CCR) of the fingerprint

Matching. CCR for fusion based feature vector is given.

RowTRF-CorePoint

ColTRF-CorePoint



Fusion-CorePoint

FV

RowTRF-Full

Finger

ColTRF-Full

Finger

Row-Density

-FullFinger

Col-Density

-FullFinger

Fusion- Full

FingerFV

PI 86 84 80 79 88 70 65 73 72 75

0102030405060708090

100

% P

I

Partitioned Kekre's Wavelets Even Odd Function Based Fingerprint Matching Performance Comparison of PI

115

Fig. 3.55. Performance Comparison for Accuracy (Correct Classification

Rate) of All the Transforms Discussed Above for Generation of

Partitioned Complex Plane in Transform Domain

Table 3.9

(a) Summary of Fingerprint Matching Tests for Partitioned Complex

Plane for Finger Core Point ROI Testing

Sr. Transform Successful Failure Total %Accuracy (CCR)

1 Walsh 457 73 530 86.20

2 Hartley 455 75 530 85.84

3 DCT 420 110 530 79.20

4 Kekre’s Transform 433 97 530 81.70

5 Kekre’s Wavelet 447 83 530 84.40

(b) Summary of Fingerprint Matching Tests for Partitioned Complex

Plane for Full Segmented Finger Testing

Sr. Transform Successful Failure Total %Accuracy (CCR)

1 Walsh 425 105 530 80.19

2 Hartley 410 120 530 77.36

3 DCT 403 127 530 76.04

4 Kekre’s Transform 411 119 530 77.55

5 Kekre’s Wavelet 406 124 530 76.60

86.2 85.84 79.2 81.7 84.4

80.19 77.36 76.04 77.55 76.6

0

10

20

30

40

50

60

70

80

90

100

Walsh Hartley DCT Kekre’s Transform Kekre’s Wavelet

%Accuracy (CCR)-Finger Core %Accuracy (CCR)-Full Finger

Partitioned Complex Plane Fingerprint Matching Testing Summary - % Accuracy (CCR) Comparison

116

Walsh transform based feature vectors give highest CCR followed by

Hartley Transform and Kekre’s Wavelets. DCT based feature vectors

has lowest accuracy for fingerprint matching. Specifically fingerprint

core point ROI based feature vectors have higher CCR as compared

to full segmented fingerprint. This is shown in Table 3.9 (a) & (b)

respectively. This shows the localizing core point or high curvature

point gives consistent texture pattern for feature vector extraction

and has higher matching rate.

3.1.5 Summary

In this chapter fingerprint matching using Kekre’s wavelets and

partitioned complex plane in transform domain of Walsh, Hartley,

Kekre’s Transform, DCT & Kekre’s wavelets is discussed. The

Kekre’s wavelets in the first approach are used for texture feature

extraction of the full fingerprint the Kekre’s wavelet based feature

vector gives 93% PI and 74% of correct classification ratio (CCR).


Partitioned Walsh, Hartley, DCT, Kekre’s Transform & Kekre’s Wavelet.

(Performance Index is Compared)

In another approach partitioned complex Walsh plane is used for

feature vector generation. Cal, Sal functions from intermediate

Walsh transform on rows and columns of fingerprint input image is

RowTRF-CorePoint

ColTRF-CorePoint

Row-Density -CorePoint

Col-Density -CorePoint

Fusion- CorePoint

FV

RowTRF-Full

Finger

ColTRF-Full

Finger

Row-Density -FullFinger

Col-Density -FullFinger

Fusion- Full

FingerFV

Walsh 85 88 80 82 95 80 70 66 69 81

Hartley 88 89 82 80 94 83 77 70 71 84

DCT 80 75 71 75 79 75 67 66 63 70

Kekre 76 84 80 81 83 64 72 68 69 81

KWT 86 84 80 79 88 70 65 73 72 75

0102030405060708090

100

Pe

rfo

rman

ce In

de

x

Performance Comparison of Walsh, Hartley, DCT, Kekre's Transform & Kekre's Wavelet Partitioned

Complex Plane in Transform Domain

117

used to find mean & density (Cal + jSal) points in complex Walsh

plane. These feature vectors are fused with DC & Sequency

information to achieve higher EER. First row in the table shown in

Fig. 3.56 shows EER for Walsh transform based feature vectors.

The complex Walsh Plane based on Cal & Sal functions of walsh

transform is applied to Hartley, DCT, Keker’s Transform & Kekre’s

Wavelets. The Cal & Sal functions here are referred as Even & Odd

Functions. The intermediate transform are used to generate

complex plane plots of (Even + jOdd) points. The table in Fig. 3.56

shows the PI comparison, Walsh & Hartley transforms have best PI

as well as Correct Classification Rate (CCR). This section has

discussed various correlation based fingerprint matching methods.

In the next sections different palmprint & Finger-knuckle print

matching algorithms will be discussed.

Fingerprint Feature Extraction & Matchingshodhganga.inflibnet.ac.in/bitstream/10603/9044/7/07... ·...

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Transcript of Fingerprint Feature Extraction & Matchingshodhganga.inflibnet.ac.in/bitstream/10603/9044/7/07... ·...