International Conference and Workshop on Emerging Trends in Technology (ICWET 2011) – TCET, Mumbai, India

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Finger-Knuckle-Print Verification using Kekre’s WaveletTransform

H B KekreComputer Science DepartmentMPSTME, NMIMS University

Mumbai, India+91-9323557897

hbk@yahoo.com

V A BharadiComputer Science DepartmentMPSTME, NMIMS University

Mumbai, India+91-9819125676

vinu_bharadi@rediffmail.comABSTRACTFinger-Knuckle-Print is an emerging biometric trait. Because ofhigh degree of uniqueness and low requirement of user co-operation it has got potential to become building block of futurebiometric security systems. In this paper we propose finger-knuckle-print verification using kekre’s wavelets. Kekre’swavelets are based on kekre’s transform and easy to construct. Wediscuss the feasibility of using kekre’s wavelet to extract spectralfeatures of the finger-knuckle-print and use them for verification.In this paper we have used wavelet energy feature, we havecompared the results with Haar wavelets. Kekre’s wavelet basedfeatures give moderate accuracy and performance is same as Haarwavelets.

Categories and Subject DescriptorsI.4.7 Image Processing and Computer vision

General TermsMeasurement, Performance, Design, Experimentation, Security,Human Factors, Verification.

KeywordsBiometrics, Finger-Knuckle-Print, Kekre’s Wavelets.

1. INTRODUCTIONWith the advancement in the technology various methods ofperson identification are possible because of availability ofaffordable and co-operative sensors as well as capable processingcomputers and storage media. Another driving force behindwidespread use of biometrics is the terrorism and need of bettermechanism to protect sensitive areas where public interaction ismore, like airports and railway stations. The methods arenumerous, and are based on different personal characteristics.Voice, lip movements, hand geometry, face, odor, gait, iris, retina,fingerprint are the most commonly used authentication methods.All of these and behavioral characteristics are called biometrics[1], [2].The biometrics is most commonly defined as measurablepsychological or behavioral characteristic of the individual thatcan be used in personal identification and verification [3], [4].

The biometrics is mainly concerned with ‘what you are’ ratherthan ‘what you carry’. The driving force of the progress in thisfield is, above all, the growing role of the Internet and therequirements of society [4],[5]. Therefore, considerableimplementations can be found in the area of electronic commerceand electronic banking systems and security applications of vitalinstallations [6].The biometrics has a significant advantage over traditionalauthentication techniques (namely smartcards, PIN numbers,passwords etc.) due to the fact that biometric characteristics of aperson are not easily transferable, are unique of every person, andcannot be lost, stolen or broken. The choice of one of thebiometric solutions depends on several factors [2]:

User acceptance Level of security required Accuracy Cost and implementation time

Fingerprint, Palm-print, Speech, Face, Iris, Retina, HandGeometry, Ear Geometry are commonly used biometric means ofhuman authentication [1],[2],[3],[4] besides there are otherbiometric traits also. Any part of human body is unique and wecan use it as biometric trait provided we have a scanner forcapturing that area.Finger-knuckle-print (hereafter referred as FKP) is one ofemerging biometric traits, as scanner or capturing hardware forthis has been developed and database for research purpose isavailable [7]. The finger-knuckle-print (FKP) refers to the imageof the outer surface of the finger phalangeal joint. TypicalKnuckle-Print image is shown in Fig. 1, taken from the PolyUFKP database. Researchers at Hong Kong PolyU University havedeveloped scanner for FKP [9] this is shown in Fig. 1 (a).To implement a good biometric security system, we need to verifythe biometric trait using feature vector [1],[2],[7],[8]. The featurevector is the information extracted from captured data. To extractthe feature vector we need to segment the region of interest whichcontains information relevant for feature extraction, this is calledas Region of Interest (ROI) [9],[10],[11]. A typical ROI extractedfrom FKP image is shown in Fig. 2.

(a)

Permission to make digital or hard copies of all or part of this work forpersonal or classroom use is granted without fee provided that copies arenot made or distributed for profit or commercial advantage and thatcopies bear this notice and the full citation on the first page. To copyotherwise, or republish, to post on servers or to redistribute to lists,requires prior specific permission and/or a fee.ICWET’11, February 25–26, 2011, Mumbai, Maharashtra, India.Copyright © 2011 ACM 978-1-4503-0449-8/11/02…$10.00

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(b)Figure 1. (a) Finger Knuckle Print Capture Device [9] (b)Typical Finger-Knuckle-Print Image from Hong KongPolytechnic University FKP Database [7].Wavelet Transform has been widely used to extract localizedspectral information in the given data. In this paper we have useda new family of wavelets called kekre’s wavelets. The kekre’swavelets are derived from kekre’s transform [12]. This will bediscussed in coming sections. In the next section we discuss thedifferent approaches for FKP verification.

Figure 2. Region of Interest (ROI) segmented from FKPshown in Fig. 1.

2. FINGER-KNUCKLE-PRINT AS ABIOMETRIC TRAITAmong different kinds of biometric traits, hand-based biometricshas been attracting considerable attention over recent years.Fingerprint, palmprint, hand geometry, hand vein [1],[2],[4], andinner-knuckle-print [17],[18] have been proposed and discussedin the literature. The popularity & widespread use of hand-basedbiometrics should be attributed to its high user acceptance. In fact,the image pattern in the finger knuckle surface is highly uniqueand thus can serve as a distinctive biometric identifier [8]. FKPbeing recent has been yet to be thoroughly discovered. Thecurrent research has shown great potential in FKP to be used as anefficient and accurate biometric trait [8],[9],[10],[11].Hand geometry, especially 3D features from finger surface hasbeen used in [13],[14] as a biometric traits but specific localizedpart has not been proposed. They used curvature based shapeindex to represent the finger back surface, rather than texture richFinger-knuckle surface.Ravikanth & Kumar [15],[16] have proposed use of finger backsurface as biometric feature; the whole back surface of hand iscaptured and then pre-processed to isolate the finger knuckle.They used subspace analysis using PCA & LDA for FKP analysis,in [10] L. Zang et al. have discussed this as a sub-optimalapproach for FKP verification.L. Zang et al. have captured FKP using a specially developeddevice which essentially captures finger knuckle in a localizedway, without much redundancy as only the concerned fingers

back surface is captured[8],[9],[10],[11]. Band limited phase onlycorrelation function is proposed in [11] by them which give EERin the range of 5.5% to 0.31 %. In [9] they have proposed a local-global feature fusion for FKP verification; Local features areextracted using a bank of Gabor filters convolved with FKP ROIand global features are taken from band limited phase onlycorrelation function.In this paper propose use of wavelet based features, specificallywavelet energy of the FKP ROI for verification purpose. We areusing a new family of wavelets called kekre’s wavelets. Wediscuss this in the next section.

3. KEKRE’S WAVELETSKekre’s wavelets are orthogonal family of wavelets. Forgeneration of kekre’s wavelets we need basis function as in caseof other families, this basis functions are generated from Kekre’sTransform matrix.

3.1 Kekre’s Transform [12],[19]Let us generate the Kekre’s Matrix [K] for size m x m where mcan be any integer not necessarily the power of 2 as required formany other conventional transforms. This matrix has all 1’s on themain diagonal and upper triangle of the matrix. The sub-diagonaljust below the main diagonal has the value (-m + i) where ‘m’ isthe order of matrix and ‘i’ is the column number. Rests of theelements of lower triangle below the sub diagonal are all zeros.The general form of Kekre’s matrix [K] can be written as

The formula for generating the element Kxy of Kekre’s transformmatrix is,

(1)

The properties of Kekre’s Transform are as follows:1) The Kekre’s transform is real and orthogonal transform.

a. [K]T [ K]=[µ] (2)Where [k]T is transpose of [K] and [µ] is a diagonalmatrix and its elements are given by µ11 = m

µii = (m-i+1)(m-i+2) (3)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 fortransforming a column vector of dimension mx1. For anormal matrix transformation we require m2 multiplicationsand m (m-1) additions.

3) The transform of a vector f is given byF = [K] f (4)

And inverse is given by

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f = [K]T [µ]-1 F (5)

3.2 Kekre’s Wavelets [12]Kekre’s Wavelet transform is derived from Kekre’s transform.From NxN Kekre’s transform matrix, we can generate Kekre’sWavelet transform matrices of size (2N)x(2N), (3N)x(3N),……,up to maximum (N2)x(N2). For example, from 5x5 Kekre’stransform matrix, we can generate Kekre’s Wavelet transformmatrices of size 10x10, 15x15, 20x20 and 25x25.

Figure 3. Kekre’s Transform (KT) matrix of size NxN.

In general MxM Kekre’s Wavelet transform matrix can begenerated 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. MxM Kekre’s Wavelet transform matrix generated from NxNKekre’s transform matrix is shown in Fig 4. First ‘N’ number ofrows of Kekre’s Wavelet transform matrix is generated byrepeating every column of Kekre’s transform matrix P times. Togenerate remaining (M-N) rows, extract last (P-1) rows and last Pcolumns from Kekre’s transform matrix and store extractedelements in to temporary matrix say T of size (P-1) x P . Fig. 4shows extracted elements of Kekre’s transform matrix stored in T.In general MxM Kekre’s Wavelet transform matrix can begenerated 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. MxM Kekre’s Wavelet transform matrix generated from NxNKekre’s transform matrix is shown in Fig 4. First ‘N’ number ofrows of Kekre’s Wavelet transform matrix is generated byrepeating every column of Kekre’s transform matrix P times. Togenerate remaining (M-N) rows, extract last (P-1) rows and last Pcolumns from Kekre’s transform matrix and store extractedelements in to temporary matrix say T of size (P-1) x P . Fig. 4shows extracted elements of Kekre’s transform matrix stored in T.

Figure 4.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

(3.43)First row of T is used to generate (N+1) to 2N rows of Kekre’sWavelet transform matrix. Second row of T is used to generate(2N+1) to 3N rows of Kekre’s Wavelet transform matrix, Likewise last row of T is used to generate ((P-1) N + 1) to PN rows[12].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 thePalmprint image using these wavelet matrices.

3.2.1 Properties of Kekre’s Wavelet Transform:1. Orthogonal- The transform matrix K is said to be orthogonal ifthe following condition is satisfied.

[K][K]T = [D], Where D is a diagonal matrix.Kekre’s Wavelet Transform matrix satisfies this property andhence it is orthogonal. The diagonal matrix value of Kekre’stransform matrix of size NxN can be computed as

(6)

2. Asymmetric- As the Kekre’s transform is upper triangularmatrix, it is asymmetric.

3. Non Involutional - An involutionary function is a function thatis its own inverse. So involution transform is a transform which isinverse transform of itself. Kekre’s transform is non-involutiontransform.

4. Transform on Vector -The Kekre’s Wavelet transform on acolumn vector f is given by

F = [KW] f (7)And inverse is given by

f = [KW]T [D]-1 F (8)5. Transform on 2D Matrix- Kekre’s Wavelet transform on 2Dmatrix f is given by

[F] = [KW] [f] [KW]T (9)Obtaining Inverse:

Calculate Diagonal matrix D as,[D] = [KW][KW]T (10)

Inverse is calculated as[f] = [KW]T [ Fij / Dij ] [KW] (11)

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

(a)

(b)

Figure 5. (a) Orientation of Bbocks for feature extraction (b)Three blocks of 128X128 Pixels.

4. FKP FEATURE EXTRACTION USINGKEKRE’S WAVELETSThe Feature vector is extracted using Kekre’s Wavelets. We areusing Wavelet Energy Feature [21]. We are using Kekre’sWavelet and comparing the results with Haar Wavelets. TheRegion of Interest (ROI) is a texture rich surface (consisting ofWrinkles) as shown in Fig. 5(a). The wavelets will capturelocalized spectral information from the ROI. We have the ROI ofSize 256 X 128 Pixels; we divide the ROI in three Blocks of 128X 128 Pixels size as follows,Each block shown in Fig. 5(b) is of 128X128 Pixels size, now wecan implement wavelet transform on it. We take wavelet transformup to 3 Levels (128, 64 and 32). At each level we have four set ofwavelet coefficients LL, LH, LH, HH. LL component is used fornext level after down sampling the inverse of LL only waveletcoefficients. We find the sum of coefficients in LH, HL & HHBlocks. This is given by [21],

-1 -12

0 0[ , ]

W W

LCi j

WE WC i j

(3.61)

L=0, 1, 2; C = 0(LH), 1(HL), 2(HH) & W is the Size of WaveletComponent (64, 32, 16)

Figure 6. Wavelet Coefficients blocks for Wavelet EnergtyFeature.

We have three decomposition levels, and each level gives 3Wavelet Energy (WE) values, hence for each block of FKP image

we get total 9 Values. Such three blocks are there hence for aFinger-Knuckle-Print there are total 27 values in a feature vector.Currently we are using sum of all WE coefficients in a component(LH, HL or HH). This is shown in Fig. 6.

01 22 0

01 22 2

.. .. ,..,

..KW

WE WE

WWE WE

(3.62)

We have taken the values as it is without normalization. Suchfeature vectors are generated for both Kekre’s Wavelets and Haarwavelet. To find the matching between two FKP’s we take theEuclidian distance between two feature vectors W1 & W2 (bothKekre’s Wavelet & Haar).

1

01 2

N

n nn

E D W W

(Where N=27) (3.63)

The feature vector generation and distance measurement methoddiscussed here will be used for FKP verification. We haveextracted this feature vector for the segmented FKP ROI usingKekre’s Wavelets and Haar Wavelets, kekre’s waveletsperformance is compared with that of Haar Wavelets. This isdiscussed in next section.

5. FKP RECOGNITION RESULTS &DISCUSSIONSWe have used POLYU FKP [7] database for testing our method.The testing code is written in Microsoft Visual C# 2005 (.NETFramework 2.0). Testing is performed on AMD Athlon 64 FX 1.8GHz processor, with 1.5GB RAM and Windows XP SP3 (32 Bit)Operating System. We have extracted feature vector using Kekre’swavelet and Haar Wavelet. Total 512 tests were performed onFKP database. In this experiment we have mainly analyzeddiscrimination capacity of Kekre’s wavelets and their feasibility inspectral feature extraction.We have performed intra-class and inter-class matching. This willbe used to analyze genuine and imposter identification capabilityof the FKP based verification. The Kekre’s Wavelet FeatureVector’s distance for Genuine FKP matching (Intra-class) andimposter (Forgery) FKP matching (Inter-class) with theprobability of occurrence is shown in Fig. 7. The graph shows thattwo different classes formed for the genuine and forgery class.The distance vs. probability plot clearly indicates that there aretwo separate classes of distance; the Genuine Distance class andForgery (Imposter) Distance class, separated by a threshold of475.Furthermore we have performed TAR-TRR analysis [1],[2] forboth Kekre’s Wavelets and Haar Wavelet based feature vector, wehave performed this analysis on the data of above mentioned 512tests. Euclidian distance based classification was used, it wasfound that Haar Wavelets and Kekre’s wavelets give same EqualError Rate (EER)[1] of 80% for True Acceptance Rate (TAR) Vs.True Rejection Rate (TRR) analysis. The EER for FalseAcceptance Rate vs. False Rejection Rate (FRR) was found to be20%; as shown in Fig. 8 (a) & (b).

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Figure 7. Kekre’s Wavelet Distance ProbabilityTwo separate classes belonging to Genuine and Forgery tests are clearly visible. Overlapping is higher due to localized coefficients

are not consider but full componentwise sum is used for generating feature vector.

(a)

(b)

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Figure 8. TAR Vs. TRR Plot for Kekre’s and Haar Wavelet

Table I gives the summary of testing for Haar & Kekre’sWavelets.

Table 1Performance Summary

Sr. Type ofWavelet

EER (TAR-TRR)

EER (FAR-FRR)

1 Kekre’sWavelet

80% 20%

2 HaarWavelet

80% 20%

As compared to the systems suggested in [8],[9],[10],[11] thecurrent system as lower performance level, but this is mainly dueto the simpler classifier used. If a Neural Network based classifierwith proper training is used the system can achieve better EER.Another thing is that we have used the Kekre’s Wavelet transform(KWT) for first time for pattern recognition, KWT is simpler togenerate and involves only integer values in wavelet matriceshence faster calculations can be achieved; it gives results same asHaar Wavelets. This makes kekre’s Wavelet Transform veryattractive for extraction for Spectral information for patternRecognition.

6. CONCLUSIONIn this paper we have proposed use of a new family of waveletscalled as Kekre’s Wavelets for Finger-Knuckle-Print Verification.Kekre’s Wavelet are faster than Haar wavelet as the TransformMatrix has only integer values. The proposed system givesmoderate EER of 80% bute performance is equal to HaarWavelets. This indicates that kekre’s wavelets have great potentialto be used for spectral feature extraction. The performance can beimproved by using neural network based classifier with propertraining.

7. ACKNOWLEDGMENTSAuthors are very thankful to L. Zhang, Assistant Professor,Biometric Research Centre (UGC/CRC), The Hong KongPolytechnic University, for providing the Finger-Knuckle-Printdatabase. This database has been a key resource for this research.

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