Master Thesis - Department of Computer Science

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We exploit classifier space in two ways: 1. LDA and 2. Nonparametric LDA. LDA and nonparametric LDA are discussed in Section 4.4.2.1 and Section 4.4.2.2, respectively. We combine face and fingerprint (two modalities for person authentication) using our proposed algorithm, described in this section. As already discussed in Section 5.2, our aim is to improve combined performance by conditionally replacing response vector Di(x) by our proposed measure, ¯ Di(x), in DP(x) to obtain ¯ DP (x), classifier- wise by using train and validation response vector sets (obtained on two disjoint validation sets, validation1 and validation2). Now for each of the L classifier, we construct train, validation and test response vector sets, denoted by RV RV T R i , RV V A i and RV T S i T R i , RV V A i T S and RVi , where i = 1, 2, ..., L. Precisely, form the sets of the i th rows of the DP’s constructed from validation1 validation2 and test set feature vectors respectively. Now let validation1 validation2 and test set feature vectors for i th classifier are denoted by: (i) validation1 feature vector set: {ux11 , ux21 M T R , . . . , ux i 1 12 mc M T R , ux , . . . , ux , . . . , ux i C }, (ii) validation2 feature vector set: {vx11 , vx21 M V A , . . . , vx i 1 12 mc M V A , vx , . . . , vx , . . . , vx i C }, and (iii) test feature vector set: {tx11 , tx21 M T S , . . . , tx i 1 , tx 12 , . . . , tx mc , . . . , tx M T S i C }, where for i th classifier the number of response vectors per class for the three disjoint T R sets are M i , M V A i , M T S i respectively. The superscript “mc” on a feature vector (e.g. ux mc ) denotes the m th sample from c th class of the corresponding set. So the response vector sets can be visualized as: T R RVi ≡ {Di(ux 11 ), . . . , Di(ux V A RVi ≡ {Di(vx 11 ), . . . , Di(vx T S RVi ≡ {Di(tx 11 ), . . . , Di(tx M T R i 1 ), Di(ux 12 ), . . . , Di(ux mc M T R ), . . . , Di(ux i M V A i 1 ), Di(vx 12 ), . . . , Di(vx mc M V A ), . . . , Di(vx i M T S i 1 ), Di(tx 12 ), . . . , Di(tx mc ), . . . , Di(tx M T S i C )}. C )}, C )}, The steps of our algorithm is given below for L classifiers, even though we are dealing with the case where L = 2. 106
5.3.1 The Algorithm The steps of our algorithm are as follows: 1. For i= 1,2,..., L do 1.1 Evaluate performance of classifier Di on validation response vector set RV V A i and denote it by P DIR(RV Di 1.2 Use train response vector set RV T R i V A i based on LDA or nonparametric LDA. 1.3 Evaluate the performance of classifier Di on RV ). of classifier Di to construct eigenmodel V A i V A constructed in previous step. For m = 1, 2, ..., Mi select each Di(x mc ) from set RV V A i and do the following: in the eigenmodel and c = 1, 2, ..., C, (a) Project Di(x mc ) on LDA or nonparametric LDA-based eigenmodel. (b) Calculate the class scores by measuring the Euclidean distance from Di(x mc ) to the nearest sample from every class in the eigenmodel to generate ¯ Di(x mc ). (c) Use minimum membership rule on ¯ Di(x mc ) to produce crisp class label for x mc . (d) Cross check the generated class label with actual class label of x mc . Calculate the performance accuracy on RV If P EM Di V A (RVi ) > P DIR Di (RV continue for next classifier. V A i V A i and denote it by P EM Di V A (RVi ). ) then continue, else go back to step 1.1 to 1.4 For an unknown test sample x, select Di(x) from set RV ¯Di(x) using the following steps. T S i and calculate (a) Project Di(x) on LDA or nonparametric LDA-based eigenmodel generated in step 1.2. (b) Calculate the new class scores for x as ¯ Di(x) by measuring the Eu- clidean distance from Di(x) to the nearest response vector from every class in the eigenspace. The elements of RV T S i are now ¯ Di(x) instead of Di(x). 107
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DEVELOPMENT OF EFFICIENT METHODS FO
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To My Parents, Sisters and Dearest
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Mirnalinee, Shreyasee, Lalit, Manis
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LDC Linear Discriminant Classifier
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3 An Efficient Method of Face Recog
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A.6 Minutiae Matching . . . . . . .
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4.1 Effect of increasing number of
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List of Figures 2.1 Summary of appr
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3.7 Area difference between genuine
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Abstract Biometrics is a rapidly ev
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CHAPTER 1 Introduction The issues a
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1.1.1 Applications Biometrics has b
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• Spoof Attacks: An impostor may
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• A new approach for multimodal b
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CHAPTER 2 Literature Review This re
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ange [23], infrared scanned [137] a
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u 2 x 2 u 1 x 1 (a) PCA basis (b) P
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PCA Projection Class 1 Class 2 LDA
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F DIFS DFFS F (a) (b) F 1 L Figure
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image A of m rows and n columns is
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faces of 40 subjects. • Others: A
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malizing the vector components, the
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Figure 2.5: A fingerprint image wit
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features (gradient coherence, inten
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Figure 2.7: Examples of minutiae; A
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according to the local orientation
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• Parallel Mode: This operational
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can address the problem of noisy se
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Prior to Matching Sensor Level Feat
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determined by logistic regression.
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Class-indifferent Methods • Decis
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3. The final DS soft vector is calc
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on three face databases and compare
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for a face. This was illustrated by
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Image Rows h(.) g(.) 2 2 Columns Fi
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in the accuracy of face recognition
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(a) (a1) (a2) (a3) (b) (b1) (b2) (b
Page 75 and 76: Genuine Impostor Scores Scores 1 0
Page 77 and 78: Error d1 = (1 − TZeroF RR) d2 = |
Page 79 and 80: The algorithm for obtaining the sub
Page 81 and 82: each subject, 42 samples (flashes f
Page 83 and 84: Table 3.3: Peak Recognition Accurac
Page 85 and 86: Table 3.5: Peak Recognition Accurac
Page 87 and 88: Table 3.7: Performance of Ekenel’
Page 89 and 90: Table 3.9: Performance of Ekenel’
Page 91 and 92: to our proposed method. Section 4.2
Page 93 and 94: plored both of the spaces to captur
Page 95 and 96: project only the class means in ran
Page 97 and 98: ΩNull and ΩRange represents the
Page 99 and 100: Thus, calculation of the QR factori
Page 101 and 102: 4.3.3 Algorithm for Feature Fusion
Page 103 and 104: The architecture of our proposed me
Page 105 and 106: T R T S denoted by RVNull and RVNul
Page 107 and 108: x DNull DRange DP (x) DNull(x) DRan
Page 109 and 110: C 2 C 1 C 1 C 2 C X X 2 M X M X 2 1
Page 111 and 112: iii) Project all class means onto n
Page 113 and 114: Table 4.1: Effect of increasing num
Page 115 and 116: Table 4.3: Effect of increasing num
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Page 119 and 120: Table 4.6: Performance of Dual Spac
Page 121 and 122: 5.1 Introduction In recent years, t
Page 123 and 124: This means for a classifier D: r i
Page 125: validation1, validation2 and test.
Page 129 and 130: 5.4 Experimental Results In this ch
Page 131 and 132: sets. • We put as much as possibl
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Page 135 and 136: LDA and LDA produce the same accura
Page 137 and 138: space. If the training data uniform
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Page 141 and 142: also be introduced. But class speci
Page 143 and 144: These stages are discussed in the f
Page 145 and 146: (a) (b) Figure A.2: Input fingerpri
Page 147 and 148: (a) (b) Figure A.4: Orientation ima
Page 149 and 150: (i) For each block centered at (i,
Page 151 and 152: (a) (b) Figure A.7: Enhanced images
Page 153 and 154: (a) (b) Figure A.10: (a) and (b) sh
Page 155 and 156: (a) (b) Figure A.12: Binarized imag
Page 157 and 158: (a) (b) Figure A.14: Thinned images
Page 159 and 160: (a) (b) Figure A.16: Thinned finger
Page 161 and 162: Paired Minutiae Minutiae with unmat
Page 163 and 164: Bibliography [1] FVC 2002 website.
Page 165 and 166: [25] Li-Fen Chen, Hong-Yuan Mark Li
Page 167 and 168: [49] Lin Hong, Yifei Wan, and Anil
Page 169 and 170: [71] L. Lam and C. Y. Suen. Applica
Page 171 and 172: IEEE Tran. on Pattern Analysis and
Page 173 and 174: of-the-Art Systems. IEEE Tran. on P
Page 175 and 176: and Human Communication, pages 374-
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Master Thesis - Department of Computer Science

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