Master Thesis - Department of Computer Science

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We try to enhance the performance of decision fusion by exploitation of individual classifier space on the basis of availability of contextual information. Contextual information refers to the fact that, when a sample of a particular subject is presented the similarity it shows for different classes is subject specific. This means that if the outputs of a classifier output for the samples of a specific class are well clustered and distinct from other clusters, there exists a scope of using this information to enhance the class separability at classifier output space in order to improve the individual classifier’s performance. This will in turn enhance the performance of fusion. Face and fingerprint are the two modalities to be combined in our case. Prior knowledge (training data at decision level) about each classifier space helps us to know that subject-wise contextual information is present in case of face but not for fingerprint. Fingerprint classifier is unable to show subject-wise contextual information because of it’s sensitivity to the number, occurrence and distribution of matched minutiae between two fingerprints. Hence in our approach, we try to improve the face space as much as possible and then combine with fingerprint. For enhancing the performance of face classifier, we use the classifier output (known as response vectors) on a validation set as the training data at fusion level for building up an LDA or nonparametric LDA-based eigenmodel and thereby enhancing class-separability. 5.2 Theoretical Basis Let x ∈ R n be a feature vector and {1, 2, ......, C} be the set of C classes. A classifier is called a mapping: D : R n → [0, 1] C The output of a classifier D will be called as response vector and denoted by RD(x), a C dimensional vector, where: RD(x) = (r 1 D(x), r 2 D(x), ....., r C D(x)) , r i D(x) ∈ [0, 1] (5.1) The components {ri D (x)} can be regarded as estimates of the posterior probabilities of (dis)similarity or (dis)belief provided by classifier D, for all classes, for a sample x. 102
This means for a classifier D: r i D (x) = P (i|x), i = 1, 2, ....., C. (5.2) Response vector is also known as the soft class label provided by a classifier. The decision of a classifier can be hardened to a crisp class label c, where c ∈ {1, 2, ......, C}, by maximum (minimum) membership rule, based on the fact that elements of response vector represent similarity (dissimilarity): D(x) = arg max r c c D(x). (5.3) In a traditional multiple classifier system, a feature vector x is classified into one of the C classes using L classifiers {D1, D2, ......, DL}, using the feature vectors xl, l = 1, 2, ..., L respectively. Measurement level (also called response vector level) combination strategies give final decision by fusing the response vectors from multiple classifiers. Formally, for a feature vector x, response vectors from multiple classifiers can be organized as a matrix called decision profile (DP): ⎡ ⎤ ⎡ ⎤ ⎢ d1,1(x) ⎢ . . . ⎢ DP (x) = ⎢ di,1(x) ⎢ . . . ⎣ dL,1(x) . . . . . . . . . . . . . . . d1,j(x) . . . di,j(x) . . . dL,j(x) . . . . . . . . . . . . . . . d1,C(x) ⎥ ⎢ D1(x) ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ . . . ⎥ ⎢ . . . ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ di,C(x) ⎥ = ⎢ Di(x) ⎥ ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ . . . ⎥ ⎢ ⎥ ⎢ . . . ⎥ ⎦ ⎣ ⎦ dL,C(x) DL(x) We denote i th row of the above matrix as Di(x) = [di,1(x), ....., di,C(x)], where di,j(x) is the degree of support given by classifier Di to the hypothesis that x belongs to class j. Di(x) is the response vector of classifier Di for the sample x. The task of any combination rule is to construct ˜ D(x), the fused output of L classifiers as: ˜D(x) = F(D1(x), . . . , Di(x), . . . , DL(x)). (5.4) Some fusion techniques known as class-conscious [68], do column-wise class-by-class operation on DP(x) matrix to obtain ˜ D(x). Example of this type of fusion techniques are: sum, product, min, max, etc [60]. Another fusion approach known as class- indifferent [68], use entire DP(x) to calculate ˜ D(x). The later needs training at fusion level in the sense that it has to create one or more than one templates per class from 103
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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
Page 71 and 72: in the accuracy of face recognition
Page 73 and 74: (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: 5.1 Introduction In recent years, t
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Page 127 and 128: 5.3.1 The Algorithm The steps of ou
Page 129 and 130: 5.4 Experimental Results In this ch
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Page 135 and 136: LDA and LDA produce the same accura
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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
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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
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of-the-Art Systems. IEEE Tran. on P
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and Human Communication, pages 374-
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Master Thesis - Department of Computer Science

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