Master Thesis - Department of Computer Science

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X 1 X i X C (a) Covariance Sum method on XNull and XRange, to obtain W Dual . or (b) Gramm-Schmidt Orthonormalization method on [W Null orthonormal basis W Dual . 7. Select optimal feature set by using either opt ,W Range opt (a) Forward Selection procedure to select optimal features W Dual opt based on class separability criterion given in Eqn. 4.28. or (b) Backward Selection in the same manner to form W Dual opt . 8. Project all training samples on W Dual opt . 9. Recognition stage: (a) Project probe sample, presented for recognition, on W Dual opt . ], to obtain from W Dual (b) Find distance of the projected probe to nearest training sample from each class. (c) Label the probe with the class corresponding to the minimum distance value. µ1 µi µC Null Space of Sw Range Space of Sw XNull x 1 Null x i Null x C Null XRange x 1 Range x i Range x C Range W Null opt W Range opt Fusion W Dual Figure 4.3: Architecture of our proposed method of feature fusion. 82 Backward/ Forward Selection W Dual opt
The architecture of our proposed method is given in Fig. 4.3 where X i denote the training set for class i. XNull and XRange are the two sets of means projected on null space and range space separately. W Null Opt and W Range Opt are the sets of discriminative directions available in null space and range space and W Dual Opt represents the optimal combined discriminative directions obtained from both spaces. The decision fusion strategy is described in the following section. 4.4 Decision Fusion The response vectors obtained from null and range classifiers are combined using three decision fusion techniques. Among them sum rule and product rule [59], [60] are adopted from already existing literature and third one is proposed by us. The response vectors on a sample x obtained from null and range classifiers can be expressed as a matrix of size 2 × C and is denoted by DP (x) [68], ⎡ ⎢ DP (x) = ⎣ d1Null (x) . . . diNull (x) . . . dCNull (x) d1 Range(x) . . . di Range(x) . . . dC ⎤ ⎡ ⎥ ⎢ ⎦ = ⎣ Range(x) DNull(x) ⎤ ⎥ ⎦ DRange(x) (4.29) The task of a combination rule, F, is to construct ˜ D(x) = [ ˜ d 1 (x), . . . , ˜ d i (x), . . . ˜ d C (x)], the fused soft class label provided by two classifiers as: ˜D(x) = F(DNull(x), DRange(x)) (4.30) The fused soft class label can be hardened to a crisp class label c, by maximum/ minimum membership rule, based on the fact that measurements of a response vector represent similarity/dissimilarity: L(x) = arg max c where L(x) represents the class label assigned to x. 4.4.1 Existing Techniques for Decision Fusion ˜d c (x). (4.31) Given DP (x), sum and product rules operate class-wise on each column of DP (x) to produce ˜ D(x) [60, 68]. • Sum Rule: Sum Rule computes the soft class label vectors using: ˜d j (x) = d j Null (x) + djRange(x), j = 1, ...., C (4.32) 83
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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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Page 69 and 70: Image Rows h(.) g(.) 2 2 Columns Fi
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Page 75 and 76: Genuine Impostor Scores Scores 1 0
Page 77 and 78: Error d1 = (1 − TZeroF RR) d2 = |
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Page 83 and 84: Table 3.3: Peak Recognition Accurac
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Page 87 and 88: Table 3.7: Performance of Ekenel’
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Page 91 and 92: to our proposed method. Section 4.2
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(a) (b) Figure A.10: (a) and (b) sh
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(a) (b) Figure A.12: Binarized imag
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(a) (b) Figure A.14: Thinned images
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(a) (b) Figure A.16: Thinned finger
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Paired Minutiae Minutiae with unmat
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Bibliography [1] FVC 2002 website.
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[25] Li-Fen Chen, Hong-Yuan Mark Li
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[49] Lin Hong, Yifei Wan, and Anil
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[71] L. Lam and C. Y. Suen. Applica
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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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