Master Thesis - Department of Computer Science

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Fig. 3.1 shows the block diagram of the proposed method. Fig. 3.1 (a) shows the generation of the subband face. The face image is decomposed into several subbands using the analysis filter of 2D Discrete Wavelet Transform (2D-DWT). The 2D-DWT is successively applied to the approximations to obtain a dyadic decomposition [38]. The subbands thus obtained can be used to reconstruct the original face using the inverse DWT (by synthesis filters). The subband face is obtained from selected subbands by partial reconstruction of the original face. Fig. 3.1 (b) shows that the subband face is transformed from image-space to feature-space by applying subspace methods (PCA , LDA, 2D-PCA, 2D-LDA and DCV). The details of the subspace methods used for integrating with subband face representation are provided in section 2.1.1.1. The features thus obtained are matched using the nearest neighbor strategy. 3.2 Subband Face Representation A set of suitable wavelet subbands are selected to generate the subband face using IDWT, for recognition using PCA, LDA, 2D-PCA, 2D-LDA and DCV. The method of reconstructing a subband face is described in the following. 3.2.1 Wavelet Decomposition The wavelet transform [38] is expressed as a decomposition of a signal f(x) ∈ L 2 (R) into a family of functions which are translations and dilations of a mother wavelet function ψ(x). The 2D wavelet transform uses a family of wavelet functions and its associated scaling function to decompose the original image into different subbands, namely the low-low (LL), low-high (LH), high-low (HL) and high-high (HH) subbands, which are also known as A (approximations), H (horizontal details), V (vertical details), D (diagonal details), respectively. Fig. 3.2 shows the 2D-DWT performed using low pass h(.) and high pass g(.) filters [83]. The decomposition pro- cess can be recursively applied to the low frequency channel (LL) to generate dyadic decomposition at the next level. Fig. 3.3 shows a face image, and its level-1 and level-3 dyadic decompositions using the 4-tap Daubechies [30] wavelet filter. Lowest level approximation subband 48
Image Rows h(.) g(.) 2 2 Columns Figure 3.2: Two dimensional discrete wavelet transform (DWT) for an image: The low pass filter h(.) and the high pass filter g(.) are applied along the rows initially followed by downsampling by a factor of two. This is followed by filtering using h(.) and g(.) along the columns and downsampled by factor of two. of the wavelet decomposition can be further decomposed using the DWT, giving a multi-level dyadic subband decomposition of the face. In the following subsection, the method of reconstructing a subband face using selective wavelet-decomposed subbands is discussed. 3.2.2 Subband Face Reconstruction A face image of a person contains common (approximations) as well as discriminatory (details) information with respect to faces of all other persons. The discriminatory information is due to structural variations of the face which are acquired as intensity variations at different locations of the face. The location and degree of intensity variations in a face of an individual are unique features which discriminate one from the rest of the population. The similarity of a face with respect to another is in the global appearance and structure of the face. These information (similar and discriminatory) are segregated at different subbands using different levels of decomposition of the face image. Wavelet decomposition helps to split the features of a face in different subbands with “approximations” containing the common (smooth) parts of the face and “details”, at certain levels of decomposition, containing the discriminatory (vari- 49 h(.) g(.) h(.) g(.) 2 2 2 2 LL LH HL HH
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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
Page 17 and 18: 3.7 Area difference between genuine
Page 19 and 20: Abstract Biometrics is a rapidly ev
Page 21 and 22: CHAPTER 1 Introduction The issues a
Page 23 and 24: 1.1.1 Applications Biometrics has b
Page 25 and 26: • Spoof Attacks: An impostor may
Page 27 and 28: • A new approach for multimodal b
Page 29 and 30: CHAPTER 2 Literature Review This re
Page 31 and 32: ange [23], infrared scanned [137] a
Page 33 and 34: u 2 x 2 u 1 x 1 (a) PCA basis (b) P
Page 35 and 36: PCA Projection Class 1 Class 2 LDA
Page 37 and 38: F DIFS DFFS F (a) (b) F 1 L Figure
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Page 41 and 42: faces of 40 subjects. • Others: A
Page 43 and 44: malizing the vector components, the
Page 45 and 46: Figure 2.5: A fingerprint image wit
Page 47 and 48: features (gradient coherence, inten
Page 49 and 50: Figure 2.7: Examples of minutiae; A
Page 51 and 52: according to the local orientation
Page 53 and 54: • Parallel Mode: This operational
Page 55 and 56: can address the problem of noisy se
Page 57 and 58: Prior to Matching Sensor Level Feat
Page 59 and 60: determined by logistic regression.
Page 61 and 62: Class-indifferent Methods • Decis
Page 63 and 64: 3. The final DS soft vector is calc
Page 65 and 66: on three face databases and compare
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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
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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
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Page 107 and 108: x DNull DRange DP (x) DNull(x) DRan
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Page 111 and 112: iii) Project all class means onto n
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Page 115 and 116: Table 4.3: Effect of increasing num
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Table 4.6: Performance of Dual Spac
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5.1 Introduction In recent years, t
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This means for a classifier D: r i
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validation1, validation2 and test.
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5.3.1 The Algorithm The steps of ou
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5.4 Experimental Results In this ch
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sets. • We put as much as possibl
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argument is invalid in the context
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LDA and LDA produce the same accura
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space. If the training data uniform
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face for each subject, and compare
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also be introduced. But class speci
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These stages are discussed in the f
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(a) (b) Figure A.2: Input fingerpri
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(a) (b) Figure A.4: Orientation ima
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(i) For each block centered at (i,
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(a) (b) Figure A.7: Enhanced images
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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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