Master Thesis - Department of Computer Science

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(a) (b) (c) Figure 3.3: (a) Original face, (b) the level-1 wavelet decomposition of the face image into subbands A, H (top) and V , D (bottom) and (c) level-3 dyadic wavelet decomposition. All subband signals are normalized individually. ations) information. Since level-1 decomposition may not be adequate to effectively isolate these pair of visual features, it is necessary to explore multi-resolution, multi- channel representation at higher levels to obtain a suitable isolation. With higher levels of decomposition, the approximation will have increasing effect of smoothening (with lesser subband bandwidth) on the face image, and the details will have more of the discriminatory information. At a certain higher level of decomposition, the entire discriminatory information will remain in the details and approximation will contain the common (or similar) structural information. In order to eliminate the similarity and retain the discrimination, the approximation is suppressed (by replacing with zeros) and the face image is reconstructed using IDWT. The details at lower levels (1 or 2) of decomposition also do not contain any useful information. This can be realized from the fact that humans do not need an image at a very large resolution to identify an individual. Too low a resolution, on the other hand, is not adequate to hold all of the discriminatory information. Hence there exists an optimal resolution at which the image contains most of the discriminatory and less (or no) redundant pixels (information). Thus it is often necessary to eliminate certain details at lower levels of decomposition to discard redundant image pixels or noise if present in the signal. Thus the subbands which only contain the discriminatory information for face recognition are selected for representation and the others are discarded. Based on the explanation presented above, we propose an efficient method of face recognition using subband face representation which provides an improvement 50
in the accuracy of face recognition. We will verify the efficiency of subband face representation using experimental results, which will be discussed in section 3.4. Fig. 3.4 shows the block diagram of IDWT that is used to reconstruct the original image from different subbands at level-1 decomposition. Fig. 3.5 shows the block diagram of the subband face reconstruction from level-2 subbands, by suppressing (replacing the coefficients by zeros) only the approximation coefficients at level-2. The subband face thus obtained will hence not posses the spectral energies in the [0 − Π/4] subband which correspond to a smoothed version (i.e. average structure) of the face image. LL LH HL HH 2 2 2 2 Rows h(.) g(.) h(.) g(.) 2 2 Columns h(.) g(.) Reconstructed image Figure 3.4: Two dimensional inverse discrete wavelet transform (IDWT) for an image. The rows are initially upsampled by factor of two and filtered using low pass h(.) and high pass g(.) filters. This is followed by upsampling along columns by a factor of two and applying the low pass h(.) and high pass g(.) filters along the columns to get the reconstructed image. Fig. 3.6 shows the original face images along with the subband faces generated by suppressing the approximations at different levels. The face image in Fig. 3.6 (a) is illuminated from the left and the corresponding subband faces shown in Figs. 3.6 (a1- a3) have the effect of illumination reduced or almost eliminated. This can also be observed for the face image in Fig. 3.6 (b) which is illuminated from the right, and its corresponding subband faces in Figs. 3.6 (b1-b3) do not posses similar amount of illumination variation. Fig. 3.6 (c) shows a face with frontal illumination, where the intensity variations (edges) of the subband faces in Figs. 3.6 (c1-c5) are stronger than the gray level image. It is also noticeable that the suppression of approximation 51
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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
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
Page 39 and 40: image A of m rows and n columns is
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
Page 67 and 68: for a face. This was illustrated by
Page 69: Image Rows h(.) g(.) 2 2 Columns Fi
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
Page 117 and 118: (Original face) (Null face) (Range
Page 119 and 120: 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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