Master Thesis - Department of Computer Science

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2. Compute the gradients ϱx(i, j) and ϱy(i, j) at each pixel (i, j). The gradient operation in our case is done by sobel operator. 3. Estimate the local orientation of each block centered at pixel (i, j) using the following equation, γx(i, j) = γy(i, j) = i+ W 2 � u=i− W 2 i− W 2 � u=i− W 2 θ(i, j) = 1 2 tan−1 j+ W 2 � v=j− W 2 j− W 2 � v=j− W 2 � γy(i, j) γx(i, j) 2ϱx(u, v)ϱy(u, v), (A.4) � ϱ 2 x (u, v)ϱ2y (u, v)� , (A.5) � . (A.6) where θ(i, j) is the least square estimate of the local ridge orientation at the block centered at pixel (i, j) and represents the direction which is orthogonal to the dominant direction of the Fourier spectrum of the W × W window. 4. Noise, corrupted ridge and valley structures may result incorrect estimation of local ridge orientation. As local ridge orientation varies slowly in a local neighborhood low-pass filtering can be used to correct θ(i, j). For low-pass filtering the orientation image is converted to a continuous vector field and is defined as, Φx(i, j) = cos(2θ(i, j)), (A.7) Φy(i, j) = sin(2θ(i, j)). (A.8) where Φx(i, j) and Φy(i, j) are the x and y components of the vector field, respectively. The low-pass filtering can be done as follows, Φ ′ x (i, j) = Φ ′ y (i, j) = D Φ 2� u=− D Φ 2 D Φ 2� u=− D Φ 2 D Φ 2� v=− D Φ 2 D Φ 2� v=− D Φ 2 D(u, v)Φx(i − uW, j − vW ), (A.9) D(u, v)Φy(i − uW, j − vW ). (A.10) where D is a two-dimensional low-pass filter with unit integral and DΦ × DΦ specifies the size of the filter. 5. Compute the local ridge orientation at (i, j) using, O(i, j) = 1 2 tan−1 � � ′ Φ y(i, j) 126 Φ ′ x (i, j) (A.11)
(a) (b) Figure A.4: Orientation images of two input fingerprints shown in Fig. A.2. Figure A.5: A X-signature with w = W and l = H in our case. The orientation image of the input fingerprint images shown in Fig A.2 are given in Fig A.4. A.1.4 Ridge Frequency Image In a local neighborhood, where no minutiae and singular points appear, the gray levels along ridges and valleys can be modeled as a sinusoidal shaped wave along a direction normal to the local ridge orientation (Fig. A.5). So, local ridge frequency is 127
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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
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Genuine Impostor Scores Scores 1 0
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Error d1 = (1 − TZeroF RR) d2 = |
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The algorithm for obtaining the sub
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each subject, 42 samples (flashes f
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Table 3.3: Peak Recognition Accurac
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Table 3.5: Peak Recognition Accurac
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Table 3.7: Performance of Ekenel’
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Table 3.9: Performance of Ekenel’
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to our proposed method. Section 4.2
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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
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Page 107 and 108: x DNull DRange DP (x) DNull(x) DRan
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Page 113 and 114: Table 4.1: Effect of increasing num
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Page 119 and 120: Table 4.6: Performance of Dual Spac
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Page 125 and 126: validation1, validation2 and test.
Page 127 and 128: 5.3.1 The Algorithm The steps of ou
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Page 135 and 136: LDA and LDA produce the same accura
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Page 145: (a) (b) Figure A.2: Input fingerpri
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Page 151 and 152: (a) (b) Figure A.7: Enhanced images
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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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