Master Thesis - Department of Computer Science

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(a) 6 7 0 1 2 5 6 7 0 1 2 3 5 3 4 4 (i, j) 4 4 (b) 3 5 3 2 1 1 0 0 7 6 5 2 7 6 (c) Average local intensity is minimum Average local intensity is maximum Figure A.11: (a) The eight directions; (b) The 9 × 9 mask for computing slit-sums; (c) For ridge pixels, average local intensity or slit-sum is minimum along the direction of the ridge and maximum along the normal direction of ridge. A slit-sum method with local threshold proposed by Stock and Swonger [118] is used to binarize a image. This method uses pixel alignment along eight (8) discrete directions, 0, π/8, 2π/8, ..., 7π/8 (see Fig. A.11(a)) and a 9×9 mask (see Fig. A.11(b)) to center at the pixel of interest. The basic idea here is that for each pixel that belongs to ridge line, there exists an orientation whose average local intensity is lower than those of remaining orientations (see Fig. A.11(c)). The gray-level values along eight directions are added respectively to obtain each slit-sum by using the following equations, S0 = H(i, j + 4) + H(i, j + 2) + H(i, j − 2) + H(i, j − 4), S1 = H(i − 2, j + 4) + H(i − 1, j + 2) + H(i + 1, j − 2) + H(i + 2, j − 4), S2 = H(i − 4, j + 4) + H(i − 2, j + 2) + H(i + 2, j − 2) + H(i + 4, j − 4), S3 = H(i − 4, j + 2) + H(i − 2, j + 1) + H(i + 2, j − 1) + H(i + 4, j − 2), S4 = H(i − 4, j) + H(i − 2, j) + H(i + 2, j) + H(i + 4, j), S5 = H(i − 4, j − 2) + H(i − 2, j − 1) + H(i + 2, j + 1) + H(i + 4, j + 2), S6 = H(i − 4, j − 4) + H(i − 2, j − 2) + H(i + 2, j + 2) + H(i + 4, j + 4), S7 = H(i − 2, j − 4) + H(i − 1, j − 2) + H(i + 1, j + 2) + H(i + 2, j + 4). where S0, S1, ..., S7 represent the sum of gray-level values for eight discrete direction (slit). Let Smax, Smin and Ssum be the maximum, minimum and sum of the 134
(a) (b) Figure A.12: Binarized images of two input fingerprints shown in Fig. A.2. slit-sums calculated in eight different directions. That is, Smax = max i=0,..,7 Si, Smin = min i=0,..,7 Si, Ssum = 7� Si i=0 Finally, the binarized image can be obtained by applying one of the following equations. B(i, j) = B(i, j) = B(i, j) = ⎧ ⎪⎨ 1 if H(i, j) ≥ Ssum/12 ⎫ ⎪⎬ ⎪⎩ 0 Otherwise ⎪⎭ ⎧ ⎪⎨ 1 ⎫ ⎪⎬ if (Smax + Smin) ≥ Ssum/4 ⎪⎩ 0 Otherwise ⎪⎭ ⎧ ⎪⎨ 1 ⎫ ⎪⎬ if (4H(i, j)Smax + Smin) ≥ 3Ssum/8 ⎪⎩ 0 Otherwise ⎪⎭ (A.31) (A.32) (A.33) We used the first equation for obtaining binarized image. Fig. A.12 shows the binarized output for the input fingerprints shown in Fig. A.2. A.4 Image Thinning For thinning, we used the method proposed by Zhang and Suen [142]. The input for this method is a binary fingerprint image with pixels of ridge and valley having value 1 (black) and value 0 (white), respectively. A 3 × 3 window as shown in Fig. A.13 135
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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
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project only the class means in ran
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ΩNull and ΩRange represents the
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Thus, calculation of the QR factori
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4.3.3 Algorithm for Feature Fusion
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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
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Master Thesis - Department of Computer Science

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