Master Thesis - Department of Computer Science

More documents

Recommendations

Info

Q = � (q 1 x, q 1 y, β 1 ), ....., (q Q x , q Q y , β Q ) � . (A.35) where |P| = P , |Q| = Q, and (p i x , pi y , αi ) are the three features associated with the i th minutiae in set P. The basic assumption made here is that the second point set Q is a rotated, scaled, and translated version of the first set P, where points may be shifted by random noise, some points may be added and some points deleted. The task of fingerprint registration is to recover this unknown transformation. Since we do not know whether the two fingerprints are the same or not (i.e., images of the same finger), we attempt to find the ’best’ transformation in the sense that when applying the transformation to the minutiae points of the set P, as many of these points as possible overlap with the minutiae points from the set Q. Two overlapping points are considered as a match only if they have the same direction. There may be minutiae points in either set that do not match with any point in the other set. The matching score is computed for each transformation after discretizing the set of all allowed transformations. Consider a transformation Fs,θ,∆x,∆y : R 2 → R 2 , given by, ⎛ ⎜ Fs,θ,∆x,∆y ⎝ x ⎞ ⎛ ⎞ ⎛ ⎟ ⎜ ⎠ = s ⎝ y cosθ −sinθ sinθ ⎟ ⎜ ⎠ ⎝ cosθ x ⎞ ⎛ ⎟ ⎜ ⎠ + ⎝ y ∆x ⎞ ⎟ ⎠ , ∆y (A.36) where s, θ, and (∆x, ∆y) are the scale, rotation, and shift parameters, respectively. The space of transformations consists of quadruples (s, θ, ∆x, ∆y), where each pa- rameter is discretized into a finite set of values: s ∈ s1, .., sK , θ ∈ θ1, ..., θL, ∆x ∈ ∆x1, ..., ∆xM and ∆y ∈ ∆y1, ..., ∆yN Matching scores for the transformations are collected in the accumulator array A, where the entry A(k, l, m, n) counts the evidence for the transformation Fsk,θl,∆xm,∆yn. The array A is filled as follows: For each pair (p, q), where p = (pi x , piy ) is a point in the set P and q = (q j x, q j y) is a point in the set Q, find all possible transformations that map p to q and increment the evidence for these evidence for these transformations in array A. For every pair of values, (sk, θl), there is exactly one shift vector (∆x, ∆y) t such that Fsk,θl,∆x,∆y(p) = q, and it can be obtained as, ⎛ ⎜ ⎝ ∆x ⎞ ⎛ ⎟ ⎜ ⎠ = q − sk ⎝ ∆y cosθl ⎞ −sinθl sinθl ⎟ ⎠ p. cosθl (A.37) 140
Paired Minutiae Minutiae with unmatched angle Unmatched Minutiae Unmatched Minutiae (a) (b) (c) (d) Query fingerprint Minutia Database fingerprint minutia Bounding box Figure A.17: Various cases in minutiae matching. (a) Matched Minutiae; (b) Minutiae with unmatched angle; (c) and (d) Unmatched minutia. The values ∆x and ∆y need to be quantized to the nearest bins corresponding to ∆xm and ∆yn. A.6.2 Minutia Pairing The minutiae need to be paired or matched if their component or features (x, y, α) are equal within some tolerance after registration. For minutia pairing, we use a bounding box (also called tolerance box) of specific width and angle tolerance in order to accommodate the shift in the minutia angle attribute. One bounding box is drawn for every minutiae of query fingerprint image to search for it’s match. We can obtain four possible cases during matching: (i) Minutiae from both fingerprints match in all components, hence denoted by paired minutiae (Fig. A.17(a)), (ii) The minutia from query fingerprint matches with minutia from database in x and y coordinate, but direction remain unmatched. These minutiae are called minutiae with unmatched angle (Fig. A.17(b)), (iii) No minutia from database fingerprint falls within bounding box of the minutia from query image (Fig. A.17(c)) and (iv) No minutia from database fingerprint matches with the minutia from query image (Fig. A.17(d)). In last two cases, the minutia from query image is denoted by unmatched minutia. In our case, bounding box size is set to 50. Angle tolerance is set to 0.1 radians. 141
Page 1 and 2:
DEVELOPMENT OF EFFICIENT METHODS FO
Page 3 and 4:
To My Parents, Sisters and Dearest
Page 5 and 6:
Mirnalinee, Shreyasee, Lalit, Manis
Page 7 and 8:
LDC Linear Discriminant Classifier
Page 9 and 10:
3 An Efficient Method of Face Recog
Page 11 and 12:
A.6 Minutiae Matching . . . . . . .
Page 13 and 14:
4.1 Effect of increasing number of
Page 15 and 16:
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
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 and 70:
Image Rows h(.) g(.) 2 2 Columns Fi
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
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
Page 121 and 122: 5.1 Introduction In recent years, t
Page 123 and 124: This means for a classifier D: r i
Page 125 and 126: validation1, validation2 and test.
Page 127 and 128: 5.3.1 The Algorithm The steps of ou
Page 129 and 130: 5.4 Experimental Results In this ch
Page 131 and 132: sets. • We put as much as possibl
Page 133 and 134: argument is invalid in the context
Page 135 and 136: LDA and LDA produce the same accura
Page 137 and 138: space. If the training data uniform
Page 139 and 140: face for each subject, and compare
Page 141 and 142: also be introduced. But class speci
Page 143 and 144: These stages are discussed in the f
Page 145 and 146: (a) (b) Figure A.2: Input fingerpri
Page 147 and 148: (a) (b) Figure A.4: Orientation ima
Page 149 and 150: (i) For each block centered at (i,
Page 151 and 152: (a) (b) Figure A.7: Enhanced images
Page 153 and 154: (a) (b) Figure A.10: (a) and (b) sh
Page 155 and 156: (a) (b) Figure A.12: Binarized imag
Page 157 and 158: (a) (b) Figure A.14: Thinned images
Page 159: (a) (b) Figure A.16: Thinned finger
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-
show all

Master Thesis - Department of Computer Science

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?