Master Thesis - Department of Computer Science

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• Product Rule: Product Rule computes the soft class label vectors as: ˜d j (x) = d j Null (x) ∗ djRange (x), j = 1, ...., C (4.33) 4.4.2 Proposed Technique for Decision Fusion Unlike sum rule and product rule, our technique of decision fusion learns each of the classifier’s behavior by using training data at decision level. Learning a classifier involves training with the response of that classifier. So the response vectors on a validation set of a database which is disjoint from training and testing set can be used as training information at decision level for learning the behavior of a classifier. We employ LDA and nonparametric LDA on training information at decision level to build up discriminative eigenmodel. Then response vectors of the input test images are projected in that eigenmodel and for each test response vector, the similarity measures for the respective classes in the eigenmodel provide a new response vector which replaces the old test response vector. To accomplish the whole task, we divide our database into three disjoint subsets, training, validation and testing sets. Now the training set along with validation set and testing set respectively constructs the “training response vector set” and “testing response vector set”, respectively at classifier output space. Then “training response vector set” is used as training data to construct a LDA or nonparametric LDA-based eigenmodel at classifier response level. Here, we formally define validation and testing set which are independent of any classifier. Let, the validation and testing set of a database are denoted by XV A and XT S and can be defined as, XV A = [vx 1 1 , vx12 , . . . , vx1V , vx21 , . . . , vxij , . . . , vxCV ], (4.34) XT S = [tx 1 1, tx 1 2, . . . , tx 1 S, tx 2 1, . . . , tx i j, . . . , tx C S ]. (4.35) where vx i j represents the jth validation sample from class i and V is the number of validation samples per class. Similarly, j th testing sample from class i is denoted by tx i j and number of testing samples per class is represented as S. The “training response vector set” and “testing response vector set” for null space classifier are 84
T R T S denoted by RVNull and RVNull and are represented as, RV RV T R Null ≡ {DNull(vx 1 1 ), DNull(vx 1 2 ), . . . , DNull(vx 1 V ), DNull(vx 2 1 ), . . . , DNull(vx 2 V ), . . . , DNull(vx i j), . . . , DNull(vx C V )} (4.36) T S Null ≡ {DNull(tx 1 1 ), DNull(tx 1 2 ), . . . , DNull(tx 1 S ), DNull(tx 2 1 ), . . . , DNull(tx 2 S), . . . , DNull(tx i j), . . . , DNull(tx C S )} (4.37) Considering “training response vector set”, RV T R Null , as training as well as testing set, we calculate an accuracy denoted by A Original Null , with the condition that same samples are never compared. So, the calculation of A Original Null 1. For i = 1 to V ∗ C involves the following steps: (i) Select a response vector DNull(vxc j ) where i = (c − 1) ∗ V + j from the set T R RVNull . (ii) Calculate the Euclidean distance of DNull(vx c j) from all other response T R vectors in the set RVNull . (iii) Find the class label of the response vector providing minimum distance from DNull(vx c j) and assign it to DNull(vx c j). (iv) Cross check the obtained class label with the original label. 2. Calculate A Original Null as Number of correctly labeled response vectors T otal number of response vectors of response vectors is V ∗ C in this case. Then RV T R Null ∗100%. Total Number is used to construct an LDA or nonparametric LDA based eigenmodel. As the length of a response vector is equal to the number of classes (C) present in a database, we obtain C eigenvectors in the eigenmodel. Let, the C eigenvectors in the order of decreasing eigenvalues be represented by EVNull = [e 1 Null, ...e i Null, ..., e C Null]. We obtain C eigensubspaces ESV i Null ’s for i = 1, 2..., C where ith eigensubspace ESV i Null contains first i eigenvectors from the set EVNull. Thus C th eigensubspace, ESV C Null , is same as EVNull. The performance of i th eigensubspace ESV i Null on “training response vector set”, which is denoted by A ESV i Null Null , is evaluated by projecting RV T R Null onto ESV i Null and calculating accuracy in the same manner as described for the calculation of A Original Null . For each eigensubspace, we compare its performance with 85
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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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(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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