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Classification (R, L, W, A, T) R L W A T
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Results (a)
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Results (b)
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Figure 15.1. Block diagram of two different approaches to solve identi cation problem:
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(a) Classi cation followed by veri cation; (b) Indexing followed by veri cation.
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15.2 Technical Approach
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masks for minutiae feature extraction and integrates newly developed classi cation [9] and indexing [8] techniques with the same veri cation algorithm that optimizes a criterion function. (c) It presents extensive comparisons between classi cation- and indexing-based techniques for identi cation.
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TECHNICAL APPROACH
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15.2.1 Minutiae Extraction Using Learned Feature Extraction Masks
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There are many approaches in the literature for the minutiae extraction [10, 16]. As compared to the other approaches, we extract minutiae using learned masks for all the results reported in this chapter. For each ngerprint, rst the background is removed. Local orientation is computed in each local 16 16 block. The ngerprint is adaptively smoothed, binarized, and thinned using the local orientation information. Potential minutiae are found using crossing number [2]. Finally, learned feature extractor masks obtained during of ine processing are adaptively applied to purify the potential minutiae. 15.2.1.1 Of ine Learning of Feature Extraction Masks
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A mask is a 2D lter that is concerned with detecting a minutia. Since a minutia can be an endpoint or a bifurcation, two masks are to be learned, one for each kind of feature. For simplicity, we use endpoints as the example to explain our learning approach. The mask for bifurcations is learned by following a similar process. Figure 15.2 shows an ideal endpoint mask T that consists of two submasks, Tr (length Lr ) and Tg (length Lg ), which denote the mask for ridge and gap, respectively. For simplicity, we assume Lr = Lg . H and L are the height and the length of the mask T, and L = Lr + Lg . The values of each pixel in Tr and Tg are 1 and 0, respectively. Suppose (a) a ridge end E in a binary ngerprint is as ideal as the ideal mask T, (b) the local orientation at the ridge end is l , (c) the correlations between the mask T and the ideal ridge end E with the orientation l and l + are f l and f l + , respectively, and (d) the difference between f l and f l + is l , that is,
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(15.1)
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Illustration of an ideal endpoint mask T.
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15
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A Comparison of Classi cation- and Indexing-Based Approaches
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where f l = (h,l) (T E ) {T (h, l) E l (h, l) } and E l (h, l) is the ridge with orienl tation l and the mask T (h, l) is applied along the ridge. Training Data. Suppose (a) examples of endpoints and bifurcations are obtained from M ngerprint images FIk , where k = 1,2, . . . , M; (b) in the kth ngerprint image FIk , there are Nk feature locations (xk,i , yk,i ), where i = 1,2,3 , . . . , Nk ; (c) in the local area around (xk,i , yk,i ), Ik,i (m, n) is the gray-scale value at pixel (m, n) of the image FIk , where xk,i d1 m xk,i + d1 , yk,i d2 n yk,i + d2 , d1 and d2 are constants; and (d) G = {(xk,i , yk,i )}. Then, for each pixel in G, we carry out the following steps: (1) Estimate the local orientation k,i at pixel (xk,i , yk,i ) in the local area; (2) adaptively smooth Ik,i (m, n) in the local area; (3) adaptively binarize Ik,i (m, n) in the local area. The details of these steps are the same as those in the run-time minutiae extraction, which are discussed in Section 15.2.1.2. Optimzation for Feature Extracton Masks Learning. Suppose (a) the mask is T(h, l), where 1 h H, 1 l L, and H = 2d1 + 1 and L = 2d2 + 1; (b) Bk,i (h, l) is the binary image of Ik,i (m, n); and (c) B k,i k,i (h, l) is the rotated binary image of Bk,i (h, l), rotation angle is k,i , which is the local orientation at pixel (xk,i , yk,i ). According to Eq. (15.1), the objective of learning algorithm can be de ned as [11]
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