Figure 6 Extracting principal lines from two different palmprints.
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Fig. 1. Three typical palmprint images. Fig. 2 shows two examples of the MFRAT whose sizes are 7x 7 and 14 x 14, respectively, and whose lines, L(0;), are at directions of 2/12, 27/12,..., and 62/12, respectively. Due to space limitation, the remaining lines L(0;) at directions of 71/12, 82/12,..., and 127/12, are not depicted here. If the line in the MFRAT is 1 pixel wide, p should be an odd num- ber in order to clearly define the center of Te In 14 x 14 MEFRAT, the center area of Zz; contains four pixels, thus the di- rections and the energies of these four pixels could be calculated In this way, the directions and energies of all pixels are cal- culated if the center of lattice Zz move over an image pixel by pixel (or pixels by pixels). For an image / (x, y) of size m xn, if the values of all pixels are replaced by their directions and en- ergies, two new images, Direction_image and Energy_image, can be created, respectively, i.e. Fig. 2. The 7 x 7 and the 14 x 14 MFRAT. (a) and (g) 0; = 2/12; (b) and (h) 02 = 27/12; (c) and (i) 03 = 32/12; (d) and (j) 04 = 47/12; (e) and (k) 05 = 5n/12; (f) and (1) 0 = 6/12. Fig. 3. Images appearing in feature extraction stage. (a) Original image; (b) Energy_image; (c) Lines_image; (d) LA_image; (e) LB_image; (f) R(LA_image, (g) R(LB_image); (h) thinning lines of (d). Fig. 5. Principal lines extracted from the same palm, but different images. Fig. 4. Pixel-to-pixel comparison and pixel-to-area comparison. Fig. 7. Extracting principal lines using different parameters. (a) M =500, p= 14, N= 12, and W =2; (b) M= 1800, p= 14, N=12, and W =2; (c) p=7, N=12, W=1, and M = 1000; (d) p= 22, N= 12, W =2, and M = 1000. ‘ig. 8. The directional energies of lines detected from Figs. 3(a) and 6(c) by Gabor filter with different parameters. (a) and (b) u = 0.2, o =3.5, and the size f filter is 20 x 20; (c) and (d) u = 0.0916, g = 5.6179, and the size of filter is 35 x 35. Fig. 9. The directional energies of lines detected from Figs. 3(a) and 6(c) by using 9 x 9 and 17 x 17 MFRAT. (a) and (b) p=9, N = 12, and W = 1; (c) and (d) p=17, N=12, and W=1. Fig. 10. Enhanced palmprint image and extracted palm lines using 9 x 9 MFRAT. (a) and (b) Enhanced palmprint image; (c) and (d) extracted palm lines from (a) and (b). Fig. 12. Palm lines detected from Figs. 3(a) and 6(c) using Wu’s approach. Fig. 11. Palm lines detected from Figs. 3(a) and 6(c) using Liu’s approach. Fig. 13. Comparing Wu’s approach with proposed approach. (a) Original palmprint image containing wide principal lines. (b) Magnitude of second derivativ detected from (a) by using Wu’s approach. (c) Directional energies detected from (a) by using 9 x 9 MFRAT (N = 12 and W = 1). (d) Directional energie detected from (a) by using 17 x 17 MFRAT (N = 12, and W = 1). Fig. 14. Experimental results of verification. (a) and (b) Genuine and imposter distributions of matching scores for Databases I and II. (c) and (d) FAR and FRR curves for Databases I and II. Experimental results near cross-over points (boldface) in Fig. 14 Table 1 Fig. 16. The principal lines from two people with similar structure, but witl dissimilar position. Fig. 15. ROC curves of the proposed approach, Palmcode, Wu’s approach and Liu’s approach. Fig. 17. The principal lines from two people with similar structure anc position. Matching scores among different palmprint images in Fig. 18 Table 2 Fig. 18. Eight palmprint images from different people, which have similar principal lines.
