III WVC 2007 - Iris.sel.eesc.sc.usp.br - USP

WVC'2007 - III Workshop de Visão Computacional, 22 a 24 de Outubro de 2007, São José do Rio Preto, SP.occluded pixels. Let’s further Z * jf and Z * jg denote thevectors defined as*ZjfZjf n0 otherwise*Zjg n , for ZZjgn0 otherwisen,for Z f nZf nj gnZ gnjjjEq. 3Equation 2 states that Z * jf and Z * jg derive from Z j fand Z j g by setting to zero the elements affected byocclusion. Let’s now z j f and z j g be the vectors formedonly by the elements respectively of Z * jf and Z * jg forwhich Z * jf(n)0 and Z * jg(n+m) 0. The length M of z j fand z j g will depend not only on the number and positionof the pixels under occlusion in both images beingcompared but also on m. Clearly, for a given value of mthe information in Z j f and Z j g relative to non occludedareas is totally contained in z j f and z j g.For that reason the dissimilarity, as given in Equation1, should be computed only on z j f and z j g..A simple manipulation leads to the conclusion that:Mp1zjf ( p)zjg(p)0 z f z gjjN 1n0Z*jZf*j*nZgn mfj*Z gjEq.45. Performance AnalysisA software prototype implementing the methodproposed in this work was built for performanceassessment. Experiments were conducted using irisimages of Casia database. Image samples that could notbe properly segmented were discarded from theanalysis. As a result a total of 263 images, coming from15 different subjects, were used in the evaluation.The analysis was limited to the verification mode. Atotal of 33453 image pairs selected from the 263 imageswere used in the analysis, whereby 32295 pairs ofdifferent eyes (negatives) and 1158 pairs of the sameeye (positives).A program implementing the method proposed in [3]was applied to perform iris normalization. All theimages used in these experiments were normalized into16x256 intensity matrices. An occlusion mask wasdrawn manually for each normalized image.The wavelet used in our experiment was taken fromthe Gaussian derivatives family (first derivative of theGaussian probability density function).Figure 7 shows the histograms of the overalldissimilarity for positives and negatives produced by theoriginal Boles method as well as by the proposedmethod.This reasoning leads to the proposal of a newdissimilarity function to cope with occlusion as given bydjmN 1 (*j j*nZgn m*Z fn0j jf , g)1Eq. 5*|| Z f |||| Z g ||The dissimilarity of two irises f and g is given inoriginal Boles’ method by the plain average of the 48values produced by the application of Equation 1 to eachrow of the zero crossing representation matrices. Thiswork proposes the use of a weighted mean instead of thesimple mean, whereby the weights are given by thenumber of non zeroed values in Z * jf(n) and Z * jg(n),according to the formula48 djm f , g kjj 1Dm48Eq. 6 kjj 1where d jm (f,g) is given by Equation 5 and k j is thenumber of non zeroed values in the j-th row of the zerocrossing representations of both images. Again, theoverall dissimilarity D between f and g is computed asin Equation 2, using the results produced by Equation 6for D m .Figure 7. Histograms of Positives and NegativesThe superiority of our method can be seen byobserving the area of overlap below the curves forpositives and negatives. The larger is this area, the morefrequent is the occurrence of either false positives orfalse negatives increases. Figure 7 shows that theoverlap of the region below both curves is significantlysmaller for our method than for Boles` method. If weconsider as acceptance threshold the dissimilarity valuefor which the normalized frequency is equal forpositives and negatives, the overlap area isapproximately three times larger for Boles` method thanfor our approach.287