Grouping based Non-additive Verification

Acknowledgments 26 tency of data features along the hypothesized boundary, but also its \inconsistency" with its larger neighborhood. In terms of perceptual grouping, a \good" hypothesis should form a \good" group. Therefore, any score method may beneet substantially from using perceptual grouping information. The non-additive score proposed here shows a signiicant improvement relative to the use of a simple additive score. It should improve other methods, especially when diicult veriication scenes are considered. The method can be applied, in principle, to many perceptual grouping cues. This method does not depends on any speciic grouping cue, and allows the use of any cue, as long as we know its statistics. Other grouping cues may measure symmetry properties, color, texture, motion parameters etc. 6 Acknowledgments We would like to thank Andrew Zisserman for drawing our attention to the need of better veriication methods. Some Hough experiments, done by Michael Hooman, emphasized the weaknesses of additive score veriication. Thanks to Elscint for providing the CT images. Conclusion 25 5 Conclusion We proposed here a new veriication paradigm, which does not rely on the size of the consistent features set but rather on grouping information, which is extracted from the image independently of the object hypothesizing mechanism. The method is controlled by one parameter, which should be selected based on the expected error mechanism. We proved that this method is consistent, in the statistical sense; That is, in the presence of only one object in the scene, the correct hypothesis is expected to get the highest score. A compact form of the grouping-based score function is suggested, which is also more intuitive. This score may be interpreted as the joint log likelihood ratio, comparing the tested hypothesis against the empty hypothesis. This criterion is \local", and depends only on data features associated with the hypothesized object, and their direct neighbors. In addition, it provides an eecient way to calculate the score, in a linear time (with respect to the number of data features associated with the hypothesis). This avoids the need to compute the grouping cues for the entire graph. Our experimentation shows that while additive approaches (based on the consistent set size) for veriication work well for easy tasks, our approach works better in many diicult cases. The integration of the proposed grouping based veriication criterion with the more traditional consistent set size criterion, is currently under study. One may argue that the …