Technical Report CIS-2004-03

Title: On the distribution of Saliency
Authors: Alexander Berengolts, Michael Lindenbaum
Abstract: The calculation of salient structures is one of the early and basic ideas of perceptual organization in Computer Vision. Saliency algorithms typically mark edge-points with some saliency measure, growing with the length and smoothness of the curve on which this edge-point lies. We propose here a modified saliency estimation mechanism, which is based on probabilistically specified grouping cues and on curve length distributions. In the context of the proposed method, the Shaashua and Ullman saliency mechanism [SU88] may be interpreted as a process trying to detect the curve with maximal expected length. The proposed approach lends itself to different types of generalizations, and in particular, to saliencies based on different cues, in a systematic rigorous way. To demonstrate this, we created a saliency process that is based on grey level similarity. The proposed saliency allows, in principle, to specify many saliency functions depending on the length distribution. We show, however, that only a limited class of saliency functions may be rigorously optimized by a local process. Following this negative result we focus on probabilistic analysis of expected length saliencies. Using ergodicity and asymptotic analysis, we derive the saliency distribution associated with the main curves and with the rest of the image.We then extend this analysis to finite-length curves. Based on the derived distributions, we show how to set a threshold on the saliency for deciding optimally between figure and background (we provide an approximate explicit expression), how to choose cues that are usable for saliency, and how to estimate bounds on the saliency performance.
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