On the distribution of saliency

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 the smoothness of the curve on which this edge-point lies. We consider a generalization [M. Lindenbaum and A. Berengolts, 2000] of the Ullman-Shaashua saliency measure (1998) and aim to analyze the saliency measure in a probabilistic context: regarding the basic grouping information (grouping cues) as random variables, we use ergodicity and asymptotic analysis to derive the saliency distribution associated with the main curves ("figure") and with the rest of the image ("background"). We further consider finite-length curves and analyze their saliency values. We observed several discrepancies between the observed distributions and the predictions we supply, discuss their sources and propose a way to account for them. Then, based on the derived distributions we show how to set threshold on the saliency for deciding optimally between figure and background, how to choose cues which are usable for saliency, and how to estimate bounds on the saliency performance.