We propose a new measure of perceptual saliency and quantitatively compare its ability to detect natural shapes in cluttered backgrounds to five previously proposed measures. As defined in the new measure, the saliency of an edge is the fraction of closed random walks which contain that edge. The transition probability matrix defining the random walk between edges is based on a distribution of natural shapes modeled by a stochastic motion. Each of the saliency measures in our comparison is a function of a set of affinity values assigned to pairs of edges. Although the authors of each measure define the affinity between a pair of edges somewhat differently, all incorporate the Gestalt principles of good-continuation and proximity in some form. In order to make the comparison meaningful, we use a single definition of affinity and focus instead on the performance of the different functions for combining affinity values. The primary performance criterion is accuracy. We compute false-positive rates in classifying edges as signal or noise for a large set of test figures. In almost every case, the new measure significantly outperforms previous measures.