Measuring convexity for figure/ground separation

In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Convexity has a stronger influence on figural organization than other global shape properties, such as symmetry (G. Kanizsa, 1979), and yet there has been very little work on convexity properties in computer vision. We present a model for figure/ground segregation which exhibits a preference for convex regions as the figure (i.e., the foreground). The model also shows a preference for smaller regions to be selected as figures, which is also known to hold for human visual perception (K. Koffka, 1935). The model is based on the machinery of Markov random fields/random walks/diffusion processes, so that the global shape properties are obtained via local and stochastic computations. Experimental results demonstrate that our model performs well on ambiguous figure/ground displays which were not captured before. In particular in ambiguous displays where neither region is strictly convex, the model shows preference to the "more convex" region, thus offering a continuous measure of convexity in agreement with human perception.