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.

We have been developing a stochastic model for figure-ground separation. The model selects/constructs the foreground with preference for figures with “more convex” shapes. When these models are applied to illusory figures they yield perceptually accurate selection of figure and background. The approach is based on an “entropy” measure of a region diffusion Markov model from a set of local figure/ground hypothesis. The contour boundaries are implicitly represented, via the thresholding of the diffusion result. What optimal properties do the illusory contours satisfies? We show that the entropy criteria selects contours such as to minimize a Taylor series of the even derivatives with respect to the length of the contour. The coefficients are positive and they get exponentially smaller as the derivatives increase. The zeroth order term suggest that small length contours are preferred, the second order terms suggests that curvature-like term is minimized (with less strength compared to the zero order one), and higher order derivatives give additional contour smoothness constraints.

All illusory surface figures yield a perception of a surface occluding another one or the background. Occluded surfaces yield completion, a phenomena known as amodal completions. It is intriguing that for some images illusory surfaces are perceived, but not for other images. Also, illusory surfaces may have portions occlude. We aim to understand these phenomena. Our approach detects intensity edges and junctions. From the junctions we seek to find an optimal image organization, i.e., multiple ordered surfaces with the ordering accounting for salience. The most salient being the figure, while the other surfaces are classified as background. A decision of which surface is the visible one (on rep) is made locally, at each pixel, allowing the salient surface (figure) to have portions occluded, i.e., with amodal completions. We account for a variety of imagery not explained before.