Illusory contours occur in a wide variety of circumstances in nature. A striking man- made example is the Kanizsa triangle. A common factor in all such figures is the perception of a surface occluding part of a background, i.e. illusory contours are always accompanied by illusory surfaces. The detection of occlusion cues suggest various different local surface configurations, leading to a large combinatorial set of global surface configurations, each one constituting an image organization. We address the problems of why and how the image organizations that yield illusory contours arise. Our approach is to: (i) detect occlusions; (ii) assign surface-states at these locations that reflect the presence of a particular surface configuration; (iii) apply a Bayesian model to diffuse this local surface information; (iv) define an entropy measure for each image organization to select the best one(s) as the one(s) giving the lowest entropy values. We note that: (a) the illusory contours arise from the surface boundaries, and hence we do not propagate/extend intensity edges directly; (b) the overlapping surfaces provide an explanation for amodal completions. The model reproduces various qualitative and quantitative aspects of illusory contour perception and has been supported by a series of experiments.