This paper offers computational theory and an algorithmic framework for perceptual organization of image contours arising from static occluding surfaces of constant lightness. We articulate constraints and biases underlying the inference of such physical events as visible surface overlap and invisible (modal and amodal) surface boundaries, from ambiguous visual evidence including visible contrast edges and L-type and T-type junctions. For any given scene, an energy or cost function is constructed over interpretation labels for nodes of a sparse graph, or belief net. Annealing-style optimization permits local cues to propagate smoothly to give rise to a global solution. We demonstrate that this approach leads to correct interpretations (in the sense of agreeing with human percepts) of popular simple ``Colorforms'' figures known to induce illusory contours, as well as more difficult figures where interpretations acknowledging accidental alignment are preferred.