Topological Requirements of Figural Completion

Figural completion, in its most common form, is the preattentive inference of the shape and location of the occluded parts of visible surfaces. Yet it also underlies illusory contour phenomena, which are associated with completion of occluding, rather than occluded surfaces. Phenomenological accounts, such as Kanizsa'ss5], though insightful, lack the precision necessary to formulate a computational theory. The mathematics relevant to understanding the problem is the topology of surfaces. Accordingly, the topology of surfaces is reviewed with the aim of more precisely characterizing the computational goal underlying gural completion. A contour labeling scheme incorporating a minimum set of necessary constraints on the appearance of boundaries in at scenes is then deened. These constraints, when enforced at points of contour intersection, are subsequently shown to be both necessary and suucient, in the sense that sets of contours satisfying the labeling scheme can always be interpolated to form topologically valid surfaces. Abstract Figural completion, in its most common form, is the preattentive inference of the shape and location of the occluded parts of visible surfaces. Yet it also underlies illusory contour phenomena, which are associated with completion of occluding, rather than occluded surfaces. Phenomenological accounts, such as Kanizsa'ss5], though insightful, lack the precision necessary to formulate a computational theory. The mathematics relevant to understanding the problem is the topology of surfaces. Accordingly, the topology of surfaces is reviewed with the aim of more precisely characterizing the computational goal underlying gural completion. A contour labeling scheme incorporating a minimum set of necessary constraints on the appearance of boundaries in at scenes is then deened. These constraints, when enforced at points of contour intersection, are subsequently shown to be both necessary and suucient, in the sense that sets of contours satisfying the labeling scheme can always be interpolated to form topologically valid surfaces.