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Perceptual grouping is an important mechanism of early visual process-ing. This paper presents a computational approach to perceptual grouping ir dot patterns. Detection of perceptual organization is done in two steps. The first step, called the lowest level grouping, extracts the perceptual segments of dots that group together because of their relative locations. The grouping is accomplished by interpreting dots as belonging to interior or border of a perceptual segment, or being along a perceived curve, or being isolated. The Voronoi neighborhood of a dot is used to represent its local geometric environment. The grouping is seeded by assigning to dots their locally evident perceptual roles and iteratively modifying the initial estimates to enforce global Gestalt constraints. This is done through independent modules that pos-sess narrow expertise for recognition of typical interior dots, border dots, curve dots and isolated dots, from the properties of the Voronoi neighborhoods. The results of the modules are allowed to influence and change each other so as to result in perceptual components that satisfy global, Gestalt criteria such as border or curve smoothness and component compactness. Such lateral communication among the modules makes feasible a perceptual interpretation of the local structure in a manner that best meets the global expectations. Thus, an integration is performed of multiple constraints, active at different perceptual levels and having different scopes in the dot pattern, to infer the lowest level perceptual structure. The result of the lowest level grouping phase is the partitioning of a dot pattern into different perceptual segments or tokens. Unlike dots, these segments possess size and shape properties in addition to locations. The second step further groups the lowest level tokens to identify any hierarchical structure present. The grouping among tokens is again done based on a variety of constraints including their proximity, orientations, sizes, and terminations, integrated so as to mimic the perceptual roles of these criteria. The result of the grouping of lowest level tokens is even larger tokens. The hierarchical grouping process repeats until no new groupings are formed. The final result of the implementation described here is a hierarchical representation of the perceptual structure in a dot pattern. Our representation of perceptual structure allows for "focus of attention" through the presence of multiple levels, and for "rivalry" of groupings at a given level through the probabilistic interpretation of groupings present.
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