Perceptual Grouping Of Dot Patterns

Abstract

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 per­ ceptual 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 glo­ bal 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 neighbor­ hoods. The results of the modules are allowed to influence and change each other so as to result in perceptual components that satisfy global, Gestalt cri­ teria 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 seg­ ments or tokens. Unlike dots, these segments possess size and shape proper­ ties 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 cri­ teria. 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. ties of tokens being grouped, and their image plane relationships. Since the detected image organization ultimately captures the organization of the scene, application of these rules should be a useful step towards image interpretation. Thus, grouping is a form of early inference about the structure of objects in the scene being viewed without the explicit use of three-dimensional domain specific knowledge.18 The image plane entities, or tokens, that may be grouped include blobs, edge segments, and geometrical features of image regions. This paper is con­ cerned with grouping of the simplest of the image plane entities - dots in a dot pattern. The goal is to develop a set of rules, as well as a computational pro­ cess that makes use of the rules for identifying the groupings of the dots per­ ceived by the humans. In this paper we present an algorithm to extract groupings in dot patterns and the resulting spatial structure perceived by humans. Section 2 describes in more detail the phenomenon of perceptual grouping, puts in perspective the nature of the problem addressed in this paper, and explains the relevance and significance of the results. Section 3 discusses a representation of geometric structure by Voronoi neighborhoods that captures significant geometrical aspects of the dot pattern. Section 4 presents an algorithm for extracting per­ ceptual structure from these geometric structural precursors. Section 5 presents an algorithm for extracting structural information from dots at multi­ ple levels. In Section 6 we make some general observations on the work described in this paper.