Accessibility,
a criterion for regularity and hierarchy in visual pattern codes

Peter A. van der Helm, Emanuel L. J. Leeuwenberg

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Abstract. In research on visual shape perception, various models have been designed for the encoding of visual patterns, in order to predict the human interpretation of such patterns. Each of these encoding models provides a few coding rules to obtain codes of a pattern, each code describing regularity and hierarchy in that pattern. Some of these models employ the minimum principle which states that the human interpretation of a pattern is reflected by the simplest code of that pattern. Despite empirical support, these encoding models suffer from three fundamental problems. First, although many coding rules can be proposed, no encoding model provides a psychological basis for those few coding rules that have been chosen (cf. Simon, 1972). Second, the minimum principle seems to require an unrealistic search for simplest pattern codes since, for any pattern, the number of possible codes is combinatorially explosive (cf. Hatfield & Epstein, 1985). Third, the quantification of simplicity is controversial and is suspected to depend too much on artifacts of the employed encoding model (cf. Hatfield & Epstein, 1985). The present study provides a coherent solution to these problems, based on the concept of accessibility. The concept of accessibility simply implies that regularity and hierarchy in the code of a pattern correspond directly to regularity and hierarchy in the pattern itself. This correspondence is specified by the notions of holographic regularity and transparent hierarchy. These two notions are based on a strictly formal analysis of regularity and hierarchy, and lead to just a few coding rules which, essentially, describe only three classes of regularities: Iterations, symmetries, and so-called alternations. Furthermore, the concept of accessibility enables an efficient and largely parallel encoding process, in which the simplest code of a pattern can be obtained without generating the explosive number of all possible codes (see also van der Helm & Leeuwenberg, 1986; van der Helm, 1988). Finally, the concept of accessibility gives rise to an improved and promising quantification of simplicity.

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