Coding theory of visual pattern completion.

Abstract

It is possible to construct a line drawing that represents one object partly hidden behind another, and most subjects complete the interrupted figure and see the hidden object as whole. This article is addressed to two problems: (a) What are the necessary and sufficient conditions for such figural completion to occur, and (b) exactly what will be seen behind the occluding figure---that is, what completion will be made? Leeuwenberg's coding model for line drawings was used to analyze a number of such figures, along with the hypothesis that figural completion occurs whenever it results in a simplification of final code of the whole figure. Data from previous experiments along with results from two new experimental studies were collected and shown to agree with this hypothesis. Of various possible figural completions or "mosaic" interpretations, subjects chose the ones resulting in the simplest overall code. However, the above conclusions are correct only if "simple" is precisely defined as the smallest information load in a completely reduced code. Other possible theories of figural completion, both structuralist and Gestalt, may invoke familiarity, particular "cues," like T-shaped intersections, simplicity of the hidden figure, symmetry, and good continuation. All such possibilities were considered in the experiments and shown to fail, wrongly predicting at least one figure. The coding-theory analysis, on the other hand, made correct predictions for all of the 25 figures used.

Reconciling simplicity and likelihood principles in perceptual organization.

“…This general approach has been applied in a variety of contexts, from the organization of simple sequences, such as the example just considered (Leeuwenberg, 1969;Restle, 1970;Simon, 1972;Simon & Kotovsky, 1963;Vitz & Todd, 1969), to judgments of "figural goodness" (Hochberg & McAllister, 1953), the analysis of Johansson's (1950) experiments on the perception of motion configurations (Restle, 1979), and figural completion (Buffart, Leeuwenberg & Restle, 1981 ). It has also been advanced as a general framework for understanding perceptual organization (e.g., Attneave & Frost, 1969;Leeuwenberg, 1971;Leeuwenberg & Boselie, 1988).…”

“…Psychologists have used two approaches to operationalize the notion of brevity of encoding: Shannon's (1948) information theory (Attneave, 1959;Garner, 1962 ) and the tradition known as coding theory (Hochberg & McAlister, 1953;Restle, 1979;Simon, 1972), one elaboration of which is structural information theory (Buffart, Leeuwenberg & Restle, 1981 ). I consider these in turn.…”

Competing global and local completions in visual occlusion.

“…During past decades several studies on visual occlusion and amodal completion have been done by various researchers (cf. Boselie, 1988;Boselie & Wouterlood, 1989;Buffart, Leeuwenberg, & Restle, 1981;Chapanis & McCleary, 1953;Dinnerstein & Wertheimer, 1957;Gerbino & Salmaso, 1987;Kanizsa & Gerbino, 1982;Kellman & Shipley, 1991;Sekuler & Palmer, 1992;van Lier, van der Helm, & Leeuwenberg, 1994;. In the literature two types of amodal completion are frequently described: According to a global completion, the completed shape is as simple as possible, and according to a local completion, the completion itself is as simple as possible.…”

The Search for Simplicity: A Fundamental Cognitive Principle?

“…T his viewpoint is ech oed in the prop osal in the G estalt tradition that perceptual organization is ch osen to maximize``pra È gn anz' ' (K offka, 1935/ 1962), a notion closely related to simplicity, wh ich aim s to integrate the range of speci® c G estalt principles of perceptual organization (good for m , good continuation, and so on ). M or eover, H ochberg and M cAlister (1953) explicitly identi® ed the goal of perceptual or ganization as m axim izing simplicity, and this work, was followed by a variety of related prop osals, wh ere sim plicity is m easured in different ways (Buffar t, L eeuwen berg, & Restle, 1981;G ar ner, 1962, 1974L eeu wenberg, 1969, 1971. M oving from perception to the psychological p rocesses involved in scienti® c inference, simp licity has also frequently been invoked as an impor tant gu iding principle.…”