Symmetry, repetition, and figural goodness: an investigation of the Weight of Evidence theory

Abstract

Considerable evidence has accumulated on the superiority of symmetry over repetition in the study of figural goodness. The Weight of Evidence theory of figural goodness (WoE) provides a mathematically rigorous, elegant, and testable account of how factors like symmetry and repetition affect figural goodness. In this study we investigate implications of the WoE approach. More specifically, we examine (1) embedded patterns versus simple elements, (2) the number of elements in a pattern, and (3) long-range dependencies within a pattern. Data from two experiments illustrate cases in which figures made of simple repetitions have higher figural goodness than some kinds of symmetrical patterns; thus, the generality of the symmetry over repetition phenomenon is questioned. We discuss our results with respect to WoE and suggest ways to further develop the theory.

Introduction

Different perceptual patterns appear to us more regular than others. The two upper patterns in Fig. 1 are composed of the same contours, but in one case they are organized to form a symmetrical grouping of high regularity or figural goodness, and in the other contours are repeated to form a figure that appears less regular. The effects of figural goodness can be operationalized in several ways. For example, a random noise element has been introduced into the lower two patterns in Fig. 1. The noise element is readily noticeable in the ‘good’ left pattern but less so on the ‘bad’ right one. Intuitively, the noise element more easily segments away from the good figure, while there is less basis for segmentation of figure and noise in the bad pattern.

Theories of figural goodness attempt to explain why some novel configurations of perceptual elements are perceived as more regular than others. A widely reported phenomenon is that the symmetry of perceptual elements is more important than repetition to perception of goodness (Baylis and Driver, 1994, Bruce and Morgan, 1975, Corballis and Roldan, 1974), at least when the relevant contours are perceived as belonging to the same object (Baylis & Driver, 1995). The Weight of Evidence model of figural goodness (henceforth WoE; van der Helm and Leeuwenberg, 1996, van der Helm and Leeuwenberg, 1999) can account for the advantage of symmetry over repetition, as well as an impressive range of other figural goodness phenomena. Apart from its empirical plausibility, the theory has received considerable theoretical attention because it is also mathematically tractable and elegant. In the present work we examine the aspects of WoE that account for the commonly observed advantage of symmetry over repetition. In doing so, we identify cases which question the generality of the symmetry over repetition phenomenon.

We next briefly review previous accounts of figural goodness that motivate the importance of the WoE theory.