Complexity and structure in visual patterns.

Abstract

A series of seven experiments investigated the determinants of judged pattern complexity, with emphasis on the identification and measurement of structural variables. In an exploratory study, it was found that the determinants of pattern complexity could be separated into quantitative variables (number of turns, amount of contour), which set an upper bound on complexity, and structural variables, which reduced perceived complexity from the upper bound value. Results indicated that a wide variety of structural features, those generated by similarity transformations and related opponent-color transformations, were perceptually effective in reducing perceived complexity. In addition, it seemed that partial or approximate structure was effective in reducing perceived complexity. Later experiments developed and extended these results. Partial or approximate symmetry was shown to have a systematic effect on perceived complexity. The relative effectiveness of 10 different structural relations within patterns was determined. Patterns of varying degrees of organization were shown to determine a family of power functions, and this result rendered the expression of effects of structure equivalent to multiplicative reductions in pattern quantity. In addition, the effects of partial structure were shown to follow approximately a squared-area law. Finally, pair-comparison scaling was shown to yield results comparable to magnitude-estimation scaling, and multiple pattern structures were found to act as alternative, rather than additive, influences upon perceived complexity. Developmental and individual differences in complexity judgment are described. Results are discussed for their implications concerning patterns as stimuli in other experimental and naturalistic situations and are considered in relation to existing theories of pattern perception.

A Review of Capacity Limitation From Visual Perception to Short-Term Visual Memory of a Single Curved Contour

“…Similar to the study conducted by Chipman (1977), Sakai and Inui (2000) conducted experiments involving psychological complexity estimation using a set of contours with different numbers of convex parts at a constant P/√A value. The results showed that psychological complexity was predicted by the number of convex parts rather than P/√A.…”

“…Real correlations between numbers of turns in BPs and P 2 /A have been shown to be very strong (Chipman, 1977). To determine which of the two physical variables was more effective with psychological complexity, Chipman (1977) conducted an estimated experiment using a set of BPs that included different numbers of turns at a constant P 2 /A value. The results showed that estimations of psychological complexity were higher for patterns with higher, relative to lower, numbers of turns, even though they all possessed constant P 2 /A values.…”

“…(1) Physical complexity of the curved contour One of the ways in which the physical complexity of BPs can be measured involves perimeter 2 /area (P 2 /A; Attneave, 1957;Chipman, 1977). Parts with high curvature, such as turns in BPs, are important in patterns (Attneave, 1954), and convex/concave parts of curved contours correspond to turns in BPs.…”

Symmetropy, an entropy-like measure of visual symmetry

“…In general, the goodness and the complexity of a pattern seem to be directly related not only to the amount of total symmetry but also to the amount of partial symmetry in the pattern (Chipman, 1977;Howe, 1980). Therefore, we now define a measure of partial symmetry and another related measure.…”

“…Although Fourier (sine-cosine) functions also have this property, they do not have the following property: The two-dimensional Walsh functions take only two values, +1 and -1. This property facilitates the compattern complexity (Chipman, 1977). It would be useful, therefore, to develop a quantitative and objective measure of symmetry in order to predict perceptual organization.…”