Shape discrimination and the judgement of perfect symmetry: Dissociation of shape from size

Abstract

We measured the accuracy with which subjects judged that a square or circle was perfectly symmetrical i.e. that aspect ratio ( a/b) was exactly unity (where a and b were, respectively, the vertical and horizontal dimensions). Errors were remarkably small, ranging from 0.7 to 0.4% for the judgement of squareness and from 1.4 to <0.1% for the judgement of circularity. Precision in judging aspect ratio was measured by requiring subjects to judge whether the aspect ratio ( a/b) TEST of a test rectangle was greater or less than the aspect ratio ( a/b) REF of a reference rectangle. Similar measurements were made for elliptical targets. To ensure that subjects based judgements on aspect ratio rather than a, b or ( a − b), the area of each successive presentation was varied randomly. The just-discriminable percentage change of aspect ratio was as low as 1.6% at ( a/b) REF = 1.0 (i.e. for a square or circular reference), and rose progressively as ( a/b) REF was made progressively larger or smaller than 1.0. Aspect ratio discrimination threshold was independent of mean area over a sixteen-fold range of 0.25–4.0 deg 2. For both rectangles and ellipses, the best value of aspect ratio discrimination threshold corresponded to a precision of encoding a and b of 14 sec arc or better. In further experiments, the method of constant stimuli was used to measure an aspect ratio aftereffect produced by adapting separately to rectangles of ( a/b) ADAPT equal to 1.5, 1.0 and ( 1/1.5). Similar aftereffects were obtained whether the area of the test stimulus was fixed or varied randomly from trial to trial, and whether the test stimulus was rectangular or elliptical. The aftereffect could not be explained in terms of fatigue of neurons sensitive to linear dimension a or b. Nor could the aftereffect be explained in terms of the “contour repulsion” hypothesis, or in terms of orientation discrimination. We conclude (1) that the same neural mechanism determines aspect ratio discrimination threshold for rectangles and ellipses and (2) that this mechanism is sensitive to aspect ratio independently of linear dimensions. We propose that aspect ratio perception is determined by the balance of excitation of two pools of neurons that are selectively sensitive to different, but overlapping ranges of ( a/b). One pool prefers aspect ratios ≫ 1.0 and the others prefer aspect ratios < 1.0. We suppose that the two pools respond identically to changes in area ( a * b). The aspect ratio aftereffect occurs when one pool is fatigued more than the other, thus altering the balance of excitation. This hypothesis can explain why aspect ratio discrimination is best at ( a/b) REF = 1.0 , why co-varying changes of area are not confounded with changes of ( a/b), and why aspect ratio discrimination threshold is not affected by mean area.