Spatial Causality in Bilateral Symmetry Detection

Abstract

We studied the influence of spatial scale on the detection of vertical and horizontal bilateral symmetry. The causality principle in scale - space theory states that increasing the spatial scale in a representation can only result in a decrease of structure. Consequently, a pattern can be random on the fine scale and symmetric on the coarse scale, never the reverse. Stimuli were bilaterally symmetric or random patterns, black-and-white on a grey background, with a circular aperture. The minimal scale was systematically varied and stimuli ranged from conventional noise patterns, through Dalmatian texture, to cow-like patterns. Observers had to judge whether a briefly presented pattern was ‘symmetric’ or ‘random’. Symmetric patterns resulted in a high accuracy (95%) with no influence of scale, and reaction times with a small linear decrease for increasing scale. Random patterns yielded an accuracy increasing from 70% at the smallest scale to 95% at the middle scales. Reaction times showed a similar pattern: largest at the smallest scales and decreasing to values equal to the symmetric condition at the middle scales. Results were similar for vertical and horizontal bilateral symmetry, though the effect for small scales in the random condition was more pronounced in the horizontal case. We conclude that bilateral symmetry is processed at multiple scales with coarse structures available slightly earlier than fine ones. The dramatic decrease of performance for fine-scale patterns is due to the causality effect; random patterns are judged as symmetric when the smallest scale information is not (yet) available.