No abstract

The human visual system is more sensitive to symmetry than to repetition. According to the so-called holographic approach [J. Math. Psychol. 35 (1991) 151; Psychol. Rev. 103 (1996) 429; Psychol. Rev. 106 (1999) 622], however, this perceptual difference between symmetry and repetition depends strongly on spatial scaling. This was tested in three experiments, using symmetry and repetition stimuli that consisted of black and white patches, with patch size as the critical variable. In Experiment 1, patch size was increased in the entire pattern, yielding fewer but larger patches (or blobs). This is known to have hardly any effect on symmetry but, as found now, it does have a strengthening effect on repetition. In the second experiment, we increased patch size in subpatterns only, yielding salient blob areas. This again strengthens repetition but, as double-checked in experiment 3, it can weaken symmetry. These results agree with the holographic approach, and enable an integration of computational, algorithmic, and implementational aspects of vision.

No abstract

As a rule, the discriminability of multiple symmetries from random patterns increases with the number of symmetry axes, but this number does not seem to be the only determinant. In particular, multiple symmetries with orthogonal axes seem better discriminable than multiple symmetries with nonorthogonal axes. In six experiments on imperfect two-fold symmetry, we investigated whether this is due to extra structure in the form of so-called correlation rectangles, which arise only in the case of orthogonal axes, or to the relative orientation of the axes as such. The results suggest that correlation rectangles are not perceptually relevant and that the percept of a multiple symmetry results from an orientation-dependent interaction between the constituent single symmetries. The results can be accounted for by a model involving the analysis of symmetry at all orientations, smoothing (averaging over neighboring orientations), and extraction of peaks.

The effect of temporal image segmentation on symmetry perception was investigated by means of stimuli composed of one part surrounding another. The two parts could be presented synchronously or with a temporal offset (20-100 ms), and each part could be either symmetrical or random. The task was to discriminate completely symmetrical (S) stimuli (in Experiment 1) or completely random (R) stimuli (in Experiment 2) from partially symmetrical (PS) stimuli in which one part was symmetrical and the other random. The R stimuli showed an asynchrony effect but the S stimuli did not. Furthermore, in both experiments, the PS stimuli showed an asynchrony effect when the symmetrical part was presented last but not when the symmetrical part was presented first (independent of whether it was the surrounded part or the surrounding part). Both results suggest that symmetry is strong enough to override this kind of temporal image segmentation.