HIGHER-ORDER STRUCTURE IN REGULARITY DETECTION

In three experiments a simple Euclidean transformation (reflection, tr anslation, rotation) was applied to collections of twelve dots in such a way that they contained equal lower-order structure, defined on the pairwise grouping of elements with their partner following transforma tion (e.g. parallel virtual lines), but differed in the presence vs ab sence of higher-order structure, defined on pairs of pairwise grouping s (e.g. virtual quadrangles with correlated angles). Based on the much better performance levels (d') in the case of additional higher-order structure, we conclude that global regularities are easier to detect when the local correspondences are supported by higher-order ones form ed between them. These enable the lower-order groupings to spread out across the whole pattern very rapidly (called bootstrapping). As a pre liminary attempt to specify these principles, we proposed a working mo del with two basic components: first, a function expressing the cost o f a perceptual grouping or the lack of regularity, and, secondly, an a lgorithm based on simulated annealing to minimize the cost function. T he simulation results obtained with our current implementation of thes e principles showed satisfactory qualitative agreement with human regu larity detection performance. Finally, the theory was shown to capture the essence of a large number of grouping phenomena taken from divers e domains such as detection of symmetry in dot patterns, global struct ure in Glass and vector patterns, correspondence in stereoscopic trans parency and apparent motion. Therefore, we are convinced that, in prin ciple, the mechanism used by the human visual system to detect regular ity incorporates something like bootstrapping based on higher-order st ructure. We regard this as a promising step towards unraveling the int riguing mechanisms of classic Gestalt phenomena.