Shapes, shocks and wiggles

We earlier introduced an approach to categorical shape description based on the singularities (shocks) of curve evolution equations. The approach rela tes to many techniques in computer vision, such as Blum's grassfire transfo rm, but since the motivation was abstract it is not clear that it should al so relate to human perception. We now report that this shock-based computat ional model can account for recent psychophysical data collected by Burbeck and Pizer. In these experiments subjects were asked to estimate the local centers of stimuli consisting of rectangles with 'wiggles' (sides modulated by sinusoids). Since the experiments were motivated by their 'core' model, in which the scale of boundary detail is proportional to object width, we conclude that such properties are also implicit in shock-based shape descri ptions. More generally, the results suggest that significance is a structur al notion, not an image-based one, and that scale should be defined primari ly in terms of relationships between abstract entities, not concrete pixels . (C) 1999 Elsevier Science B.V. All rights reserved.