Shapes, shocks and wiggles

摘要

We earlier introduced an approach to categorical shape description based on the singularities (shocks) of curve evolution equations. The approach relates to many techniques in computer vision, such as Blum's grassfire transform, but since the motivation was abstract it is not clear that it should also relate to human perception. We now report that this shock-based computational 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 descriptions. More generally, the results suggest that significance is a structural notion, not an image-based one, and that scale should be defined primarily in terms of relationships between abstract entities, not concrete pixels.