Explorations of Shape Space

Using a small number of prototypical reference objects to span the internal shape representation space has been suggested as a general approach to the problem of object representation in vision (Edelman, 1995c). We have investigated the ability of human subjects to form the low-dimensional metric shape representation space predicted by this approach. In each of a series of experiments, which involved pairwise similarity judgement, and delayed match to sample, subjects were confronted with several classes of computer-rendered 3D animal-like shapes, arranged in a complex pattern in a common high-dimensional parameter space. We combined response time and error data into a measure of view similarity, and submitted the resulting proximity matrix to non metric multidimensional scaling (MDS). In the two-dimensional MDS solution, views of the same shape were invariably clustered together, and, in each experiment, the relative geometrical arrangement of the view clusters of the different objects reflected the true low-dimensional structure in a parameter space (star, triangle, square, line) that defined the relationships between the stimuli classes. These findings are now used to guide the development of a detailed computational theory of shape vision based on similarity to prototypes.