Constancy and Similarity

Pizlo, Rosenfeld, and Weisss6] suggest that people perceive two 2-D shapes as the same (i.e., there is shape constancy) when one shape might be a perspective image of the other. We argue that this hypothesis is both too broad and too restrictive. Their view is too broad because, as we show, two such images can appear quite diierent when there is signiicant perspective distortion. Their view is too restrictive because factors such as context and the complexity of the shapes compared can play a role in judgements of shape constancy. Moreover, Pizlo et al.'s formulation is asymmetric in requiring that one of the images be considered the model which produces the other. One can consider removing this asymmetry by judging shapes as the same when they could be two perspective views, taken with the same camera, of a third planar shape. We show that this is true if and only if the images are projectively equivalent. However, Pizlo et al. have convincingly rejected projective equivalence as a model of shape constancy.