Skeleton-Based Shape Similarity

Many aspects of visual perception, including the classification of shapes into known categories and the induction of new shape categories from examples, are driven by shape similarity. But there is as yet no generally agreed, principled measure of the degree to which two shapes are "similar. " Here, we derive a measure of shape similarity based on the Bayesian skeleton estimation framework of Feldman and Singh (2006). The new measure, called generative similarity, is based on the idea that shapes should be considered similar in proportion to the posterior probability that they were generated from a common skeletal model rather than from distinct skeletal models. We report a series of experiments in which subjects were shown a small number (1, 2, or 3) of 2D or 3D "nonsense " shapes (generated randomly in a manner designed to avoid known shape categories) and asked to select other members of the "same " shape class from a larger set of (random) alternatives. We then modeled subjects' choices using a variety of shape similarity measures drawn from the literature, including our new measure, skeletal cross-likelihood, a skeleton-based measure recently proposed by Ayzenberg and Lourenco (2019), a nonskeletal part-based similarity model proposed by Erdogan and Jacobs (2017), and a convolutional neural network model (Vedaldi & Lenc, 2015). We found that our new similarity measure generally predicted subjects' selections better than these competing proposals. These results help explain how the human visual system evaluates shape similarity and open the door to a broader view of the induction of shape categories.