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Nathan Destler, Manish Singh, Jacob Feldman; Bayesian shape similarity based on 3D shape skeletons. Journal of Vision 2018;18(10):418. doi: https://doi.org/10.1167/18.10.418.
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Shape similarity is a fundamental component of object recognition and shape matching, but computation of shape similarity is poorly understood. In previous work, we proposed a simple similarity measure based on the cross-likelihood of the respective maximum posterior shape skeletons in a Bayesian framework. In the current work we introduce a more principled approach to shape similarity, and also extend it to the 3D case. The new similarity measure is proportional to the posterior probability that two shapes were generated from a common skeletal model, relative to the probability that they were generated from distinct models. One of the key terms entering in this ratio is a probabilistic version of the "edit distance" between one shape skeleton and the other, which expresses how likely one skeleton is to be a transformation of the other. To validate the model, we first applied it to previously-collected human shape discrimination thresholds for (2D) shapes, exploring the degree to which subjects' ability to discriminate simple shapes can be accounted for via skeleton-based similarity. Next, we collected new data in which participants were asked to assign 3D shapes to categories induced from positive and negative examples. In Exp. 1, subjects were asked to classify novel shapes based on a single positive and single negative example. In Exp. 2, subjects were asked to classify shapes based on multiple positive examples (and a single negative example), allowing us to evaluate how subjects' classifications, as well as those of the similarity model, vary as a function of the dissimilarity within the training set. As within-category dissimilarity rises, both the subjects' and the model's responses induce a more "generalized" skeletal model with a topologically simplified structure, entailing a broader category distribution. We interpret these results within the framework provided by the Bayesian approach to shape similarity and shape matching.
Meeting abstract presented at VSS 2018
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