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Erica Briscoe, Manish Singh, Jacob Feldman; Shape skeletons and shape similarity. Journal of Vision 2008;8(6):718. doi: https://doi.org/10.1167/8.6.718.
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© ARVO (1962-2015); The Authors (2016-present)
Human judgments of shape similarity are notoriously difficult to capture with a simple similarity metric; traditional measures based on contour features often show dramatic failures. A critical problem underlying contour-based similarity measures is their failure to respect the global configuration of object parts. We propose a shape similarity measure based on an extension of previous work on Bayesian shape skeleton estimation (Feldman & Singh, VSS 2006; PNAS 2007). The maximum a posteriori shape (MAP) skeleton, defined as the skeletal structure most likely to have generated a given shape, provides a robust and intuitive estimate of a shape's part structure. Here we extend the probabilistic machinery of Bayesian shape analysis to motivate a shape similarity measure that is based on the probability that two shapes share a common generative origin. To validate this similarity measure we ran a series of experiments. Exp. 1 involves simple shapes that vary according to their number of perceived parts. Similarity judgments exhibit a gross discontinuity when part structure changes qualitatively, e.g. from one part to two, even when this apparent change arises from a small change in contour properties. This pattern of results cannot be explained by conventional contour-based measures, but naturally falls out of the skeleton-based similarity measure, which automatically assigns greater dissimilarity to shapes whose estimated shape skeletons are topologically distinct. Follow-up experiments using more complex shapes show comparable results: shapes with qualitatively similar skeletons show greater similarity, while differences in skeleton structure (i.e. changes in part structure) are associated with increased dissimilarity. Finally, we argue that the derivation of a similarity metric from an overt probabilistic shape model provides a well-motivated account of the previously inaccessible connection between shape representation and shape categorization.
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