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Jacob Feldman, Manish Singh; Bayesian estimation of the shape skeleton. Journal of Vision 2006;6(6):23. doi: https://doi.org/10.1167/6.6.23.
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© ARVO (1962-2015); The Authors (2016-present)
Skeletal representations of shape have attracted enormous interest ever since their introduction by Blum (1973). But computation of the shape skeleton is notoriously problematic, (e.g. extremely sensitive to noise in the bounding contour). In conventional approaches, the shape skeleton has generally been defined by a fixed geometric construction and computed via a deterministic procedure. We introduce a new probabilistic approach to computing the shape skeleton, in which the shape is conceived as the outcome of a stochastic generative process in which a skeleton is randomly generated, and then sprouts “ribs” of random lengths, whose endpoints when joined define the shape's bounding contour. This stochastic shape model includes a prior probability density over shape skeletons (a generalization of our previous work on contour information), and a likelihood density over shapes given a skeleton. Then computation of the shape skeleton becomes a conventional Bayesian estimation problem, in which the observer estimates the skeleton that maximizes the posterior probability of the observed shape (the “MAP skeleton”). Equivalently, the procedure can be seen as minimizing the description length of the shape, i.e. the sum of the negative log prior (complexity) of the skeleton plus the negative log likelihood of the shape given the skeleton. In this approach, small deformations along the bounding contours do not lead to substantial changes in the skeleton, but rather are modeled as noise in the stochastic rib-length function. We present examples showing that the MAP skeleton corresponds closely to the intuitive branching structure for a variety of shapes.
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