Bayesian estimation of the shape skeleton

Skeletal representations of shape have attracted enormous interest ever since their introduction by Blum [Blum H (1973) J Theor Biol 38:205–287], because of their potential to provide a compact, but meaningful, shape representation, suitable for both neural modeling and computational applications. But effective computation of the shape skeleton remains a notorious unsolved problem; existing approaches are extremely sensitive to noise and give counterintuitive results with simple shapes. In conventional approaches, the skeleton is defined by a geometric construction and computed by a deterministic procedure. We introduce a Bayesian probabilistic approach, in which a shape is assumed to have “grown” from a skeleton by a stochastic generative process. Bayesian estimation is used to identify the skeleton most likely to have produced the shape, i.e., that best “explains” it, called the maximum a posteriori skeleton. Even with natural shapes with substantial contour noise, this approach provides a robust skeletal representation whose branches correspond to the natural parts of the shape.