Skeleton pruning as trade-off between skeleton simplicity and reconstruction error

Skeletons can be viewed as a compact shape representation in that each shape can be completely reconstructed from its skeleton. However, the usefulness of a skeletal representation is strongly limited by its instability. Skeletons suffer from contour noise in that small contour deformation may lead to large structural changes in the skeleton. A large number of skeleton computation and skeleton pruning approaches has been proposed to address this issue. Our approach differs fundamentally in the fact that we cast skeleton pruning as a trade-off between skeleton simplicity and shape reconstruction error. An ideal skeleton of a given shape should be the skeleton with a simplest possible structure that provides a best possible reconstruction of a given shape. To quantify this trade-off, we propose that the skeleton simplicity corresponds to model simplicity in the Bayesian framework, and the shape reconstruction accuracy is expressed as goodness of fit to the data. We also provide a simple algorithm to approximate the maximum of the Bayesian posterior probability which defines an order for iteratively removing the end branches to obtain the pruned skeleton. Presented experimental results obtained without any parameter tuning clearly demonstrate that the resulting skeletons are stable to boundary deformations and intra class shape variability.