Ligature Instabilities in the Perceptual Organization of Shape

Although the classical Blum skeleton has long been considered unstable, many have attempted to alleviate this defect through pruning. Unfortunately, these methods have an arbitrary basis, and, more importantly, they do not prevent internal structural alterations due to slight changes in an object's boundary. The result is a relative lack of development of skeleton representations for indexing object databases, despite a long history. Here we revisit a subset of the skeleton—called ligature by Blum—to demonstrate how the topological sensitivity of the skeleton can be alleviated. In particular, we show how the deletion of ligature regions leads to stable hierarchical descriptions, illustrating this point with several computational examples. We then relate ligature to a natural growth principle to provide an account of the perceptual parts of shape. Finally, we discuss the duality between the problems of part decomposition and contour fragment grouping.