Ligature instabilities in the perceptual organization of shape

Although the classical Blum skeleton has long been considered unstable, man y have attempted to alleviate this defect through pruning. Unfortunately, t hese methods have an arbitrary basis, and, more importantly, they do not pr event internal structural alterations due to slight changes in an object's boundary. The result is a relative lack of development of skeleton represen tations for indexing object databases, despite a long history. Here we revi sit 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 d escriptions, illustrating this point with several computational examples. W e then relate ligature to a natural growth principle to provide an account of the perceptual parts of shape. Finally, we discuss the duality between t he problems of part decomposition and contour fragment grouping, (C) 1999 A cademic Press.