Statistical Shape Modeling Using Morphological Representations

The aim of this paper is to propose tools for statistical analysis of shape families using morphological operators. Given a series of shape families (or shape categories), the approach consists in empirically computing shape statistics (i.e., mean shape and variance of shape) and then to use simple algorithms for random shape generation, for empirical shape confidence boundaries computation and for shape classification using Bayes rules. The main required ingredients for the present methods are well known in image processing, such as watershed on distance functions or log-polar transformation. Performance of classification is presented in a well-known shape database.