A geometric approach to shape clustering and learning

Using a geometric analysis of shapes introduced in [E. Klassen, et al., 2003], we present algorithms for: (i) hierarchical clustering of objects according to the shapes of their contours, and (ii) learning of simple probability models on a shape space from a collection of observed contours. We propose a tree (or a hierarchical) structure for clustering observed shapes. Clustering at any level is performed using a modified k-mean algorithm; means of individual clusters provide shapes for clustering at the next higher level. To impose a probability model on the shape space, we use a finite-dimensional Fourier approximation of functions tangent to the shape space at the sample mean. Examples are presented for demonstrating these ideas using shapes from the surrey fish database.