Unsupervised Shape Clustering using Diffusion Maps

The quotient space of all smooth and connected curves represented by a fixed number of boundary points is a finite-dimensional Riemannian manifold, also known as a shape manifold. This makes the preservation of locality a critically important issue when reducing the dimensionality of shapes on the manifold. We present a completely unsupervised clustering algorithm employing diffusion maps for locality-preserving embedding of shapes onto a much lower-dimensional space. The algorithm first obtains a non-linear low-dimensional embedding of shape context features of outer boundary contours of the shapes. Considering the embedded coordinates as a new minimalist representation of shapes, a clustering of shapes is obtained using a finite mixture model. The proposed clustering algorithm is computationally efficient, as it relies on clustering in a very lowdimensional space, and produces much improved results (88.6% for a 7-class dataset) as compared to clustering with conventional linear projections.