  Unsupervised clustering of curves according to their shapes is an important
problem with broad scientific applications. The existing model-based clustering
techniques either rely on simple probability models (e.g., Gaussian) that are
not generally valid for shape analysis or assume the number of clusters. We
develop an efficient Bayesian method to cluster curve data using an elastic
shape metric that is based on joint registration and comparison of shapes of
curves. The elastic-inner product matrix obtained from the data is modeled
using a Wishart distribution whose parameters are assigned carefully chosen
prior distributions to allow for automatic inference on the number of clusters.
Posterior is sampled through an efficient Markov chain Monte Carlo procedure
based on the Chinese restaurant process to infer (1) the posterior distribution
on the number of clusters, and (2) clustering configuration of shapes. This
method is demonstrated on a variety of synthetic data and real data examples on
protein structure analysis, cell shape analysis in microscopy images, and
clustering of shaped from MPEG7 database.
