A Bayesian Approach for Construction of Sparse Statistical Shape Models Using Dirichlet Distribution

Statistical shape models (SSMs) made using point sets are important tools to capture the variations within shape populations. One popular method for construction of SSMs is based on the Expectation-Maximization (EM) algorithm which establishes probabilistic matches between the model and training points. In this paper, we propose a novel Bayesian framework to automatically determine the optimal number of the model points. We use a Dirichlet distribution as a prior to enforce sparsity on the mixture weights of Gaussians. Insignificant model points are determined and pruned out using a quadratic programming technique. We apply our method to learn a sparse SSM from 15 manually segmented caudate nuclei data sets. The generalization ability of the proposed model compares favorably to a traditional EM based model