Hierarchical Generative Modeling and Monte-Carlo EM in Riemannian Shape Space for Hypothesis Testing

Abstract

Statistical shape analysis has relied on various models, each with its strengths and limitations. For multigroup analyses, while typical methods pool data to fit a single statistical model, partial pooling through hierarchical modeling can be superior. For pointset shape representations, we propose a novel hierarchical model in Riemannian shape space. The inference treats individual shapes and group-mean shapes as latent variables, and uses expectation maximization that relies on sampling shapes. Our generative model, including shape-smoothness priors, can be robust to segmentation errors, producing more compact per-group models and realistic shape samples. We propose a method for efficient sampling in Riemannian shape space. The results show the benefits of our hierarchical Riemannian generative model for hypothesis testing, over the state of the art.