A Global Criterion for the Computation of Statistical Shape Model Parameters Based on Correspondence Probabilities

A fundamental problem when building a statistical shape model (SSM) is the correspondence problem. We present an approach for unstructured point sets where one-to-one correspondences are replaced by correspondence probabilities between shapes which are determined using the Expectation Maximization - Iterative Closest Points registration. We propose a unified MAP framework to compute the model parameters which leads to an optimal adaption of the model to the observations. The optimization of the MAP explanation with respect to the observation and the generative model parameters leads to very efficient and closed-form solutions for (almost) all parameters. Experimental results on synthetic data and brain structures as well as a performance comparison with a statistical shape model built on one-to-one correspondences show the efficiency and advantages of this approach.