A class of probabilistic shape models

Deformable models are related to other data representation methods. It was recently proposed a class of models based on a fuzzy energy function which includes many well known algorithms (snakes, elastic nets, fuzzy and hard c-means and Kohonen maps). This paper describes a probabilistic extension of these algorithms in a Bayesian framework, using Gibbs-Boltzman distributions. It is shown that the new class of models minimizes an energy function with an additional term: the log partition function. The role of the log partition function in probabilistic versions of snakes, c-means and elastic nets is studied and analytic expressions are derived in the case of probabilistic snakes. The log partition function produces an additional force field which improves the performance of these algorithms in some applications