Probabilistic shape models: the role of the partition function

Deformable models have been intensively investigated during the last decade. Several well known algorithms, proposed in other contexts can also be included in this class (e.g., Kohonen maps, elastic nets and fuzzy c-means). In all these methods the model parameters are obtained in a deterministic framework by the minimization of an energy function. This paper proposes a novel class of probabilistic shape models related to the unified framework presented by Abrantes and Marques (see IEEE Trans. Image Processing, p.1507-21, 1996). Shape modelling is addressed as a MAP estimation problem, by assuming that the image features are random variables with Gibbs-Boltzmann distribution, and provides extensions for several well known algorithms. The main difference between the proposed algorithms and the original ones lies on the partition function which depends on the model parameters and influences the shape estimates. For example, it is shown that in snakes the partition function generates short-range repulsive forces between the model units which prevent their collapse when they are attracted by common data