Geometrical and Topological Informations for Image Segmentation with Monte Carlo Markov Chain Implementation

Image segmentation methods based on Markovian assumption consist in optimizing a Gibbs energy function which depends on the observation field and the segmented field. This energy function can be represented as a sum of potentials defined on cliques which are subsets of the grid of sites. The Potts model is the most commonly used to represent the segmented field. However, this model only expresses a potential on classes for nearest neighbor pixels. In this paper, we propose the integration of global informations, like the size of a region, in the local potentials of the Gibbs energy. To extract these informations, we use a representation model well known in geometric modeling: the topological map. Results on synthetic and natural images are provided, showing improvements in the obtained segmented fields.