A Bayesian approach to image segmentation using Adaptive Finite Element Method

Mathematical methods for image segmentation are a research field currently widely investigated both from a theoretical point of view and from an application driven one. Starting from the classical formulation of Mumford and Shah's functional for image segmentation, several variants have been proposed along the years. In this poster we propose to present a brief overview of the so-called region-based functionals for image segmentation. The deterministic model proposed by Chan and Vese is extended by means of a probabilistic approach based on a Bayesian idea, without an a priori known dependency on the prior probability distribution. This leads to an improved model able to recognize the boundaries of the objects even in presence of noisy sources and non-uniform spatial patterns. From the computational point of view, a descent algorithm is derived by means of a level-set formulation and a discretization based on Finite Element Method and Adaptive Finite Element Method is proposed. Some application to sinthetic and real images are proposed.