Abstract: An efficient snake formulation should conform to the idea of picking the smoothest curve among all the shapes approximating an object of interest. In current geodesic snakes, the regularizing curvature also affects the convergence stage, hindering the latter at concave regions. In the present work, we make use of characteristic functions to define a novel geodesic formulation that decouples regularity and convergence. This term decoupling endows the snake with higher adaptability to non-convex shapes. Convergence is ensured by splitting the definition of the external force into an attractive vector field and a repulsive one. In our paper, we propose to use likelihood maps as approximation of characteristic functions of object appearance. The better efficiency and accuracy of our decoupled scheme are illustrated in the particular case of feature space-based segmentation.

Abstract: Deformable models have received much popularity due to their ability to include high-level knowledge on the application domain into low-level image processing. Still, most proposed active contour models do not sufficiently profit from the application information and they are too generalized, leading to non-optimal final results of segmentation, tracking or 3D reconstruction processes. In this paper we propose a new deformable model defined in a statistical framework to segment objects of natural scenes. We perform a supervised learning of local appearance of the textured objects and construct a feature space using a set of co-occurrence matrix measures. Linear Discriminant Analysis allows us to obtain an optimal reduced feature space where a mixture model is applied to construct a likelihood map. Instead of using a heuristic potential field, our active model is deformed on a regularized version of the likelihood map in order to segment objects characterized by the same texture pattern. Different tests on synthetic images, natural scene and medical images show the advantages of our statistic deformable model.