A Variational Model for Object Segmentation Using Boundary Information and Statistical Shape Prior Driven by the Mumford-shah Functional

In this paper, we propose a variational model for object segmentation using the active contour method, a geometric shape prior and the Mumford-Shah functional. We propose an energy functional composed by three terms: the first one is based on image gradient, which detects edges, the second term constrains the active contour to get a shape compatible with a statistical model of the target shape, which provides robustness against missing shape information due to cluttering, occlusion and gaps, and the third part drives globally the shape prior towards a homogeneous intensity region. The minimization of the functional gives a system of coupled ordinary and partial differential equations which steady state, computed in a level set framework, provides the solution of the segmentation problem. We mathematically justify our segmentation variational model by proving the existence of a solution minimizing the energy functional in the space of functions of bounded variation. Applications of the proposed model are presented on various synthetic and real-world images.