A Generalized Level Set Formulation of the Mumford-Shah Functional with Shape Prior for Medical Image Segmentation

Image segmentation is an important research topic in medical image analysis area. In this paper, we firstly propose a generalized level set formulation of the Mumford-Shah functional by a sound mathematical definition of line integral. The variational flow is implemented in level set framework and thus implicit and intrinsic. By embedding a weighted length term to the original Mumford-Shah functional, the paper presents a generic framework that integrates region, gradient and shape information of an image into the segmentation process naturally. The region force provides a global criterion and increases the speed of convergence, the gradient information allows for a better spatial localization while the shape prior makes the model especially useful to recover objects of interest whose shape can be learned through statistical analysis. The shape prior is represented by the zero-level set of signed distance maps of images and is well consistent with level set based variational framework. Experiments on 2-D synthetic and real images validate this novel method.