An efficient variational multiphase motion for the Mumford-Shah segmentation model

We propose here a new multiphase level set model for image segmentation, using Mumford-Shah techniques in the piecewise-constant case. The proposed model is also a generalization of our active contour model without edges based on a two-phase segmentation. In order to handle multiple individual segments and complex topologies (such as multiple junctions), we propose a new and efficient multiphase representation by level sets: The necessary number of level set functions is considerably reduced (we need only n level set functions to represent 2ⁿ phases or segments), and in addition we have overcomed the problems of vacuum and overlap, naturally arising in multiphase problems. Finally, we show how the model can be used in image segmentation, for synthetic and real (possible noisy) pictures.