Multi-Region Active Contours with a Single Level Set Function

Segmenting an image into an arbitrary number of coherent regions is at the core of image understanding. Many formulations of the segmentation problem have been suggested over the past years. These formulations include, among others, axiomatic functionals, which are hard to implement and analyze, and graph-based alternatives, which impose a non-geometric metric on the problem. We propose a novel method for segmenting an image into an arbitrary number of regions using an axiomatic variational approach. The proposed method allows to incorporate various generic region appearance models, while avoiding metrication errors. In the suggested framework, the segmentation is performed by level set evolution. Yet, contrarily to most existing methods, here, multiple regions are represented by a single non-negative level set function. The level set function evolution is efficiently executed through the Voronoi Implicit Interface Method for multi-phase interface evolution. The proposed approach is shown to obtain accurate segmentation results for various natural 2D and 3D images, comparable to state-of-the-art image segmentation algorithms.