Active contours for multi-region image segmentation with a single level set function

Segmenting the image into an arbitrary number of parts is at the core of image understanding. Many formulations of the task have been suggested over the years. Among these are axiomatic functionals, which are hard to implement and analyze, while graph-based alternatives impose a non-geometric metric on the problem. We propose a novel approach to tackle the problem of multiple-region segmentation for an arbitrary number of regions. The proposed framework allows generic region appearance models while avoiding metrication errors. Updating the segmentation in this framework is done by level set evolution. Yet, unlike most existing methods, evolution is executed using a single non-negative level set function, through the Voronoi Implicit Interface Method for a multi-phase interface evolution. We apply the proposed framework to synthetic and real images, with various number of regions, and compare it to state-of-the-art image segmentation algorithms.