Segmenting an image into similar parts is important for low level image understanding. Many formulations of the segmentation task have been suggested over the years. While axiomatic functionals, such as the Mumford-Shah functional, are hard to implement and analyze, graph-based alternatives often impose articial measures on the problem. The latter are usually simple to optimize and implement at the expense of giving up some desired properties. Here, we tackle the most basic image quantization, or piecewise constant segmentation problem, while regularizing the boundaries between the regions according to a weighted Euclidean arc-length. The problem is shown to be related to the original Mumford-Shah functional, and formalized as a level set evolution equation. Yet, unlike most existing methods, the evolution is executed using a single non-negative level set function, through the Voronoi Implicit Interface Method [21] for a multi-phase interface evolution. The proposed framework has been tested on a number of synthetic and real images, with dierent num
['Anastasia Dubrovina', 'Guy Rosman', 'Ron Kimmel']
Active Contours for Multi-region Image Segmentation with a Single Level Set Function