Statistically consistent image segmentation

A long studied and important image processing problem is image segmentation. In this paper theoretical properties of some image segmentation methods are investigated. More precisely, we are interested if these methods are statistically consistent, that is, if they can accurately recover the number of segments together with their boundaries in the image as the number of pixels tends to infinity. Major focus is given to the class of methods that is based on the minimum description length principle. A small numerical experiment is conducted to support our theoretical results.