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.

1. INTRODUCTION

Image segmentation aims to partition an image into a set of nonoverlapping regions so that pixels within the same region are homogeneous with respect to some characteristic (e.g., greyvalue or roughness), while pixels from adjacent regions are significantly different with respect to the same characteristic. It is a fundamental problem in image processing, as very often it is necessary to group the highly localized pixels into more global and meaningful segmented objects to facilitate the extraction of useful information. In this paper greyvalue is the image characteristic that forms the basis for segmentation.