Design of statistical measures for the assessment of image segmentation schemes

Image segmentation is discussed for years in numerous papers, but assessing its quality is mainly dealt with in recent works. Quality assessment is a primary concern for anyone working towards better segmentation tools. It both helps to objectively improve segmentation techniques and to compare performances with respect to other similar algorithms. In this paper we use a statistical framework to propose statistical measures capable to describe the performances of a segmentation scheme. All the measures rely on a ground-truth segmentation map that is supposed to be known and that serves as a reference when qualifying the results of any segmentation tool. We derive the analytical expression of several transition probabilities and show how to calculate them. An important conclusion from our study, often overlooked, is that performances can be content dependent, which means that one should adapt a measure to the content of an image.