<title>Random sets in image processing</title>

Abstract

Image processing is properly viewed as modeling and estimation in two dimensions. Image are often projections of higher dimensional phenomena onto a 2D grid. The scope of phenomena that can be imaged is unbounded, thus a wealth of image models is required. In addition, models should be constructed according to rigorous mathematics from first principles. One such approach is random- set modeling. The fit between random sets and our intuitive notion of image formation is natural, but poses difficult mathematical and statistical problems. We review the foundation of the random set approach in the continuous and discrete setting and present several highlights in estimation and filtering for binary images.