Pixel labeling in a second-order Markov mesh

Abstract

In this paper, we address the pixle labeling problem under the assumption that contextual information in the picture is encoded in the transition probabilities of a second-order Markov mesh random field. We show that the problem can be solved by a linear algorithm generalizing Devijver's F-G-H algorithm. In order to label the current pixel, all the dependencies inside a triangular past neighborhood are taken into account. However, the computation of the probability of the labels lying at the border of the neighborhood is based upon an hypothesis. The complexity of the algorithm increases with the size of the considered neighborhood. Some experiments illustrating the theory proposed show how to recover an artificial binary image from its noisy version and how the size of the considered neighborhood influences the recovering. The very good results justify the use of this algorithm and moreover show that a best compromise between computer-time and precision leads to the F-G-H algorithm.