Optimal boundary detection on grey-tone image

Abstract

The paper is devoted to the problem of optimal boundary detection for a two-object image. The objects have different average brightnesses under conditions of stationary noise. There is no a priori information about the average brightness of the objects, the type and parameters of noise density distribution functions, the shapes of the objects or the boundary length. However, the location of an initial point belonging to an object contour is presumed to be known. It is shown that an unknown contour line can only be found among level lines. A graph is constructed from a group of level lines passing through the initial point. The problem of finding the optimal path on the graph is solved according to a pre-defined quality criterion. The investigation included previously known criteria (maximization of gradient sums, the average gradient maximization) as well as some proposed by the authors (average risk minimization, as applied to a segmentation task, and alternative choice). The efficiency of the criteria is tested on a set of image models with different signal-to-noise ratios. An effective suboptimal tracking algorithm is developed for practical tasks of grey-tone image segmentation.