Resistance-geodesic distance and its use in image processing and segmentation

Abstract

In many clustering and image-segmentation algorithms, measuring distances is used to decide whether two image points belong to a single or, respectively, to two different image segments. In more complicated images, measuring the distances along the surface that is defined by the image function may be more relevant than the Euclidean distance. The geodesic distance, i.e. the shortest path in the corresponding graph, has become popular. The problem is that it is determined on the basis of only one path that can arise accidentally as a result of imperfections in image. Using the k shortest paths solves the problem only partially since more than one path can arise accidentally too. In this paper, we introduce the resistance-geodesic distance with the goal to reduce the possibility that a false accidental path will be used for computing. Firstly, the effective conductance is computed for each pair of neighbouring nodes to determine the local width of the path that could run through the arc connecting them. The width is then used for determining the costs of arcs; the arcs with a small width are penalised. The usual methods for computing the shortest path in graph are then used to compute the final distances. We present the corresponding theory as well as the experimental results.