The k-max distance in graphs and images

Abstract

In this paper, we propose a new distance called the k - max distance that is intended for graphs and images. The length of a path is defined as the sum of the k maximum arc weights along the path. The distance between two nodes is the length of the shortest path between them. We show that the k max distance is a metric. The algorithm for computing the k - max distance is presented. Certain positive properties of the k - max distance are shown, namely in the context of measuring the distances for image segmentation. The comparison with the geodesic distance, the max- arc distance, the minimum barrier distance, and the random walker technique is carried out in the segmentation of real- life images.