The Boolean map distance: Theory and efficient computation

Abstract

We propose a novel distance function, the boolean map distance (BMD), that defines the distance between two elements in an image based on the probability that they belong to different components after thresholding the image by a randomly selected threshold value. This concept has been explored in a number of recent publications, and has been proposed as an approximation of another distance function, the minimum barrier distance (MBD). The purpose of this paper is to introduce the BMD as a useful distance function in its own right. As such it shares many of the favorable properties of the MBD, while offering some additional advantages such as more efficient distance transform computation and straightforward extension to multi-channel images.