The boolean map distance: theory and efficient computation

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

Distance Transform Computation for Digital Distance Functions

International audienceIn image processing, the distancetransform (DT), in which each object grid point is assigned the distance to the closest background grid point, is a powerful and often used tool. In this paper, distancefunctions defined as minimal cost-paths are used and a number of algorithms that can be used to compute the DT are presented. We give proofs of the correctness of the algorithms

Path-Based Distance with Varying Weights and Neighborhood Sequences

International audienceThis paper presents a path-based distance where local displacement costs vary both according to the displacement vector and with the travelled distance. The corresponding distance transform algorithm is similar in its form to classical propagation-based algorithms, but the more variable distance increments are either stored in look-up-tables or computed on-the-fly. These distances and distance transform extend neighborhood-sequence distances, chamfer distances and generalized distances based on Minkowski sums. We introduce algorithms to compute, in Z2, a translated version of a neighborhood sequence distance map with a limited number of neighbors, both for periodic and aperiodic sequences. A method to recover the centered distance map from the translated one is also introduced. Overall, the distance transform can be computed with minimal delay, without the need to wait for the whole input image before beginning to provide the result image