Extended concepts

In the previous section, we described a number of different methods that were proposed to solve the same complex problem: computing the distance from any pixel in an image to the nearest object pixel. In contrast, several authors explored variations on the definition of this problem. In this section, we present three such variations.

First, we consider geodesic distances constrained by restricted domains [122,167]. Distances are only defined and computed on a part of the image, that can be either convex or non-convex. Secondly, we present the k-distance transformation [175], that computes the k distances to the k nearest object pixels. The usual DT is of course a particular case of k-DT with k=1. Finally, we present distances defined on gray-scale images [139,5,170,108,152,156]. On such images, a great variety of metrics can be defined. We present some of those and an efficient general purpose algorithm to compute the related DTs.