Weighted digital distance transforms in four dimensions Original Research Article

A digital distance transformation converts a binary image in Zn to a distance transform, where each picture element in the foreground (background) has a value measuring the closest distance to the background (foreground). In a weighted distance transform, the distance between two points is defined by a minimal path consisting of a number of steps between neighbouring picture elements, where each type of possible step is given a length-value, or a weight. In 4D, using 3×3×3×3 neighbourhoods, there are four different weights. In this paper, optimal real and integer weights are computed for one type of 4D weighted distance transforms. The most useful integer transform is probably 〈3,4,5,6〉, but there are a number of other ones listed. Two integer distance transforms are illustrated by their associated balls.