A Unified Linear-Time Algorithm for Computing Distance Maps

Distance maps of binary images contain. for each pixel, the distance between that pixel and the pixel of value 0 closest to it. They have important uses in computer vision, pattern recognition, morphology and robotics ( IO]. Many algorithms have been proposed for computing distance maps for a variety of distances such as the Li, L,, octagonal and Euclidean distances ]%I I-131. Recently, Kolounzakis and Kutsulakos [ 91 gave an O( N2 log N) time algorithm for computing accurate Euclidean distance maps. It computes a distance map column by column, using a divide and conquer approach to each column. They also pointed out that their algorithm is available for other distances such as the LI distance. Dividing rows and columns alternately, Chen and Chuang [4] reduced the time complexity to 0( N’) which is optimal. Breu et al. [ 21 also gave an 0( N*) time algorithm which is based on the construction of the Voronoi diagram. In this paper we give a simple unified algorithm for computing distance maps. The algorithm runs in O( N2) time for an input of N x N binary image. It was first developed for the Euclidean distance in 181.