Parallel computation of exact Euclidean distance transform

Abstract

Distance transform is extensively used in image processing, such as expanding, shrinking, thinning, computing shape factor, etc. There are many approximate Euclidean distance transform (EDT) algorithms in the literature, but finding the exact Euclidean distance transform (EDT) with respect to the Euclidean distance metric is better in various application fields. Unless the digital image is very small, it is rather time consuming to find the exact Euclidean distance transform of an image. So, it is important to improve the computing speed. In this paper we study the parallel computation of the exact Euclidean distance transform for two parallel architectures: the EREW PRAM model and the SIMD hypercube computer. The parallel algorithm is given for the computation of exact Euclidean distance transform for all pixels with respect to black pixels in an N × N black and white image. The running time is O(log 2 N) both in the EREW PRAM model and the hypercube computer with N × N processors.