A parallel algorithm for weighted distance transforms

Abstract

This paper presents a parallel algorithm for the weighted distance transform and the nearest feature transform of an n/spl times/n binary image. We show that the algorithm runs in O(log n) time using n/sup 2//log n processors on the EREW PRAM and in O(log log n) time using n/sup 2//log log n processors on the common CRCW PRAM. We also show that the algorithm runs in O(n/sup 2//p/sup 2/+n) time an a p/spl times/p mesh and in O (n/sup 2//p/sup 2/+(n log p)/p) time on a p/sup 2/ processor hypercube (for 1/spl les/p/spl les/n). The algorithm is cost optimal on the PRAMs, on the mesh (for 1/spl les/p/spl les//spl radic/n) and on the hypercube (for 1/spl les/p/spl les/n/log n). We show that the time complexity on the EREW PRAM is time optimal.