A Parallel Algorithm for Weighted Distance Transforms

This paper presents a parallel algorithm for the weighted distance transform and the nearest feature transform of an n n binary image. We show that the algorithm runs in O(log n) time using n2= logn processors on the EREW PRAM and in O(log log n) time using n2= log log n processors on the common CRCW PRAM. We also show that the algorithm runs in O(n2=p2 + n) time on a p p mesh and in O(n2=p2 +(n log p)=p) time on a p2 processor hypercube (for 1 p n). The algorithm is cost optimal on the PRAMs, on the mesh (for 1 p pn) and on the hypercube (for 1 p n= logn). We show that the time complexity on the EREW PRAM is time optimal.