A cost optimal parallel algorithm for weighted distance transforms
The distance transform and the nearest feature transform are useful operations in image processing. These transforms are based on various kinds of distance functions because the distance functions have different efficiency or usefulness. In this paper, we consider these transforms based on the weighted distance, which is a generalization of many distances, such as city block, chessboard and chamfer distances. This paper presents a parallel algorithm for these transforms of an nn binary image. The algorithm runs in O time using processors on the EREW PRAM and in O time using processors on the common CRCW PRAM. The algorithm also runs in O(n2/p2+n) time on a pp mesh and in O time on a p2 processor hypercube (for 1?p?n). From these complexities, the algorithm is cost optimal on all models. Also we obtained an lower bound for the transform on the CREW PRAM. This implies that the algorithm is time optimal on the EREW PRAM.
parallel algorithm distance transform nearest feature transform pram mesh hypercube