A simple parallel algorithm for the medial axis transform of binary images

The medial axis transform (MAT) is an image representation scheme. For a binary image, the MAT is defined as a set of upright maximal squares which consist of pixels of value 1 entirely. The MAT plays an important role in image understanding. The paper presents a parallel algorithm for computing the MAT of an n/spl times/n binary image. We show that the algorithm can be performed in O(log n) time using n2/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 can be performed in O(n/sup 2//p/sup 2/+n) time on 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).