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×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 n²/log log n processors on the common CRCW PRAM. We also show that the algorithm can be performed 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⩽√n) and on the hypercube (for 1⩽p⩽n/log n)