3D Block-Based Medial Axis Transform and Chessboard Distance Transform on the CREW PRAM

Abstract

Traditionally, the block-based medial axis transform (BB-MAT) and the chessboard distance transform (CDT) were usually viewed as two completely different image computation problems, especially for three dimensional (3D) space. We achieve the computation of the 3D CDT problem by implementing the 3D BB-MAT algorithm first. For a 3D binary image of size N3, our parallel algorithm can be run in O(logN) time using N3processors on the concurrent read exclusive write (CREW) parallel random access machine (PRAM) model to solve both 3D BB-MAT and 3D CDT problems, respectively. In addition, we have implemented a message passing interface (MPI) program on an AMD Opteron Model 270 cluster system to verify the proposed parallel algorithm, since the PRAM model is not available in the real world. The experimental results show that the speedup is saturated when the number of processors used is more than four, regardless of the problem size.