Fast algorithms for block-based medial axis transform on the LARPBS

Many parallel algorithms have been proposed for computing the two-dimensional block-based medial axis transform (2D_BB_MAT). Unfortunately, almost all of them are dedicated for solving 2D_BB_MAT problem and are very difficult to be extended for solving the 3D_BB_MAT problem. In this paper, an O(1) time algorithm for solving the 2D_BB_MAT of a binary image P of size N × N on an LARPBS is first developed. The running time of this algorithm has a smaller constant factor compared with those of all the other previous proposed O(1) time algorithms. Then this algorithm is extended for computing the 3D_BB_MAT of a binary image V of size N × N × N in O(1) time on an LARPBS. The running time of this algorithm has a small constant factor also. To the best of our knowledge, this is the first parallel algorithm proposed for solving the 3D_BB_MAT problem known.