Optimal parallel algorithms for computing the chessboard distance transform and the medial axis transform on RAP

The distance transform (DT) and the medial axis transform (MAT) are two important image operations. They are both used to extract the information about the shape and the position of the foreground pixels relative to each other. Many applications of these transforms are applied in the fields of image processing and computer vision, such as expanding, shrinking, thinning and computing shape factor, etc. Each of these two transforms is essentially a global operation. Unless the digital image is very small, all global operations are prohibitively costly. In order to provide the efficient transform computations, it is considerably desired to develop parallel algorithms for these two operations. In this paper, we provide the fastest parallel algorithms to compute the chessboard distance transform (CDT) which is a DT based on the chessboard metrics, and the medial axis transform (MAT). Each of the transforms of a 2-D binary image array of size N×N can be computed in O(1) time on the 2-D 2N×2N reconfigurable array of processors (RAP)