Parallel computation of the 3-D Euclidean distance transform on the SlMD hypercube computer

The processing of three-dimensional (3-D) objects from 3-D digital image data is an important task in the image processing and the computer vision fields. The distance transform (DT) is extensively applied in the image processing and computer vision areas as a key operation. In a two or three-dimensional image array, the computation of distance transform (DT) is an important task. With the increasing application of 3-D voxel images, it is useful to consider the distance transform of a 3-D digital image array. In order to provide the efficient transform computations, parallelism is employed. We develop parallel algorithms for the three-dimensional Euclidean distance transform (3D-EDT) on the SIMD hypercube computer. The time complexity of our parallel algorithm is O(log²N) for an N×N×N image array using N³ processors. A generalized parallel algorithm for the 3D-EDT is also proposed and it runs O((N/p)³log(N)+(N/p)²log²p) time for an N×N×N binary image array on the SIMD hypercube computer using p³ PE´s, where 1≤p≤N.