Constant-time algorithm for computing the Euclidean distance maps of binary images on 2D meshes with reconfigurable buses

The computation of Euclidean distance maps (EDM), also called Euclidean distance transform, is a basic operation in computer vision, pattern recognition, and robotics. Fast computation of the EDM is needed since most of the applications using the EDM require real-time computation. It is shown in L. Chen and H.Y.H. Chuang Information Processing Letters, 51, pp. 25–29 (1994)] that a lower bound Ω(n²) is required for any sequential EDM algorithm due to the fact that in any EDM algorithm each of the n² pixels has to be scanned at least once. Recently, many parallel EDM algorithms have been proposed to speedup its computation. Chen and Chuang proposed an algorithm for computing the EDM on an n×n mesh in O(n) time L. Chen and H.Y.H. Chuang Parallel Computing, 21, pp. 841–852 (1995)]. Clearly, the VLSI complexities of both the sequential and the mesh algorithm described in L. Chen and H.Y.H. Chuang Parallel Computing, 21, pp. 841–852 (1995)] are AT²=O(n⁴), where A is the VLSI layout area of the design and T is the computation time using area A when implemented in VLSI. In this paper, we propose a new and faster parallel algorithm for computing the EDM problem on the reconfigurable VLSI mesh model. For the same problem, our algorithm runs in O(1) time on a two-dimensional n²×n² reconfigurable mesh. We show that the VLSI complexity of our algorithm is the same as those of the above sequential algorithm and the mesh algorithm, while it uses much less time. To our best knowledge, this is the first constant-time EDM algorithm on any parallel computational model.