Efficient Parallel Algorithms for Distance Maps of 2-D Binary Images Using an Optical Bus

Computing a distance map (distance transform) is an operation that converts a two-dimensional (2-D) image consisting of black and white pixels to an image where each pixel has a value or a pair of coordinates that represents the distance to or location of the nearest black pixel. It is a basic operation in image processing and computer vision fields, and is used for expanding, shrinking, thinning, segmentation, clustering, computing shape, object reconstruction, etc. This paper examines the possibility of implementing the problem of finding a distance map for an image efficiently using an optical bus. The computational model considered is the linear array with a reconfigurable pipelined bus system (LARPBS), which has been introduced recently based on current electronic and optical technologies. It is shown that the problem for an image can be implemented in (log log log ) bus cycles deterministically or in (log ) bus cycles with high probability on an LARPBS with processors. By high probability, we mean a probability of (1 ) for any constant 1. We also show that the problem can be solved in (log log ) bus cycles deterministically or in (1) bus cycles with high probability on an LARPBS with 3 processors. Scalability of the algorithms is also discussed briefly. The same problem can be solved using an LARPBS of processors in (( ) log log log ) time deterministically or in (( ) log ) time with high probability for any practical machine size of . For processor arrays with practical sizes, a bus cycle is roughly the time of an arithmetic operation. Hence, the algorithm compares favorably to the best known parallel algorithms for the same problem in the literature