Nearest neighbor problems on a mesh-connected computer

Given a binary image registered on a mesh-connected computer, the image is formed on n×n pixels distributed one pixel per processing element (PE). Two algorithms for computing the nearest neighbor are proposed. The first algorithm involves an image formed of two kinds of PEs, those having a point (marked PEs) and those not having a point (unmarked PEs). For each marked PE the Euclidean distance that separates this marked PE from the nearest other marked PE is determined. The second algorithm involves an image containing black components. The nearest-neighbor black component for each given black component is determined. When the algorithm has been completed, every PE of each black component `knows´ the coordinates of the nearest PE belonging to the nearest black component. It is shown that using the operations of connection and disconnection of communication channels to link two nonneighbor PEs, each problem can be solved in a number of operations less than n if n is sufficiently large for a mesh-connected computer of n×n dimension