Parallel Detection of Concavities in Cellular Blobs

This paper reports some results on the use of parallel-structured computers to detect and describe concavities in simply connected planar regions (``domains´´ or ``blobs´´). We show, in particular, how these concavities may be obtained by a parallel filling-in process-somewhat like pouring liquid into several cups simultaneously. It has been shown that the concavities and concavity tree of a regular cellular blob (i.e., a digitized simply connected planar region) can be obtained by the use of a sequential algorithm that finds the minimum-perimeter polygon (MPP) passing through the boundary cells of the cellular blob. In this paper we show how any such MPP may be computed by a sequence of simultaneous local operations in a parallel-structured computer. We also show that the ratio of computation times for sequential algorithms to those for parallel algorithms operating on the cellular image of a large circular blob is approximately proportional to the square root of the blob´s perimeter, assuming the size of the vertex-detecting window is fixed and large enough to detect one or more vertices of the MPP. We also show that filling in the concavities by a sequence of parallel local operations terminates to an approximation of the cellular hull (i.e., the digitization of the convex hull of the original blob) in a finite time, and that this approximation is a subset of the cellular hull.