The prism machine: An alternative to the pyramid

The author defines a prism machine as a stack of n cellular arrays, each of size 2/sup n/ x 2/sup n/, with cell (i,j) on level k connected to cells (i,j), (i + 2/sup k/, j), and (i, j + 2/sup k/) (modulo 2/sup n/) on level k + 1. The author shows that such a machine can perform many useful types of operations on a 2/sup n/ X 2/sup n/ image in O(n) time. These include histogramming; the discrete Fourier transform; and various types of convolution and polynomial fitting operations having kernels of sizes 2/sup k/, k ,= 1,2,..., n. The latter operations are performed in every position, rather than in positions spaced 2/sup k/ apart as in the case of a pyramid. The connections in a prism resemble those in a hypercube, except that the author allows only connection in two ''directions'' at a time. The prism requires n times as many cells as a hypercube, but each cell has only a bounded number of neighbors instead of the O(n) neighbors in a hypercube. The author shows elsewhere that the between-level connections in a prism have a simple optical implementation. The prism requires more cells than a hypercubemore » or pyramid, but in practical cases the increase would be less than an order of magnitude. On the other hand, the prism has a very simple interconnection structure in which each cell has only a small number of neighbors, and in particular there are only three connections (per cell) between levels. Thus the prism deserves serious consideration as a possible architecture for image processing and analysis.« less