Simulating essential pyramids

Pyramid computers, and more generally pyramid algorithms, for image processing have the advantage of providing regular structure with a base naturally identified with an input image and a logarithmic height that permits rapid reduction of information. It is shown that it is possible to simulate systematically the effect of having a separate, so-called `essential´ pyramid over each object, greatly simplifying algorithm development since algorithms can be written assuming that there is only a single object. This approach can yield optimal or nearly optimal algorithms for the pyramid computer and can also be used on nonpyramid architectures such as the hypercube, mesh-of-trees, mesh, mesh with row and column buses, mesh with reconfigurable buses, and PRAM (parallel random-access machine). For several of these architectures, the simulated essential pyramids can simultaneously execute an algorithm nearly as fast as a pyramid computer over a single object