HYPERMATRIX ALGEBRA - APPLICATIONS IN PARALLEL IMAGE-PROCESSING

A unique algebraic methodology is presentedfor implementing parallel tasks on multistage multidimensional architectures. Such architectures are motivated by the potential of digital optical and optoelectronic computing. Structured tasks can be decomposed from their initial algebraic casting and shown to match known canonical forms representing desirablecomputing structures such as 2D Omega processor. Algebraic manipulation of two-dimensional data structures—typical in image processing—requires more powerful operations than those afforded by classical matrixalgebra. To this end, hypermatrix algebra provides acompact treatment of multidimensional objects and associated operations. Mappings of linear transformations are demonstrated including 2D Hadamard transformations, matrix rotations, and transposition. © 1993 Academic Press, Inc.