Relationship of image algebra to the optical processing of signals and imagery

Abstract

A method is proposed for the optical implementation of image algebra (IA) which would map the graph of a transformed IA expression directly to an optical architecture. The IA is a concise, mathematically rigorous notation which unifies linear and nonlinear mathematics in the image domain. Due to its clarity and inherent parallelism, the IA has been successfully employed in the specifications of image- and signal-processing algorithms for parallel computers such as the ERIM Cyto-SS, Honeywell Prep, and Thinking Machines' Connection Machine (CM-1 and CM-2). In this study, we consider the utility of IA as a descriptor of optical processing, as well as the optical implementation of image-algebraic operations over a finite subset of the Euclidean plane. For real-valued imagery, many IA operations can be realized via magnitude-only computation. Thus, incoherent illumination could be employed. Algorithmic examples are derived from the signal- and image-processing literature, as well as from set and graph theory, and include insertion sorting, cellular automata, morphological image operations, and morphological neural nets. Complexity analyses and implementational issues are discussed in terms of functional properties of the IA operator set, subject to optical propagation constraints.