JOURNAL OF PARALLEL AND DISTRJBUTED COhfPUTlNG 4,7-44 ( 1987) Image Algebra Techniques for ParallelImage Processing* GERHARD X. RD-~ER Computer and Information Sciences Department, University of Florida, Gainesville, Florida 3261 I AND PAUL D. GADER Mathematics Department, University of Florida, Gainesville, Florida 32611 Received March 2 1,1986 An imagealgebra hasbeendefinedwhich is capable of expressing a wide variety of gray-level image-to-image transformations. The purposeof this paper is fourfolld: ( 1) to introduce the reader to the basicconcepts of the imagealgebra; (2) to show how it suggests a general-purpose cellular pyramid array processor for real time image processing tasks, (3) to demonstrate how the imagealgebra can be usedto formulate. the problem of mapping algorithmsto specific hardware; and (4) to show how alge- braic techniques can be used to develop systematic methods for deriving parallel dgOIithIllS. 0 1987 Academic F’rw, Inc. 1. IN-~RoDuCTI~N Current practice in the development and implementation of image pro- cessing algorithms makes little use of any standardized, mathematically rig- orous, efficient algebraic system that is speci!kally designed for image manip ulation. Yet vast increases in image prowssing activities in the military, in- dustrial, and academic communities have resulted in a deluge of different image processing operations and architectures. There are approximately as many different image processing languages as there are different image pro- * The results in this paper represent an expanded versionof research presented at the 1985 IEEEComputer Society Workshopon Computer Architecturefor PatternAnalysis and Image Database Management[ 131. 0743-73 15187 S3.00 Copyright 0 1987 by Acdcmic Pw.ss, Inc. AU righis of reproduction in any form reacmd.