International Journal of Computer and Information Sciences, VoL 12, No. 6, 1983 Cellular Topology and Its Applications in Image Processing Lawrence A. Ankeney ~ and Gerhard X. Ritter 2,3 Received June 1983; revised October 1983 In this paper the interaction between Minkowski algebra, nondiscrete cellular topologies and some well known basic cellular image processing operations is investigated. It is shown that some useful topological measures can be extracted from these basic image operations and that these operations can be viewed from a nonalgebraic and purely topological point of view. KEY WORDS: Cellular computers; cellular automatons; cellular topology; Minkowski algebra; neighborhood transform; cellular image processing. 1. INTRODUCTION There seems to be little awareness within the mathematical community as to the many diverse applications of topology in the areas of pattern recognition and image processing. In fact, applications of topology outside the realm of mathematics is generally thought to be either rare or nonexisting. We hope to remedy this situation a little by presenting several image processing operations that permit image processing algorithms to be considered from a purely topological point of view. In particular, we use topological notions to define highly parallel neighborhood operations for filtering, data compression and image matching. Some of these operations will be novel, while others date back to Minkowski's development of the geometry of numbers in 1897. i Air Force Armament Laboratory, Eglin Air Force Base, Florida 32542. 2 Department of Mathematics and Center for Information Research, University of Florida, Gainesville, Florida 32611. 3 The author wishes to acknowledge support for this research by the Air Force Office of Scientific Research/AFSC, United States Air Force, under Contract F49620-C-82-0035. The United States Government is authorized to reproduce and distribute reprint for governmental purposes nothwithstanding any copyright notation hereon. ,$33 0091-7036/83/1200-0433503.0o/0 9 1983Plenum Publishing Corporation