A Computational Model of Mathematical Morphology

Abstract

Using mathematical morphology, recent research has clarified the geometrical properties of topological transformation procedures such as skeletonization and boundary detection, which are typical operations for shape analysis. Further, mathematical morphology has derived what we must compute parallelly for shape analysis. Mathematical morphology, however, does not provide how we must compute parallelly each operation because the theory is based on integral geometry and is not based on the theory of parallel computation. A well-defined language clarifies how algorithms should be compute parallelly.¹ Then, it is necessary to introduce a language to describe the parallelism of morphological operations. The theory of computation² is unfamiliar to image analysis society. Then, just as mathematical morphology brought new methodology to image analysis society, the computational theory will enrich shape analysis.