Neighborhood Decomposition of Convex Structuring Elements for Mathematical Morphology on Hexagonal Grid
In this paper, we present a new technique to find the optimal neighborhood decomposition for convex structuring elements used in morphological image processing on hexagonal grid. In neighborhood decomposition, a structuring element is decomposed into a set of neighborhood structuring elements, each of which consists of the combination of the origin pixel and its six neighbor pixels. Generally, neighborhood decomposition reduces the amount of computation required to perform morphological operations such as dilation and erosion. Firstly, we define a convex structuring element on a hexagonal grid and formulate the necessary and sufficient condition to decompose a convex structuring element into the set of basis convex structuring elements. Secondly, decomposability of a convex structuring element into the set of primal bases is also proved. Furthermore, cost function is used to represent the amount of computation or execution time required for performing dilations on different computing environments and by different implementation methods. The decomposition condition and the cost function are applied to find the optimal neighborhood decomposition of a convex structuring element, which guarantees the minimal amount of computation for morphological operations. Example decompositions show that the decomposition results in great reduction in the amount of computation for morphological operations.
KeywordsCost Function Mathematical Morphology Morphological Operation Primal Basis Hexagonal Grid
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