An Optimal Decomposition Algorithm for Convex Structuring Elements

볼록 구조자룰 위한 최적 분리 알고리듬

In this paper, we present a new technique for the local decomposition of convex structuring elements for morphological image processing. Local decomposition of a structuring element consists of local structuring elements, in which each structuring element consists of a subset of origin pixel and its eight neighbors. Generally, local decomposition of a structuring element reduces the amount of computation required for morphological operations with the structuring element. A unique feature of our approach is the use of linear integer programming technique to determine optimal local decomposition that guarantees the minimal amount of computation. We defined a digital convex polygon, which, in turn, is defined as a convex structuring element, and formulated the necessary and sufficient conditions to decompose a digital convex polygon into a set of basis digital convex polygons. We used a set of linear equations to represent the relationships between the edges and the positions of the original convex polygon, and those of the basis convex polygons. Further. a cost function was used represent the total processing time required for computation of dilation/erosion with the structuring elements in a decomposition. Then integer linear programming was used to seek an optimal local decomposition, that satisfies the linear equations and simultaneously minimize the cost function.