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A Greedy Algorithm for Decomposing Convex Structuring Elements

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Abstract

This paper presents a greedy algorithm for decomposing convex structuring elements as sequence of Minkowski additions of subsets of the elementary square (i.e., the 3 × 3 square centered at the origin). The technique proposed is very simple and it is based on algebraic and geometric properties of Minkowski additions. Besides its simplicity, the advantage of this new technique over other known algorithms is that it generates a minimal sequence of not necessarily convex subsets of the elementary square. Thus, subsets with smaller cardinality are generated and a faster implementation of the corresponding dilations and erosions can be achieved. Experimental results, proof of correctness and analysis of computational time complexity of the algorithm are also given.

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  1. Departamento de Ciência da Computação do IME-USP, Rua do Matão 1010, 05508-090, São Paulo, SP, Brasil

    Ronaldo Fumio Hashimoto & Junior Barrera

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  1. Ronaldo Fumio Hashimoto
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  2. Junior Barrera
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Hashimoto, R.F., Barrera, J. A Greedy Algorithm for Decomposing Convex Structuring Elements. Journal of Mathematical Imaging and Vision 18, 269–289 (2003). https://doi.org/10.1023/A:1022847527229

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