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A Combinatorial Optimization Technique for the Sequential Decomposition of Erosions and Dilations

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Abstract

This paper presents a general algorithm for the automatic proof that an erosion (respectively, dilation) has a sequential decomposition or not. If the decomposition exists, an optimum decomposition is presented. The algorithm is based on a branch and bound search, with pruning strategies and bounds based on algebraic and geometrical properties deduced formally. This technique generalizes classical results as Zhuang and Haralick, Xu, and Park and Chin, with equivalent or improved performance. Finally, theoretical analysis of the proposed algorithm and experimental results are presented.

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Authors and Affiliations

  1. Departamento de Ciência da Computação, IME-USP, Rua do Matão 1010, 05508-900, São Paulo, SP, Brasil

    Ronaldo Fumio Hashimoto

  2. Departamento de Ciência da Computação, IME-USP, Rua do Matão 1010, 05508-900, São Paulo, SP, Brasil

    Junior Barrera

  3. Departamento de Ciência da Computação, IME-USP, Rua do Matão 1010, 05508-900, São Paulo, SP, Brasil

    Carlos Eduardo Ferreira

Authors
  1. Ronaldo Fumio Hashimoto
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  2. Junior Barrera
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  3. Carlos Eduardo Ferreira
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Hashimoto, R.F., Barrera, J. & Ferreira, C.E. A Combinatorial Optimization Technique for the Sequential Decomposition of Erosions and Dilations. Journal of Mathematical Imaging and Vision 13, 17–33 (2000). https://doi.org/10.1023/A:1008373522375

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