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Voronoi random field and its application to the fuzzy post office problem

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Abstract

In this paper, we consider a random field, which is a generalization of Voronoi diagrams to probabilistic metric spaces. This random field is defined at each point of the space as a random variable that represents the nearest generator. As an application, relation to the post office problem for fuzzy point sets that was posed by Aurenhammer–Stockl–Welzl is investigated. This problem is also considered on digital pictures and an efficient numerical method to compute the probabilities is provided. The proposed method gives the probabilities of the random field in O(M 2 + M N) time, where M is the number of pixels in the input pictures and N is the number of generators, while a straightforward calculation takes O(M 3 N 2) time.

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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo, 113-8656, Japan

    Takaharu Yaguchi

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  1. Takaharu Yaguchi
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Correspondence to Takaharu Yaguchi.

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Yaguchi, T. Voronoi random field and its application to the fuzzy post office problem. Japan J. Indust. Appl. Math. 27, 425–441 (2010). https://doi.org/10.1007/s13160-010-0019-4

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  • DOI: https://doi.org/10.1007/s13160-010-0019-4

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