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  1. 学術雑誌論文
  2. Journal of Computational Science

Use of several non-Euclidean metrics to compute distances between every two points in a plane bounded convex set

https://hiroshima-cu.repo.nii.ac.jp/records/2000200
https://hiroshima-cu.repo.nii.ac.jp/records/2000200
b2c61b6f-3b4b-4296-88cf-c06da684b54b
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JOCS85_102494.pdf JOCS85_102494.pdf (1005.7 KB)
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Item type デフォルトアイテムタイプ(シンプル)(1)
公開日 2025-02-18
タイトル
タイトル Use of several non-Euclidean metrics to compute distances between every two points in a plane bounded convex set
言語 en
作成者 岩田, 一貴

× 岩田, 一貴

en IWATA, Kazunori

ja 岩田, 一貴

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権利情報
言語 en
権利情報 © 2024 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
主題
主題Scheme Other
主題 Integral approximation
主題
主題Scheme Other
主題 Non-Euclidean metric
主題
主題Scheme Other
主題 Distribution of distances
主題
主題Scheme Other
主題 Plane bounded convex set
主題
主題Scheme Other
主題 Hough transform
内容記述
内容記述タイプ Abstract
内容記述 We consider movements between two chosen points in a plane-bounded set. The length of the movement between two points is measured by the Euclidean metric. We can then obtain the distribution of distances regarding the bounded set by repeatedly measuring the lengths of the movements. When we select two points uniformly in a bounded set, the shape of the bounded set affects the distribution. The distribution is easily computable by integral approximation and usefully remains invariant under the group of congruence transformations on the bounded set. For these reasons, some fundamental methods based on this distribution have been used in shape analysis. Thus, this distribution is important to some practical methods based on the Euclidean metric. Although some articles have been devoted to the study of non-Euclidean metrics in pattern recognition including shape analysis, only a few attempts have so far been made using the distribution of such non-Euclidean metrics. In this paper, we present the expression for the distributions with several non-Euclidean metrics using a density for the set of lines. This expression can be efficiently calculated as a sum of distributions, by generating a finite set of lines. We concentrate on a bounded convex set in the plane to define a non-Euclidean metric. In examples of such metrics on the convex set, we discuss those well-known in taxicab and projective geometries. In the experimental results using several convex sets, we visualize the distributions with the non-Euclidean metrics by plotting their graphs. Comparing the distribution based on the Euclidean metric with those based on the non-Euclidean metrics, we reveal several differences among the distributions.
言語 en
内容記述
内容記述タイプ Other
内容記述 This work was supported by JSPS, Japan KAKENHI [grant number 22K12171].
言語 en
出版者
出版者 Elsevier B.V.
言語
言語 eng
資源タイプ
資源タイプ識別子(シンプル) http://purl.org/coar/resource_type/c_6501
資源タイプ(シンプル) journal article
関連情報
識別子タイプ DOI
関連識別子 https://doi.org/10.1016/j.jocs.2024.102494
助成情報
研究課題番号URI https://kaken.nii.ac.jp/ja/search/?kw=22K12171
研究課題番号 22K12171
研究課題名 距離計量学習を用いた形状データのクラスタリング手法の開発
言語 ja
書誌情報 en : Journal of Computational Science

巻 85, p. none-102494, ページ数 9, 発行日 2025-02
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