WEKO3
アイテム
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/2000200b2c61b6f-3b4b-4296-88cf-c06da684b54b
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
JOCS85_102494.pdf (1005.7 KB)
|
.png)
|
| 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
|
|||||||||
| 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 |
|||||||||
