{"title":"闭合曲线的离散Fréchet距离","authors":"Evgeniy Vodolazskiy","doi":"10.1016/j.comgeo.2022.101967","DOIUrl":null,"url":null,"abstract":"<div><p>The paper presents a discrete variation of the Fréchet distance between closed curves, which can be seen as an approximation of the continuous measure. A rather straightforward approach to compute the discrete Fréchet distance between two closed sequences of <em>m</em> and <em>n</em> points using binary search takes <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mi>log</mi><mo></mo><mi>m</mi><mi>n</mi><mo>)</mo></math></span> time. We present an algorithm that takes <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo></mo><mi>m</mi><mi>n</mi><mo>)</mo></math></span> time, where <span><math><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> is the iterated logarithm.</p></div>","PeriodicalId":51001,"journal":{"name":"Computational Geometry-Theory and Applications","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Discrete Fréchet distance for closed curves\",\"authors\":\"Evgeniy Vodolazskiy\",\"doi\":\"10.1016/j.comgeo.2022.101967\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The paper presents a discrete variation of the Fréchet distance between closed curves, which can be seen as an approximation of the continuous measure. A rather straightforward approach to compute the discrete Fréchet distance between two closed sequences of <em>m</em> and <em>n</em> points using binary search takes <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mi>log</mi><mo></mo><mi>m</mi><mi>n</mi><mo>)</mo></math></span> time. We present an algorithm that takes <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo></mo><mi>m</mi><mi>n</mi><mo>)</mo></math></span> time, where <span><math><msup><mrow><mi>log</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> is the iterated logarithm.</p></div>\",\"PeriodicalId\":51001,\"journal\":{\"name\":\"Computational Geometry-Theory and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Geometry-Theory and Applications\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0925772122001109\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Geometry-Theory and Applications","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0925772122001109","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
The paper presents a discrete variation of the Fréchet distance between closed curves, which can be seen as an approximation of the continuous measure. A rather straightforward approach to compute the discrete Fréchet distance between two closed sequences of m and n points using binary search takes time. We present an algorithm that takes time, where is the iterated logarithm.
期刊介绍：
Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems.
Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.
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