{"title":"Discrete Analytical Hyperplanes","authors":"Eric Andres , Raj Acharya , Claudio Sibata","doi":"10.1006/gmip.1997.0427","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents the properties of the discrete analytical hyperplanes. They are defined analytically in the discrete domain by Diophantine equations. We show that the discrete hyperplane is a generalization of the classical digital hyperplanes. We present original properties such as exact point localization and space tiling. The main result is the links made between the arithmetical thickness of a hyperplane and its topology.</p></div>","PeriodicalId":100591,"journal":{"name":"Graphical Models and Image Processing","volume":"59 5","pages":"Pages 302-309"},"PeriodicalIF":0.0000,"publicationDate":"1997-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/gmip.1997.0427","citationCount":"126","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Graphical Models and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1077316997904275","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 126
Abstract
This paper presents the properties of the discrete analytical hyperplanes. They are defined analytically in the discrete domain by Diophantine equations. We show that the discrete hyperplane is a generalization of the classical digital hyperplanes. We present original properties such as exact point localization and space tiling. The main result is the links made between the arithmetical thickness of a hyperplane and its topology.
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