{"title":"Oriented Surfaces in Digital Spaces","authors":"Herman G.T.","doi":"10.1006/cgip.1993.1029","DOIUrl":null,"url":null,"abstract":"<div><p>We define a <em>digital space</em> to be a pair consisting of an arbitrary nonempty set <em>V</em> and a symmetric binary relation π on <em>V</em> with respect to which <em>V</em> is connected. Our intent is to investigate the notion of an oriented surface in this general environment. Our terminology reflects this: we refer to elements of <em>V</em> as <em>spels</em> (short for \"spatial elements\"), to artibrary nonempty subsets of π as <em>surfaces</em>, and we define the notions of the <em>interior</em> and the <em>exterior</em> of a surface. We introduce the notion of a <em>near-Jordan</em> surface, its interior and exterior partition <em>V</em>. We call a symmetric binary relation on <em>V</em> that contains π a <em>spel-adjacency</em>. For spel-adjacencies κ and λ, we call a surface κλ-<em>Jordan</em> if it is near-Jordan, its interior is κ-connected, and its exterior is λ-connected. We prove a number of results which characterize κλ-<em>Jordan</em> surfaces in general digital spaces and in <em>binary pictures</em> (in which there is an assignment of a 1 or a 0 to elements of <em>V</em>).</p></div>","PeriodicalId":100349,"journal":{"name":"CVGIP: Graphical Models and Image Processing","volume":"55 5","pages":"Pages 381-396"},"PeriodicalIF":0.0000,"publicationDate":"1993-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1006/cgip.1993.1029","citationCount":"119","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"CVGIP: Graphical Models and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1049965283710291","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 119
Abstract
We define a digital space to be a pair consisting of an arbitrary nonempty set V and a symmetric binary relation π on V with respect to which V is connected. Our intent is to investigate the notion of an oriented surface in this general environment. Our terminology reflects this: we refer to elements of V as spels (short for "spatial elements"), to artibrary nonempty subsets of π as surfaces, and we define the notions of the interior and the exterior of a surface. We introduce the notion of a near-Jordan surface, its interior and exterior partition V. We call a symmetric binary relation on V that contains π a spel-adjacency. For spel-adjacencies κ and λ, we call a surface κλ-Jordan if it is near-Jordan, its interior is κ-connected, and its exterior is λ-connected. We prove a number of results which characterize κλ-Jordan surfaces in general digital spaces and in binary pictures (in which there is an assignment of a 1 or a 0 to elements of V).