{"title":"The space efficiency of quadtrees","authors":"Charles R Dyer","doi":"10.1016/0146-664X(82)90020-X","DOIUrl":null,"url":null,"abstract":"<div><p>The space efficiency of the quadtree representation is investigated for the case in which a single 2<sup><em>m</em></sup> by 2<sup><em>m</em></sup> square region occurs in a 2<sup><em>n</em></sup> by 2<sup><em>n</em></sup> image. When the square is equally likely to occur at any position, it is shown that the average and worst case numbers of nodes in the quadtree are both on the order of the region's perimeter plus the logarithm of the image's diameter.</p></div>","PeriodicalId":100313,"journal":{"name":"Computer Graphics and Image Processing","volume":"19 4","pages":"Pages 335-348"},"PeriodicalIF":0.0000,"publicationDate":"1982-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0146-664X(82)90020-X","citationCount":"110","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Graphics and Image Processing","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0146664X8290020X","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 110
Abstract
The space efficiency of the quadtree representation is investigated for the case in which a single 2m by 2m square region occurs in a 2n by 2n image. When the square is equally likely to occur at any position, it is shown that the average and worst case numbers of nodes in the quadtree are both on the order of the region's perimeter plus the logarithm of the image's diameter.
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