{"title":"S/sup 2/-微分同态流形上曲率有界形状函数的局部逼近","authors":"Jianping Wang, I. Greenshields","doi":"10.1109/ACSSC.1993.342446","DOIUrl":null,"url":null,"abstract":"The explosive growth in the availability of three-dimensional imaging technologies (such as magnetic resonance imagery (MRI) and computer-assisted tomography (CAT)) has transformed the issue of three-dimensional shape description from a purely abstract exercise in differential geometry to one with practical implications. The paper explores the problem of constructing a rotationally-invariant \"sampling lattice\" for objects which are diffeomorphic to the unit sphere whose shape functions are L/sup 2/ and bounded in norm with respect to their Laplacian by using local R/sup 2/ approximations to the S/sup 2/ shape functions. The approach used follows a line of argument presented by Daubechies (1990).<<ETX>>","PeriodicalId":266447,"journal":{"name":"Proceedings of 27th Asilomar Conference on Signals, Systems and Computers","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1993-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Local approximation of curvature-bounded shape functions on S/sup 2/-diffeomorphic manifolds\",\"authors\":\"Jianping Wang, I. Greenshields\",\"doi\":\"10.1109/ACSSC.1993.342446\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The explosive growth in the availability of three-dimensional imaging technologies (such as magnetic resonance imagery (MRI) and computer-assisted tomography (CAT)) has transformed the issue of three-dimensional shape description from a purely abstract exercise in differential geometry to one with practical implications. The paper explores the problem of constructing a rotationally-invariant \\\"sampling lattice\\\" for objects which are diffeomorphic to the unit sphere whose shape functions are L/sup 2/ and bounded in norm with respect to their Laplacian by using local R/sup 2/ approximations to the S/sup 2/ shape functions. The approach used follows a line of argument presented by Daubechies (1990).<<ETX>>\",\"PeriodicalId\":266447,\"journal\":{\"name\":\"Proceedings of 27th Asilomar Conference on Signals, Systems and Computers\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1993-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of 27th Asilomar Conference on Signals, Systems and Computers\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ACSSC.1993.342446\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of 27th Asilomar Conference on Signals, Systems and Computers","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACSSC.1993.342446","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Local approximation of curvature-bounded shape functions on S/sup 2/-diffeomorphic manifolds
The explosive growth in the availability of three-dimensional imaging technologies (such as magnetic resonance imagery (MRI) and computer-assisted tomography (CAT)) has transformed the issue of three-dimensional shape description from a purely abstract exercise in differential geometry to one with practical implications. The paper explores the problem of constructing a rotationally-invariant "sampling lattice" for objects which are diffeomorphic to the unit sphere whose shape functions are L/sup 2/ and bounded in norm with respect to their Laplacian by using local R/sup 2/ approximations to the S/sup 2/ shape functions. The approach used follows a line of argument presented by Daubechies (1990).<>
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