{"title":"内轴子集的稳定性和同伦","authors":"F. Chazal, A. Lieutier","doi":"10.2312/SM.20041396","DOIUrl":null,"url":null,"abstract":"Medial Axis is known to be unstable for non smooth objects. For an open set <i>O</i>, we define the Weak Feature Size, wfs, minimum distance between <i>O</i><sup>c</sup> and the critical points of the function distance to <i>O</i><sup>c</sup>. We introduce the \"Lambda-Medial Axis\" of <i>O</i>, Mλ, a subset of the Medial Axis of <i>O</i> which captures the Homotopy type of <i>O</i> when λ < wfs. We show that, at least for some \"regular\" values of λ, M<inf>λ</inf> remains stable under Hausdorff distance perturbations of <i>O</i><sup>c</sup>.","PeriodicalId":405863,"journal":{"name":"ACM Symposium on Solid Modeling and Applications","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2004-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"47","resultStr":"{\"title\":\"Stability and homotopy of a subset of the medial axis\",\"authors\":\"F. Chazal, A. Lieutier\",\"doi\":\"10.2312/SM.20041396\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Medial Axis is known to be unstable for non smooth objects. For an open set <i>O</i>, we define the Weak Feature Size, wfs, minimum distance between <i>O</i><sup>c</sup> and the critical points of the function distance to <i>O</i><sup>c</sup>. We introduce the \\\"Lambda-Medial Axis\\\" of <i>O</i>, Mλ, a subset of the Medial Axis of <i>O</i> which captures the Homotopy type of <i>O</i> when λ < wfs. We show that, at least for some \\\"regular\\\" values of λ, M<inf>λ</inf> remains stable under Hausdorff distance perturbations of <i>O</i><sup>c</sup>.\",\"PeriodicalId\":405863,\"journal\":{\"name\":\"ACM Symposium on Solid Modeling and Applications\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2004-06-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"47\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM Symposium on Solid Modeling and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2312/SM.20041396\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Symposium on Solid Modeling and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2312/SM.20041396","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Stability and homotopy of a subset of the medial axis
Medial Axis is known to be unstable for non smooth objects. For an open set O, we define the Weak Feature Size, wfs, minimum distance between Oc and the critical points of the function distance to Oc. We introduce the "Lambda-Medial Axis" of O, Mλ, a subset of the Medial Axis of O which captures the Homotopy type of O when λ < wfs. We show that, at least for some "regular" values of λ, Mλ remains stable under Hausdorff distance perturbations of Oc.
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