Shape dimension and approximation from samples

被引：18

作者：

Dey, TK ^{[1
]}

Giesen, J ^{[1
]}

Goswami, S ^{[1
]}

Zhao, WL ^{[1
]}

机构：

[1] Ohio State Univ, Dept CIS, Columbus, OH 43210 USA

来源：

DISCRETE & COMPUTATIONAL GEOMETRY | 2003年 / 29卷 / 03期

关键词：

Sample Point; Engineering Application; Empirical Result; Detection Algorithm; Topological Dimension;

D O I：

10.1007/s00454-002-2838-9

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

There are many scientific and engineering applications where an automatic detection of shape dimension from sample data is necessary. Topological dimensions of shapes constitute an important global feature of them. We present a Voronoi-based dimension detection algorithm that assigns a dimension to a sample point which is the topological dimension of the manifold it belongs to. Based on this dimension detection, we also present an algorithm to approximate shapes of arbitrary dimension from their samples. Our empirical results with data sets in three dimensions support our theory.

引用

页码：419 / 434

页数：16

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