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Discrete & Computational Geometry

, Volume 29, Issue 3, pp 419–434 | Cite as

Shape Dimension and Approximation from Samples

  •  Dey
  •  Giesen
  •  Goswami
  •  Zhao

Abstract. 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.

Keywords

Sample Point Engineering Application Empirical Result Detection Algorithm Topological Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

  •  Dey
    • 1
  •  Giesen
    • 1
  •  Goswami
    • 1
  •  Zhao
    • 1
  1. 1.Department of CIS, Ohio State University, Columbus, OH 43210, USA tamaldey@cis.ohio-state.edu,giesen@cis.ohio-state.edu,goswami@cis.ohio-state.edu,zhaow@cis.ohio-state.eduUS

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