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Discrete and Computational Geometry pp 329–345Cite as

Detecting Undersampling in Surface Reconstruction

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Part of the book series: Algorithms and Combinatorics ((AC,volume 25))

Abstract

Current surface reconstruction algorithms perform satisfactorily on well sampled, smooth surfaces without boundaries. However, these algorithms face difficulties with undersampling. Cases of undersampling are prevalent in real data since often these data sample a part of the boundary of an object, or are derived from a surface with high curvature or non-smoothness. In this paper we present an algorithm to detect the boundaries where dense sampling stops and undersampling begins. This information can be used to reconstruct surfaces with boundaries, and also to localize small and sharp features where usually undersampling happens. We report the effectiveness of the algorithm with a number of experimental results. Theoretically, we justify the algorithm with some mild assumptions that are valid for most practical data.

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Author information

Authors and Affiliations

  1. Department of Computer and Information Science, Ohio State University, Columbus, OH, 43210, USA

    Tamal K. Dey

  2. Department of Computer and Information Science, Ohio State University, Columbus, OH, 43210, USA

    Joachim Giesen

  3. Institut für Theoretische Informatik, ETH Zentrum, CH-8092, Zürich, Switzerland

    Joachim Giesen

Authors
  1. Tamal K. Dey
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  2. Joachim Giesen
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Editor information

Editors and Affiliations

  1. Department of Computer and Information Science, Polytechnic University, Six Metro Tech Center, Brooklyn, NY, 11201, USA

    Boris Aronov

  2. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Saugata Basu

  3. City College and Courant Institute, 251 Mercer St., New York, NY, 10012, USA

    János Pach

  4. School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Micha Sharir

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© 2003 Springer-Verlag Berlin Heidelberg

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Dey, T.K., Giesen, J. (2003). Detecting Undersampling in Surface Reconstruction. In: Aronov, B., Basu, S., Pach, J., Sharir, M. (eds) Discrete and Computational Geometry. Algorithms and Combinatorics, vol 25. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55566-4_15

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  • DOI: https://doi.org/10.1007/978-3-642-55566-4_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62442-1

  • Online ISBN: 978-3-642-55566-4

  • eBook Packages: Springer Book Archive

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