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The conformal alpha shape filtration

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Abstract

Conformal alpha shapes are a new filtration of the Delaunay triangulation of a finite set of points in ℝd. In contrast to (ordinary) alpha shapes the new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha shapes. The local scale parameter conforms to the local geometry and is motivated from applications and previous algorithms in surface reconstruction. We show how conformal alpha shapes can be used for surface reconstruction of non-uniformly sampled surfaces, which is not possible with alpha shapes.

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Authors and Affiliations

  1. Department of Computer Science, ETH Zürich, Zürich, Switzerland

    Joachim Giesen & Mark Pauly

  2. INRIA, Sophia Antipolis, France

    Frederic Cazals

  3. Department of Computer Science, Stanford University, Stanford, CA, USA

    Afra Zomorodian

Authors
  1. Joachim Giesen
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  2. Frederic Cazals
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  3. Mark Pauly
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  4. Afra Zomorodian
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Correspondence to Joachim Giesen.

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Giesen, J., Cazals, F., Pauly, M. et al. The conformal alpha shape filtration . Visual Comput 22, 531–540 (2006). https://doi.org/10.1007/s00371-006-0027-1

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  • DOI: https://doi.org/10.1007/s00371-006-0027-1

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