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Size Analysis of Nearly Regular Delaunay Triangulations

Author

Listed:
  • Ian L. Dryden

    (University of Leeds)

  • Charles C. Taylor

    (University of Leeds)

  • Mohammad Reza Faghihi

    (Islamic Republic of Iran)

Abstract

Consider a nearly regular point pattern in which a Delaunay triangulation is comprised of nearly equilateral triangles of the same size. We propose to model this set of points with Gaussian perturbations about a regular mean configuration. By investigating triangle subsets in detail we obtain various distributions of statistics based on size, or squared size of the triangles which is closely related to the mean (squared) distance to the six nearest neighbors. A scaleless test statistic, corresponding to a coefficient of variation for squared sizes, is proposed and its asymptotic properties described. The methodology is applied to an investigation of regularity in human muscle fiber cross-sections. We compare the approach with an alternative technique in a power study.

Suggested Citation

  • Ian L. Dryden & Charles C. Taylor & Mohammad Reza Faghihi, 1999. "Size Analysis of Nearly Regular Delaunay Triangulations," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 97-117, July.
    • Handle: RePEc:spr:metcap:v:1:y:1999:i:1:d:10.1023_a:1010064208174
    DOI: 10.1023/A:1010064208174
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    References listed on IDEAS

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    1. Ian L. Dryden & Mohammad Reza Faghihi & Charles C. Taylor, 1997. "Procrustes Shape Analysis of Planar Point Subsets," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 353-374.
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