Modeling three-dimensional morphological structures using spherical harmonics

Li Shen, Hany Farid, Mark A. McPeek

Research output: Contribution to journalArticle

122 Scopus citations


Quantifying morphological shape is a fundamental issue in evolutionary biology. Recent technological advances (e.g., confocal microscopy, laser scanning, computer tomography) have made the capture of detailed three-dimensional (3D) morphological structure easy and cost-effective. In this article, we develop a 3D analytic framework (SPHARM - spherical harmonics) for modeling the shapes of complex morphological structures from continuous surface maps that can be produced by these technologies. Because the traditional SPHARM methodology has limitations in several of its processing steps, we present new algorithms for two SPHARM processing steps: spherical parameterization and SPHARM registration. These new algorithms allow for the numerical characterization of a much larger class of 3D models. We demonstrate the effectiveness of the method by applying it to modeling the cerci of Enallagma damselflies.

Original languageEnglish (US)
Pages (from-to)1003-1016
Number of pages14
Issue number4
StatePublished - Apr 1 2009


  • Enallagma cerci
  • Fourier descriptors
  • Morphological evolution
  • Shape analysis
  • Spherical harmonics

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics
  • Genetics

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