Modeling three-dimensional morphological structures using spherical harmonics.

Evolution. 2009 Apr;63(4):1003-16. Epub 2009 Oct 17. // Links

Modeling three-dimensional morphological structures using spherical harmonics.

Shen L, Farid H, McPeek MA.

Center for Neuroimaging, Division of Imaging Sciences, Department of Radiology, Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, 950 W Walnut St, R2 E124, Indianapolis, Indiana 46202, USA. shenli@iupui.edu 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.