Quantitative analysis of three-dimensional landmark coordinate data

The advantages of using three-dimensional (3D) data in the description and analysis of biological forms are obvious: these data provide realistic, geometrically integrated models of the forms under study, and can be rotated, translated and dissected electronically for viewing. 3D coordinate data can be collected from several sources including computed tomographic images, stereo photographs, specially designed microscopes, and digitizers. But once collected, how can these data be analyzed to address biologically relevant research questions? This paper demonstrates the capabilities of two analytical techniques, finite-element scaling analysis and Euclidean distances matrix analysis, in the comparison of 3D biological forms. Examples include studies of growth of the craniofacial complex, and analyses of differences in form between members of biologically defined groups (e.g. species, sexes, diagnostic categories).