A Fourier analytic procedure to describe complex morphological shapes.

Most time-dependent processes such as growth are characterized by changes in size and shape. An accurate assessment of such morphological changes at specific points in time and over time has remained problematic. The conventional metrical approach, consisting of a comparatively few and subjectively chosen distances, angles, and ratios remains an inefficient descriptor of complex shapes. This is not to say that conventional metrics have no utility (their use depends on the application), but rather that they cannot measure more than a fraction of the informational content present in complex shapes. An alternative approach to conventional metrics has been developed using a Fourier analytic procedure. The Fourier function chosen provides an accurate representation of the morphological form. As the Fourier coefficients are orthogonal it is possible to partition out the effect of size to facilitate comparisons based solely on shape. The application of this Fourier procedure to describe morphological shapes is illustrated with data drawn from craniofacial as well as postcranial skeletal materials.