Fourier Biometrics: Harmonic Amplitudes as Multivariate Shape Descriptors
Jean L. Younker, Robert Ehrlich · Systematic Biology · 1977
Fourier analysis in closed form provides a highly efficient method for measuring overall morphological similarity and identifying specific types of morphological variation. In shape analysis of ostracode outlines, continuous variation representing phylogenetically induced changes as well as shape families reflecting taxonomic categories can be recognized. Two-dimensional shape is described by a series of terms in a Fourier expansion of periphery radius as a function of polar angle for members of the ostracode genus Rabilimis and for six genera of Hemicytheridae. Raw data, consisting of Cartesian coordinates of the two-dimensional outline are converted to polar coordinates using the center of gravity of the form as a reference point. Coefficients of each term in the expansion represent the contribution of a fundamental harmonic form to the total shape description. When morphological variability is partitioned across the harmonic amplitude spectrum so that individual coefficients represent separate sources of morphological variation, removal of specific harmonics allows comparison of variation resulting from genetic vs. nongenetic factors.