Fourier Biometrics: Harmonic Amplitudes as Multivariate Shape Descriptors

Abstract

Fourier analysis in closed form provides a highly efficient method for measuring overall morphological similarity and identifying specific types of morhological variation. In shape analysis of ostracod outlines, continuous variation representing phylogenetically induced changes and 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 ostracod genus Rabilimis and for 6 genera of Hemicytheridae [Hemicythere, Elofsonella, Baffincythere, Finmarchinella, Muellerina, Bensonocythere]. Raw data consisting of Cartesian coordinates of the 2-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.