Improvements To The Method Of Fourier Shape Analysis As Applied In Morphometric Studies

Fourier outline shape analysis is a powerful tool for the morphometric study of two‐dimensional form in organisms lacking many biologically homologous landmarks. Several improvements to the method are described herein; these modifications are incorporated into the new computer programs Hangle, Hmatch and Hcurve. First, automated tracing of outlines using image capture software, although desirable, results in high frequency pixel ‘noise’ that can corrupt the Fourier analysis. Program Hangle eliminates this noise using optional and variable levels of outline smoothing. Secondly, a widely used Fourier technique, elliptic Fourier analysis (EFA, Kuhl and Giardina 1982), yields coefficients that are not computationally independent of each other, a condition that hampers and compromises statistical analysis. In addition, EFA increasingly downweights successively more detailed features of the outline. Program Hangle solves both of these problems. Lastly, Fourier methods in general are sensitive to the placement of the starting position of the digitized trace. This problem is acute when the organisms under study have no unambiguously defined, homologous point on the outline from which to start the trace. Program Hangle allows the user to normalize for starting position using various properties of individual outlines. Alternatively, Hmatch takes a new approach and can be used to normalize using properties of the entire population under study.key words: Fourier shape analysis, morphometric studies, new computer programs, foraminiferal outlines.