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

Abstract

ABSTRACT. 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 modi®cations 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 coef®cients 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 de®ned, 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.

Sensory Evolution and Ecology of Early Turtles Revealed by Digital Endocranial Reconstructions

“…Although this approach uses only two-dimensional outlines (in contrast to three-dimensional landmarks), it allows quantification of shape data for geometries lacking homologous landmarks (Haines and Crampton, 2000). For shape analysis, a sagittal cross-section through the surface model of each brain (i.e., digital cast of the endocranial cavity) was produced in Avizo for each reconstruction.…”

A morphometric approach to conch ontogeny of <i>Cymaclymenia</i> and related genera (Ammonoidea, Late Devonian)

“…Data collection was done using the program tpsDig (Rohlf, 2006); we used 500 coordinates for each outline (Simon et al, 2010). Fourier analysis is probably the most frequently used method for outline analyses (Wills, 2001); for the analysis of complex forms, the use of the elliptical Fourier analysis is required (Kuhl and Giardinia, 1982;Ferson et al, 1985;Temple, 1992;Crampton, 1995;Haines and Crampton, 2000). The transformation of the outline data into periodical functions is here achieved by the programs hangle and hmatch, in which 22 Fourier coefficients were calculated (Simon et al, 2010(Simon et al, , 2011.…”

Comparison of maxillary first molar occlusal outlines of Neandertals from the Meuse River Basin of Belgium using elliptical Fourier analysis

“…This chain code was used to create the elliptical Fourier descriptors of each outline at a 20 harmonic resolution, by recording deviations of each individual outline shape from a normalized ellipse using trigonometric functions to calculate negative and positive perturbations. These are recorded as the amplitudes of the harmonics derived from four elliptical Fourier coefficients which describe subtle aspects of shape (Lestrel 1974;1997;Kuhl and Giardina 1982;Haines and Crampton 2000;Iwata and Ukai 2002). Contour analysis of human posterior teeth has been previously conducted on Neandertals and modern humans (Benazzi et al 2011a, b;2012;Bailey et al 2014;2016;Bauer et al 2016).…”