Improvements to the method of Fourier shape analysis as applied in morphometric studies

Fourier outline shape analysis is a powerful tool for the morphometric stud y 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 MANGLE, HMATC H and HCURVE. First, automated tracing of outlines using image capture soft ware, although desirable, results in high frequency pixel 'noise' that can corrupt the Fourier analysis. Program MANGLE eliminates this noise using op tional and variable levels of outline smoothing. Secondly, a widely used Fo urier technique, elliptic Fourier analysis (EFA, Kuhl and Giardina 1982), y ields 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 ou tline. Program MANGLE solves both of these problems. Lastly, Fourier method s 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 st art the trace. Program MANGLE allows the user to normalize for starting pos ition using various properties of individual outlines. Alternatively, HMATC H takes a new approach and can be used to normalize using properties of the entire population under study.