SHAPE: A Computer Program Package for Quantitative Evaluation of Biological Shapes Based on Elliptic Fourier Descriptors

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Abstract
Quantitative evaluation of the shapes of biological organs is often required in various research fields, such as agronomy, medicine, genetics, ecology, and taxonomy. Elliptic Fourier descriptors (EFDs), proposed by Kuhl and Giardina (1982), can delineate any type of shape with a closed two-dimensional contour and have been effectively applied to the evaluation of various biological shapes in animals (Bierbaum and Ferson 1986; Diaz et al. 1989; Ferson et al. 1985; Rohlf and Archie 1984) and plants (Furuta et al. 1995; Iwata et al. 1998; McLellan 1993; Ohsawa et al. 1998; White et al. 1988). Quantization of shapes is a prerequisite for evaluating the inheritance of morphological traits in quantitative genetics. There are many reports showing that measurements based on EFDs are helpful for such quantization of the shapes of plant and animal organs. For instance, Iwata et al. (2000) conducted a diallele analysis of the shape of Japanese radish (Raphanus sativus L.) roots, using the principal component scores of the EFDs as shape characteristics. Quantitative trait loci (QTL) analysis has also been conducted using the principal component scores of EFDs concerning the shape of the male genitalia of Drosophila species (Laurie et al. 1997; Liu et al. 1996). The shape evaluation method based on EFDs can be a powerful tool for analyzing biological shapes, but it is not easy for a researcher to use this method because it involves several complex procedures, such as image processing, contour recording, derivation of the descriptors, and multivariate analysis of the descriptors.

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