6533b7d4fe1ef96bd1262a7c

RESEARCH PRODUCT

Geometric Measurement Analysis Versus Fourier Series Analysis for Shape Characterization Using the Gastropod Shell (Trivia) as an Example

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Varied and efficient methods have been developed to describe and quantify natural objects. The most common ones use superimposition techniques (e.g. Procrustes methods; Bookstein, 1991), decomposition into harmonics (Fourier series and functions, wavelets; Anstey and Delmet, 1973; Christopher and Waters, 1974; Gevirtz, 1976; Lestrel, 1997; Toubin and others, 1999; Verrecchia, Van Grootel, and Guillemet, 1996; Younger and Ehrlich, 1977), analysis of spiral functions (e.g. Raup parameters; Raup, 1961, 1966; Tursch, 1998), and combinations of parameters from elementary geometry (e.g. circularity index, lengthening; Coster and Chermant, 1989; Schmidt-Kittler, 1986; Viriot, Chaline, and Schaaf, 1990). In general, these methods are used independently of one another, without evaluation of their respective efficiencies. This paper compares two of these techniques (Fourier descriptors and combinations of elementary geometric parameters) using image analysis of Trivia shells. The example studied was a cowry-like shell called Trivia (Gasteropoda, Prosobranchia, Triviidae). Although the soft parts, color, number of ribs, and shell shape allow for present-day species to be distinguished (Lebour, 1933; Pelseneer, 1926, 1932), only the number of ribs and the shape can be used to differentiate fossil taxa. Moreover, Trivia species are only distinguishable by subtle variations in their shape that are difficult to describe with qualitative methods (Tursch, 1992). The opaque outer whorl entirely hides the spire, making its characterization impossible using rolling parameters (e.g. Raup’s parameters). The shells in the