A Fourier-wavelet representation of 2-D shapes: sexual dimorphism in the Japanese cranial base

Abstract

We present a new approach called computational shape analysis, which utilizes a Fourierwavelet representation for characterizing shape features of 2-D forms commonly encountered in a wide set of sub-disciplines within the biological sciences. The morphology of interest consists of the human cranial base (CB) as depicted on lateral cephalometric radiographs. Given a complex irregularly bounded form in Cartesian coordinate space, we first compute elliptical Fourier functions (EFFs) using a set of closely-spaced pseudo-homologous (x, y) points, starting at basion, to create a precise analog of the closed contour. This computed contour is then scaled (size-standardization) and rotated (positional-orientation) to provide for a common normalization. This insures that the representation is invariant with respect to starting point, size and orientation. Utilizing the EFFs, global aspects of the CB can then be extracted. The coordinates derived from the EFF were subsequently submitted to a continuous wavelet transform (CWT). Wavelet coefficients were then computed to identify localized features. The significant advantage of wavelets is that they are able to objectively identify changes in boundary curvature, thereby depicting localized aspects not easily attainable with other methods. Utilizing a sample of 297 Japanese cranial base outlines, statistically-significant differences in sex and archeological age were found. Although archeological age differences were present, they were small and largely random in character, suggesting stability in the CB structures. The presence of sexually dimorphic differences is consistent with earlier data derived from studies of Macaca nemestrina. In the current study, these differences in sexual dimorphism were present for every group starting with the Yayoi period and continuing up to the Modern period. Consequently, one may infer that the pattern of sexual dimorphism documented in the Japanese CB, is a primate pattern with an ancient evolutionary history. Wavelets were particularly useful in objectively identifying this sexual dimorphism. The results demonstrate that the Fourier-wavelet representation is a practical approach for numerically describing and visually depicting both global and localized features.

Sexual dimorphism using elliptical Fourier analysis: shape differences in the craniofacial complex

“…Results based on the M. nemestrina cranial base prompted further studies using human data to see if a similar pattern of sexual dimorphism could be discerned (Lestrel et al, 2004a(Lestrel et al, , 2005). An early initial longitudinal study using conventional Fourier analysis hinted at cranial base shape differences due to sex, but these shape changes, while present, were not recognized or followed up at the time (Lestrel and Roche, 1986).…”

“…Thus, while Fourier coefficients or their amplitudes are useful for capturing the global aspects of a form, the localization or identification of local aspects is not readily possible. A method that has been recently developed to circumvent this constraint and will recognize any changes in curvature, are wavelets (see Lestrel et al, 2004aLestrel et al, , 2005 for an extended discussion of these issues).…”

“…The standardized headfilms of the cranial base were traced onto matte acetate sheets and 54 points located (Lestrel et al, 2004a). Digitizing was carried out with a Calcomp DrawingBoard III.…”

“…Of the seven centroid-based distances chosen to characterize the cranial base, a distance of primary interest from the centroid to the superior aspect, or tip of the dorsum sellae (point 26), was found to be significant for the group contrast at P < 0.05, while the sex contrast was significant at the P < 0.005 level. Details of the measurements used can be found in Lestrel et al (2004a).…”

Sexual dimorphism in chin shape: Implications for adaptive hypotheses

“…We believe that the most effective way to quantify chin shape is to use elliptical Fourier functions analysis. This morphometric approach has been applied to a variety of biological traits (Inoue, 1990;Lestrel, 1997;Seiffert and Kappelman, 2001;Lestrel et al, 2004;Athreya, 2006), including primate mandibular symphyses (Chen et al, 2000;Daegling and Jungers, 2000;Schmittbuhl et al, 2001Schmittbuhl et al, , 2002Schmittbuhl et al, , 2007Guy et al, 2008;Brown and Maeda, 2009). EFFA is essentially a technique for computing a trigonometric function that can be used to describe a curve, or in this case the shape of an outline.…”