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

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  • Fourier wavelet representation of 2 D shapes sexual dimorphism in the Japanese cranial base

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We present a new approach called computational shape analysis, which utilizes a Fourier-wavelet 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.<br>

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