Sexual dimorphism in the Japanese cranial base: a Fourier-wavelet representation.

An approach, computational shape analysis (CSA), is presented here which utilizes a Fourier-wavelet representation to numerically describe shape features of biological forms. Two elements are involved: 1) elliptical Fourier functions (EFFs), to provide estimates of global aspects, and 2) continuous wavelet transforms (CWTs) to generate an objective estimate of localized features. EFFs are computed, using a set of pseudohomologous points, to create a precise analog of the boundary. This computed contour is then normalized by scaling and rotated in two-dimensional space to insure a representation that is invariant with respect to starting point, size, and orientation. The predicted point coordinates derived from the EFFs are submitted to CWT for further processing. Wavelet coefficients are then computed to identify localized features, localization being a subjective process with EFFs. The advantage of wavelets is that they eliminate the inevitable subjectivity inherent in the choice of measurements. To test the usefulness of CSA, a sample of cranial base (CB) lateral radiographic outlines was available. Five archaeological periods, Yayoi, Kofun, Kamakura, Edo, and Modern, were utilized (n = 297). Statistically significant differences in sex and archaeological age were found. Although archaeological age differences were present, they were small and random in character, suggesting stability in the CB structures. In contrast, sexually dimorphic differences were present in every group from the Yayoi to the Modern period. This presence of sexually dimorphic differences in shape was consistent with earlier studies of M. nemestrina, G. gorilla, and P. troglodytes. Consequently, it is suggested that the pattern of sexual dimorphism documented in the Japanese CB is a primate pattern with an ancient evolutionary history. The results demonstrate, both visually and numerically, that CSA is a powerful approach for describing both global and localized features of craniofacial structures such as the CB.