March 2019
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133 Reads
Shape quantification generally requires the positioning of landmarks, either to measure distances and angles, or to compare Cartesian coordinates. However, the definition of homologous landmarks is sometimes very challenging, especially for smooth objects. Several methods have been proposed to circumvent this problem, such as sliding semi-landmarks. Here we present a method based on spherical harmonics, a generalization of elliptic Fourier analysis for 3D continuous surfaces. Our objective was to test whether spherical harmonics are an efficient tool to (1) quantify the 3D shape of an object and (2) compare 3D shapes between objects. We used the virtual endocranial surfaces of 72 primates representing 5 hominid species. The surfaces were first centred, aligned and scaled using Avizo software. Subsequent analyses were performed using SPHARM-MAT software. The first two steps, parametrization and expansion, corresponded to the computation of the spherical harmonic coefficients describing each specimen. The last step, registration, performed the alignment of the spherical representation of all the specimens, allowing inter-individual comparisons. Accurate surface reconstructions were obtained using a limited number of spherical harmonics, but artefacts tended to appear for small-scale shape deformations. The combination of several registration methods led to a reasonable alignment of all the surface reconstructions. Multivariate statistics on spherical harmonic coefficients discriminated all species, except within the genus Pan (chimpanzees). Though, interspecific differences were less clear than in analyses conducted on the coordinates of homologous landmarks, probably because the landmarks were mainly placed on the endocranial base, which is less homogenous than the smooth endocranial vault.