Elliptical Fourier descriptors for contours in three dimensions: a new tool for morphometrical analysis in biology.

Elliptical Fourier descriptor analysis is a method for the morphometric study of curves. It has been used in the two-dimensional plane for closed contours, but rarely for lines in the three-dimensional space. The method consists of an expansion of a contour as a sum of ellipses. In this article, we study three-dimensional contours, i.e. lines embedded in the three-dimensional space. We compute for the first time the relations between the Fourier coefficients and its geometric parameters. We then use these relations for normalization and reorientation of three-dimensional contours. Such an algorithm can be used to perform inter-individual comparisons between contours, regardless of differences in viewpoint or global size. Human and small animal illustrative examples using biomedical X-ray CT imaging data of open bone structures demonstrate the interest and potential of the method for morphological analysis.

Subtle Morphological Changes in the Mandible of Tabby Mice Revealed by Micro-CT Imaging and Elliptical Fourier Quantification.

X-linked hypohidrotic ectodermal dysplasia (XLHED) is a genetic disorder due to a mutation of the EDA gene and is mainly characterized by an impaired formation of hair, teeth and sweat glands, and craniofacial dysmorphologies. Although tooth abnormalities in Tabby (Ta) mutant mice - the murine model of XLHED - have been extensively studied, characterization of the craniofacial complex, and more specifically the mandibular morphology has received less attention. From 3D micro-CT reconstructions of the left mandible, the mandibular outline observed in lateral view, was quantified using 2D elliptical Fourier analysis. Comparisons between Ta specimens and their wild-type controls were carried out showing significant shape differences between mouse strains enabling a clear distinction between hemizygous Ta specimens and the other mouse groups (WT and heterozygous Eda(Ta/+) specimens). Morphological differences associated with HED correspond not only to global mandibular features (restrained development of that bone along dorsoventral axis), but also to subtle aspects such as the marked backward projection of the coronoid process or the narrowing of the mandibular condylar neck. These modifications provide for the first time, evidence of a predominant effect of the Ta mutation on the mandibular morphology. These findings parallel the well described abnormalities of jugal tooth row and skeletal defects in Ta mice, and underline the role played by EDA-A in the reciprocal epithelial-mesenchymal interactions that are of critical importance in normal dental and craniofacial development.