title: Elliptical Fourier descriptors for contours in three dimensions: a new tool for morphometrical analysis in biology.
abstract: 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.
authors.affiliation: Preclinical Imaging Lab, biophysique et médecine nucléaire, hôpitaux universitaires de Strasbourg, Strasbourg cedex, France. jeremy.godefroy.01@normalesup.org
authors.forename: Jérémy E
authors.initials: JE
authors.lastname: Godefroy
authors.forename: Fabien
authors.initials: F
authors.lastname: Bornert
authors.forename: Catherine I
authors.initials: CI
authors.lastname: Gros
authors.forename: André
authors.initials: A
authors.lastname: Constantinesco
mesh_terms: D000465:Algorithms; D000715:Anatomy / Q000379:methods*; D000818:Animals; D003627:Data Interpretation, Statistical; D053360:Ectodermal Dysplasia, Hypohidrotic, Autosomal Recessive / Q000473:pathology; D005260:Female; D005539:Foramen Magnum / Q000473:pathology; D005583:Fourier Analysis; D006801:Humans; D007091:Image Processing, Computer-Assisted; D021621:Imaging, Three-Dimensional / Q000379:methods; D008297:Male; D051379:Mice; D009038:Motion; D018401:Sample Size; D014057:Tomography, X-Ray Computed