title: Statistical analysis of arch shape with conic sections.
abstract: Arcs of conic sections are used to model the shapes of human dental arches and to provide a basis for the statistical and graphical analysis of a population of shapes. The Bingham distribution, an elliptical distribution on a hypersphere, is applied in order to model the coefficients of the conic arcs. It provides a definition of an 'average shape' and it quantifies variation in shape. Geometric envelopes of families of conic arcs whose coefficients satisfy a quadratic constraint are used to depict the distribution of shapes in the plane and to make graphical inferences about the average shape. The methods are demonstrated with conic arcs fitted to a sample of 66 maxillary dental arches.
mesh_terms: D003724:Dental Arch / Q000033:anatomy & histology*; D008433:Mathematics; D008953:Models, Anatomic; D013223:Statistics as Topic