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Surface de symétrie d’une structure 3D : application à l’étude des déformations scoliotiques du dos

Abstract : In this thesis we are interested in the study of the symmetry of 3D meshes. Usually, this is defined as an orthogonal symmetry with respect to a plane. However, this characterisation is only fully relevant in case of "straight" bilateral structures. For our case about scoliotic deformations of the back surface, the analysis of asymmetries is very imprecise.Therefore we propose to generalise the notion of 3D mesh symmetry by defining an orthogonal symmetry with respect to any non-planar surface.After having studied the limits of plane symmetry, we suggest a new method to calculate a surface of symmetry for a 3D mesh. This iterative algorithm is based on the decomposition of the studied structure into a set of adaptive bands, defined orthogonally to a symmetry curve, and then on the calculation of local symmetry planes for each of these bands. These bands are later interpolated to obtain the surface of symmetry. A particular focus is put into the robustness of the algorithm, which must be able to adapt to the various possible deformations of the mesh.We then propose a method able to compute a curved and standardised asymmetry map from the surface of symmetry.Lastly, we present an application of our contributions for the study of scoliosis-induced deformities.We then show that the study of the surface of symmetry of the back makes it possible to categorise the different types of scoliosis and build a 3D model of the spine, without resorting to radiative imaging.
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Submitted on : Tuesday, May 26, 2020 - 11:21:57 PM
Last modification on : Wednesday, September 9, 2020 - 3:08:40 AM


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Marion Morand. Surface de symétrie d’une structure 3D : application à l’étude des déformations scoliotiques du dos. Modélisation et simulation. Université Montpellier, 2019. Français. ⟨NNT : 2019MONTS107⟩. ⟨tel-02628542⟩



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