Morphing de maillage et indexation de forme pour la modélisation du fémur humain

This thesis aims at designing new mesh morphing methods that provide generality, robustness, automation, and accuracy in generating patient specific mesh. The approach consists to fit a carefully designed mesh on target geometry of another patient. We first propose a method based on the morphing of meshes in the planar domain. The process of morphing projects surface meshes on a common planar domain and makes use of a technique based on radial basis functions constrained by a set of anatomical corresponding points on the two geometries. However, this first approach may fail when the two shapes are very different. Therefore, we extend the method by directly morphing the 3D mesh without the intermediate step of planar parameterization. Although this is a simplification of the original method, this method yields excellent results in terms of robustness and accuracy on a large database of 140 femurs with a high inter-subject anatomical variability. Moreover, our morphing technique allows us mapping this database into an iso-topological representation, such that we can operate on the meshes as on a finite-dimensional vector space. This opens the door to many important applications. As an example, a principal component analysis is applied to build a statistical model of femur shapes and then, we show how this model can be efficiently used to recover a 3D femur shape from a single X-ray image.