Modélisation et description par graphes pour des formes géométriques complexes Application aux structures de l’oreille

Abstract

This thesis work focuses on the reconstruction and description of complex geometric shapes. An application to the modeling of ear structures is presented and serves as a framework throughout this work. It is divided into two parts. The first part presents the development of amulti-structure reconstruction approach of volumetric data fromdeformable models. This approach is applied to volumes obtained by cone beam CT (CBCT) for the reconstruction of the structures of the inner ear and the ossicular chain. The second part presents the development of a 3D shape description approach for the analysis and comparison of triangulated models. The originality of this approach is based on the computation of a shape graph that characterizes in a compact way both the geometry and the topology of the object, relying on the differential analysis of the input mesh. This approach is applied to the detection of local surface deformations on reconstructed 3D models of the inner ear. In the first part, we present an approach for semi-automatic reconstruction of middle and inner ear structures using generic 3D deformable surface models. This approach has the advantage of being completely independent of access to large databases needed for statistical and machine learning methods, as these data are almost non-existent for the problem of modeling ear structures from CBCT acquisitions. First, the user has to position a set of control points in the data volume for each of the four structures of the inner and middle ear. Each mesh is then finely deformed in an iterative way. This deformation is decomposed into two steps: a segmentation step, which allows us to find the boundaries of the structure in the volume while taking into account the neighboring structures as neighborhood constraints; and a regularization step, which allows themaintenance of the general shape of the structure as well as a globally smooth aspect. Finally, we validate three aspects of the method: the quality of the reconstructions, the reproducibility and the influence of free parameters. The results indicate a higher quality than the methods proposed in the literature for data of similar quality, as well as a better robustness. In the second part, we present the development of an approach for the description and local comparison of the surface of topologically complex shapes. First, a Reeb graph is constructed froma curvature function to describe the global shape of a 3D model. We present an algorithmic improvement that allows the construction of the graph on any type of triangulated surface while ensuring that it is homeomorphic to the theoretical Reeb graph. We also propose a filtering operator based on the geometric properties of the surface that allows to eliminate the related components that present a surface ratio below a threshold. The shape index is used as a curvature function to guarantee the invariance to scaling and remeshing of the Reeb graph. In a second step, a partition of the graph into several subgraphs is performed using a spectral partitioning algorithm. Then, the subgraphs of two similar surfaces are matched by computing the graph editing distance between each pair. This approach is then applied to the detection of malformations on the semicircular canals between a group of asymptomatic patients and a group of patients with scoliosis. Preliminary results indicate a significant difference between the two groups of models.

Date	6 Dec 2021
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Jean-Luc Mari (Supervisor), Jacques A. de Guise (Supervisor) & Matthieu Schmittbuhl (Supervisor)