Traitements d'images sur surfaces et variétés avec mise en application au patrimoine culturel 3D
François Lozes · HAL (Le Centre pour la Communication Scientifique Directe) · 2015
In this thesis, we are interesting in transposing and solving PDEs and variationalproblems on general surfaces or manifolds. PDEs and variational methods are one of themost important tools widely used for modeling and solving inverse problems, e.g., in imageprocessing and computer vision. Recently, many of these methods were extended to non-localforms. However, most of the research works on local or non-local processing focus only onimage processing on Euclidean spaces.In this thesis, we propose an approach to transpose and to solve PDEs on surfaces andpoint clouds. This latter approach is based on the representation of point clouds by weightedgraphs and the framework of Partial differential Equations (PdEs). This approach requiresno pre-processing of point clouds, and allow to extend and to adapt non-local PDEs bychanging only the topology of the graph.