Invariance à la reparamétrisation en apprentissage profond géométrique : applications à la synthèse de mouvements de corps et de visages humains

3D shape data is especially challenging to process because of its scarcity and complexity. Still, being able to compute plausible deformations of such shapes is critical for many applications, from augmented reality to mechanical engineering and biomedical imaging. Learning-based frameworks have shown tremendous performance when dealing with text and image data. However, leveraging this efficiency for deformable 3D data faces multiple challenges due to its non-Euclidean and high-dimensional characteristics.Surface meshes are a natural discretization of 3D shape data. When acquired in a raw state, these meshes are said to be unregistered, which means the arrangement of vertices and faces of the mesh is not precisely known. This observation is often overlooked, and many algorithms—especially learning-based ones—are designed for registered data with a known structure. This induces limitations in the applicability of such algorithms to real-world scenarios if the model cannot generalize to unseen discretizations.This thesis presents advancements regarding the problem of predicting surface deformations that remain robust when input meshes are remeshed, and we present several contributions in this regard in the manuscript.First, we propose a novel loss function for unsupervised learning of facial and expression deformations from a template mesh using an autoencoder framework. Then, we expand the latent structure to induce locality by combining local and global features, enabling partial deformations and interpolations. Building on a similar idea, we extend this neural feature field for deformations with an additional modality (audio) to propose the first talking-head model that can generalize across different mesh structures. Finally, we adapt this framework in a sequential manner to model long-range motions such as walking and running.Together, these contributions address common and challenging limitations of deep deformation models for surface data.