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GeoDeep4Mesh: Geometric Deep Learning on the Mesh Manifold

3 Février 2022

Catégorie : Doctorant

The core of this proposed project is on developing mathematically principled generative frameworks for deep learning on non-Euclidean domains such as graphs and manifolds. This project will touch upon some of the most challenging problems in different fields such as computer vision and graphics, where generative models are crucial. The research topic itself is very timely in terms of need and applicability of the systems targeted. This research also seeks to advance fundamental tools, that are not only of high relevance in terms of intellectual merit but also in broad impact.


Key words:

Geometric deep learning; generative models in non-Euclidean domains; face and body analysis

Centre de Recherche en Informatique, Signal et Automatique de Lille (UMR 9189 CRIStAL), Villeneuve d'Ascq, France.
Mohamed Daoudi ( mohamed(dot)daoudi(at)univ-lille(dot)fr )
Deise Santana Maia ( deise(dot)santanamaia(at)univ-lille(dot)fr )



While deep learning methods have been studied for quite a long time on regular domains like for images, learning solutions capable of working on non-Euclidean data like graphs, meshes or point clouds have been defined more recently. This area of research is attracting more and more interest for the potential applications in many disparate domains, going from modeling of social networks, molecules matching and design, to surface classification and recognition. This has originated a new area of investigation broadly known as Geometric Deep Learning. In this thesis proposal, we aim at investigating new solutions for learning on 2D manifolds. On the one hand, our idea is to attack the problem by proposing equivariant networks capable of accounting for 3D transformations as well as embedding new metrics in the loss that are computed on the surface. On the other hand, we will propose generative models for meshes and point clouds that also account for the temporal dimension.

International collaborations
In this project, we will collaborate with the Media Integration and Communication Center (MICC), of the University of Florence, a Center of Excellence established in 2001 by the Italian Ministry of Education and Research. MICC is internationally reknown, with a top-record of publications, participation in several international, European and national projects, and the organization of top-level events like the ACM MM, ECCV and ICPR conferences.
Full description
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Giorgos Bouritsas, Sergiy Bokhnyak, Stylianos Ploumpis, Stefanos Zafeiriou, and Michael M. Bronstein. Neural 3D morphable models: Spiral convolutional networks for 3D shape representation learning and generation. In 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019, pages 7212–7221. IEEE, 2019.
Michael M. Bronstein, Joan Bruna, Taco Cohen, and Petar Velickovic. Geometric deep learning: Grids, groups, graphs, geodesics, and gauges, 2021.
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Luca Cosmo, Antonio Norelli, Oshri Halimi, Ron Kimmel, and Emanuele Rodol`a. LIMP: learning latent shape representations with metric preservation priors. In Andrea Vedaldi, Horst Bischof, Thomas Brox, and Jan-Michael Frahm, editors, Computer Vision - ECCV 2020 - 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part III, volume 12348 of Lecture Notes in Computer Science, pages 19–35. Springer, 2020.