Teaching and Talks

Preparation and supervision of labs: Introduction to geometry processing, learning on shapes, neural shape representations. Website

Supervision of lab sessions: Introduction to computer sience, Object Oriented Programming, Web design. Java, HTML, CSS.

Teaching of first year bachelors, and assistance for exercises. Design of midterm exams.

In this series of lecture, we present geometric deep learning from its roots: we start by the raise of deep learning and the failures of classical deep learning on 3D shapes, and present most popular approaches of the recent years, both on point clouds and surfaces. Then, we present the adaptation of modern approache, such as the transformer to the specific challenges of 3D shapes. We conclude by presenting the remaining open challenges in modern geometric deep learning for surfaces.

Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for improved accuracy and generality. However, most existing methods in this area restrict the learning aspect only to the feature functions and still rely on axiomatic modeling for formulating the training loss or for functional map regularization inside the networks. This limits both the accuracy and the applicability of the resulting approaches only to scenarios where assumptions of the axiomatic models hold. In this work, we show, for the first time, that both in-network regularization and functional map training can be replaced with data-driven methods. For this, we first train a generative model of functional maps in the spectral domain using score-based generative modeling, built from a large collection of high-quality maps. We then exploit the resulting model to promote the structural properties of ground truth functional maps on new shape collections. Remarkably, we demonstrate that the learned models are category-agnostic, and can fully replace commonly used strategies such as enforcing Laplacian commutativity or orthogonality of functional maps. Our key technical contribution is a novel distillation strategy from diffusion models in the spectral domain. Experiments demonstrate that our learned regularization leads to better results than axiomatic approaches for zero-shot non-rigid shape matching.

In this talk, we present first the inherent challenges of deep learning on 3D surfaces, in the context of shape analysis. We present the early approaches to tackle this problem and explain why they were failing. We then present two modern architectures: PointNet, a key component in many modern point cloud architecture, and DiffusionNet, a backbone that is still used in state-of-the-art shape matching approaches. We also discuss the need to regularize latent spaces of shapes to reproduce faithful interpolation in the latent space.

We analyze human poses and motion by introducing three sequences of easily calculated surface descriptors that are invariant under reparametrizations and Euclidean transformations. The key idea behind these descriptors is our convexity hypothesis: we suggest that most human poses are (almost) uniquely defined by their convex hull. We formulate the descriptors by associating to each finitely-triangulated surface two functions on the unit sphere: for each unit vector \( \vec{u} \) we compute the weighted area of the projection of the surface onto the plane orthogonal to \( \vec{u} \) and the length of its projection onto the line spanned by u. The \( L_2 \) norms and inner products of the projections of these functions onto the space of spherical harmonics of order \( k \) provide us with three sequences of Euclidean and reparametrization invariants of the surface. The use of these invariants reduces the comparison of 3D+time surface representations to the comparison of polygonal curves in \( \mathbb{R}^n \). The experimental results on artificial datasets are promising. Moreover, a slight modification of our method yields good results on noisy, real applications.

The analysis of 3D human bodies is a fundamental problem with applications in healthcare, virtual reality, animation, and motion understanding. We introduce the main challenges of representing human shape and pose, as well as the need for geometric invariances when building shape spaces. We review classical approaches, from handcrafted descriptors, statistical body models such as SMPL to Riemannian shape analysis. In a second part, we introduce deep learning methods for 3D data such as PointNet and mesh-based CNNs. We also introduce recent techniques to build a disentangled latent representations for human shape and pose. We conclude the talk by presenting our recent learned Riemannian approach to overcome current limitations of deep learning for 3D human body analysis.