mva_geom

Geometry Processing and Geometric Deep Learning

Lecturers:

• Etienne Corman (junior CNRS researcher, LORIA)
• Julie Digne (senior CNRS researcher, LIRIS)
• Maks Ovsjanikov (Professor at Ecole Polytechnique, LIX)

Goals of the course

This course will introduce students to advanced topics in modern geometric data analysis (the field known as Geometry Processing) with focus on: a) mathematical foundations (discrete differential geometry, mapping, optimization), and b) deep learning for best performing methods.

We will give an overview of the foundations in surface-based analysis and processing before moving to modern techniques based on deep learning for solving problems such as 3D shape classification, correspondence, parametrization, etc. Finally, we will cover recent approaches for generating geometry, from both the mesh and shape-based perspectives.

Planning 2024 (tentative dates)

Courses take place in room 1Z53 at ENS Paris Saclay on Wednesdays. Courses are from 1 pm to 3:20 pm followed by lab work from 3:40 to 5:40 pm.

• Oct. 2nd: Lecture 1 (E. Corman): Intro to Discrete Differential Geometry. Basic differential operators on surfaces in both the smooth and discrete settings. Operator discretization through FEM. Geodesics. Functions, derivatives, integration, convolution on surfaces.
• Oct. 9th: Lecture 2 (E. Corman): Discrete Differential Geometry part 2. Spectral methods + manipulating geometry, Curvature. Shape deformation, Optimization of geometric energies. Surface parameterization. Mappings between surfaces. Basic surface topology, and topological constraints.
• Oct. 16th: Lecture 3 (M. Ovsjanikov): Extrinsic learning approaches for regular data in 2D and 3D. Intrinsic approaches. Convolution on surfaces and triangle meshes. Geodesic CNNs and their variants. Spectral methods, pros and cons. Learning via diffusion.
• Oct. 30th: Lecture 4 (M. Ovsjanikov): Projection-based approaches. Learning on Point clouds. Common point-based architectures (PointNet, PointNet++, DGCNN, KPConv, etc.). Applications (surface reconstruction, point cloud filtering).
• Nov. 6th: Lecture 5 (J. Digne): Neural fields for surface representation, generation and analysis. Neural Radiance fields and Neural Fields regularization. DeepSDF, Occupancy networks, Fast Fourier Features.
• Nov. 13th: Lecture 6 (J. Digne): Generative Modeling (how to generate the surface structure). Local synthesis. E.g., geometric texture synthesis. In-painting. Mesh generation, Differentiable meshing.
• Nov 20th: Paper reading presentations