Neural Geometry Processing

Class Info

**Instructor:**Noam Aigerman

**When:**Tuesday and Thursday, 16:30 - 18:30

**Where:**Room Z-315, Claire-McNicoll building

**Contact:**noam.aigerman@umontreal.ca

**Logistics (coursework, lecture notes etc.)**on Piazza

Description

*Neural Geometry Processing*is an emerging field, stemming from the application of deep learning to 3D problems using Geometry Processing. Similarly to (non-neural) Geometry Processing, Neural Geometry Processing is indesciplinary and develops methods and theory using concepts from mathematical fields such as differential geometry and algebra, as well as algorithms from computational geometry and vision. This course aims to give the students the necessary tools to approach research in this field and make further excursions into it independetly.

Syllabus (tentative)

Including both frontal lectures and reviewing state-of-the-art papers:

- Fundamental mathematical theory, from a geometric perspective
- Linear Algebra - linear transformations, coordinate systems, linear basis, eigendvectors, SVD
- Multivariate Calculus - gradient, jacobian, chain rule, implicit function, laplacian, continuity, injectivity
- Point Clouds
- Meshes
- Neural Surfaces
- Encoders - PC, Mesh CNN's, Diffusion Based
- Descriptors and Encoding - Curvature, Heat Kernel Signature, Wave Kernel
- Implicit functions
- Voxel-based methods
- Signed Distance Fields
- Reconstruction Methods - Marching Cubes, Dual Contouring, Poisson Reconstruction
- Hybrid Representations
- Mappings, Deformations
- Neural Radiance Fields
- Differentiable Rendering
- Generative Techniques - diffusion, Score Distillation, CLIP

Evaluation

30% class participation, 40% homework + mini-project, 30% paper reading+presentation