Mathematical methods for image synthesis

Lecturers: Nicolas Bonneel, Julie Digne

This class will expose mathematical tools encountered at various stages of the image synthesis pipeline. These methods are widely used in computer graphics research.
  1. Monte-Carlo methods for 3d rendering (Nicolas, weeks 1,2)
  2. Optimal transport (Nicolas, weeks 3,4)
  3. Image and video processing -- mostly with Poisson equation! (Nicolas, weeks 5,6)
  4. Spectral mesh processing (Julie, weeks 7,8)
  5. Markov random fields (Julie, week 9)
  6. Sparse minimization (Julie, week 10)
  7. Dictionary Learning and Application to Image Processing (Julie)

Prerequisites: Knowledge of basic geometric data structures and basic linear algebra. Programming.

Evaluation: Students will be graded on one short project related to the course, implemented in the language students feel the most comfortable with, and one article reading. Both the project and chosen paper will be presented at the end of the semester. If a project is taken from Nicolas' part, the reading should be taken from Julie and vice-versa.

Project presentation schedule:
Time Name
10:15 Dimitri
10:35 Fabrice
10:55 Martin
11:15 Simon
11:35 Etienne
11:55 Loïs

Nicolas Bonneel and Julie Digne are junior CNRS researchers at LIRIS lab.

Nicolas Bonneel develops mathematical tools for computer graphics, with particular attention to optimal transport, with applications to geometry, video processing, and rendering. After obtaining his PhD at INRIA Sophia-Antipolis in 2009, and years of post-docs at UBC (Vancouver), INRIA Nancy and Harvard University (Cambridge), he joined LIRIS in the geometry teams GéoMod and M2Disco in 2014.

Julie Digne focuses her research on geometry processing and applied math. She obtained her PhD, advised by Jean-Michel Morel, in 2010 in applied mathematics at Ecole Normale Supérieure de Cachan. She graduated from ENS Cachan (Master's degree: Mathématiques Vision Apprentissage). Her PhD thesis was awarded the Jacques Hadamard Foundation for Mathematics PhD award. In 2010-2012, she was a post-doc at INRIA in collaboration with Caltech. She joined the GéoMod team at LIRIS, University of Lyon in 2012.