This class will expose mathematical tools encountered at various stages of the image synthesis pipeline. These methods are widely used in computer graphics research.

- Monte-Carlo methods for 3d rendering (Nicolas, weeks 1,2)
- Importance sampling, Monte-Carlo convergence rate
- The rendering equation: a Fredholm equation of the second kind
- Lecture notes: PDF version, PPTX version
- Readings and project
- Optimal transport (Nicolas, weeks 3,4)
- Monge and Kantorovich formulations
- Differential geometry of optimal transport
- Numerical methods (Sinkhorn algorithm, Power Diagrams, ...)
- Applications to images and rendering
- Lecture notes: PDF version, PPTX version
- Readings and project
- Image and video processing -- mostly with Poisson equation! (Nicolas, weeks 5,6)
- Variational formulation / PDE
- Numerical methods
- Applications (image stitching, content-aware copy/paste, video filtering, gradient based rendering, fluid simulation, ...)
- Other cool non-Poisson image and video processing techniques
- Lecture notes: PDF version, PPTX version
- Readings and project
- Spectral mesh processing (Julie, weeks 7,8)
- A Fourier basis on surface meshes, Laplace Beltrami definition
- Application to mesh processing: denoising, compression
- Shape correspondence linearization through functional maps
- Lecture notes: PDF version
- Readings and project
- Markov random fields (Julie, week 9)
- Definition, graphical model formulation
- Maximum a posteriori inference: belief propagation and graph cuts
- Application to Segmentation and Texture Synthesis
- Lecture notes: PDF version
- Readings and project
- Sparse minimization (Julie, week 10)
- Regularization with sparse prior, sparsity inducing norms
- Dictionary learning and basis selection, pursuit algorithms and convergence proofs
- Application to image processing
- Lecture notes: PDF version
- Readings and project
- Dictionary Learning and Application to Image Processing (Julie)
- Lecture notes: PDF version

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.