# Parameterization of the Indirect Illumination Manifold

- Working environment: INRIA Rhone-Alpes, Montbonnot
- Advisor: Cyril Soler
- Keywords:
**Global illumination, Non linear dimensionality reduction, real time rendering, GPU Programming**
- Possibility to continue on a PhD:
**Yes**

## Summary

The simulation of "global illumination" consists in numerically solving an integral equation that expresses the equilibrium of light energy in a scene.

For practical reasons, one usually separates the "direct" illumination, that denotes light directly comes from the light sources and bounces on a single object before reaching the camera, from the "indirect" illumination, which may bounces an arbitrary number of times in the scene before reaching the camera.

The distribution of indirect illumination depends very smoothly on the positions of the light sources, and therefore only occupies a restricted sub-space of the full span of possible distributions of light energy in a scene, when illumination conditions are changed.

Consequently, we believe that it is possible to compute a low dimensional parameterization of the manifold of indirect illumination distributions.

We would like to use this parameterization to perform real-time calculations of global illumination in video games that react to the players' position and actions, as well as performing relighting tasks into static images.

## Proposed steps and sub-projects:

The work will include the following tasks, which may be re-defined of course depending on possible interesting finding and new routes the student will envisions during the year:

- read about the simulation of global illumination, the linear operator formulation of light transport, and non linear dimensionality reduction techniques
- build a 1st prototype that allows manifold exploration, based on a numerical interpolation of precomputed distributions of light
- conduct an theoretical error analysis to determine how far interpolated distributions are from simulated ones
- experiment on the dimensionality of the manifold depending on the types of scenes
- subsidiarily use the parameterization to compute the eigenfunctions of the light transport operator which should also belong to that manifold.

The PhD candidate should have a solid background in mathematics and computer graphics, and be proficient in C++.
Knowledge in GPU programming is a plus but not required. The candidate should speak english or french.

## Contact

Send an email to *cyril.soler - at - inria.fr*