Research on Graphics

I've come to graphics relatively recently (in the year 2000), and up to now I've been working on the following projects:

Voxelglobal illumination (global illumination using voxels)
Geometric modeling using linear programming
Visualization for neurosurgery
I wrote a textbook on graphic algorithms (in French)

Voxel Global Illumination

I've proposed a Voxel method for radiosity which was published as a poster at DGCI'2002. This is a completely new approach to global illumination. Basically, when we want to render a 3D scene, we approximate the surfaces of all the objects by a voxel surface (see the topological part of my research for a theoretical study of such discrete surfaces).
Once we have a discrete scene composed of voxels, encoded in an octree data structure, we discretize both surfaces and directions in the space in the continuous diffuse illumination equation (a classical equation used in radiosity), thus obtaining a discrete equation. As in classical radiosity, this discrete equation fullfils the requirements for applying (say) the Gauss-Seidel method, so we can numerically compute a solution of the equation.

This method has been much improved and made practical by my PhD student Pierre Chatelier, who made substantial optimization (providing optimal complexity for the visibility problem) and generalized the method for general BRDF. Lukasz Piwowar is currently improving the method a lot, by providing unaliased display which enables to reduce the number of voxels dramatically, and including all source code in a comprehensive software.

The method is being developped with a parallel algorithm for cluster by my student Rita Zrour, under the joint supervision of Fabien Feschet.

Here is a recent test image (sponza atrium) :

Here are a few more images, some of which are voxel global illumination combined with local specular models:

out of the labyrinth, don't get too close to the sun !

Here are the two first images, (with only lambertian reflexion and aliased display) ever obtained by our method
(at that time, the method was very slow and nobody took it seriously. It was published as a poster):

Result of radiosity, display by z-buffer

same scene as above, other viewpoint, display by z-buffer.

Geometric modeling

My research on geometric modeling up to now consists in the joint supervision with Yan Gerard of the PhD student Thibault Marzais, Who designed a linear programming approach to (piecewise) polynomial surfaces fitting experimental data (clouds of points). The advantage of this method compared to least square methods is that we optimize the uniform error instead of a statistical error.