Using discrete topology and geometry for Rendering
Rendering
My research's field is computer graphics, and more specifically 3D rendering. It has a high number of applications such as cinema, video games, publicity, architecture or scientific visualization.
I mainly focus on physically based rendering, principally pathtracing based methods. Those techniques perform a light transport simulation by tracing random paths in the scene. The light contribution reaching the camera is estimated for each pixel to produce the final image.
In the pathintegral framework, the color of a pixel is expressed by an integral over the space of paths passing through this pixel. MonteCarlo methods allow to estimate this value by sampling random paths and computing a weighted sum of paths contributions. To be efficient, sampling distributions must be carefully chosen to maximize the number of samples in regions of high energy. This task is challenging because of the high dimensionality of the sample space and the complexity of scenes that are used in production (mixture of heterogeneous materials, high number of occlusions). When bad sampling distributions are used, the estimator exposes high variance which appears as noise and fireflies in the final image. In that case, it can take hours to render a clean image. This is of course a huge problem when rendering animations that are composed of thousands of frames.
A common problem is the rendering of scenes containing lot of occlusions separating the camera from the light sources. In that case, most paths sampled with current methods have zero contribution. To address this problem, I take advantage of a discrete topological skeleton of the empty space of the scene.
Topological skeleton
A topological skeleton of a 3D object is a subset of that object having the same topology. It means that it has the same holes and connexity. Usually, we want the skeleton to keep the same shape as the original object and to be centered. It allows to keep meaningful information about the geometry of the object while being sparse. To obtain that kind of skeleton, we apply a thinning algorithm on a voxelization of the object.
For rendering, I use a topological skeleton of the empty space of the 3D scene. Indeed, light travels through that space. Having a simple topological description of that space allows to develop rendering algorithms that take care of this information to reach better performance.
The skeletons I use are represented by graphs embeded in 3D space. Each node of these graphs store the radius of a maximal ball centered in empty space at the position of the node. This geometric information allows to evaluate the volume of empty space arround different portions of the skeleton. Both the graph structure and the radius information help to build meaningful probability distributions based on geometry and topology instead of materials. With the skeleton, we are able to guide rays directly towards high energy regions of the scene.
List of publications
HAL: Laurent Noël
PhD Thesis
Discrete Shape Analysis for Global Illumination
International conferences

Skeleton based Vertex Connection Resampling for Bidirectional Pathtracing
Laurent Noël and Venceslas Biri, in 23rd Pacific Conference on Computer Graphics and Applications, PG 2015, Beijing, China, October 79, 2015.
Article  Source code  Bibtex 
Portal Extraction Based on an Opening Labeling for Ray Tracing
Laurent Noël and Venceslas Biri, in 12th International Symposium on Mathematical Morphology, ISMM 2015, Reykjavik, Iceland, May 2729, 2015. 10.1007/9783319187204_3
Article  Bibtex 
RealTime Global Illumination for Games using Topological Information
Laurent Noël and Venceslas Biri, in Annual International Conference on Computer Games Multimedia & Allied Technology, January 2014. Best Student Research Award. 10.5176/22511679_CGAT14.17
Article  Bibtex 
A 3D Curvilinear Skeletonization Algorithm with Application to Path Tracing
John Chaussard, Laurent Noël, Venceslas Biri, and Michel Couprie. DGCI'13, page 119130. (2013) 10.1007/9783642370670_11
Article  Bibtex
International journals

RealTime Global Illumination using Topological Information
Laurent Noël and Venceslas Biri, GSTF Journal on Computing (JoC)4.1 (Oct 2014): 110.
Article  Bibtex
National conferences

Echantillonage préférentiel multiple exploitant un squelette curviligne pour le lancer de rayons
Laurent Noël, John Chaussard, Venceslas Biri. Association Française d'Informatique Graphique (AFIG). 2012.
Article
Miscellaneous

Coarse irradiance estimation using curvilinear skeleton
Laurent Noël, John Chaussard, Venceslas Biri, in SIGGRAPH '12 ACM SIGGRAPH 2012 Posters. 10.1145/2342896.2343014
Article  Bibtex