Using discrete topology and geometry for Rendering

My research focuses on the use of discrete topology and geometry to render images of 3D scenes. The main discrete entity I use is a centered topologic skeleton of the empty space of the scene. It allows to describe both topologic and geometric features of the scene with a sparse structure.


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 path-tracing 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 path-integral framework, the color of a pixel is expressed by an integral over the space of paths passing through this pixel. Monte-Carlo 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 7-9, 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 27-29, 2015. 10.1007/978-3-319-18720-4_3
    Article - Bibtex
  • Real-Time 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. 10.5176/2251-1679_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 119-130. (2013) 10.1007/978-3-642-37067-0_11
    Article - Bibtex

International journals

  • Real-Time Global Illumination using Topological Information
    Laurent Noël and Venceslas Biri, GSTF Journal on Computing (JoC)4.1 (Oct 2014): 1-10.
    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.


  • 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