On the Effective Dimension of Light Transport

Christian Lessig and Eugene Fiume



Abstract: Light transport is often characterized within a high-dimensional space although practitioners have long known that it commonly behaves as a much lower-dimensional phenomenon. We study the effective dimension of light transport over a neighborhood on the scene manifold and show that under plausible assumptions the dimensionality is characterized by the spectrum of the spatio-spectral concentration problem. This allows us to improve existing estimates for the dimension in computer graphics using a more insightful derivation and for the first time we obtain optimal representations. The relevance of our results for existing rendering applications is discussed.


Publications

Christian Lessig and Eugene Fiume, On the Effective Dimension of Light Transport, To appear in Computer Graphics Forum (Proceedings of Eurographics Symposium on Rendering 2010). (preprint,slides)

Code

The Matlab code which was used to generate the figures in the paper can be downloaded: only source code, source code with precomputed data.

Slepian Functions

A short note providing more background information on Slepian functions is available here.


Acknowledgement

We thank Tyler de Witt and Jos Stam for helpful discussion. The implementation of Slepian functions by Frederik Simons was also valuable for our research.

lessig (at) dgp (dot) toronto (dot) edu May 2010