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.
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)
The Matlab code which was used to generate the figures in the paper can be downloaded: only source code, source code with precomputed data.
A short note providing more background information on Slepian functions is available here.
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.