Premium
On the Effective Dimension of Light Transport
Author(s) -
Lessig Christian,
Fiume Eugene
Publication year - 2010
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2010.01736.x
Subject(s) - rendering (computer graphics) , curse of dimensionality , computer science , dimension (graph theory) , computer graphics , relevance (law) , dimensionality reduction , manifold (fluid mechanics) , space (punctuation) , computer graphics (images) , theoretical computer science , algorithm , computer vision , artificial intelligence , mathematics , pure mathematics , mechanical engineering , political science , law , engineering , operating system
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.