On the Effective Dimension of Light Transport

• Published in: Computer graphics forum Vol. 29; no. 4; pp. 1399 - 1403
• Main Authors: Lessig, Christian, Fiume, Eugene
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.2010
• Subjects: Analysis; and texture; C (programming language); Computer graphics; Computer Graphics [I.3.7]: Three-Dimensional Graphics and Realism-[Color; Computer Graphics [I.3.7]: Three‐Dimensional Graphics and Realism—[Color, shading, shadowing, and texture]; Computer programming; Derivation; Estimates; Manifolds; Optimization; Rendering; Representations; shading; shadowing; Studies; Transport
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/j.1467-8659.2010.01736.x

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.