1. The Mutual Information-based Oracle
Information-Theoretic Oracle Based on Kernel Smoothness
for Hierarchical Radiosity
Miquel Feixas, Jaume Rigau, Philippe Bekaert *, and Mateu Sbert
Girona Graphics Group, IIiA, Universitat de Girona, Spain
* Max-Plank-Institut fuer Informatik, Germany
Information Theory Principles applied to Visibility and Radiosity
A scene contains and transfers information. This exchange of information creates a dependence or correlation between the different parts of a scene.
Continuous mutual information quantifies with maximum accuracy the information transfer in a scene.
Continuous mutual information is the least upper bound to discrete mutual information. Refinement increases discrete mutual information.
Visibility Mutual Information
Radiosity
Scene meshing has to accurately represent illumination variations
Continuous mutual information
Discrete mutual information
In the radiosity equation, the geometric factor is weighted by the receiver reflectance and the source radiosity.
Discretisation error
Radiosity Equation
For a Scene
Refinement Criteria (Oracles)
Power-based
Smoothness-based
Patch-to-patch
The Mutual Information-based Oracle
Basic Principles
MI-based Oracle
Advantages of MI-based Oracle
Among different discretisations of the same scene, the most accurate one is the one with the highest discrete mutual information. Objective: to maximize the discrete mutual information.
The difference between continuous and discrete mutual information expresses the loss of information transfer due to the discretisation.
This difference can be interpreted as the discretisation error or the benefit to be gained by refining. It also represents the variation of the radiosity kernel.
It preserves illumination details
It avoids overrefinement in smoothly lit areas
It is more robust than a classic smoothness-based oracle
Similarly to the radiosity equation, the geometric discretisation error is weighted by the receiver reflectance and the source radiosity.
Monte Carlo
Integration
Power-based
Smoothness-based
MI-based
Smoothness-based
MI-based
Smoothness-based
MI-based
For the radiosity computation rays have been used.
For the radiosity computation rays have been used.
Oracles have been implemented on the Hierarchical Monte Carlo Radiosity algorithm in the RenderPark system (
10 additional element-to-element random lines have been used to evaluate the smoothness-based and MI-based oracles
Saarbrücken, Germany
September 2-6