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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 400000 rays have
been used.
For the radiosity computation 116000 rays
have been used.

• Oracles have been implemented on the
  Hierarchical Monte Carlo Radiosity algorithm in
  the RenderPark system (www.renderpark.be)
• 10 additional element-to-element random lines
  have been used to evaluate the smoothness-based
  and MI-based oracles