*"It is not only important, it is essential!"* Dr. Strangelove

The importance of a light distribution indicates its contribution to an image or a region of interest. Importance can be used to focus ray tracing and global illumination calculations where they matter most for image accuracy, and thereby speed up rendering significantly.

The use of importance started in neutron transport simulations for development of the hydrogen bomb (right after World War II), but it has found more peaceful uses since then. Importance was used -- in different disguises -- from 1983 to accelerate ray tracing. Smits et al. formally introduced the use of importance for global illumination in 1992. Since then, importance has been used to optimize finite element methods (radiosity and radiance) and various Monte Carlo methods (path tracing, random walk radiosity, stochastic relaxation radiosity, ray bundles, and photon particle tracing for photon maps). Importance also provides the theoretical foundation for algorithms such as bidirectional path tracing.

Importance is an adjoint of light. There are six commonly used representations of light (incident and exitant radiance, radiosity, irradiance, and incident and exitant power), six corresponding representations of importance (incident and exitant directional importance, incident and exitant diffuse importance, and incident and exitant power importance), and several different inner products used to define adjoints. Some methods use a continuous framework while other use a discrete approximation, and different authors use different notation and terminology. So it is all quite confusing! This paper is an attempt to clarify and categorize the use of importance in rendering so far.

Importance is also known as "visual importance", "potential", "visual potential", "value", or "potential value".

Here are two annotated bibliographies of references describing the use of adjoints and importance:

importance_background.bib contains references to mathematics texts on adjoints in general and to articles and books about the use of importance in nuclear physics (where importance is an adjoint of neutron density).

importance_graphics.bib contains references to articles, dissertations, and books about the use of importance (defined as an adjoint of light) in ray tracing and global illumination. The entries are divided into six categories: 1) theoretical results in rendering, 2) "classic" ray tracing and distribution ray tracing, 3) finite element methods, 4) Monte Carlo methods, 5) volume ray tracing and participating media, 6) overviews. The entries are sorted chronologically within each category.

These two bibliographies are in BibTeX format and are intended to supplement Ian Ashdown's excellent radbib bibliography. Many thanks to Philippe Bekaert who pointed out some of these references. Please send me e-mail if you see errors or know of any references that should be added.

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