Dec 16, 1998

Publications by Henrik Wann Jensen, Mental Images, Berlin:

• Efficient Simulation of Light Transport in Scenes with Participating Media using Photon Maps, SIGGRAPH'98.
• Adaptive Sampling and Bias Estimation in Path Tracing, 1997.
• Rendering Caustics on Non-Lambertian Surfaces, CGF'97 & GI'96.
• Global Illumination using Photon Maps, 1996.

BibTeX references.

This paper presents a new method for computing global illumination in scenes with participating media. The method is based on bidirectional Monte Carlo ray tracing and uses photon maps to increase efficiency and reduce noise. We remove previous restrictions limiting the photon map method to surfaces by introducing a volume photon map containing photons in participating media. We also derive a new radiance estimate for photons in the volume photon map. The method is fast and simple, but also general enough to handle nonhomogeneous media and anisotropic scattering. It can efficiently simulate effects such as multiple volume scattering, color bleeding between volumes and surfaces, and volume caustics (light reflected from or transmitted through specular surfaces and then scattered by a medium). The photon map is decoupled from the geometric representation of the scene, making the method capable of simulating global illumination in scenes containing complex objects. These objects do not need to be tessellated; they can be instanced, or even represented by an implicit function. Since the method is based on a bidirectional simulation, it automatically adapts to illumination and view. Furthermore, because the use of photon maps reduces noise and aliasing, the method is suitable for rendering of animations.

One of the major problems in Monte Carlo based methods for global illumination is noise. This paper investigates adaptive sampling as a method to alleviate the problem. We introduce a new refinement criterion, which takes human perception and limitations of display devices into account by incorporating the tone-operator. Our results indicate that this can lead to a significant reduction in the overall RMS-error, and even more important that noisy spots are eliminated. This leads to a very homogeneous image quality.

As most adaptive sampling techniques our method is biased. In order to investigate the importance of this problem, a nonparametric bootstrap method is presented to estimate the actual bias. This provides a technique for bias correction and it shows that the bias is most significant in areas with indirect illumination.

This paper presents a new technique for rendering caustics on non-Lambertian surfaces. The method is based on an extension of the photon map which removes previous restrictions limiting the usage to Lambertian surfaces. We add information about the incoming direction to the photons and this allows us to combine the photon map with arbitrary reflectance functions. Furthermore we introduce balancing of the photon map which not only reduces the memory requirements but also significantly reduces the rendering time. We have used the method to render caustics on surfaces with reflectance functions varying from Lambertian to glossy specular.

This paper presents a two pass global illumination method based on the concept of photon maps. It represents a significant improvement of a previously described approach both with respect to speed, accuracy and versatility. In the first pass two photon maps are created by emitting packets of energy (photons) from the light sources and storing these as they hit surfaces within the scene. We use one high resolution caustics photon map to render caustics that are visualized directly and one low resolution photon map that is used during the rendering step. The scene is rendered using a distribution ray tracing algorithm optimized by using the information in the photon maps. Shadow photons are used to render shadows more efficiently and the directional information in the photon map is used to generate more optimal sampling directions and to limit the recursion in the distribution ray tracer by providing an estimate of the radiance on all surfaces with the exception of specular and highly glossy surfaces. Noise and blur at discontinuities in the radiance estimate is reduced by using a cone filter.

The results presented demonstrate global illumination in scenes containing procedural objects and surfaces with diffuse and glossy reflection models. The implementation is also compared with the Radiance program.

Idea: Simplify the representation of the illumination instead of the geometry (of the scene).

NB: The author identifies "caustics" with "specular reflections"... (?)

Two passes (steps):

1. creation of photon maps,
2. rendering.

Pass 1: Construction of the Photon Maps

• Photon map is used to
  • generate optimized sampling directions;
  • reduce the number of shadow rays;
  • render caustics;
  • limit the number of reflections traced.
• Photon map is constructed :
  • by emitting a large number of photons (energy packets) from each light source;
  • by tracing each photon through the scene (path tracing);
  • upon hiting a surface, a photon is stored in a photon map and Russian roulette is used to determine the photon'state: absorption or reflection;
  • upon reflection, the new direction is obtained through a BRDF;
  • photons are stored in a balanced kd-tree.
• Caustic photon map:
  1. created by emitting (high densities of) photons towards specular objects in the scene;
  2. storing these photons as they hit diffuse surfaces;
  3. caustics are rendered by visualizing a radiance estimate based directly on the caustic photon map: high densities required
     • NB: Never compute caustics via Monte Carlo sampling since this proves impractical in most situations.
• Global photon map:
  1. created by emitting photons towards all objects;
  2. used as a rough approximation of the light/flux within the scene;
  3. not visualized directly.
• Shadow photons:
  1. created by tracing rays with origin at the light source through the entire scene:
     • at 1st intersection point a "normal" photon is stored,
     • at the next intersection points "shadow" photons are stored.
  2. used during the rendering step to reduce the number of shadow rays.

Pass 2: Rendering

Based on Monte Carlo ray tracing (except for caustics), where the pixel radiance is computed by averaging a number of sample estimates.

Page created & maintained by Frederic Leymarie, 1998.
Comments, suggestions, etc., mail to: leymarie@lems.brown.edu