1. Photon Density Estimation using Multiple Importance Sampling
Yusuke Tokuyoshi
1 Introduction
4 Weighting Function
In global illumination rendering, final gathering (or path tracing) and caustics photon map [Jensen 2001] are frequently used. However, photon mapping generate estimation results with many noises on glossy surfaces as in the upper images of section 5. We solve this problem using MIS (multiple importance sampling) [Veach 1997]. The advantages of our method are an easy implementation, lower overheads, and good estimation results without delicate parameter tuning.
MIS is often used to calculate direct illumination of area light sources. However, our target is caustics photons emitted from area light sources or environment maps. In this poster, we introduce a weighting function of density estimation for MIS.
We introduce the following weighting function. (The derivation is in
glass
light source
N : number of emitted photons
Le(x′, ω′) : emitted radiance at the position x′ and the direction ω′
θ : angle between the reflected direction ω and the surface normal
ΔA : area covered by the nearest neighbor photons
Φ : total radiant flux of the light sources
α : when ray first intersects a non-perfect specular surface,
α = number of oversamples per pixel, otherwise α=1
m2 : number of sample rays
p2(ω) : PDF of the BSDF model
2 Multiple Importance Sampling
MIS is a strategy to combine several sampling techniques using a weighting function. Let wi is the weighting function of sample technique i:
To calculate the above weighting function, we store Le(x′,ω′) in each photon. Therefore photon data structure increase by 1 float size.
qi is the product of the sample number and the PDF (probability distribution function) of sample model i. β is the parameter of this heuristic. In this poster, we use β = 2 because [Veach 1997] says it is reasonable value.
Photons vs. Rays
glass
light source
glass
light source
glass
glossy
light source
3 Combining Photons and Rays
perfect
specular
perfect specular
light source
caustics path
indirect light path
Photon Mapping
for Caustics
Final Gathering or Path Tracing
for Indirect Light
Case1: Search Radius
Large →
Small →
Case2: Light Source
Small →
Large →
Case3: Material
Diffuse →
Glossy →
5 Results
General Method
In this poster, caustics are calculated by caustics photon maps. And indirect illumination is calculated by sample rays (final gathering or path tracing). If a scene has area light sources, sample rays contain some caustics paths. Generally, these caustics paths are not used for calculation of caustics. Our idea is combining caustics photons and caustics paths using MIS for reducing noises. Let w1 be the weight of density estimation, and let w2 be the weight of sample rays distributed according to the BSDF.
80.0 secs
61.4 secs
84.6 secs
Proposed Method
Combining Photons and Rays using Weighting Function w1 and w2
88.8 secs
62.4 secs
88.7 secs
(73757 photons)
(64809 photons)
( photons)
(640x480 pixel, max 500 paths/pixel, CPU: Core i7 860)
References
Our renderer is available at
JENSEN, H. W Realistic Image Synthesis Using Photon Mapping. A. K. Peters.
VEACH, E Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University