Photon Density Estimation using Multiple Importance Sampling Yusuke Tokuyoshi (yusuke.tokuyoshi@gmail.com) 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 http://www.vidro-project.com/publications/pdemis09.html) 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) (342100 photons) (640x480 pixel, max 500 paths/pixel, CPU: Core i7 860) References Our renderer is available at http://www.vidro-project.com/ JENSEN, H. W. 2001. Realistic Image Synthesis Using Photon Mapping. A. K. Peters. VEACH, E. 1997. Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University