Variance Reduction for Monte Carlo Rendering
Monte Carlo (MC) integration is a common technique for rendering images with distributed effects such as antialiasing, depth of field, motion blur, and global illumination.
It simulates a variety of sophisticated light transport paths in a unified manner; it estimates pixel values by using stochastic point samples in the integral domain.
Despite its generality and simplicity, however, the MC approach converges slowly and suffers from noisy images because of large variance.
There are serveal categories of methods for variance reduction of MC rendering, such as filtering, importance sampling, caching and interpolation.
Among them, we have developed methods following the paradigms of importance sampling and filtering and adaptive sampling.
Filtering and adaptive sampling.
We applied Stein's Unbiased Risk Estimator (SURE) to adaptive sampling and reconstruction to reduce noise in Monte Carlo rendering.
SURE is a general unbiased estimator for mean squared error (MSE) in statistics.
With SURE, we are able to estimate error for an arbitrary reconstruction kernel, enabling us to use more effective kernels rather than being restricted to the symmetric ones used in previous work.
It also allows us to allocate more samples to areas with higher estimated MSE. Adaptive sampling and reconstruction can therefore be processed within an optimization framework.
We also proposed an efficient and memory-friendly approach to reduce the impact of noisy geometry features where there is depth of field or motion blur.
Experiments show that our method produces images with less noise and crisper details than previous methods.
The paper was presented in ACM SIGGRAPH Asia 2012.
Importance sampling is an effective strategy for reducing such variance.
It requires to efficiently approximate the integral kernel of the rendering equation, a triple product of incident lighting, material properties and visibility.
Among them, visibility is often ignored because its estimation demands expensive shadow ray casting or shadow map construction.
Such neglect limits the effectiveness of importance sampling.
We proposed an efficient method for estimating average visibility to improve the effectiveness of importance sampling.
Our method is based on the observation that visibility terms in the many-light transport matrix exhibit local structures if shading points and lights are properly clustered.
By clustering lights and shading based on their geometric properties, we can estimate the average visibility between each pair of light cluster and shading cluster with only a small number of shadow rays.
Based on the average visibility, light clusters are locally refined for each shading cluster if necessary.
With the estimated visibility, the importance function becomes more accurate and MC rendering becomes much more efficient.
The paper has been published by IEEE TVCG.
We proposed a scalable algorithm for rendering translucent materials with complex lighting.
The method represents the light transport with a diffusion approximation by a dual-matrix representation with the Light-to-Surface and Surface-to-Camera
By exploiting the structures within the matrices, the proposed method can locate surface samples with little contribution by using only subsampled matrices and avoid wasting computation on these samples.
The decoupled estimation of irradiance and diffuse BSSRDFs also allows us to have a tight error bound, making the adaptive diffusion approximation more efficient and accurate.
Experiments show that our method outperforms previous methods for translucent material rendering, especially in large scenes with massive translucent surfaces shaded by complex illumination.
The paper has been accepted by IEEE TVCG.
- SURE-based Optimization for Adaptive Sampling and Reconstruction
- ACM SIGGRAPH Asia 2012
- VisibilityCluster: Average Directional Visibility for Many-Light Rendering
- IEEE TVCG 2013
- Dual-Matrix Sampling for Scalable Translucent Material Rendering
- IEEE TVCG 2015
This research is supported by:
- NTU 103R7609-5
- NTU 102R7609-5
- NTU 101R7609-5
cyy -a-t- csie.ntu.edu.tw