Perceptual Error Optimization for Monte Carlo Rendering

Error in Monte Carlo, quasi-error in Quasi-Monte Carlo

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account ...

An error formula for Monte Carlo based portfolio optimization

One–period utility based portfolio optimization is a classic method in financial economics [13]. The theory is extremely well developed, and extends in many directions, for example to dynamic portfolio optimization in continuous time [12]. Nonetheless, the solutions to these problems, characterized theoretically, often remain dismayingly difficult to compute in practise. Very often, finance pra...

Monte Carlo Methods in Rendering

Population Monte Carlo Samplers for Rendering

We present novel samplers and algorithms for Monte Carlo rendering. The adaptive image-plane sampler selects pixels for refinement according to a perceptually-weighted variance criteria. The hemispheric integrals sampler learns an importance sampling function for computing common rendering integrals. Both algorithms, which are unbiased, are derived in the generic Population Monte Carlo statisti...

Bayesian Collaborative Denoising for Monte Carlo Rendering

The stochastic nature of Monte Carlo rendering algorithms inherently produces noisy images. Essentially, three approaches have been developed to solve this issue: improving the ray-tracing strategies to reduce pixel variance, providing adaptive sampling by increasing the number of rays in regions needing so, and filtering the noisy image as a post-process. Although the algorithms from the latte...