Robust control variates optimization for rendering
Date:
Abstract
Monte Carlo integration is a recurrent problem in computer graphics. This numerical esti- mation is error prone and many methods have been developed to limit it magnitude. One of them is the use of control variate to simplify the integration problem. When using a suitable control variate, it is possible to significantly reduce the complexity of the integra- tion problem and thus the amount of error produced. On the other hand, using the bad control variate can increase the error. The major difficulty of these methods is to choose robustly these control variate. We propose an optimization-based method that ensures a variance reduction compared to a Monte Carlo estimator. This method uses the samples of a Monte Carlo estimator to build a reliable estimate of the integrated function. We then use this estimate as a control variate function. Under certain simple conditions, it is provable that this estimator has a reduced variance over to a Monte Carlo one. This method can be used as a substitute of Monte Carlo estimator in many problems. We have demonstrated its applicability to different light transport simulation problems.