Adaptive Splitting Factors with Error Estimation for Monte Carlo Rendering

Abstract

Splitting methods for variance reduction in Monte Carlo (MC) rendering are proposed in this thesis. We can reduce the variance of MC estimators by efficiently increasing the number of samples per dimension in the multi-dimensional model. The main problem of splitting is how to determine splitting factors, which are the number of samples in each dimension. In this thesis, splitting is applied in the shadow and secondary rays at the first bounce of the paths. Splitting factors are estimated by using error estimation methods such as mutual information, R_squared change and adjusted R_squared change. Those methods can estimate the error for each dimension of random parameters in MC rendering. Sample colors and random parameters for generating the rays in MC rendering are used as input variables in error estimators. For verifying proposed splitting factors, the toy scenes which are affected by direct or indirect illumination and ground truth splitting factors are used. The results of the proposed splitting method are presented by comparing the results of plain path tracing (PT). Finally, the limitation and future works of the proposed methods is given at the end of this thesis.