Efficient Quadrature Rules for Illumination Integrals: From Quasi Monte Carlo to Bayesian Monte Carlo (Synthesis Lectures on Computer Graphics and Animation)

Description

Rendering photorealistic images is a costly process which can take up to several days in the case of high quality images. In most cases, the task of sampling the incident radiance function to evaluate the illumination integral is responsible for an important share of the computation time. Therefore, to reach acceptable rendering times, the illumination integral must be evaluated using a limited set of samples. Such a restriction raises the question of how to obtain the most accurate approximation possible with such a limited set of samples. One must thus ensure that sampling produces the highest amount of information possible by carefully placing and weighting the limited set of samples. Furthermore, the integral evaluation should take into account not only the information brought by sampling but also possible information available prior to sampling, such as the integrand smoothness. This idea of sparse information and the need to fully exploit the little information available is present throughout this book. The presented methods correspond to the state-of-the-art solutions in computer graphics, and take into account information which had so far been underexploited (or even neglected) by the previous approaches. The intended audiences are Ph.D. students and researchers in the field of realistic image synthesis or global illumination algorithms, or any person with a solid background in graphics and numerical techniques. Introduction The Global Illumination Problem Illumination Integral Evaluation Motivation Book Overview Spherical Fibonacci Point Sets for QMC Estimates of Illumination Integrals Introduction Background QMC on the Unit Square QMC Rules on the Unit Sphere QMC Point Sets Hemispherical Projections Summary Spherical Fibonacci Point Sets QMC for Illumination Integrals Results Experimental Setup Predicting the Estimate Error Experimental Estimate Error Conclusion Bayesian Monte Carlo for Global Illumination Introduction and Motivation Representing a Function Using a Smooth Model Linear Basis Functions Model Bayesian Regression Bayesian Monte Carlo BMC Quadrature Equations Reducing the Number of Hyperparameters Summary Applying BMC to Global Illumination Spherical Gaussians for Fast Quadrature Computation Prior GP: a Global Model with Local Adaptation From the Hemisphere to the Gaussian Lobe Precomputations The Rendering Algorithm Results Experimental Environment Hyperparameters Learning Comparison: BMC vs. QMC Skipping the Learning Step Conclusion Posterior Distribution Bibliography Authors' Biographies