A Gaussian process-based approach to rendering

Abstract

[en] Many physically-based image rendering algorithms use the illumination integral to determine the color of each pixel in the rendered image. This integral has a component that can be sampled but has no known analytical expression, so it cannot be computed directly and must be evaluated with approximation methods. Among these we can find the Monte Carlo (MC) and the Bayesian Monte Carlo (BMC) integration methods. MC integration consists in defining a random variable such that its expected value is the solution to the integral, and then repeatedly sampling that random variable to estimate the true value. In contrast, BMC models the function to be integrated using a Gaussian Process, which allows for the incorporation of prior information. While MC is conceptually simple and straightforward to implement, it has a slower convergence rate compared to BMC. BMC, on the other hand, allows for better estimates with the same number of samples, even without prior information, by taking into account all available information about the samples, in particular the covariance of the sample locations. In this thesis, I implemented the MC and the BMC algorithms for integration, and compared their performances in two settings: for the estimation of a single integral with a known true value and for image rendering using the root-mean-squared error (RMSE). My results showed that the error of BMC converged much faster compared to MC in both settings, mirroring the existing literature on the topic. In addition, I experimented with the use of a constant prior in the BMC method, and found promising results for single integral estimation, although further work is needed to successfully apply this finding to image rendering.