Reduction of stochastic noise in physically-based rendering algorithms.

The use of computer graphics has become commonplace in industry, games, films, architectural visualizations, etc. Over the years, there has been an increasing demand for more realism and more graphical fidelity. To achieve this realism, current state-of-the-art illumination algorithms are based on ray tracing, which simulates the physical transport of light through three-dimensional scenes. While ray tracing is conceptually simple, the underlying problem is a recursive integral equation, which has to be evaluated for each pixel. Solving this integral equation is usually done using stochastic methods, like Monte Carlo integration. However, using stochastic algorithms inevitably leads to variance on the numerical outcomes which appears as noise in rendered images.

In this dissertation, we aim to reduce this noise by improving the efficiency of the illumination algorithms. First, we present a novel view on the visibility evaluation between two points in a three-dimensional scene. Traditionally, the visibility is evaluated by testing all the geometrical primitives for intersection with a line segment spanned by two points. However, we propose a method to stochastically evaluate the visibility by only testing a random subset of the geometrical primitives, while still converging to the correct solution.

Second, we present a new algorithm which accelerates the evaluation of the visibility between two points in a three-dimensional scene by leveraging cheap geometrical proxies. While simplified versions complex geometry are already commonly used to accelerate visibility operations, naively substituting the simplified geometry for the original geometry will introduce artefacts and bias. In contrast, our method remains unbiased by stochastically using either the simplified geometry or a combination of the simplified geometry and the original geometry for intersection testing.

Finally, we propose a semi-analytical technique to evaluate the direct illumination. Instead of sampling the light sources using point samples, we propose to use line samples where the contribution of a line sample is evaluated analytically. Using line samples to evaluate the direct illumination instead of point samples reduces the dimension of the integral equation, which can lead to higher orders of convergence when specialized distributions are used to generate the line samples.