Practical sampling for ray-based rendering

Many methods for realistic rendering, including ray tracing, distribution ray tracing, and path tracing, are based on the underlying operation of intersecting geometric rays with objects in a scene. In effect, these programs are light simulators, where each ray represents the path of light between emitters, reflective surfaces, or the virtual camera. Tracing the number of photons that form real images is prohibitive, so rendering programs must select a representative sample of the light within a scene to simulate. Formally, light transport in a scene is described by an integral equation. Since the rendering integrand is multidimensional and discontinuous, point sampling methods such as Monte Carlo and quasi-Monte Carlo integration are commonly used to estimate the value of the integral. A critical component of these methods is the selection of random points in the domain of integration. This dissertation examines effective methods for selecting these points. This dissertation offers the following contributions. We provide an experimental framework for comparing image difference algorithms, and use this framework to show that humans are more likely to agree with advanced perceptually-based methods than simpler methods such as RMS error. We also compare the performance of several point sets commonly used in multidimensional sampling, and show that low-discrepancy points tend to produce better images than blue noise points or other point sets. According to our comparisons, random-edge discrepancy in multiple dimensions is a good predictor of the quality of images rendered with a given point set. We also compute the distortion of various transformation functions, and show that the distortion induced by a transformation has little effect on image quality. Finally, we argue that at low sampling rates, variance may be more important than expected value, and show how inconsistent estimators with low variance may yield better images than unbiased estimators with relatively more variance.