[Wal98]
Cornell University Program of Computer Graphics 

Density Estimation Techniques For Global Illumination.Bruce J. Walter.PhD thesis, Cornell University, 1998. In this thesis we present the density estimation framework for computing viewindependent global illumination solutions. The framework consists of three phases: particle tracing, density estimation, and decimation. Monte Carlo particle tracing is used to accurately simulate the light transport under a general spectral geometricoptics based physical model. Next kernel density estimation is used to reconstruct perceptual illumination functions. Finally decimation is used to optimize the resulting mesh for compactness and rapid interactive display as Gouraudshaded triangles. The three principal contributions of this work are the framework's separation of transport and function reconstruction computations, its ability to produce accurate solutions with precisely known error characteristics, and the techniques that we introduce to improve its efficiency and accuracy. Particle tracing's generality allows us to eliminate or delay many common simplifying assumptions and improves our accuracy and error analysis. Delaying the density estimation until particle tracing is complete allows us to make better use of the expensive particle data. The separation of global transport and local representation computations also reduces the computational complexity of each phase, enhances the framework's scalability, and exposes abundant opportunities for parallelism. Another advantage is that we can solve directly for the radiant exitance without needing to estimate the more complicated spectral radiance function. Despite its advantages, if naively implemented the framework would be prohibitively expensive. Thus we also introduce several techniques that significantly improve its accuracy and efficiency. These include the separation of luminance and chromaticity bandwidths, perceptuallymotivated noise visibility predictors, statistical bias detection techniques to automatically enhance underresolved illumination features, a local polynomial density estimation method to eliminate boundary bias, and wavelength importance sampling to reduce the spectral noise. Results of the framework are shown for some complex environments and compared against measured data for a simple scene. The strength of our framework is that it can simulate a wider variety of lighting effects, with fewer simplifying assumptions, and more precise error analysis that current viewindependent methods. Furthermore, because of its accuracy, our density estimation framework solutions are used as reference solutions for judging the quality and effectiveness of more approximate but faster rendering methods.  
