Spectral Optimization of kD-Sample Points for Integrands in Realtime-Path Tracing

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Since several years, Monte Carlo-raytracing methods, such as path tracing, are standard in offline rendering, and the future of real-time rendering. Limited computation time per image in this scenario, however, make robust and efficient rendering algorithms necessary which are able to produce images with low variance and high temporal stability with only few, or even a single, computed light transport path per pixel. The most important ingredient of efficient Monte Carlo-methods -- next to importance sampling, denoising and outlier removal, where much progress has been made in recent years -- is the generation of sets of sample points for the numeric integration, which are able to reduce the perceived integration error in rendered images.For this, the proposed project shall exceed the known techniques for stratification or low-discrepancy sampling (e.g. used in quasi-Monte Carlo methods) and explore new approaches which are better suited for real-time raytracing. In this setting, in contrast to offline methods, it is not possible to strive for convergence of the Monte Carlo-integration within every single pixel. Instead, a good distribution of sample points across the integration dimensions and in a local pixel neighborhood, and by this the reduction of low-frequency components of the error in image space, is of utmost importance. This also allows for a best possible variance reduction and low bias if post-filtering for denoising is applied subsequently. The necessity of good sample distributions and at the same time the relatively low dimensionality motivates a precomputation of distributions, which, in contrast, would not be attractive for offline rendering due to variable and high path lengths.The interplay between a distribution of sample points and the frequency spectrum of the error in image space is complex and subject to our studies. For this, we will analyze and model realistic integrands. For moderate dimensionality, this can be achieved using Fourier transformations of dense sampling of the integrand performed with instrumented raytracing implementations. Visualizations of the resulting spectra will provide insights in the structure of realistic integrands and help to develop generic models, which later will not require sampling of specific 3D scenes anymore.A prediction of the spectrum of the error in image space for a given distribution of sample points enables us to optimize the spectrum of sample points such that frequency components of the error, which are perceived as distracting, or are difficult or impossible to remove with post-filtering, are mitigated. Optimization approaches for sample points according to these spectra are also subject of this project. The goal is that all these costly precomputations are only performed once for each class of integrands, and at runtime precomputed sample points can simply be read from tileable textures.