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dc.contributor.authorSingh, Gurpriten_US
dc.contributor.authorMiller, Baileyen_US
dc.contributor.authorJarosz, Wojciechen_US
dc.contributor.editorZwicker, Matthias and Sander, Pedroen_US
dc.description.abstractRecently researchers have started employing Monte Carlo-like line sample estimators in rendering, demonstrating dramatic reductions in variance (visible noise) for effects such as soft shadows, defocus blur, and participating media. Unfortunately, there is currently no formal theoretical framework to predict and analyze Monte Carlo variance using line and segment samples which have inherently anisotropic Fourier power spectra. In this work, we propose a theoretical formulation for lines and finite-length segment samples in the frequency domain that allows analyzing their anisotropic power spectra using previous isotropic variance and convergence tools. Our analysis shows that judiciously oriented line samples not only reduce the dimensionality but also pre-filter C0 discontinuities, resulting in further improvement in variance and convergence rates. Our theoretical insights also explain how finite-length segment samples impact variance and convergence rates only by pre-filtering discontinuities. We further extend our analysis to consider (uncorrelated) multi-directional line (segment) sampling, showing that such schemes can increase variance compared to unidirectional sampling. We validate our theoretical results with a set of experiments including direct lighting, ambient occlusion, and volumetric caustics using points, lines, and segment samples.en_US
dc.publisherThe Eurographics Association and John Wiley & Sons Ltd.en_US
dc.subjectComputing methodologies
dc.subject> Ray tracing
dc.subjectMathematics of computing
dc.subject> Stochastic processes
dc.subjectComputation of transforms
dc.titleVariance and Convergence Analysis of Monte Carlo Line and Segment Samplingen_US
dc.description.seriesinformationComputer Graphics Forum
dc.description.sectionheadersMonte Carlo before Coffee

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  • 36-Issue 4
    Rendering 2017 - Symposium Proceedings

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