N-dimensional Gaussians for Fitting of High-Dimensional Functions

Our method optimizes N-dimensional Gaussians to approximate high-dimensional anisotropic functions in a few minutes. Our parameterization, culling, and optimization-controlled refinement allow us to quickly estimate Gaussian parameters to represent various complex functions.

Authors

Stavros Diolatzis

Intel Corporation

Tobias Zirr

Intel Corporation

Alexandr Kuznetsov

Intel Labs

Georgios Kopanas

Inria, Université Côte d'Azur

Anton Kaplanyan

Intel Corporation

This article was first published in arXiv*.

Our method optimizes N-dimensional Gaussians to approximate high-dimensional anisotropic functions in a few minutes. Our parameterization, culling, and optimization-controlled refinement allow us to quickly estimate Gaussian parameters to represent various complex functions. We show two applications:

  • 10D+ Application (top): Synthetic scenes for which we can render G-buffers, such as world position, albedo, and roughness, can be shaded with global illumination through our 10D+ Gaussian mixture. Even though the Gaussians are evaluated on the surfaces, their representation power can efficiently estimate the appearance of reflections and transmittance with correct parallax effects. Apart from the G-buffers, we support the variability of moving objects and light sources as extra dimensions.
  • 6D Application (bottom): Real-world scenes with complex, view-dependent effects can be modeled efficiently through our six-dimensional Gaussian mixture. The six dimensions of world position and view direction give the parameterization the same representation power for both diffuse and view-dependent effects, reconstructing complex effects like the one through the magnifying glass.

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Graphics Research at Intel