Conditional Product Next Event Estimation for Gaussian Process Implicit Surfaces

Abstract

We propose a new next-event estimation (NEE) technique for Gaussian Process Implicit Surfaces (GPISes). We show that the distribution of surface normals available for sampling at a GPIS hit point collapses from 2D to 1D as the GPIS realizations approach heightfields, causing existing NEE to fail entirely in this limit. We analyze this collapse and develop a new strategy that directly importance samples the resulting 1D arc of valid scattering directions restricted to the spherical cap towards a light source. Our technique enables NEE on heightfield GPISes for the first time and provides substantial variance reduction for highly anisotropic near-heightfield configurations. We combine our strategy with existing techniques via multiple importance sampling for robust performance across all degrees of anisotropy, and support arbitrary emitter shapes via sphere proxies.

Downloads and Links

Publication:

Paper (Author's Version), PDF (37 MB)

Paper (compressed), PDF (2.5 MB)

Official Publisher's Version (External Link)

Slides:

Slides, PDF (18 MB)

Slides, Powerpoint (105 MB)

Code:

Source Code, GitHub (External Link)

Data:

Scene Data (78 KB)

Video

Interactive result comparisons

Below you can view interactive comparisons of the full OpenEXR rendered results from the paper. You can also find low-dynamic range versions below each thumbnail if you prefer.

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  Dragon (Anisotropic, Surface-like)Fig. 1LDR version
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  Veach (Mesh Light)Fig. 7LDR version
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  Veach (Isotropic)Fig. 8LDR version
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  Veach (Anisotropic)Fig. 8LDR version
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  Dragon (Isotropic, Surface-like)Fig. 9LDR version
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  Dragon (Anisotropic, Volumetric)Fig. 9LDR version
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  Veach (Anisotropic along XY)Fig. 10LDR version
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  ShaderballLDR version

Cite

@article{shi26conditional,
    author  = {Shi, Song and Xu, Kehan and Jarosz, Wojciech},
    title   = {Conditional Product Next Event Estimation for Gaussian Process Implicit Surfaces},
    journal = {Computer Graphics Forum},
    year    = {2026},
    month   = jul,
    volume  = {45},
    number  = {4},
    doi     = {10.1111/cgf.70535},
}

Copyright Disclaimer

© 2026 The Authors. Computer Graphics Forum published by Eurographics — The European Association for Computer Graphics and John Wiley & Sons Ltd. This is the author's version of the work, posted here for your personal use. Not for redistribution. The definitive version is available at the publisher's site.