Conditional product next event estimation for Gaussian process implicit surfaces

1Dartmouth College

In Computer Graphics Forum (Proceedings of EGSR), 2026

Teaser
Equal-sample comparison of the dragon scene with a heightfield-like GPIS. The previous NEE method [XBdEJ25] struggles under high anisotropy (top-left inset) since the set of admissible paths approaches a lower-dimensional manifold. Our CPNEE technique importance samples the 1D arc of valid scattering directions restricted to the light's spherical cap, recovering a clean result in the same number of samples (top-right). Combining all three strategies (unidirectional, emitter NEE, and CPNEE) via multiple importance sampling (MIS) yields robust performance across arbitrary degrees of anisotropy (bottom-right).
Abstract Downloads More Cite Related

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

Acknowledgements

We thank the anonymous reviewers for their helpful suggestions and the members of the Dartmouth Visual Computing Lab for valuable discussions. This work was supported by NSF award 2440472.

Cite

Song Shi, Kehan Xu, Wojciech Jarosz. Conditional product next event estimation for Gaussian process implicit surfaces. Computer Graphics Forum (Proceedings of EGSR), 45(4), July 2026. 
@article{shi26cpnee,
    author    = {Shi, Song and Xu, Kehan and Jarosz, Wojciech},
    title     = {Conditional Product Next Event Estimation for {Gaussian} Process Implicit Surfaces},
    journal   = {Computer Graphics Forum (Proceedings of EGSR)},
    day       = {1},
    month     = jul,
    volume    = {45},
    number    = {4},
    year      = {2026},
    doi       = {10/rngs},
    publisher = {The Eurographics Association and John Wiley \\& Sons Ltd.}
}
© The Author(s). This is the author's version of the work. It is posted here by permission of The Eurographics Association for your personal use. Not for redistribution. The definitive version is available at diglib.eg.org.