Practical Gaussian process implicit surfaces with sparse convolutions

In ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia), 2025

Our novel sparse convolution representation for Gaussian Process Implicit Surfaces (GPISes) enables, for the first time, the visualization of single non-stationary realizations (split screen, middle right) alongside their ensemble-averaged light transport (right). The single realization allows examining the underlying structures of the stochastic geometry that lead to the aggregate rough surface or volumetric appearance. Furthermore, our algorithm (middle left) significantly boosts rendering efficiency for ensemble light transport compared to previous work by Seyb et al. 2024 (left) at equal time (40 min). The rightmost column presents magnified insets comparing the two methods, with speedup quantified by the ratio of mean squared error (MSE). This improvement stems from a combination of our efficient sparse convolution representation and the ability to perform next-event estimation even on specular micro-surfaces.

Abstract

A fundamental challenge in rendering has been the dichotomy between surface and volume models. Gaussian Process Implicit Surfaces (GPISes) recently provided a unified approach for surfaces, volumes, and the spectrum in between. However, this representation remains impractical due to its high computational cost and mathematical complexity. We address these limitations by reformulating GPISes as procedural noise, eliminating expensive linear system solves while maintaining control over spatial correlations. Our method enables efficient sampling of stochastic realizations and supports flexible conditioning of values and derivatives through pathwise updates. To further enable practical rendering, we derive analytic distributions for surface normals, allowing for variance-reduced light transport via next-event estimation and multiple importance sampling. Our framework achieves efficient, high-quality rendering of stochastic surfaces and volumes with significantly simplified implementations on both CPU and GPU, while preserving the generality of the original GPIS representation.

Downloads

• Publication

  • Paper, PDF (20MB)
  • Publisher's official version (may require a subscription)
  • SIGGRAPH Asia 2025 poster, PDF (14.5MB)

• Slides

  • Presentation slides, MP4 (107MB)

• Video

  • Video (full-quality), MP4 (233MB)
  • Video (web-quality), MP4 (77MB)

• Data

  • Supplemental archive, ZIP (37MB) - offline version of the interactive comparisons below.

• Code

  • Reference C++ implementation
  • Interactive demos on ShaderToy.com
  • GitHub repo with source code for all the above ShaderToy demos

Videos

Visual overview

In this paper we make the rendering of Gaussian process implicit surfaces (GPIS) practical. We achieve this with a novel procedural noise formulation and by enabling next-event estimation for specular BRDFs.

A key challenge in rendering is the surface vs. volume dichotomy. Seyb et al. [2024] proposed Gaussian process implicit surfaces (GPIS) as a unified approach, covering surfaces, volumes, and the rich continuum in between. However, the representation remained prohibitively expensive to render.

Our paper reformulates Gaussian processes as a type of procedural noise – specifically, sparse convolution noise, simulated by placing kernels at random locations. This allows us to leverage the decades of work in graphics on efficient procedural noise synthesis and to express GPISes in a language familiar to practitioners in our field.

This formulation allows for a much simpler and faster implementation. We can now render GPISes efficiently, including both a single realization and the full ensemble light transport, even on the GPU. Try out our online Shadertoy demos:
2D GPIS and 3D GPIS.

We also enabled next-event estimation (NEE) for GPISes with specular BRDFs by deriving the analytic distribution of normals. This lets us replicate the UNI/NEE/MIS comparison from the classic Veach MIS scene, but where each plate is represented as a GPIS.

When combined, these improvements provide massive rendering speedups compared to our prior work (over 9000X in this chess set inset!).

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Interactive result comparisons

Below you can view interactive comparisons comparing our method to various previous approaches.

Figure 7: Shaderball

Figure 12: Veach MIS

Figure 14: Dragon

Figure 15: Dragon

Figure 16: Chess Set

Figure 15: Statue

Figure 17: Coffee Mug

Acknowledgements

We thank Dario Seyb for insightful discussions on GPIS and Jeffrey Liu for providing helpful feedback. This work was partially supported by NSF awards 1844538 and 2440472. We used assets licensed under CC0 in many figures of this paper and thank the original creators for providing them: shader ball [Takikawa et al. 2022], chess set (polyhaven.com, by Riley Queen), dragon (OpenVDB sample models), two statues (threedscans.com), and coffee mug (Sketchfab). We pair-programmed with an LLM to refine the code and layout of several programmatically generated figures: Figs. 2, 3, 5, 6 and 19.

Cite

@article{xu25practical,
    author  = {Xu, Kehan and Bitterli, Benedikt and d'Eon, Eugene and Jarosz, Wojciech},
    title   = {Practical {G}aussian Process Implicit Surfaces with Sparse Convolutions},
    journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH Asia)},
    year    = {2025},
    month   = dec,
    volume  = {44},
    number  = {6},
    doi     = {10.1145/3763329}
}

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