SOF: Sorted Opacity Fields
for Fast Unbounded Surface Reconstruction

SIGGRAPH Asia 2025

Lukas Radl¹ Felix Windisch¹ Thomas Deixelberger²
Jozef Hladky² Michael Steiner¹ Dieter Schmalstieg^1,3 Markus Steinberger^1,2

² ³

Paper Video Code Pre-Trained Models Extracted Meshes

SOF enables rapid extraction of unbounded meshes from 3D Gaussians.

Sorted Opacity Fields

Our contributions can be summarized as follows:

A novel, more robust depth estimate, and incorporating per-pixel sorting within GOF!
A novel extent-based loss, along with a regularizer which aligns the level-set with the depth during optimization!
A highly efficient parallelization scheme for Marching Tetrahedra, which improves performance by almost an order of magnitude!

When combined,

this yields a highly efficient framework for unbounded mesh extraction! Check out or code and paper for technical details.

Qualitative Mesh Comparison

Here, we compare the meshes extracted from our method to the ones obtained from state-of-the-art Gaussian Opacity Fields!

BibTeX

If you find our work useful, consider using a citation.

@inproceedings{radl2025sof,
  author    = {Radl, Lukas and Windisch, Felix and Deixelberger, Thomas and Hladky, Jozef and Steiner, Michael and Schmalstieg, Dieter and Steinberger, Markus},
  title     = {{SOF: Sorted Opacity Fields for Fast Unbounded Surface Rconstruction}},
  booktitle = {SIGGRAPH Asia Conference Proceedings},
  year      = {2025}
}

Related Work

Gaussian Opacity Fields: Efficient Adaptive Surface Reconstruction in Unbounded Scenes. Yu et al., 2024. ACM TOG 43(6).
StopThePop: Sorted Gaussian Splatting for View-Consistent Real-Time Rendering. Radl and Steiner et al., 2024. ACM TOG 43(4).

SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction