SOF: Sorted Opacity Fields for Fast Unbounded Surface Reconstruction

TL;DR

SOF introduces a novel method for fast, accurate surface reconstruction from 3D Gaussian representations, significantly improving mesh quality and processing speed in large-scale, unbounded environments.

Contribution

The paper presents Sorted Opacity Fields (SOF), a new approach with hierarchical resorting and a specialized Marching Tetrahedra algorithm for efficient, high-fidelity surface extraction from Gaussian-based scene representations.

Findings

Achieves higher reconstruction accuracy than previous methods.

Reduces meshing time by up to an order of magnitude.

Cuts total processing time by more than a factor of three.

Abstract

Recent advances in 3D Gaussian representations have significantly improved the quality and efficiency of image-based scene reconstruction. Their explicit nature facilitates real-time rendering and fast optimization, yet extracting accurate surfaces - particularly in large-scale, unbounded environments - remains a difficult task. Many existing methods rely on approximate depth estimates and global sorting heuristics, which can introduce artifacts and limit the fidelity of the reconstructed mesh. In this paper, we present Sorted Opacity Fields (SOF), a method designed to recover detailed surfaces from 3D Gaussians with both speed and precision. Our approach improves upon prior work by introducing hierarchical resorting and a robust formulation of Gaussian depth, which better aligns with the level-set. To enhance mesh quality, we incorporate a level-set regularizer operating on the opacity field and introduce losses that encourage geometrically-consistent primitive shapes. In addition, we develop a parallelized Marching Tetrahedra algorithm tailored to our opacity formulation, reducing meshing time by up to an order of magnitude. As demonstrated by our quantitative evaluation, SOF achieves higher reconstruction accuracy while cutting total processing time by more than a factor of three. These results mark a step forward in turning efficient Gaussian-based rendering into equally efficient geometry extraction.