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.

翻译：近年来，三维高斯表示技术的进展显著提升了基于图像的场景重建的质量与效率。其显式特性促进了实时渲染与快速优化，然而在大型无界环境中提取精确表面仍是一项艰巨任务。现有方法多依赖于近似深度估计与全局排序启发式策略，这可能导致伪影并限制重建网格的保真度。本文提出排序不透明度场（SOF），一种旨在从三维高斯中快速精确恢复细节表面的方法。我们通过引入分层重排序机制与更贴合水平集的高斯深度鲁棒表述，改进了先前工作。为提升网格质量，我们在不透明度场上应用水平集正则化器，并引入促进几何一致基元形状的损失函数。此外，我们开发了适配于不透明度表述的并行化行进四面体算法，将网格生成时间缩短达一个数量级。定量评估表明，SOF在将总处理时间减少三倍以上的同时，实现了更高的重建精度。这些成果标志着将高效基于高斯的渲染转化为同等高效几何提取的重要进展。