Neural surface representation has demonstrated remarkable success in the areas of novel view synthesis and 3D reconstruction. However, assessing the geometric quality of 3D reconstructions in the absence of ground truth mesh remains a significant challenge, due to its rendering-based optimization process and entangled learning of appearance and geometry with photometric losses. In this paper, we present a novel framework, i.e, GURecon, which establishes a geometric uncertainty field for the neural surface based on geometric consistency. Different from existing methods that rely on rendering-based measurement, GURecon models a continuous 3D uncertainty field for the reconstructed surface, and is learned by an online distillation approach without introducing real geometric information for supervision. Moreover, in order to mitigate the interference of illumination on geometric consistency, a decoupled field is learned and exploited to finetune the uncertainty field. Experiments on various datasets demonstrate the superiority of GURecon in modeling 3D geometric uncertainty, as well as its plug-and-play extension to various neural surface representations and improvement on downstream tasks such as incremental reconstruction. The code and supplementary material are available on the project website: https://zju3dv.github.io/GURecon/.

翻译：神经表面表示在新视角合成与三维重建领域已展现出显著成功。然而，由于基于渲染的优化过程以及外观与几何通过光度损失进行耦合学习，在缺乏真实网格的情况下评估三维重建的几何质量仍然是一个重大挑战。本文提出一种新颖框架GURecon，该框架基于几何一致性为神经表面建立几何不确定性场。与现有依赖基于渲染测量的方法不同，GURecon为重建表面建模连续的三维不确定性场，并通过在线蒸馏方法进行学习，无需引入真实几何信息进行监督。此外，为减轻光照对几何一致性的干扰，我们学习并利用解耦场对不确定性场进行微调。在多个数据集上的实验证明了GURecon在三维几何不确定性建模方面的优越性，其即插即用特性可扩展至多种神经表面表示，并能提升增量重建等下游任务的性能。代码与补充材料详见项目网站：https://zju3dv.github.io/GURecon/。