用几何约束提升神经隐式表面重建精度
Geometric implicit neural representations for signed distance functions
- 在损失函数中引入法向、曲率等几何信息进行正则化
- 实现从带方向点云和多视角图像中高精度重建表面
- 适合需要精确几何形状的3D建模任务
隐式神经表示（INRs）已成为低维空间信号表示的有力框架。本文综述了专门用于近似表面场景有符号距离函数（SDFs）的INR研究，输入为带方向的点云或一组定位图像。我们将损失函数中融入法向、曲率等微分几何工具的神经SDF称为几何INRs。该3D重建方法的核心思想是在损失函数中加入额外正则化项，确保INR满足全局性质，例如SDF应具有单位梯度。我们从微分几何角度探讨了关键方法组件，包括INR定义、几何损失函数构建及采样策略。研究表明，几何INRs在从带方向点云和定位图像中重建表面方面取得了显著进展。
原文摘要 · Abstract (English)
\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating \textit{signed distance functions} (SDFs) for surface scenes, using either oriented point clouds or a set of posed images. We refer to neural SDFs that incorporate differential geometry tools, such as normals and curvatures, in their loss functions as \textit{geometric} INRs. The key idea behind this 3D reconstruction approach is to include additional \textit{regularization} terms in the loss function, ensuring that the INR satisfies certain global properties that the function should hold -- such as having unit gradient in the case of SDFs. We explore key methodological components, including the definition of INR, the construction of geometric loss functions, and sampling schemes from a differential geometry perspective. Our review highlights the significant advancements enabled by geometric INRs in surface reconstruction from oriented point clouds and posed images.
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