\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.

翻译：隐式神经表示（INRs）已成为在低维空间中表示信号的一种有前景的框架。本文综述了现有文献中关于专门用于近似表面场景符号距离函数（SDFs）的INR问题，其输入数据为定向点云或一组位姿已知的图像。我们将那些在损失函数中融入微分几何工具（如法线和曲率）的神经SDFs称为几何INRs。这种三维重建方法的核心思想是在损失函数中加入额外的正则化项，以确保INR满足函数应具备的某些全局性质——例如在SDFs情况下具有单位梯度。我们从微分几何的视角探讨了关键的方法论组成部分，包括INR的定义、几何损失函数的构建以及采样方案。我们的综述强调了几何INRs在从定向点云和位姿已知图像进行表面重建方面所带来的显著进展。