Geometric implicit neural representations for signed distance functions

$\mathit{\text{Implicit}}\mathit{\text{neural}}\mathit{\text{representations}}$ (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 $\mathit{\text{signed}}\mathit{\text{distance}}\mathit{\text{functions}}$ (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 $\mathit{\text{geometric}}$ INRs. The key idea behind this 3D reconstruction approach is to include additional $\mathit{\text{regularization}}$ 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.