Geometric implicit neural representations for signed distance functions
arXiv:2511.07206 · doi:10.1016/j.cag.2024.104085
Abstract
\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.
References in corpus (14)
- Instant Neural Graphics Primitives with a Multiresolution Hash Encoding
- Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
- Nerfstudio: A Modular Framework for Neural Radiance Field Development
- NeRF++: Analyzing and Improving Neural Radiance Fields
- MonoSDF: Exploring Monocular Geometric Cues for Neural Implicit Surface Reconstruction
- Geo-Neus: Geometry-Consistent Neural Implicit Surfaces Learning for Multi-view Reconstruction
- Exploring Differential Geometry in Neural Implicits
- Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields
- Neural Implicit Surface Evolution
- Neural Implicit Morphing of Face Images
- MARF: The Medial Atom Ray Field Object Representation
- Implicit Neural Representation of Tileable Material Textures
- ImFace++: A Sophisticated Nonlinear 3D Morphable Face Model with Implicit Neural Representations
- Enhancing Surface Neural Implicits with Curvature-Guided Sampling and Uncertainty-Augmented Representations