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arXiv · 2511.07206

Geometric implicit neural representations for signed distance functions

Luiz Schirmer·Tiago Novello·Vinícius da Silva·Guilherme Schardong·Daniel Perazzo·Hélio Lopes·Nuno Gonçalves·Luiz Velho
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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.

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Luiz Schirmer, Tiago Novello, Vinícius da Silva, Guilherme Schardong, Daniel Perazzo, Hélio Lopes, Nuno Gonçalves, Luiz Velho. 2025-11-10. Geometric implicit neural representations for signed distance functions. https://doi.org/10.1016/j.cag.2024.104085

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