Geometric implicit neural representations for signed distance functions

• URL: http://arxiv.org/abs/2511.07206v1
• Date: Mon, 10 Nov 2025 15:33:02 GMT
• Title: Geometric implicit neural representations for signed distance functions
• Authors: Luiz Schirmer, Tiago Novello, Vinícius da Silva, Guilherme Schardong, Daniel Perazzo, Hélio Lopes, Nuno Gonçalves, Luiz Velho,
• Abstract summary: Implicit neural representations (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces.<n>This survey reviews the existing literature on the specialized INR problem of approximating textitsigned distance functions (SDFs)<n>We refer to neural SDFs that incorporate differential geometry tools, such as normals and curvatures, in their loss functions as textitgeometric INRs.
• Score: 9.015149670090144
• License: http://creativecommons.org/licenses/by/4.0/
• 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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