# NeuroGF: A Neural Representation for Fast Geodesic Distance and Path Queries

arXiv: https://arxiv.org/abs/2306.00658 · HTML: https://mlsanity.com/paper/2306.00658/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 50 references that are in the map.
- First posted on arXiv 1 Jun 2023.

## Builds on (most cited first, 20 of 20)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [Neural Surface Maps](https://mlsanity.com/paper/2103.16942/) (2021)
- [NeuForm: Adaptive Overfitting for Neural Shape Editing](https://mlsanity.com/paper/2207.08890/) (2022)
- [GeoNet: Deep Geodesic Networks for Point Cloud Analysis](https://mlsanity.com/paper/1901.00680/) (2019)
- [Neural Convolutional Surfaces](https://mlsanity.com/paper/2204.02289/) (2022)
- [GraphWalks: Efficient Shape Agnostic Geodesic Shortest Path Estimation](https://mlsanity.com/paper/2205.15217/) (2022)
- [Parallel Chen-Han (PCH) Algorithm for Discrete Geodesics](https://mlsanity.com/paper/1305.1293/) (2013)
- [Parallel and Scalable Heat Methods for Geodesic Distance Computation](https://mlsanity.com/paper/1812.06060/) (2018)
- [Geodesic-Former: a Geodesic-Guided Few-shot 3D Point Cloud Instance Segmenter](https://mlsanity.com/paper/2207.10859/) (2022)

## Built on by (most cited first, 7 of 7)

- [Learning the Geodesic Embedding with Graph Neural Networks](https://mlsanity.com/paper/2309.05613/) (2023)
- [Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Models](https://mlsanity.com/paper/2505.18230/) (2025)
- [Im2SurfTex: Surface Texture Generation via Neural Backprojection of Multi-View Images](https://mlsanity.com/paper/2502.14006/) (2025)
- [A Survey of AI Methods for Geometry Preparation and Mesh Generation in Engineering Simulation](https://mlsanity.com/paper/2512.23719/) (2025)
- [LiteGE: Lightweight Geodesic Embedding for Efficient Geodesics Computation and Non-Isometric Shape Correspondence](https://mlsanity.com/paper/2512.17781/) (2025)
- [From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data](https://mlsanity.com/paper/2606.02268/) (2026)
- [Reciprocal Latent Fields for Precomputed Sound Propagation](https://mlsanity.com/paper/2602.06937/) (2026)

## Abstract (arXiv)

Geodesics are essential in many geometry processing applications. However, traditional algorithms for computing geodesic distances and paths on 3D mesh models are often inefficient and slow. This makes them impractical for scenarios that require extensive querying of arbitrary point-to-point geodesics. Although neural implicit representations have emerged as a popular way of representing 3D shape geometries, there is still no research on representing geodesics with deep implicit functions. To bridge this gap, this paper presents the first attempt to represent geodesics on 3D mesh models using neural implicit functions. Specifically, we introduce neural geodesic fields (NeuroGFs), which are learned to represent the all-pairs geodesics of a given mesh. By using NeuroGFs, we can efficiently and accurately answer queries of arbitrary point-to-point geodesic distances and paths, overcoming the limitations of traditional algorithms. Evaluations on common 3D models show that NeuroGFs exhibit exceptional performance in solving the single-source all-destination (SSAD) and point-to-point geodesics, and achieve high accuracy consistently. Besides, NeuroGFs also offer the unique advantage of encoding both 3D geometry and geodesics in a unified representation. Moreover, we further extend generalizable learning frameworks of NeuroGFs by adding shape feature encoders, which also show satisfactory performances for unseen shapes and categories. Code is made available at https://github.com/keeganhk/NeuroGF/tree/master.