# Neural Shortest Path for Surface Reconstruction from Point Clouds

arXiv: https://arxiv.org/abs/2502.06047 · HTML: https://mlsanity.com/paper/2502.06047/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 61 references that are in the map.
- First posted on arXiv 9 Feb 2025.

## Builds on (most cited first, 30 of 33)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Multi-Garment Net: Learning to Dress 3D People from Images](https://mlsanity.com/paper/1908.06903/) (2019)
- [Neural-Pull: Learning Signed Distance Functions from Point Clouds by Learning to Pull Space onto Surfaces](https://mlsanity.com/paper/2011.13495/) (2020)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [MeshUDF: Fast and Differentiable Meshing of Unsigned Distance Field Networks](https://mlsanity.com/paper/2111.14549/) (2021)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [NeuralUDF: Learning Unsigned Distance Fields for Multi-view Reconstruction of Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2211.14173/) (2022)
- [Deep Level Sets: Implicit Surface Representations for 3D Shape Inference](https://mlsanity.com/paper/1901.06802/) (2019)
- [Critical Regularizations for Neural Surface Reconstruction in the Wild](https://mlsanity.com/paper/2206.03087/) (2022)
- [CAP-UDF: Learning Unsigned Distance Functions Progressively from Raw Point Clouds with Consistency-Aware Field Optimization](https://mlsanity.com/paper/2210.02757/) (2022)
- [GIFS: Neural Implicit Function for General Shape Representation](https://mlsanity.com/paper/2204.07126/) (2022)
- [Deep Implicit Surface Point Prediction Networks](https://mlsanity.com/paper/2106.05779/) (2021)
- [Phase Transitions, Distance Functions, and Implicit Neural Representations](https://mlsanity.com/paper/2106.07689/) (2021)
- [Learning Anchored Unsigned Distance Functions with Gradient Direction Alignment for Single-view Garment Reconstruction](https://mlsanity.com/paper/2108.08478/) (2021)
- [Learning a More Continuous Zero Level Set in Unsigned Distance Fields through Level Set Projection](https://mlsanity.com/paper/2308.11441/) (2023)
- [SSRNet: Scalable 3D Surface Reconstruction Network](https://mlsanity.com/paper/1911.07401/) (2019)
- [GenSDF: Two-Stage Learning of Generalizable Signed Distance Functions](https://mlsanity.com/paper/2206.02780/) (2022)
- [3PSDF: Three-Pole Signed Distance Function for Learning Surfaces with Arbitrary Topologies](https://mlsanity.com/paper/2205.15572/) (2022)
- [StEik: Stabilizing the Optimization of Neural Signed Distance Functions and Finer Shape Representation](https://mlsanity.com/paper/2305.18414/) (2023)
- [Robust Zero Level-Set Extraction from Unsigned Distance Fields Based on Double Covering](https://mlsanity.com/paper/2310.03431/) (2023)
- [VisCo Grids: Surface Reconstruction with Viscosity and Coarea Grids](https://mlsanity.com/paper/2303.14569/) (2023)
- [Surface Extraction from Neural Unsigned Distance Fields](https://mlsanity.com/paper/2309.08878/) (2023)

## Abstract (arXiv)

In this paper, we propose the neural shortest path (NSP), a vector-valued implicit neural representation (INR) that approximates a distance function and its gradient. The key feature of NSP is to learn the exact shortest path (ESP), which directs an arbitrary point to its nearest point on the target surface. The NSP is decomposed into its magnitude and direction, and a variable splitting method is used that each decomposed component approximates a distance function and its gradient, respectively. Unlike to existing methods of learning the distance function itself, the NSP ensures the simultaneous recovery of the distance function and its gradient. We mathematically prove that the decomposed representation of NSP guarantees the convergence of the magnitude of NSP in the H1 norm. Furthermore, we devise a novel loss function that enforces the property of ESP, demonstrating that its global minimum is the ESP. We evaluate the performance of the NSP through comprehensive experiments on diverse datasets, validating its capacity to reconstruct high-quality surfaces with the robustness to noise and data sparsity. The numerical results show substantial improvements over state-of-the-art methods, highlighting the importance of learning the ESP, the product of distance function and its gradient, for representing a wide variety of complex surfaces.