# GraphWalks: Efficient Shape Agnostic Geodesic Shortest Path Estimation

arXiv: https://arxiv.org/abs/2205.15217 · HTML: https://mlsanity.com/paper/2205.15217/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 17 of 17)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Principal Neighbourhood Aggregation for Graph Nets](https://mlsanity.com/paper/2004.05718/) (2020)
- [Embodied Question Answering](https://mlsanity.com/paper/1711.11543/) (2017)
- [Walk in the Cloud: Learning Curves for Point Clouds Shape Analysis](https://mlsanity.com/paper/2105.01288/) (2021)
- [ASAP: Adaptive Structure Aware Pooling for Learning Hierarchical Graph Representations](https://mlsanity.com/paper/1911.07979/) (2019)
- [If beam search is the answer, what was the question?](https://mlsanity.com/paper/2010.02650/) (2020)
- [On NMT Search Errors and Model Errors: Cat Got Your Tongue?](https://mlsanity.com/paper/1908.10090/) (2019)
- [Finding the Stochastic Shortest Path with Low Regret: The Adversarial Cost and Unknown Transition Case](https://mlsanity.com/paper/2102.05284/) (2021)
- [A Survey of Algorithms for Geodesic Paths and Distances](https://mlsanity.com/paper/2007.10430/) (2020)
- [Learning to Generate Customized Dynamic 3D Facial Expressions](https://mlsanity.com/paper/2007.09805/) (2020)
- [Geodesic Distance Descriptors](https://mlsanity.com/paper/1611.07360/) (2016)
- [Geodesic Distance Estimation with Spherelets](https://mlsanity.com/paper/1907.00296/) (2019)
- [Revisiting Point Cloud Simplification: A Learnable Feature Preserving Approach](https://mlsanity.com/paper/2109.14982/) (2021)
- [Shortest path distance approximation using deep learning techniques](https://mlsanity.com/paper/2002.05257/) (2020)

## Built on by (most cited first, 8 of 8)

- [WiLoR: End-to-end 3D Hand Localization and Reconstruction in-the-wild](https://mlsanity.com/paper/2409.12259/) (2024)
- [Neural Sign Actors: A diffusion model for 3D sign language production from text](https://mlsanity.com/paper/2312.02702/) (2023)
- [SAGS: Structure-Aware 3D Gaussian Splatting](https://mlsanity.com/paper/2404.19149/) (2024)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [NeuroGF: A Neural Representation for Fast Geodesic Distance and Path Queries](https://mlsanity.com/paper/2306.00658/) (2023)
- [ShapeFusion: A 3D diffusion model for localized shape editing](https://mlsanity.com/paper/2403.19773/) (2024)
- [ImHead: A Large-scale Implicit Morphable Model for Localized Head Modeling](https://mlsanity.com/paper/2510.10793/) (2025)
- [GeoMM: On Geodesic Perspective for Multi-modal Learning](https://mlsanity.com/paper/2505.11216/) (2025)

## Abstract (arXiv)

Geodesic paths and distances are among the most popular intrinsic properties of 3D surfaces. Traditionally, geodesic paths on discrete polygon surfaces were computed using shortest path algorithms, such as Dijkstra. However, such algorithms have two major limitations. They are non-differentiable which limits their direct usage in learnable pipelines and they are considerably time demanding. To address such limitations and alleviate the computational burden, we propose a learnable network to approximate geodesic paths. The proposed method is comprised by three major components: a graph neural network that encodes node positions in a high dimensional space, a path embedding that describes previously visited nodes and a point classifier that selects the next point in the path. The proposed method provides efficient approximations of the shortest paths and geodesic distances estimations. Given that all of the components of our method are fully differentiable, it can be directly plugged into any learnable pipeline as well as customized under any differentiable constraint. We extensively evaluate the proposed method with several qualitative and quantitative experiments.