# LiteGE: Lightweight Geodesic Embedding for Efficient Geodesics Computation and Non-Isometric Shape Correspondence

arXiv: https://arxiv.org/abs/2512.17781 · HTML: https://mlsanity.com/paper/2512.17781/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 44 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [On the Continuity of Rotation Representations in Neural Networks](https://mlsanity.com/paper/1812.07035/) (2018)
- [Objaverse-XL: A Universe of 10M+ 3D Objects](https://mlsanity.com/paper/2307.05663/) (2023)
- [3D Menagerie: Modeling the 3D shape and pose of animals](https://mlsanity.com/paper/1611.07700/) (2016)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [3D-CODED : 3D Correspondences by Deep Deformation](https://mlsanity.com/paper/1806.05228/) (2018)
- [Deep Functional Maps: Structured Prediction for Dense Shape Correspondence](https://mlsanity.com/paper/1704.08686/) (2017)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [NeuroGF: A Neural Representation for Fast Geodesic Distance and Path Queries](https://mlsanity.com/paper/2306.00658/) (2023)
- [Loss it right: Euclidean and Riemannian Metrics in Learning-based Visual Odometry](https://mlsanity.com/paper/2401.05396/) (2023)
- [Parallel Chen-Han (PCH) Algorithm for Discrete Geodesics](https://mlsanity.com/paper/1305.1293/) (2013)

## Built on by (most cited first, 2 of 2)

- [From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data](https://mlsanity.com/paper/2606.02268/) (2026)
- [Auditing Training-Free 3D Shape Retrieval with Diffused Geodesic Moments](https://mlsanity.com/paper/2605.29004/) (2026)

## Abstract (arXiv)

Computing geodesic distances on 3D surfaces is fundamental to many tasks in 3D vision and geometry processing, with deep connections to tasks such as shape correspondence. Recent learning-based methods achieve strong performance but rely on large 3D backbones, leading to high memory usage and latency, which limit their use in interactive or resource-constrained settings. We introduce LiteGE, a lightweight approach that constructs compact, category-aware shape descriptors by applying Principal Component Analysis (PCA) to unsigned distance field (UDFs) samples at informative voxels. This descriptor is efficient to compute and removes the need for high-capacity networks. LiteGE remains robust on sparse point clouds, supporting inputs with as few as 300 points, where prior methods fail. Extensive experiments show that LiteGE reduces memory usage and inference time by up to 300× compared to existing neural approaches. In addition, by exploiting the intrinsic relationship between geodesic distance and shape correspondence, LiteGE enables fast and accurate shape matching. Our method achieves up to 1000× speedup over state-of-the-art mesh-based approaches while maintaining comparable accuracy on non-isometric shape pairs, including evaluations on point-cloud inputs.