# From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data

arXiv: https://arxiv.org/abs/2606.02268 · HTML: https://mlsanity.com/paper/2606.02268/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 53 references that are in the map.
- First posted on arXiv 1 Jun 2026.

## Builds on (most cited first, 30 of 31)

- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Point-BERT: Pre-training 3D Point Cloud Transformers with Masked Point Modeling](https://mlsanity.com/paper/2111.14819/) (2021)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Revisiting Point Cloud Classification: A New Benchmark Dataset and Classification Model on Real-World Data](https://mlsanity.com/paper/1908.04616/) (2019)
- [PointContrast: Unsupervised Pre-training for 3D Point Cloud Understanding](https://mlsanity.com/paper/2007.10985/) (2020)
- [Masked Autoencoders for Point Cloud Self-supervised Learning](https://mlsanity.com/paper/2203.06604/) (2022)
- [Point-M2AE: Multi-scale Masked Autoencoders for Hierarchical Point Cloud Pre-training](https://mlsanity.com/paper/2205.14401/) (2022)
- [Self-Supervised Pretraining of 3D Features on any Point-Cloud](https://mlsanity.com/paper/2101.02691/) (2021)
- [CrossPoint: Self-Supervised Cross-Modal Contrastive Learning for 3D Point Cloud Understanding](https://mlsanity.com/paper/2203.00680/) (2022)
- [Unsupervised Point Cloud Pre-Training via Occlusion Completion](https://mlsanity.com/paper/2010.01089/) (2020)
- [Sonata: Self-Supervised Learning of Reliable Point Representations](https://mlsanity.com/paper/2503.16429/) (2025)
- [Unsupervised Learning of Robust Spectral Shape Matching](https://mlsanity.com/paper/2304.14419/) (2023)
- [Masked Scene Contrast: A Scalable Framework for Unsupervised 3D Representation Learning](https://mlsanity.com/paper/2303.14191/) (2023)
- [Joint-MAE: 2D-3D Joint Masked Autoencoders for 3D Point Cloud Pre-training](https://mlsanity.com/paper/2302.14007/) (2023)
- [Ponder: Point Cloud Pre-training via Neural Rendering](https://mlsanity.com/paper/2301.00157/) (2022)
- [Point Cloud Pre-training with Diffusion Models](https://mlsanity.com/paper/2311.14960/) (2023)
- [The Vector Heat Method](https://mlsanity.com/paper/1805.09170/) (2018)
- [Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation](https://mlsanity.com/paper/2402.18920/) (2024)
- [Take-A-Photo: 3D-to-2D Generative Pre-training of Point Cloud Models](https://mlsanity.com/paper/2307.14971/) (2023)
- [Boundary First Flattening](https://mlsanity.com/paper/1704.06873/) (2017)
- [A Survey of Algorithms for Geodesic Paths and Distances](https://mlsanity.com/paper/2007.10430/) (2020)
- [Point-DAE: Denoising Autoencoders for Self-supervised Point Cloud Learning](https://mlsanity.com/paper/2211.06841/) (2022)
- [Learning the Geodesic Embedding with Graph Neural Networks](https://mlsanity.com/paper/2309.05613/) (2023)
- [PointVST: Self-Supervised Pre-training for 3D Point Clouds via View-Specific Point-to-Image Translation](https://mlsanity.com/paper/2212.14197/) (2022)
- [NeuroGF: A Neural Representation for Fast Geodesic Distance and Path Queries](https://mlsanity.com/paper/2306.00658/) (2023)
- [Self-supervised Learning of LiDAR 3D Point Clouds via 2D-3D Neural Calibration](https://mlsanity.com/paper/2401.12452/) (2024)
- [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)
- [FlexPara: Flexible Neural Surface Parameterization](https://mlsanity.com/paper/2504.19210/) (2025)

## Built on by (most cited first, 1 of 1)

- [SeamFlow: Structure-Aware Flow Matching on Edge Probabilities for Artist-Like UV Unwrapping](https://mlsanity.com/paper/2609.04751/) (2026)

## Abstract (arXiv)

Geometric analysis fundamentally distinguishes between textitextrinsic and textitintrinsic perspectives. The dominant paradigm in current 3D representation learning relies on either extrinsic spatial structures or high-level semantics, struggling to capture the essence of shape identity and underlying manifold topology. To bridge this gap, we introduce a novel 3D representation learning paradigm, namely PRISM, for Pre-training, which learns isometric embeddings by Recovering the Intrinsic Surface geodesic Metric. PRISM incorporates a topology-enforcing objective that explicitly constrains the structure of latent space, alongside a specialized two-stage training recipe mitigating sample imbalance inherent in the distribution of geodesic distances. Experiments demonstrate that our approach shows satisfactory accuracy, robustness, and high efficiency in geodesic distance prediction and achieves superior performance across diverse downstream tasks, including shape recognition, surface parameterization, and non-rigid correspondence. The code will be publicly available at https://github.com/AidenZhao/PRISM.