# Learning Manifolds in High-D Point Embedding for Anisotropic Surface Approximation from Unstructured Point Clouds

arXiv: https://arxiv.org/abs/2607.28855 · HTML: https://mlsanity.com/paper/2607.28855/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 76 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [ScanNet: Richly-annotated 3D Reconstructions of Indoor Scenes](https://mlsanity.com/paper/1702.04405/) (2017)
- [Fast Graph Representation Learning with PyTorch Geometric](https://mlsanity.com/paper/1903.02428/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Point Transformer V3: Simpler, Faster, Stronger](https://mlsanity.com/paper/2312.10035/) (2023)
- [Shape As Points: A Differentiable Poisson Solver](https://mlsanity.com/paper/2106.03452/) (2021)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation](https://mlsanity.com/paper/1908.01491/) (2019)
- [PCPNET: Learning Local Shape Properties from Raw Point Clouds](https://mlsanity.com/paper/1710.04954/) (2017)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [Surface Reconstruction from Point Clouds: A Survey and a Benchmark](https://mlsanity.com/paper/2205.02413/) (2022)
- [PointTriNet: Learned Triangulation of 3D Point Sets](https://mlsanity.com/paper/2005.02138/) (2020)
- [PoNQ: a Neural QEM-based Mesh Representation](https://mlsanity.com/paper/2403.12870/) (2024)
- [Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation](https://mlsanity.com/paper/2503.23670/) (2025)
- [Fast and Globally Consistent Normal Orientation based on the Winding Number Normal Consistency](https://mlsanity.com/paper/2405.16634/) (2024)
- [TetWeave: Isosurface Extraction using On-The-Fly Delaunay Tetrahedral Grids for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2505.04590/) (2025)
- [NASM: Neural Anisotropic Surface Meshing](https://mlsanity.com/paper/2410.23109/) (2024)

## Abstract (arXiv)

Dense 3D sensors in various real-world fields produce point clouds that are geometrically redundant for real-time processing. In this paper, we propose an efficient and scalable learning-based anisotropic surface approximation framework, HD-PEA, that operates directly on unstructured point clouds, integrating anisotropic optimization into reconstruction to produce compact, geometry-aligned surface representations with higher fidelity, fewer elements, and improved numerical stability compared to isotropic and adaptive meshes. Firstly, we develop a novel learning-based high-dimensional (high-d) Euclidean point embedding method to map the input point clouds into a high-d manifold embedding space. For handling large-scale point clouds without retraining and fine-tuning, a patch-based meta-embedding scheme is designed during the inference stage. Then, we develop a new tangent subspace estimation for the high-d embedding manifold approximation and anisotropic manifold reconstruction in high-d space. The main contribution of this work is to propose a scalable deep learning framework and a variety of datasets for constructing a high-d Euclidean point embedding space aimed to 3D anisotropic surface mesh approximation and Riemannian curvature tensor estimation from point clouds. We extensively evaluate our method against state-of-the-art surface reconstruction approaches using several datasets, such as Thingi10K dataset, AIM@SHAPE and Stanford 3D Scanning Repository, ScanNet dataset, and further demonstrate its generalization and usability on diverse unseen shapes and applications from these datasets.