用于非结构化点云各向异性曲面逼近的高维点嵌入学习流形
Learning Manifolds in High-D Point Embedding for Anisotropic Surface Approximation from Unstructured Point Clouds
- Wayne State University（韦恩州立大学）
- Texas A&M University（德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出HD-PEA框架，通过高维点嵌入等技术实现非结构化点云的各向异性曲面逼近，在多数据集上验证了其泛化性与可用性，性能优于现有方法。
AI中文摘要：
各类实际领域的密集3D传感器生成的点云存在几何冗余，难以实时处理。本文提出一种高效可扩展的基于学习的非结构化点云各向异性曲面逼近框架HD-PEA，直接在非结构化点云上操作，将各向异性优化融入重建，生成与几何对齐的紧凑曲面表示，相比各向异性网格和自适应网格，具有更高保真度、更少元素和更好数值稳定性。首先，开发一种新型基于学习的高维欧氏点嵌入方法，将输入点云映射到高维流形嵌入空间；为处理无需重新训练和微调的大规模点云，推理阶段设计了基于块的元嵌入方案。然后，开发一种新的切子空间估计方法，用于高维嵌入流形逼近和高维空间中的各向异性流形重建。本工作的主要贡献是提出一种可扩展深度学习框架和多种数据集，用于构建面向3D各向异性曲面网格逼近和从点云估计黎曼曲率张量的高维欧氏点嵌入空间。使用Thingi10K数据集、AIM@SHAPE、斯坦福3D扫描库、ScanNet数据集等多个数据集，对该方法与最先进的曲面重建方法进行了广泛评估，并进一步证明了其在这些数据集的各类未见形状和应用上的泛化性和可用性。
英文摘要：
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.
