首个均衡覆盖各类拓扑的3D表面数据集，助力机器学习识别复杂几何结构。
EuLearn: A 3D database for learning Euler characteristics
- 基于随机纽结构造可自缠绕的嵌入曲面，覆盖均匀变化的亏格类型。
- 原始神经网络在亏格分类任务上表现差，新采样方法提升性能显著。
- 专为图与流形数据设计非欧几里得采样，适合拓扑感知模型研究者。
我们提出EuLearn，首个均衡覆盖多种拓扑类型的表面数据集。通过基于随机纽结构建亏格均匀变化的嵌入曲面，使表面可自缠绕。EuLearn包含3D网格、点云和标量场的新拓扑数据集，旨在促进能识别拓扑特征的机器学习系统训练。我们测试了典型3D神经网络架构，发现其原始实现对亏格分类效果不佳。为此，我们开发了一种针对图与流形数据的新型非欧几里得统计采样方法，并提出基于该采样的邻接感知改进版PointNet与Transformer。结果表明，将拓扑信息融入深度学习流程可显著提升在这些高挑战性数据集上的表现。
原文摘要 · Abstract (English)
We present EuLearn, the first surface datasets equitably representing a diversity of topological types. We designed our embedded surfaces of uniformly varying genera relying on random knots, thus allowing our surfaces to knot with themselves. EuLearn contributes new topological datasets of meshes, point clouds, and scalar fields in 3D. We aim to facilitate the training of machine learning systems that can discern topological features. We experimented with specific emblematic 3D neural network architectures, finding that their vanilla implementations perform poorly on genus classification. To enhance performance, we developed a novel, non-Euclidean, statistical sampling method adapted to graph and manifold data. We also introduce adjacency-informed adaptations of PointNet and Transformer architectures that rely on our non-Euclidean sampling strategy. Our results demonstrate that incorporating topological information into deep learning workflows significantly improves performance on these otherwise challenging EuLearn datasets.
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