通过恢复几何测地距离，学习3D形状的内在表示。
From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data
- 基于测地距离重建学习形状的等距嵌入。
- 在测地距离预测和下游任务中表现优异。
- 适合需要理解形状本质拓扑的研究者。
几何分析从根本上区分了外在与内在视角。当前主流的3D表示学习方法依赖于外在空间结构或高层语义，难以捕捉形状身份的本质及底层流形拓扑。为此，我们提出一种新型3D表示学习范式PRISM（Pre-training via Recovering Intrinsic Surface Geodesic Metric），通过恢复内在表面测地度量来学习等距嵌入。PRISM引入拓扑约束目标，显式控制潜在空间结构，并采用两阶段训练策略缓解测地距离分布中的样本不平衡问题。实验表明，该方法在测地距离预测中具备良好准确率、鲁棒性和高效率，并在形状识别、表面参数化、非刚性对应等多种下游任务中取得优越性能。代码将公开于https://github.com/AidenZhao/PRISM。
原文摘要 · Abstract (English)
Geometric analysis fundamentally distinguishes between \textit{extrinsic} and \textit{intrinsic} 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 \textbf{PRISM}, for \textbf{P}re-training, which learns isometric embeddings by \textbf{R}ecovering the \textbf{I}ntrinsic \textbf{S}urface geodesic \textbf{M}etric. 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.
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