From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data
2026-06-01 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors introduce PRISM, a new way to teach computers about 3D shapes by focusing on their internal geometry rather than just their outer form or labels. Their method learns how distances work along the surface of shapes, preserving important shape features and the space's structure. They created a training process that deals with uneven data to improve learning. Tests show PRISM predicts these surface distances well and helps with tasks like recognizing shapes and matching points on flexible surfaces.
Geometric analysisExtrinsic vs. intrinsic geometry3D representation learningIsometric embeddingsSurface geodesic metricLatent spaceTopologyShape recognitionSurface parameterizationNon-rigid correspondence
Authors
Yuming Zhao, Junhui Hou, Qijian Zhang, Jia Qin, Ying He
Abstract
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.