Title: Transitioning from Extrinsic to Intrinsic: Geodesic-Driven Representation Learning for 3D Geometric Data

Abstract:

Geometric analysis is fundamentally characterized by the distinction between extrinsic and intrinsic viewpoints. Current 3D representation learning predominantly relies on either extrinsic spatial configurations or high-level semantic features, a approach that often fails to capture the core essence of shape identity and the underlying manifold topology. To address this limitation, we propose a novel representation learning framework called PRISM (Pre-training via Recovery of the Intrinsic Surface geodesic Metric). This method learns isometric embeddings by explicitly recovering the intrinsic surface geodesic metric. PRISM integrates a topology-enforcing objective that strictly constrains latent space structure, complemented by a specialized two-stage training strategy designed to mitigate the sample imbalance typically found in geodesic distance distributions. Experimental results indicate that our method delivers satisfactory accuracy, robustness, and high efficiency in predicting geodesic distances. Furthermore, it achieves superior performance across a variety of downstream applications, such as shape recognition, surface parameterization, and non-rigid correspondence. The source code will be made publicly available at https://github.com/AidenZhao/PRISM.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC