RODR: Riemannian Orthogonally Decoupled Regularization for Disentangled Manifold Representation

arXiv:2607.23958v1 Announce Type: new Abstract: Point cloud denoising is essentially a geometric recovery task that aims to reconstruct the intrinsic structure of a smooth 2D Riemannian manifold embedded in R^3 from noisy, discrete ambient-space samples. Despite the remarkable progress of modern manifold-aware encoders and generative transport models in geometric representation learning, a fundamental objective-geometry mismatch remains underexplored. Theoretically, we identified that this mismatched coupling leads to geometric gradient interference, where conflicting optimization objectives result in structural degradation and point clustering. We introduce Riemannian Orthogonally Decoupled Regularization (RODR) to reformulate the optimization trajectory by disentangling the normal (fitting) and tangential (distribution) components. Guided by a vector-attention and entropy-aware adaptive strategy, RODR effectively preserves high-fidelity geometric details while maintaining sampling uniformity. Experiments demonstrate that RODR reaches performance comparable to state-of-the-art baselines and suggests improved distribution regularity and reduced local aggregation effectively. Our work establishes a generic and interpretable framework for disentangled geometric optimization in point cloud processing.

Related

• Beyond Defenses: Manifold-Aligned Regularization for Intrinsic 3D Point Cloud Robustness
• PointCHR: Point Cloud Analysis via Curvature-Aware Hyperbolic Rectification
• From Extrinsic to Intrinsic: Geodesic-Guided Representation Learning for 3D Geometric Data

Source: arXiv cs.CV | 2026-07-28