RODR: Riemannian Orthogonally Decoupled Regularization for Disentangled Manifold Representation

2026-07-26

AI Summary

This work addresses the gradient interference caused by the coupling of geometric structure and point distribution objectives in point cloud denoising. To resolve this issue, we propose a Riemannian orthogonal decoupling regularization framework that explicitly separates normal-direction optimization (for geometric fitting) from tangential-direction optimization (for point distribution) for the first time. By leveraging a vector attention mechanism and an entropy-aware adaptive strategy, our method performs orthogonal decoupled optimization on a two-dimensional Riemannian manifold embedded in ℝ³. The approach achieves state-of-the-art denoising accuracy while significantly improving point distribution uniformity, effectively suppressing local clustering and better preserving fine geometric details.

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.

Problem

• point cloud denoising
• geometric gradient interference
• objective-geometry mismatch
• structural degradation
• point clustering

Innovation

• Riemannian manifold
• orthogonal decoupling
• geometric gradient interference
• point cloud denoising
• disentangled representation