提出RODR方法，分离点云几何优化中的法向与切向成分，提升去噪质量。
RODR: Riemannian Orthogonally Decoupled Regularization for Disentangled Manifold Representation
- 通过黎曼正交解耦正则化分离法向拟合与切向分布优化
- 在多个数据集上实现与顶尖方法相当的去噪性能，减少局部聚集
- 适用于需要高保真几何重建的点云处理任务，如三维建模
点云去噪本质上是几何恢复任务，旨在从噪声离散的R³空间采样中重构嵌入其中的平滑二维黎曼流形的内在结构。尽管现代流形感知编码器和生成传输模型在几何表征学习方面取得显著进展，但一个根本性的目标-几何不匹配问题仍被忽视。理论上，我们发现这种耦合导致几何梯度干扰，冲突的优化目标引发结构退化与点聚集。本文提出黎曼正交解耦正则化（RODR），通过解耦法向（拟合）与切向（分布）分量来重构优化轨迹。基于向量注意力与熵感知自适应策略，RODR有效保留高保真几何细节并维持采样均匀性。实验表明，RODR性能接近当前最优基准，显著改善分布规律性并降低局部聚集。本工作建立了点云处理中可解释的解耦几何优化通用框架。
原文摘要 · Abstract (English)
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.
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