AI 中文总结
研究点云去噪中目标与几何不匹配问题，提出黎曼正交解耦正则化（RODR），通过解耦法向和切向分量重新制定优化轨迹，实验表明其性能与基线相当，能改善分布规律、减少局部聚集，建立了解缠几何优化框架。
AI 中文摘要
点云去噪本质上是一项几何恢复任务，旨在从有噪声的离散环境空间样本中重建嵌入在R^3中的光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示学习方面取得了显著进展，但一个基本的目标-几何不匹配问题仍未得到充分探索。理论上，这种不匹配的耦合会导致几何梯度干扰，使结构退化和点聚类。我们引入黎曼正交解耦正则化（RODR），通过解耦法向（拟合）和切向（分布）分量来重新制定优化轨迹。在向量注意力和熵感知自适应策略的引导下，RODR有效保留高保真几何细节并保持采样均匀性。实验表明，RODR性能与现有基线相当，有效改善了分布规律性并减少了局部聚集。我们的工作为点云处理中的解缠几何优化建立了一个通用且可解释的框架。
英文摘要
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.
Comments10 pages, 4 figures
