RODR: Riemannian Orthogonally Decoupled Regularization for Disentangled Manifold Representation
2026-07-27 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors studied the problem of cleaning up 3D point clouds, which are noisy samples of smooth surfaces. They found that mixing different goals during optimization causes issues like distorted shapes and points bunching together. To fix this, they proposed a method called RODR that separates the fitting of the shape and how points are spread out, using a smart attention strategy. Their experiments show this method keeps shapes accurate and points evenly distributed, matching top-performing techniques. This work offers a clear way to improve 3D point cloud denoising by separating geometric aspects during learning.
point cloud denoisingRiemannian manifoldgeometric gradient interferencenormal and tangential componentsvector-attentionentropy-aware regularizationsampling uniformitygeometric optimizationdisentangled learningambient space
Authors
Jiayu Zhu, Wenlai Zhao
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.