# RODR: Riemannian Orthogonally Decoupled Regularization for Disentangled Manifold Representation

arXiv: https://arxiv.org/abs/2607.23958 · HTML: https://mlsanity.com/paper/2607.23958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 40 references that are in the map.
- First posted on arXiv 27 Jul 2026.

## Builds on (most cited first, 21 of 21)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Point Transformer](https://mlsanity.com/paper/2011.00931/) (2020)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Gradient Fields for Shape Generation](https://mlsanity.com/paper/2008.06520/) (2020)
- [PointCleanNet: Learning to Denoise and Remove Outliers from Dense Point Clouds](https://mlsanity.com/paper/1901.01060/) (2019)
- [Score-Based Point Cloud Denoising](https://mlsanity.com/paper/2107.10981/) (2021)
- [Equivariant Point Network for 3D Point Cloud Analysis](https://mlsanity.com/paper/2103.14147/) (2021)
- [Pointfilter: Point Cloud Filtering via Encoder-Decoder Modeling](https://mlsanity.com/paper/2002.05968/) (2020)
- [IterativePFN: True Iterative Point Cloud Filtering](https://mlsanity.com/paper/2304.01529/) (2023)
- [Deep Point Set Resampling via Gradient Fields](https://mlsanity.com/paper/2111.02045/) (2021)
- [3DMambaIPF: A State Space Model for Iterative Point Cloud Filtering via Differentiable Rendering](https://mlsanity.com/paper/2404.05522/) (2024)
- [3D Point Cloud Denoising via Deep Neural Network based Local Surface Estimation](https://mlsanity.com/paper/1904.04427/) (2019)
- [PD-Flow: A Point Cloud Denoising Framework with Normalizing Flows](https://mlsanity.com/paper/2203.05940/) (2022)
- [P2P-Bridge: Diffusion Bridges for 3D Point Cloud Denoising](https://mlsanity.com/paper/2408.16325/) (2024)
- [PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering](https://mlsanity.com/paper/2209.00798/) (2022)
- [Manifold Fitting under Unbounded Noise](https://mlsanity.com/paper/1909.10228/) (2019)
- [Noise2Score3D: Tweedie's Approach for Unsupervised Point Cloud Denoising](https://mlsanity.com/paper/2503.09283/) (2025)
- [Adaptive and Iterative Point Cloud Denoising with Score-Based Diffusion Model](https://mlsanity.com/paper/2509.14560/) (2025)

## Abstract (arXiv)

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.