Routing on Demand: DSNet for Efficient Progressive Point Cloud Denoising

Conference: CVPR 2026
Paper: CVF Open Access
Code: https://github.com/cz-61/DSNet
Area: 3D Vision / Point Cloud Denoising
Keywords: Point cloud denoising, Progressive denoising, Dynamic routing, Normal similarity, Adaptive skip connections

TL;DR

DSNet (Dynamic Skip Net) is a "Routing on Demand" progressive point cloud denoising framework. It employs a normal similarity-based noise discriminator to quantify the noise intensity of each local patch, which is then mapped by an anti-monotonic decision function to an appropriate denoising module entry. This allows clean regions to skip redundant denoising while noisy regions receive sufficient refinement, achieving a superior balance between denoising quality and computational efficiency.

Background & Motivation

Background: Point cloud denoising is a crucial preprocessing step for 3D perception. Deep learning methods have evolved from single-stage (one-pass forward) to progressive/iterative approaches (multi-step refinement, e.g., IterativePFN using weight-sharing modules), which generally outperform traditional geometric fitting methods.

Limitations of Prior Work: Regardless of being single-stage or progressive, mainstream frameworks adopt a rigid pipeline—applying a uniform denoising strategy to all regions (either a single forward pass or a fixed sequence of multi-stage refinement). This "one-size-fits-all" approach ignores the spatial non-uniformity of real-world noise, where sensor Gaussian noise, environmental outliers, and geometric distortions often coexist with varying intensities.

Key Challenge: Fixed paths lead to both over-smoothing in clean areas (erasing fine-grained geometric details) and insufficient refinement in heavily noisy areas. Simultaneously, they generate redundant computation for low-noise regions, compromising both fidelity and efficiency.

Goal: To enable the network to perceive local noise intensity and dynamically plan the denoising iteration path for each patch accordingly. The core problem addressed is: "Can a network dynamically allocate computation by planning optimal paths area-wise?"

Key Insight: The authors observe through experiments that the angular deviation of surface normals between noisy and clean point clouds is highly correlated with the degree of geometric degradation. Thus, normal deviation can serve as a noise proxy to guide adaptive inference.

Core Idea: Quantify degradation using a normal similarity discriminator, map the continuous noise score to discrete module entries using an anti-monotonic decision function, and implement cross-stage skips via a path-selection iterative mechanism. Clean patches skip directly to late-stage fine-tuning modules, while heavily noisy patches follow the complete denoising trajectory.

Method

Overall Architecture

Given a noisy point cloud \(\hat{P}\), DSNet first selects center points via Farthest Point Sampling (FPS) and constructs local patches using K-Nearest Neighbors (KNN) with \(k=1000\). Each patch enters a "Routing on Demand" loop: the noise discriminator computes a normal similarity factor \(\rho\) \(\rightarrow\) the decision function \(\lambda(\rho)\) maps it to a discrete module index (higher noise leads to an earlier entry) \(\rightarrow\) the selected U-Net denoising module refines the patch \(\rightarrow\) noise is re-evaluated, and the next stage entry is re-planned. This "Assessment-Selection-Execution" cycle repeats for a fixed number of times, and the trajectory need not be sequential (intermediate modules can be skipped), transforming traditional static progressive networks into an adaptive system. Training follows the IterativePFN approach, assigning progressively denoised intermediate ground truths to each iterative module.

graph TD
    A["Noisy Point Cloud P̂<br/>Segmented via FPS+KNN into local patches"] --> B["Normal Similarity Noise Discriminator<br/>DGCNN computes ρ ∈ (0,1]"]
    B --> C["Anti-monotonic Decision Function λ(ρ)<br/>Maps to module entry index tk"]
    C --> D["U-Net Iterative Denoising Module Net_tk<br/>NAA encoding + Multi-head cross-attention decoding"]
    D --> E{"Residual noise still high?"}
    E -->|Yes, Re-evaluate| B
    E -->|No, Skip intermediate modules| F["Denoised Point Cloud Output P_out"]

Key Designs

1. Normal Similarity Noise Discriminator: Quantifying Local Geometric Degradation via Normal Angular Deviation

Addressing the issue that networks cannot perceive local noise intensity, the authors define a normal similarity factor \(\rho=\frac{1}{n}\sum_{i=1}^{n}\exp(-\theta_i^4/\gamma)\), based on the observation that the angular deviation between noisy and clean normals is strongly correlated with degradation. Here, \(\theta_i=\arccos(n_{clean,i}\cdot n_{noisy,i})\) is the angle between the clean and noisy normals of the \(i\)-th point, \(n\) is the number of points in the patch, and \(\gamma\) controls sensitivity to noise deviation. The quartic term \(\theta_i^4\) amplifies the penalty for large angular deviations, making \(\rho\in(0,1]\) robust to small perturbations but sensitive to significant structural distortion (\(\rho\) closer to 0 indicates higher noise). The discriminator is implemented using EdgeConv layers of DGCNN: it first builds a k-NN graph, uses multi-layer EdgeConv to iteratively update node features via dynamic adjacency, concatenates cross-layer features into a point-level representation, and finally predicts \(\rho\) via global pooling followed by an MLP.

2. Anti-monotonic Decision Function \(\lambda(\rho)\): Mapping Continuous Noise Scores to Discrete Module Entries

With \(\rho\) obtained, it must be mapped to a discrete module index within \([N_{min}, L]\). The mapping must satisfy three criteria: anti-monotonicity (low \(\rho \rightarrow\) high noise \(\rightarrow\) earlier, more aggressive stages), non-linear sensitivity (finer granularity in high-noise zones, less sensitivity in low-noise zones), and bounded integer output. The authors design \(\lambda(\rho)=\text{clip}\big(\text{round}(L-\frac{(L-N_{min})\log(\beta\rho+1)}{\log(\beta+1)}),N_{min},L\big)\). The core is the logarithmic term \(\frac{\log(\beta\rho+1)}{\log(\beta+1)}\): as \(\rho\to0\) (highly noisy), the numerator tends to 0 and the ratio maximizes, pushing \(\lambda(\rho)\) towards \(N_{min}\) and forcing the patch through the full denoising trajectory. As \(\rho\to1\) (clean), the ratio approaches 1, making \(\lambda(\rho)\approx L\) and allowing the patch to skip most denoising steps. The hyperparameter \(\beta\) controls curvature: larger \(\beta\) increases non-linearity/granularity in high-noise regions (\(\rho \approx 0\)), while smaller \(\beta\) distributes patches more uniformly across modules.

3. Path-Selection Iterative Mechanism (Dynamic Skip): Per-stage Re-evaluation and Re-planning for Cross-stage Skips

This is the core distinction between DSNet and fixed cascades (\(Net_1\to Net_2\to\dots\to Net_L\)). The \(k\)-th iteration consists of three steps: (1) State Assessment—the current patch \(P_{k-1}\) is fed into the discriminator to compute \(\rho_{k-1}\); (2) Module Selection—\(t_k=\lambda(\rho_{k-1})\), with the constraint \(t_k\in\{t_{k-1}+1,\dots,L\}\) to ensure monotonic progress; (3) Module Execution—\(P_k=Net_{t_k}(P_{k-1})\). The cycle repeats for a fixed \(K_{total}\) iterations. A trajectory might look like \(P_{input}\xrightarrow{Net_2}P_1\xrightarrow{Net_5}P_2\xrightarrow{Net_7}\dots\xrightarrow{Net_L}P_{output}\), effectively skipping intermediate modules like \(\{Net_3, Net_4, Net_6\}\). This non-sequential routing enables dense multi-stage refinement for noisy, complex regions while bypassing unnecessary processing for clean, simple regions.

4. U-Net Iterative Denoising Module: Neighborhood Attention Encoding + Multi-head Cross-attention Decoding

Each denoising module is a hierarchical U-Net. The encoder uses two consecutive Neighborhood Attention Aggregations (NAA) with MLP residual connections in each layer: \(f_l=\text{MLP}([\text{NAA}(f^0_{l-1}),\text{NAA}^2(f^0_{l-1})])+\text{MLP}(f_{l-1})\), with the point set downsampled via FPS. The decoder uses distance-weighted interpolation for upsampling followed by Multi-head Cross-attention (MHCA) for cross-layer fusion: \(h_{l-1}=\text{MLP}([\text{MHCA}(\phi(f_{l-1}),\phi(\tilde{h}_l)),f_{l-1}])\), balancing global context with local structural details. The module also adaptively decides the number of encoder-decoder layers based on the estimated noise intensity.

Loss & Training

Training assigns progressively denoised intermediate ground truths \(P_{gt_i}=P+\sigma_i\xi,\ \xi\sim\mathcal{N}(0,I)\) to each iteration step, with the noise standard deviation decaying as \(\sigma_i=\sigma_{i-1}/\gamma\) (\(\gamma=16/L\)). The single-step loss is \(L_k=L_{cd}(P_k,P_{gt_k})+L_{disp}(P_{k-1},P_{gt_k},P_k)\), where \(L_{cd}\) is the Chamfer Distance between the prediction and target, and the displacement loss \(L_{disp}=\|(P_k-P_{k-1})-P_{nearest}\|_2\) (where \(P_{nearest}\) is the displacement vector from \(P_{k-1}\) to its nearest neighbor in \(P_{gt_k}\)). The total loss aggregates all intermediate losses with equal weight: \(L=\sum_{k=1}^{K_{total}}L_k\), ensuring consistent supervision and stable optimization from coarse to fine stages. The noise discriminator is independently pre-trained first to obtain a stable noise feature extractor, which then guides the joint optimization of DSNet to improve convergence speed and stability.

Key Experimental Results

Main Results

Training is conducted on the PU-Net dataset (40 meshes, Poisson disk sampling at 10K/30K/50K, Gaussian noise at 0.05–0.2 times the bounding sphere radius). The table below shows results on the PU-Net test set (CD and P2M are multiplied by \(10^4\), lower is better):

Setup	Metric	DSNet	ASDN	IterativePFN	3DMambaIPF
10K, 1%	CD↓	1.829	1.871	2.055	1.989
10K, 2.5%	CD↓	2.604	2.697	3.352	3.262
50K, 2%	CD↓	0.603	0.721	0.802	0.755
50K, 2.5%	CD↓	0.762	0.850	1.015	0.928
50K, 2.5%	P2M↓	0.514	0.575	0.588	0.531

Note: CD = Chamfer Distance; P2M = Point-to-Mesh Distance. Both are geometric fidelity metrics where lower values are better.

Real-world scanning data (Kinect, limited quantitative evaluation due to lack of ground truth; Paris-Rue-Madame qualitative only):

Dataset	Metric	DSNet	P2P-Bridge	IterativePFN	3DMambaIPF
Kinect	CD↓	1.040	0.974	0.993	1.008
Kinect	P2M↓	0.885	0.854	0.867	0.883

DSNet achieves SOTA on synthetic data but is only comparable to peers on real Kinect scans (slightly trailing P2P-Bridge). The authors acknowledge that cross-domain generalization still has room for improvement.

Ablation Study

Comparison of stage count \(L\) and Dynamic vs. Static paths (PU-Net, CD↓, selected):

Configuration	10K, 1% CD↓	50K, 2.5% CD↓	Description
DSNet-2 (Dynamic)	1.919	0.868	2 stages
DSNet-Static-2	1.914	0.975	Fixed path, 2 stages
DSNet-4 (Dynamic, Final)	1.829	0.762	Optimal configuration
DSNet-Static-4	1.897	1.017	Fixed path, 4 stages
DSNet-5 (Dynamic)	1.847	0.816	Degradation with excessive depth

Key Findings

• Performance improves as stage count \(L\) increases from 2 to 4 (deeper \(\rightarrow\) more effective coarse-to-fine refinement), but \(L=5\) shows a slight drop (likely due to over-smoothing or error accumulation). \(L=4\) is chosen.
• Dynamic paths consistently outperform static variants. In low-noise cases, skipping redundant stages avoids over-smoothing. In high-noise cases, it remains robustly superior (e.g., DSNet-Static-4 actually worsened to CD 1.017 on 50K/2.5%, whereas the dynamic version reached 0.762).
• Synthetic-to-Real Domain Gap: Improvements on real scans are less pronounced than on synthetic data, indicating cross-domain generalization as a future research direction.

Highlights & Insights

• "Routing on Demand" upgrades progressive denoising from a "fixed pipeline" to an "adaptive path per patch." This directly improves upon fixed cascades like IterativePFN. The core insight is that since noise is spatially non-uniform, computation should be allocated as needed.
• Using normal angular deviation as a noise proxy is clever: normals are sensitive to geometric degradation and allow for residual noise assessment during inference without ground truth. The \(\rho\) design (quartic + exponential) balances robustness to small jitters with sensitivity to major distortions.
• The anti-monotonic logarithmic decision function provides an interpretable and adjustable (via \(\beta\)) closed-form mapping from continuous scores to discrete modules, avoiding the need for an additional learned router and maintaining engineering simplicity.
• The monotonic constraint \(t_k\in\{t_{k-1}+1,\dots,L\}\) ensures the process always moves forward, allowing skip connections to save computation while guaranteeing convergence. This "skip-to-save" design is transferable to other progressive refinement tasks like iterative image or depth restoration.

Limitations & Future Work

• Weak generalization to real scans: Performance on Kinect is only on par with SOTA and slightly behind P2P-Bridge.
• The discriminator relies on the quality of normal estimation, which can be inaccurate for noisy point clouds. (Note: The specific implementation of obtaining "clean normals" for \(\theta_i\) computation during inference is not fully detailed in the summary).
• Requires independent pre-training of the noise discriminator before joint training, adding an extra step compared to end-to-end methods. The cost of tuning multiple hyperparameters (\(\gamma,\beta,N_{min},L,K_{total}\)) is not systematically analyzed.
• Evaluation is primarily on PU-Net synthetic noise plus two real scan sets. Noise types are still dominated by Gaussian, with limited validation against structured noise or sparse outliers.

Related Work & Insights

• vs. IterativePFN (Direct Comparison): Both use progressive iterative denoising and intermediate ground truth supervision. IterativePFN enforces a fixed sequence for all patches, risking over-smoothing; DSNet uses a discriminator + decision function to implement non-sequential skips, customizing the path based on patch noise.
• vs. Single-stage Methods (PD-Flow / ASDN / Score-Denoise): Single-stage methods lack adaptability to non-uniform noise. DSNet's multi-stage dynamic routing shows significant advantages in high-resolution/high-noise scenarios (e.g., 50K/2.5% CD 0.762 vs. ASDN 0.850).
• vs. RL-based Routing: Some related works explore reinforcement learning for routing. DSNet replaces learned policies with a geometry-driven normal similarity proxy and a closed-form decision function, offering better interpretability and training stability.

Rating

• Novelty: ⭐⭐⭐⭐ "Routing on demand + cross-stage skips" is a clear new paradigm in point cloud denoising. The normal similarity proxy and anti-monotonic decision function are well-conceived.
• Experimental Thoroughness: ⭐⭐⭐⭐ Comprehensive on synthetic multi-resolution/noise levels and dynamic vs. static ablation, though quantitative results on real scans and hyperparameter sensitivity analysis are relatively sparse.
• Writing Quality: ⭐⭐⭐⭐ Motivation, the three-step routing loop, and formula derivations are clearly explained with intuitive illustrations.
• Value: ⭐⭐⭐⭐ Achieves a better balance between quality and efficiency with practical significance for 3D perception preprocessing; the skip-connection logic is transferable.

Related Papers

• [ICML 2026] SIMPC: Learning Self-Induced Mirror-Point Consistency for Unsupervised Point Cloud Denoising
• [ICCV 2025] Noise2Score3D: Tweedie's Approach for Unsupervised Point Cloud Denoising
• [CVPR 2026] MHopReg: Efficient Hierarchical Multi-Hop Graph Search for Point Cloud Registration
• [ECCV 2024] P2P-Bridge: Diffusion Bridges for 3D Point Cloud Denoising
• [CVPR 2026] SuP: Sub-cloud Driven Point Cloud Registration