Point Cloud Denoising: Methods & Trends

• Point Cloud Denoising is the process of cleaning raw, unordered point cloud data by removing sensor and environmental noise while preserving underlying geometric structures.
• It typically involves a two-step approach—outlier removal followed by surface noise restoration—utilizing both classical geometric methods and modern deep learning techniques such as graph convolution and transformer-based modules.
• Key challenges include handling diverse noise types, maintaining fine details and sharp edges, and ensuring computational efficiency, with performance measured by metrics like Chamfer Distance and AUPR.

Searching arXiv for recent and representative point cloud denoising papers and surveys. arXiv search query: point cloud denoising survey 2025 score graph transformer I’m unable to invoke the arXiv search tool in this interface, so I will ground the article strictly in the provided arXiv records and cite them directly. Point cloud denoising (PCD) is a fundamental problem aiming to recover clean point sets while preserving underlying structures, because raw point clouds acquired in real-world environments are often corrupted with noise due to various factors such as sensor, lighting, material, environment etc, which reduces geometric fidelity and degrades downstream performance (Wang et al., 23 Aug 2025). A complementary survey formulates PCD as a two-step process—outlier removal and surface noise restoration—encompassing most scenarios and requirements of PCD (Zhang et al., 16 Aug 2025). Across the literature, denoising is treated both as a preprocessing stage for downstream tasks such as surface reconstruction and analysis, and as a geometric inference problem in which noise suppression must be balanced against preservation of sharp features, edges, and fine geometric details (Cheng et al., 2017).

1. Problem formulation, task structure, and taxonomies

Point clouds are unordered, irregular, and lack explicit structure, unlike images or grids, making direct application of convolutional operations non-trivial (Wang et al., 23 Aug 2025). The surveys identify several recurring challenges: diversity of noise types and modalities, balancing denoising with feature preservation, data and supervision limitations, and computational efficiency and scalability (Zhang et al., 16 Aug 2025). Real-world noise includes surface noise, outliers, sensor artifacts, occlusion-induced gaps, and non-uniform densities, while many learning systems are trained primarily on synthetic perturbations (Wang et al., 23 Aug 2025).

Within the two-step formulation, outlier removal identifies and removes points significantly deviating from the underlying surface, while surface noise restoration relocates remaining noisy points to their true positions on the underlying surface (Zhang et al., 16 Aug 2025). Surface noise restoration is further divided into edge-aware denoising, which emphasizes preservation of sharp geometric features and edges, and precise surface recovery, which focuses on accurate surface localization and uniformity (Zhang et al., 16 Aug 2025). The same survey distinguishes point-level and patch-level paradigms: point-level denoising uses local neighborhoods for each point, whereas patch-level denoising operates on overlapping patches and captures larger context (Zhang et al., 16 Aug 2025).

A second taxonomy organizes deep learning PCD methods from two perspectives: supervision level and modeling perspective (Wang et al., 23 Aug 2025).

Perspective	Categories	Meaning
Supervision level	Supervised; Unsupervised	Require paired noisy-clean data; or denoise without access to clean ground-truth
Modeling perspective	Reconst.; Displ.; Distrib.; Filter; Classif.	Reconstruction-Based; Displacement-Based; Distribution-Based; Filter-Based; Classification-Based

This taxonomy suggests that “point cloud denoising” is not a single algorithmic family but a collection of formulations spanning regression, filtering, density modeling, manifold regularization, and classification. A plausible implication is that comparisons across papers are often controlled as much by the assumed noise process and supervision regime as by network architecture.

2. Classical geometric and non-learning foundations

Early non-learning approaches are strongly geometric. “Density-based Denoising of Point Cloud” first uses particle-swam optimization technique for automatically approximating optimal bandwidth of multivariate kernel density estimation, then mean-shift based clustering technique to remove outliers through a thresholding scheme, and finally bilateral mesh filtering to smooth the remaining points (Zaman et al., 2016). In this pipeline, outlier suppression and surface smoothing are explicitly separated rather than learned jointly.

“Denoising a Point Cloud for Surface Reconstruction” introduces a three-stage procedure: octree-based clustering for outlier and white noise removal, statistical pruning for removing high noise perturbation, and meshless Laplacian smoothing on a sparser representative point set (Cheng et al., 2017). Its noise model explicitly includes white noise, clustered outliers, and noisy perturbation, and its design avoids surface normal estimation or implicit surface fitting (Cheng et al., 2017). The method is framed as a practical precursor to downstream reconstruction codes, especially when contamination is too severe for native reconstruction pipelines.

A more formal patch-manifold view appears in “3D Point Cloud Denoising using Graph Laplacian Regularization of a Low Dimensional Manifold Model” (Zeng et al., 2018). There, each surface patch is treated as a vector in $\mathbb{R}^{3k}$, self-similar patches are connected in a graph, and the low-dimensional manifold prior is approximated by a patch-based graph Laplacian regularizer (Zeng et al., 2018). The denoising objective is stated as

$$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$

and the graph regularizer admits a graph spectral interpretation as low-pass graph spectral filtering (Zeng et al., 2018). The same paper emphasizes that the combinatorial Laplacian preserves constant signal, which is used to explain preservation of flat surfaces and edges (Zeng et al., 2018).

“Point cloud denoising based on tensor Tucker decomposition” extends non-local patch processing by representing local surface patches as matrices, stacking similar aligned patches into a $3$rd order tensor, compressing that tensor with Tucker decomposition, applying hard thresholding in the core tensor, and averaging overlapping estimates after reconstruction (Li et al., 2019). The paper reports that the proposed algorithm outperforms the state-of-the-art graph Laplacian regularized (GLR) algorithm when the Gaussian noise is high $(\sigma=0.1)$, and that GLR is better in lower noise cases $(\sigma=0.04, 0.05, 0.08)$ (Li et al., 2019). This explicit trade-off remains characteristic of classical denoisers: stronger non-local aggregation can dominate under heavy noise, while more precise geometric modeling can dominate at lower noise.

3. Graph, patch, and non-local deep denoising

Deep learning-based PCD models are described as surpassing traditional methods in denoising performance because of strong representation capabilities and flexible architectures (Zhang et al., 16 Aug 2025). Among early graph-based systems, “Learning Graph-Convolutional Representations for Point Cloud Denoising” proposes GPDNet, a deep, fully-convolutional neural network based on graph-convolutional layers that dynamically constructs neighborhood graphs from similarity among the high-dimensional feature representations of the points (Pistilli et al., 2020). The model is fully-convolutional rather than patch-based, uses residual blocks and dynamic graph construction in feature space, and couples denoising with a surface proximity regularization term that encourages denoised points to lie close to the underlying surface (Pistilli et al., 2020).

“Non-Local Part-Aware Point Cloud Denoising” shifts emphasis from local neighborhoods to inherent non-local self-similarity in 3D objects and scenes (Huang et al., 2020). Its non-local learning unit is customized with a graph attention module to adaptively capture non-local semantically-related features over the entire point cloud, and the loss combines a conventional surface reconstruction loss with a semantic part loss so that denoising is performed in a part-aware manner (Huang et al., 2020). This framework directly addresses the limitation, noted repeatedly in the literature, that strictly local processing may miss repeated structures or semantically related regions.

Patch-based learning remains central. “MODNet: Multi-offset Point Cloud Denoising Network Customized for Multi-scale Patches” extracts low-level feature of three scales patches, embeds multi-scale geometric information for each scale feature, regresses multi-scale weights, and predicts the final displacement by adaptively weighting three scale-specific offsets (Huang et al., 2022). The paper attributes remnant noise and wrongly-removed geometric details to simple aggregation of extracted multi-scale features and argues for point-wise adaptive scale selection, especially for points close to edges and points on complex curved surfaces (Huang et al., 2022). Visualizations of adaptive weights confirm that edge points receive higher weights for medium or large scales, while smooth regions favor small-scale information (Huang et al., 2022).

“Point Cloud Denoising and Outlier Detection with Local Geometric Structure by Dynamic Graph CNN” combines denoising and outlier detection in a two-stage pipeline mirroring PointCleanNet: an outlier detector followed by a denoiser (Nakayama et al., 2023). Its main intervention is to explicitly encode local geometric structure with two types of graph convolutional layer designed based on the Dynamic Graph CNN: dynamic neighborhood graph construction in every layer, and a fixed graph built in a lower-dimensional feature space and propagated backward through each layer (Nakayama et al., 2023). Experimental results show that the proposed methods outperform the conventional method in AUPR, which indicates outlier detection accuracy, and Chamfer Distance, which indicates denoising accuracy; the static graph variant provides a trade-off, matching accuracy but offering faster computation (Nakayama et al., 2023).

4. Score fields, distribution learning, and unsupervised inference

A major conceptual shift treats denoising as ascent in a learned probability field. “Score-Based Point Cloud Denoising” models the noisy point cloud distribution as

$$q(x) := (p * n)(x) = \int_{\mathbb{R}^3} p(y)n(x-y)\,dy,$$

and interprets denoising as maximizing $\log q(x)$ by iterative updates

$x^{(t+1)} = x^{(t)} + \alpha_t \bar{s}_i(x^{(t)}),$

where the score $\nabla_x \log q(x)$ is estimated by a neural network (Luo et al., 2021). The method uses dynamically-connected graph convolutional layers for feature extraction and demonstrates potential to be applied in other tasks such as point cloud upsampling (Luo et al., 2021).

“Point Cloud Denoising via Momentum Ascent in Gradient Fields” identifies a specific weakness of iterative gradient-field denoisers: the predicted gradient could fluctuate, leading to perturbed and unstable solutions, as well as a long inference time (Zhao et al., 2022). Its remedy is momentum gradient ascent, which leverages the information of previous iterations in determining the trajectories of the points, improving the stability of the solution and reducing the inference time (Zhao et al., 2022). The paper explicitly contrasts its 15 denoising steps with 30 in the baseline (Zhao et al., 2022).

Temporal coherence is exploited in “Dynamic Point Cloud Denoising via Gradient Fields” (Hu et al., 2022). There, the gradient field is the gradient of the log-probability function of the noisy point cloud, and denoising proceeds by gradient ascent; for dynamic clouds, temporally corresponding patches are searched by treating each patch as a rigid object moving in the gradient field of an adjacent frame until the sum of gradients over the patch reaches $0$ (Hu et al., 2022). After correspondence, the temporal gradient field is averaged from current and adjacent frames. This suggests that dynamic PCD is not merely frame-wise denoising with temporal post-processing, but a correspondence problem embedded in the denoising field itself.

Distribution learning also appears outside score matching. “PD-Flow: A Point Cloud Denoising Framework with Normalizing Flows” formulates the denoising process from the perspective of distribution learning and feature disentanglement, viewing noisy point clouds as a joint distribution of clean points and noise and using normalizing flows to model the mapping between Euclidean and latent spaces (Mao et al., 2022). Noise disentanglement is then performed in latent space rather than by direct point-wise correction (Mao et al., 2022).

A fully unsupervised variant is “Noise2Score3D: Unsupervised Tweedie’s Approach for Point Cloud Denoising” (Wei, 24 Feb 2025). For Gaussian noise, it uses Tweedie’s formula

$$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$0

and performs single-step inference as

$$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$1

after learning the score function from noisy data alone (Wei, 24 Feb 2025). The same work introduces Total Variation for Point Cloud,

$$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$2

as a criterion for estimating unknown noise parameters (Wei, 24 Feb 2025). The paper reports a $$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$3x–$$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$4x speedup over competing iterative approaches (Wei, 24 Feb 2025). More recently, “Adaptive and Iterative Point Cloud Denoising with Score-Based Diffusion Model” proposes estimating the noise variation of a given noisy point cloud and determining an adaptive denoising schedule with appropriate step sizes before iterative score-based updates (Wang et al., 18 Sep 2025).

5. Geometry-aware preservation of normals, edges, and structure

A persistent theme in the literature is that effective denoising is not equivalent to aggressive smoothing. “GeoGCN: Geometric Dual-domain Graph Convolution Network for Point Cloud Denoising” formalizes this by defining two kinds of surface normals: Real Normal (RN), which preserves the local details of noisy point clouds, and Virtual Normal (VN), which avoids the global shape shrinkage during denoising (Chen et al., 2022). GeoGCN first regresses point positions by spatialbased GCN with the help of VNs, then estimates initial RNs by performing Principal Component Analysis on the regressed points, and finally regresses fine RNs by normalbased GCN (Chen et al., 2022). The paper positions local detail preservation and global shape preservation as separate but coupled constraints.

“PCDNF: Revisiting Learning-based Point Cloud Denoising via Joint Normal Filtering” casts denoising as a multitask problem in which point cloud denoising and normal filtering are optimized together (Liu et al., 2022). Its auxiliary normal filtering task is intended to help the overall network remove noise more effectively while preserving geometric features more accurately, while the shape-aware selector constructs a latent tangent space representation of the specific point by comprehensively considering the learned point and normal features and geometry priors (Liu et al., 2022). The feature refinement module then fuses point and normal features, motivated by the claim that point features are more suitable for describing geometric details and normal features are more conducive for representing geometric structures such as sharp edges and corners (Liu et al., 2022).

Transformer-based denoising is represented by “NoiseTrans: Point Cloud Denoising with Transformers” (Hou et al., 2023). The model uses transformer encoder architecture, obtains structural similarity of point-based point clouds with the assistance of the transformer's core self-attention mechanism, and introduces Local Point Attention to prevent the point cloud from being over-smooth (Hou et al., 2023). It also proposes sparse encoding so that the Transformer can better perceive the structural relationships of the point cloud and improve denoising performance on unordered point sets (Hou et al., 2023).

These designs collectively address a common misconception: that geometric fidelity is adequately captured by point-wise proximity alone. The literature repeatedly adds normals, tangent spaces, adaptive multi-scale context, or attention-based structural cues precisely because proximity-only objectives can produce remnant noise, wrongly-removed geometric details, global shape shrinkage, or over-smoothing (Huang et al., 2022).

6. Evaluation practice, applications, and current research directions

Evaluation protocols in PCD are heterogeneous but recurrent. Chamfer Distance (CD) is widely used for denoising accuracy, Point-to-Mesh Distance (P2M) for surface-wise deviation, and Mean Square Error (MSE) for coordinate error (Wei, 24 Feb 2025). In dynamic settings, Hausdorff Distance (HD) is also reported (Hu et al., 2022). For outlier removal, AUPR is used as Area Under Precision-Recall curve (Nakayama et al., 2023), while some real-time denoisers also report Precision, Recall, F1 Score, and Peak Signal-to-Noise Ratio (PSNR) (Zhang et al., 11 Dec 2025). This metric diversity reflects the dual role of PCD as both geometric restoration and outlier discrimination.

The application range in the cited literature is broad: surface reconstruction and analysis (Luo et al., 2021), immersive telepresence, autonomous driving, and surveillance for dynamic point clouds (Hu et al., 2022), as well as robotics, augmented reality, and real-world LiDAR scenes (Wang et al., 23 Aug 2025). The DGCNN-based outlier detector-denoiser explicitly links local geometric reasoning to downstream tasks like segmentation, surface reconstruction, and 3D understanding (Nakayama et al., 2023). A plausible implication is that method selection depends on whether downstream sensitivity is dominated by topology, boundary preservation, temporal consistency, or runtime.

Efficiency and scalability remain active concerns. The static-graph variant in the DGCNN outlier-denoising framework speeds up per-point computation by $$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$5 relative to dynamic computation and is able to denoise $$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$6 million points $$\min_{\mathbf{U}} \int_\mathcal{M} \mathrm{dim}(\mathcal{M}(\mathbf{U}))(\mathbf{p})\,d\mathbf{p} + \lambda \|\mathbf{V} - \mathbf{U}\|_F^2,$$7 seconds faster (Nakayama et al., 2023). “Adaptive Dual-Weighted Gravitational Point Cloud Denoising Method” approaches the problem without learning, combining octree-based spatial partitioning, adaptive voxel-based occupancy statistics, k-nearest neighbor density estimation, and a density-distance dual-weighted gravitational scoring function; it reports consistent improvements in F1, PSNR, and Chamfer Distance while reducing the single-frame processing time in multi-noise scenarios (Zhang et al., 11 Dec 2025). Such results indicate that real-time or near-real-time denoising remains a competitive design objective alongside accuracy.

The 2025 surveys identify several open challenges that organize current work: irregular and unstructured data, complex noise patterns, preservation of fine structures, non-uniform densities and outliers, lack of clean ground-truth, and computational efficiency and scalability (Wang et al., 23 Aug 2025). They also emphasize real-world generalization, because many methods rely on synthetic datasets while real-world noise distributions differ from standard synthetic noise (Zhang et al., 16 Aug 2025). In that sense, contemporary PCD research increasingly converges on hybrid priorities: outlier removal plus surface restoration, local geometry plus non-local context, and learned statistical fields plus explicit geometric constraints.