Single-step map Plug-and-Play point cloud denoising method

Abstract

The invention belongs to the technical field of three-dimensional point cloud processing and graph signal processing, and particularly relates to a single-step graph Plug-and-Play point cloud denoising method, which comprises the following steps of S1, point cloud input and graph construction; s2, carrying out pre-filtering on a multi-graph shift operator Chebyshev (Chebyshev); s3, realizing global near-end mapping based on positive definite and positive semidefinite Laplacian; s4, denoising is carried out on the local 1-Lipschitz patch; and S5, single-step fixed point updating and residual constraint are carried out. According to the method, by constructing a graph structure with a multi-graph shift operator Chebyshev pre-filtering, learning a positive-definite and positive-semidefinite graph Laplacian operator and a patch denoising network meeting 1-Lipschitz constraint, point cloud denoising can be completed by updating a fixed point once, the calculation overhead is remarkably reduced while the denoising precision is ensured, and the method has a relatively good market application prospect.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional point cloud processing and graph signal processing technology, specifically relating to a single-step graph plug-and-play point cloud denoising method. Background Technology

[0002] 3D point clouds are fundamental data representations for robot mapping, localization, manipulation, and 3D reconstruction, and are typically acquired by sensors such as LiDAR, structured light, and Time-of-Flight (TOF) depth cameras. In actual data acquisition, point clouds are inevitably affected by Gaussian noise, non-Gaussian noise, and outliers, which reduces the accuracy and robustness of subsequent modules such as registration, SLAM, and target recognition. Therefore, high-quality denoising before the point cloud enters subsequent geometry or learning modules remains essential.

[0003] Existing point cloud denoising methods can be broadly categorized into geometric model-based and learning model-based methods. Geometric model-based methods, such as local surface fitting methods based on point set surfaces and moving least squares (MLS), achieve smoothing by fitting a surface within a local neighborhood and then projecting the points back onto the surface. These methods are simple to implement and highly interpretable, but they tend to over-smooth in regions with high curvature or strong noise, smoothing out sharp edges. Graph filtering methods treat point clouds as graph signals, constructing an adjacency graph of the point cloud and performing low-pass or bilateral filtering in the graph domain to achieve a trade-off between noise suppression and structure preservation. However, traditional graph filtering still involves a trade-off between "denoising and detail preservation," the filtering parameters are difficult to adjust adaptively, and its ability to preserve complex structures in high-noise scenarios is limited.

[0004] Deep learning-based point cloud denoising methods typically employ patch regression networks, normalized flow models, latent space denoising networks combining invertible networks and graph convolutions, multi-step iterative filtering networks, and path-selective denoising networks. These methods can achieve high recovery accuracy through multi-layer feature extraction and nonlinear transformations, but they generally suffer from problems such as complex network structures, large number of parameters, high FLOPs and memory overhead, large inference latency, and a lack of strict non-extensibility constraints.

[0005] The Plug-and-Play / Regularization-by-Denoising (PnPRED) framework offers a compromise by treating the denoiser as a proximal operator in the optimization process. If the data terms are convex and the denoiser is a non-expanding map, the existence and convergence of fixed points can be theoretically guaranteed. However, existing point cloud denoising schemes based on PnP or RED suffer from several drawbacks. First, the graph Laplacian may not guarantee positive definiteness or semi-positive definiteness, leading to a non-strictly convex energy function. Second, the denoising network typically does not constrain the Lipschitz constant, potentially amplifying high-frequency noise or causing instability under strong noise. Furthermore, most implementations still require multiple iterations of the proximal operator, resulting in high overall computational latency.

[0006] Therefore, existing technologies struggle to simultaneously achieve the following while ensuring that the surface geometry and sharp structure are not compromised: theoretically supported global stability, low latency from single-step or fixed-step inference, and high accuracy and good generalization ability across various noise levels.

[0007] Glossary : Point cloud: A data set consisting of several three-dimensional points, each point containing at least three-dimensional coordinate information; A graph is a structure consisting of a set of vertices V and a set of edges E, used to represent the adjacency relationships between vertices. Graph Laplacian operator L: A matrix constructed from the edge weights of the graph, used to measure the smoothness of a graph signal on the graph. Positive definite semi-positive definite (PSD) Laplace: A graph Laplace matrix in which all eigenvalues ​​are greater than or equal to zero, used to ensure the convexity of the energy function and the stability of optimization. Graph shift operator: A linear operator that enables the propagation of first-order neighborhood information on a graph, such as a Laplace matrix or a normalized adjacency matrix; Chebyshev graph filtering: A type of graph filtering method that uses Chebyshev polynomials to approximate frequency domain filters, which can achieve local graph filtering without explicit eigenvalue decomposition; Plug-and-Play / Regularization-by-Denoising (PnPRED): An optimization framework that treats the denoiser as a regularization operator or a proximal operator, and achieves reconstruction by iteratively or step-by-step calling of the denoiser; 1-Lipschitz denoiser: A denoising operator with a Lipschitz constant no greater than 1, which does not amplify input perturbations and helps to ensure the non-extensibility and stability of the overall mapping; Conjugate Gradient (CG): An iterative method for solving symmetric positive definite linear equation systems, applicable to sparse Laplace linear systems.

[0008] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0009] The purpose of this invention is to provide a single-step graph plug-and-play point cloud denoising method. By constructing a graph structure with Chebyshev pre-filtering and multi-graph shift operator, learning a positive definite and semi-positive definite graph Laplacian operator, and a patch denoising network that satisfies 1-Lipschitz constraints, point cloud denoising can be completed with a single fixed-point update, significantly reducing computational overhead while ensuring denoising accuracy.

[0010] To achieve the above objectives, the present invention provides the following technical solution: A single-step plug-and-play point cloud denoising method includes the following steps: S1. Point cloud input and graph construction; Obtain a noisy 3D point cloud y; based on a preset neighborhood size parameter, search for nearest neighbors for each point and construct an undirected graph G of mutual nearest neighbors; S2, Chebyshev pre-filtering with multi-image shift operator; Construct at least two different graph shift operators based on graph G; For each graph shift operator S_k, a Chebyshev polynomial filter of a preset order is used to perform graph filtering on the point cloud coordinates to obtain several pre-filtered features. The pre-filtered features obtained from different graph shift operator branches are concatenated in the channel dimension and projected onto a unified feature space through linear mapping or a lightweight network to obtain the pre-filtered graph signal y0. S3. Implement global proximal mapping based on positive definite and semi-positive definite Laplace; For each edge (i,j) in graph G, construct edge features and input them into the edge weight generation network to obtain non-negative edge weights. ; By the right Construct the graph Laplace operator L, and use a positive definite and semi-positive definite construction method. This ensures that the eigenvalues ​​of L are non-negative; A linear system is constructed using the Laplacian operator L, and an iterative solver is used to solve it, yielding a globally smoothed intermediate result z. S4, local 1-Lipschitz patch noise reduction; For each point, a local patch containing the point and its neighboring points is extracted from the graph G. The patch coordinates, normals and pre-filtered features are combined to form a patch feature vector, which is then input into a patch denoising network D(·) that satisfies the 1-Lipschitz constraint to obtain a local denoising output D(z) for the globally smooth intermediate point cloud z. S5. Single-step fixed-point update and residual constraints; The globally smoothed intermediate point cloud z is combined with the patch denoising result D(z) using a convex combination to obtain the intermediate denoised point cloud after a single-step update. ; Then, the residual is limited according to the displacement between the input point cloud y and x^(1) to obtain the final output point cloud x.

[0011] Preferably, the noisy 3D point cloud y obtained in S1 contains N 3D points, each of which contains at least 3D coordinates; the expression for the undirected graph G constructed based on the point cloud is as follows: G = (V, E); Where V = {1,2,…,N} is the set of vertices; E is the set of edges.

[0012] As a preferred method, in S1, the normal and curvature of each point are estimated based on local principal component analysis, and edges that are too long or cross high curvature discontinuities are eliminated to avoid incorrectly connecting different object surfaces.

[0013] As a preferred embodiment, the expression for the linear system constructed in S3 using the Laplace operator L is as follows: ; Where L is a positive definite semi-positive definite matrix; I is an N×N identity matrix; λ represents the graph regularization coefficient, which is a real number greater than 0.

[0014] As a preferred option, the intermediate denoised point cloud obtained in S5 after a single-step update. The calculation formula is as follows: ; in, α represents the intermediate denoising result after a single-step update; α represents the fusion coefficient, with a value range of [0,1]; z represents the globally smooth intermediate point cloud obtained by solving the Laplacian near-end map; D(·) is a local patch denoising network used to denoise the local neighborhood patches of the input point cloud and output the denoising result; D(z) represents the local denoising result obtained by inputting the globally smooth intermediate point cloud z into D(·).

[0015] As a preferred option, the formula for calculating the final output point cloud x obtained in S5 is as follows: ; Where x represents the final denoised point cloud; y represents the input noisy point cloud, containing N 3D points; clip(·) is the clipping function. -y, -δ, δ) represents the vector Each dimension of y is clipped to the interval [-δ, δ]; δ represents the residual limiting threshold, which is used to limit the maximum magnitude of the updated residual.

[0016] Compared with the prior art, the present invention has the following beneficial effects: (1) The single-step graph plug-and-play point cloud denoising method of the present invention constructs a graph structure that is close to each other, and combines distance and curvature thresholds to remove long sides that cross different objects or discontinuous surfaces, so that the graph structure can more accurately reflect local geometric relationships, which is beneficial to suppressing noise while maintaining the edges and thin structure.

[0017] (2) The single-step graph Plug-and-Play point cloud denoising method of the present invention performs Chebyshev graph filtering based on at least two different graph shift operators, and splices the multi-channel filtering results and then projects them onto a unified feature space. In single-step calculation, it captures both low-frequency smoothing trends and mid-frequency geometric details, which can improve the suppression capability of different noise frequency bands.

[0018] (3) The single-step graph plug-and-play point cloud denoising method of the present invention, by representing the Laplacian as... The form is used, and B is constructed based on the non-negative weights output by the edge weight generation network, such that L is positive definite and semi-positive definite, thereby ensuring that the energy function constructed based on L is a convex function and a linear system. It can be solved stably.

[0019] (4) The single-step spectral plug-and-play point cloud denoising method of the present invention applies spectral norm constraints to the linear layers of the patch denoising network and penalizes the Jacobian norm during the training phase, thereby controlling the Lipschitz constant of the network to a range not greater than 1, so that the mapping corresponding to the network is a non-expanding mapping, which is beneficial to maintaining the overall non-expanding property after being combined with the Laplacian near-end mapping.

[0020] (5) The single-step graph plug-and-play point cloud denoising method of the present invention obtains the single-step update result by convexly combining the global Laplacian near-end result with the local patch denoising result, and limits the amplitude of the update residual, so that denoising can be completed with only one linear system solution and one network forward propagation, which significantly reduces the computational overhead and improves stability while ensuring geometric accuracy. Attached Figure Description

[0021] Figure 1This is a flowchart of the single-step graph plug-and-play point cloud denoising method of the present invention, showing the processing modules from noisy point cloud input to denoised point cloud output; Figure 2 This is a schematic diagram of the point cloud map construction module of the present invention, showing the mutual nearest neighbor relationship, normal / curvature estimation and edge culling strategy; Figure 3 This is a schematic diagram of the multi-graph shift Chebyshev pre-filtering module of the present invention, showing the splicing and projection process of different graph shift operator branches and their output features; Figure 4 This is a schematic diagram of the single-step convex combination module of Laplace proximal mapping and patch denoising of the present invention, showing the process of solving the linear system, patch extraction and denoising, and residual limiting output. Detailed Implementation

[0022] The technical solution of this invention patent will be clearly and completely described below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without inventive effort are within the scope of protection of this invention.

[0023] In the description of this invention, it should be noted that the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the invention.

[0024] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to a connection within two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0025] See attached document Figure 1-4 A single-step plug-and-play point cloud denoising method includes the following steps: Step S1: Point cloud input and graph construction; Obtain a noisy 3D point cloud y, which contains N 3D points, each of which contains at least 3D coordinates; Based on the preset neighborhood size parameter, the nearest neighbors of each point are retrieved, and an undirected graph G of mutual neighbors is constructed; the expression of the undirected graph G is as follows: G = (V, E); Where V = {1,2,…,N} is the set of vertices; E is the set of edges; Optionally, based on local principal component analysis, the normal and curvature of each point are estimated, and edges that are too long or cross high curvature discontinuities are removed to avoid incorrectly connecting different object surfaces; Step S2: Chebyshev pre-filtering using multi-image shift operator; Construct at least two different graph shift operators based on graph G, such as the normalized Laplacian operator, its powers, and the normalized adjacency matrix; For each graph shift operator S_k, a Chebyshev polynomial filter of a preset order is used to perform graph filtering on the point cloud coordinates to obtain several pre-filtered features. The pre-filtered features obtained from different graph shift operator branches are concatenated in the channel dimension and projected onto a unified feature space through linear mapping or a lightweight network to obtain the pre-filtered graph signal y0. Step S3: Implement global proximal mapping based on positive definite and semi-positive definite Laplace; For each edge (i,j) in graph G, construct edge features and input them into the edge weight generation network to obtain non-negative edge weights. (i,j) represents an undirected edge in graph G connecting vertex i and vertex j. By the right Construct the graph Laplace operator L, and use a positive definite and semi-positive definite construction method. This ensures that the eigenvalues ​​of L are non-negative; A linear system can be constructed using the Laplace operator L, expressed as follows: ; Where L is a positive definite semi-positive definite matrix; I is an N×N identity matrix; λ represents the graph regularization coefficient, which is a real number greater than 0; The intermediate result z after global smoothing is obtained by using iterative solvers such as the conjugate gradient method. Step S4: Local 1-Lipschitz patch denoising; For each point, a local patch containing the point and its neighboring points is extracted from the graph G. The patch coordinates, normals and pre-filtered features are combined to form a patch feature vector, which is then input into a patch denoising network D(·) that satisfies the 1-Lipschitz constraint to obtain a local denoising output D(z) for the globally smooth intermediate point cloud z. During the training phase, the patched denoising network controls the Lipschitz constant to be no greater than 1 through spectral norm constraints and Jacobi norm penalties, thus allowing it to be regarded as a non-extended mapping during the inference phase. In an alternative implementation, the above process can be represented as a composite mapping: , in, Extract operators for patches. Denoising the patched network; Step S5: Single-step fixed-point update and residual constraints; The globally smoothed intermediate point cloud z is combined with the patch denoising result D(z) using a convex combination to obtain the intermediate denoised point cloud after a single-step update. The calculation formula is as follows: ; in, denoises the intermediate denoising result after a single-step update; α represents the fusion coefficient, with a value range of [0,1]; z represents the globally smoothed intermediate point cloud obtained by solving the Laplacian near-end map; D(·) is a local patch denoising network used to denoise the local neighborhood patches of the input point cloud and output the denoising result; D(z) represents the local denoising result obtained by inputting the globally smoothed intermediate point cloud z into D(·); Then, the residual is limited based on the displacement between the input point cloud y and x^(1) to obtain the final output point cloud x. The calculation formula is as follows: ; Where x represents the final denoised point cloud, which serves as the denoising result of this invention; y represents the input noisy point cloud, containing N three-dimensional points; clip(·) is the clipping function, clip( -y, -δ, δ) represents the vector Each dimension of y is clipped to the interval [-δ, δ]; δ represents the residual limiting threshold, which is used to limit the maximum magnitude of the updated residual.

[0026] Example 1 : Noise reduction of point clouds in offline 3D models; In this embodiment, the input point cloud is derived from a publicly available 3D model benchmark dataset, and each model is subjected to simulated noise addition at multiple noise levels.

[0027] First, each 3D model is resampled into a point cloud with a fixed number of points, and then centered and scaled. Independent Gaussian noise is added to each point according to a preset noise standard deviation to obtain a noisy point cloud y.

[0028] Then, the single-step map plug-and-play point cloud denoising method of the present invention is executed according to steps S1 to S5, and the denoised point cloud x is output; Finally, the denoising quality was evaluated using metrics such as Chamfer distance, point-to-plane error, and normal deviation.

[0029] Experiments show that, with the same or lower computational overhead, the geometric accuracy of the method of this invention is superior to that of complex deep network methods using multi-step iterations.

[0030] Example 2 Denoising of point clouds in LiDAR scenes; In this embodiment, the input point cloud comes from an outdoor scene collected by a vehicle-mounted LiDAR.

[0031] During the graph construction phase, sensor features such as point reflection intensity and scan line number can be used as part of the edge features to improve the sensitivity of the graph structure to differences in scene geometry and materials. Local patch features can be overlaid with time frame index or trajectory information of corresponding points in historical frames to enhance robustness against dynamic objects and severe weather noise. During the training phase, synthetic noise or registered near-clean frames can be constructed as supervision signals, and the single-step graph plug-and-play framework described in this invention is still used for training and inference.

[0032] Experiments show that this embodiment can effectively suppress sensing noise and preserve details such as road boundaries and building corners in complex outdoor scenes, providing more stable geometric input for subsequent SLAM and target detection.

[0033] The single-step graph plug-and-play point cloud denoising method of this invention achieves point cloud denoising with a single fixed-point update by constructing a graph structure with pre-filtering by the multi-graph shift operator Chebyshev, learning a positive definite and semi-positive definite graph Laplacian operator, and a patch denoising network satisfying 1-Lipschitz constraints. This significantly reduces computational overhead while maintaining denoising accuracy. In addition, this invention combines the positive definite and semi-positive definite Laplacian near-end mapping with the 1-Lipschitz patch denoiser in a convex combination, so that the overall mapping is theoretically non-expanded, which improves the stability of point cloud denoising on different noise levels and different datasets, and avoids numerical divergence and error amplification caused by unconstrained deep networks or normalization flow.

[0034] This invention also provides a highly efficient point cloud denoising module that can be directly embedded into application scenarios such as robot mapping, 3D reconstruction, and point cloud registration. While maintaining geometric accuracy no less than that of complex iterative methods, it achieves low FLOPs and low memory usage, making it suitable for deployment on resource-constrained platforms.

[0035] The single-step graph plug-and-play point cloud denoising method of this invention can be used in conjunction with various existing point cloud preprocessing, registration, and 3D reconstruction algorithms. Furthermore, the graph construction strategy, patch feature selection, and training loss function can be appropriately adjusted according to specific application scenarios. Without departing from the core idea of ​​this invention, any equivalent substitutions or combinations of specific network structures, solver implementations, loss weights, etc., should be considered to fall within the protection scope of this invention.

[0036] The foregoing description of specific exemplary embodiments of the invention is for illustrative and explanatory purposes. These descriptions are not intended to limit the invention to the precise forms disclosed, and it will be apparent that many changes and variations can be made in accordance with the foregoing teachings. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application, thereby enabling those skilled in the art to implement and utilize various different exemplary embodiments of the invention, as well as various different choices and variations. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. A single-step plug-and-play point cloud denoising method, characterized in that, Includes the following steps: S1. Point cloud input and graph construction; Obtain a noisy 3D point cloud y; based on a preset neighborhood size parameter, search for nearest neighbors for each point and construct an undirected graph G of mutual nearest neighbors; S2, Chebyshev pre-filtering with multi-image shift operator; Construct at least two different graph shift operators based on graph G; For each graph shift operator S_k, a Chebyshev polynomial filter of a preset order is used to perform graph filtering on the point cloud coordinates to obtain several pre-filtered features. The pre-filtered features obtained from different graph shift operator branches are concatenated in the channel dimension and projected onto a unified feature space through linear mapping or a lightweight network to obtain the pre-filtered graph signal y0. S3. Implement global proximal mapping based on positive definite and semi-positive definite Laplace; For each edge (i,j) in graph G, construct edge features and input them into the edge weight generation network to obtain non-negative edge weights. ; By the border Construct the graph Laplace operator L, and use a positive definite and semi-positive definite construction method. This ensures that the eigenvalues ​​of L are non-negative; A linear system is constructed using the Laplacian operator L, and an iterative solver is used to solve it, yielding a globally smoothed intermediate result z. S4, local 1-Lipschitz patch noise reduction; For each point, a local patch containing the point and its neighboring points is extracted from the graph G. The patch coordinates, normals and pre-filtered features are combined to form a patch feature vector, which is then input into a patch denoising network D(·) that satisfies the 1-Lipschitz constraint to obtain a local denoising output D(z) for the globally smooth intermediate point cloud z. S5. Single-step fixed-point update and residual constraints; The globally smoothed intermediate point cloud z is combined with the patch denoising result D(z) using a convex combination to obtain the intermediate denoised point cloud after a single-step update. ; Then, the residual is limited according to the displacement between the input point cloud y and x^(1) to obtain the final output point cloud x.

2. The single-step map plug-and-play point cloud denoising method according to claim 1, characterized in that, The noisy 3D point cloud y obtained in S1 contains N 3D points, each of which contains at least 3D coordinates; the expression for the undirected graph G constructed based on the point cloud is as follows: G = (V, E); Where V = {1,2,…,N} is the set of vertices; E is the set of edges.

3. The single-step map plug-and-play point cloud denoising method according to claim 1, characterized in that, In S1, the normal and curvature of each point are estimated based on local principal component analysis. Edges that are too long or cross high curvature discontinuities are removed to avoid incorrect connections between different object surfaces.

4. The single-step map plug-and-play point cloud denoising method according to claim 1, characterized in that, The expression for the linear system constructed using the Laplace operator L in S3 is as follows: ； Where L is a positive definite semi-positive definite matrix; I is an N×N identity matrix; λ represents the graph regularization coefficient, which is a real number greater than 0.

5. The single-step map plug-and-play point cloud denoising method according to claim 1, characterized in that, The intermediate denoised point cloud obtained after a single-step update in S5 The calculation formula is as follows: ； in, α represents the intermediate denoising result after a single-step update; α represents the fusion coefficient, with a value range of [0,1]; z represents the globally smooth intermediate point cloud obtained by solving the Laplacian near-end map; D(·) is a local patch denoising network used to denoise the local neighborhood patches of the input point cloud and output the denoising result; D(z) represents the local denoising result obtained by inputting the globally smooth intermediate point cloud z into D(·).

6. The single-step map plug-and-play point cloud denoising method according to claim 5, characterized in that, The formula for calculating the final output point cloud x obtained in S5 is as follows: ； Where x represents the final denoised point cloud; y represents the input noisy point cloud, containing N 3D points; clip(·) is the clipping function. -y, -δ, δ) represents the vector Each dimension of -y is clipped to the interval [-δ, δ]; δ represents the residual limiting threshold, used to limit the maximum magnitude of the updated residual.

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