Efficient graph conditional reversible flow method and system for scalable point cloud denoising

Abstract

The present application relates to the technical field of point cloud denoising, and particularly relates to an efficient graph conditional reversible flow method and system for scalable point cloud denoising, comprising the following steps: step 1: obtaining a point cloud to be denoised and constructing initial point cloud features; step 2: constructing a shared graph context; step 3: constructing a lightweight dual-frequency graph conditional representation and generating a phased injection feature; step 4: constructing a graph residual conditional enhanced reversible flow model and performing a reversible transformation; step 5: performing reasoning path alignment residual distillation and obtaining a fast reasoning path; step 6: adopting a cache reuse reasoning strategy to reorganize a complete denoised point cloud. By introducing a graph residual conditional mechanism and a lightweight dual-frequency graph conditional modeling module into the reversible flow backbone, the local neighborhood structure, low-frequency surface structure and high-frequency detail residual information are jointly involved in point cloud latent space modeling, and the geometric consistency and detail preservation capability in the point cloud denoising process are improved.

Description

Technical Field

[0001] This invention relates to the field of point cloud denoising technology, specifically to an efficient graph-conditional reversible flow method and system for scalable point cloud denoising. Background Technology

[0002] In recent years, 3D point clouds, as an important data form for describing the spatial geometry of objects and scenes, have been widely used in fields such as 3D reconstruction, autonomous driving, robot perception, industrial inspection, digital twins, and scene understanding. Point clouds are typically acquired by LiDAR, depth cameras, 3D scanners, or multi-sensor systems. However, during actual acquisition, factors such as sensor accuracy, environmental occlusion, multipath reflection, object material, uneven sampling density, and complex weather conditions often result in point cloud data containing random noise, outliers, local perturbations, and structural errors. This noise can disrupt the local surface structure and geometric continuity of the point cloud, affecting the stability and accuracy of subsequent tasks such as registration, segmentation, recognition, reconstruction, and measurement. Therefore, how to remove noise while preserving the true geometric structure and local details of the point cloud is a crucial problem in the field of 3D point cloud processing.

[0003] Current existing technologies related to point cloud denoising methods include: Invention Patent Publication No.: CN122048708A, titled: A Three-Dimensional Point Cloud Denoising Method, Apparatus, Device, and Storage Medium. This patent performs local normal estimation on each point in the three-dimensional point cloud to be filtered, obtains the nearest neighbor of the query point based on a KD tree, calculates the joint weighted distance based on the normal vectors of the query point and its neighbors, and then determines and removes outliers based on local statistical indicators and a global threshold. This method can improve the accuracy of outlier detection by combining geometric distance and normal difference, but it mainly relies on local statistical rules and threshold determination. Its modeling ability for complex noise distributions, large-scale dense point clouds, and non-outlier surface disturbances is limited, and it is difficult to fully learn deep geometric priors in the point cloud. The invention patent publication number is CN122023176A, titled "A Deep Learning-Based Method and System for Denoising 3D Point Clouds." This patent uses dynamic edge convolution and attention enhancement to encode local features of the original 3D point cloud, extracts global features through multi-scale parallel processing, and fuses the multi-scale local and global features for decoding to predict the residual displacement vector to obtain the denoised point cloud. While this method can enhance the representation of local and global features using a deep learning model, it is essentially still a feedforward displacement regression framework. It mainly corrects the position of points through residual displacement and lacks a reversible mapping mechanism to model the relationship between noisy observations and the potential clean geometric distribution. Furthermore, multi-scale neighborhood search, dynamic edge convolution, and attention enhancement introduce additional computational overhead, leaving room for improvement in inference efficiency in scenarios with large point counts or densely sampled point clouds. The invention patent publication number is CN122049386A, entitled "A Collaborative Sensing Method, Device, and Electronic Equipment Based on Multi-Model Fusion Denoising." This patent addresses vehicle-road cooperative sensing scenarios under complex meteorological conditions. It performs semantic cognitive analysis on the raw point cloud data and meteorological information of multiple sensing nodes based on a first model. Then, based on a second model and the semantic cognitive results, it performs spatial and frequency domain denoising on the point cloud. Finally, it fuses the denoised point clouds from multiple sensing nodes to generate semantic-level collaborative sensing results. This method can improve the perception effect of multi-node point cloud fusion and complex meteorological environments by combining semantic information. However, its focus is on multi-sensor node collaborative fusion and meteorological semantic-assisted denoising, rather than efficient geometric recovery modeling for a single large-scale point cloud. Its processing flow involves multi-model analysis, joint spatial and frequency domain processing, and multi-node fusion, which may result in high system complexity and high real-time inference costs in general point cloud denoising tasks.

[0004] In summary, current technical solutions have the following limitations: 1) Local statistical or threshold determination methods rely on manual rules and local geometric indicators, making it difficult to adapt to fine-grained surface perturbations in complex noise and densely sampled point clouds; 2) While deep learning-based direct regression methods can learn point cloud features, they typically lack reversible transformation mechanisms, making it difficult to fully preserve geometric information during denoising; 3) Existing graph structure or multi-scale feature modeling methods increase the computational overhead of neighborhood search, feature aggregation, and attention, easily leading to high memory usage and latency in large-scale point cloud inference; 4) Existing methods rarely consider local graph structure modeling, latent space noise decoupling, inference path acceleration, and result reorganization efficiency simultaneously, making it difficult to balance denoising quality, geometric detail preservation, and inference efficiency in scenarios with large point counts or dense sampling.

[0005] Therefore, it is necessary to propose an efficient graph-conditional reversible flow method and system for scalable point cloud denoising. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, the present invention aims to provide an efficient graph-conditional reversible flow method and system for scalable point cloud denoising. This method introduces a graph residual conditionalization mechanism and a lightweight dual-frequency graph conditional modeling module into the reversible flow backbone, enabling local neighborhood structures to participate in latent space modeling. Simultaneously, by combining inference path-aligned residual distillation and cached reuse inference strategies, the implicit solution overhead and redundant computation in large-scale point cloud denoising are reduced, thereby improving inference efficiency while maintaining denoising quality and geometric details.

[0007] The technical solution of the present invention is as follows:

[0008] This invention provides an efficient graph-conditionally reversible flow method for scalable point cloud denoising, comprising the following steps:

[0009] Step 1: Obtain noisy point cloud Initial point cloud features are generated through point feature embedding;

[0010] Step 2: Construct a global shared graph context based on the point cloud geometric space. The global shared graph context consists of a neighborhood index set and edge weights, which can be reused in the subsequent reversible flow module to avoid repeated graph construction.

[0011] Step 3: Based on the shared graph context, perform high- and low-frequency decomposition on the initial point cloud features, use neighborhood distance statistics to generate channel gating weights to adaptively suppress high-frequency noise components, and generate staged injection condition features corresponding to each reversible flow module through multi-stage residual edge convolution layer adaptation.

[0012] Step 4: Modulate point cloud features using staged injection conditional features, calculate local geometric graph residuals based on shared graph context, embed graph residuals into Lipschitz-constrained reversible branches to construct graph conditional reversible transformation functions, and stack multiple sets of enhanced reversible flow modules through forward and inverse pairwise reversible transformations to output point cloud denoising features.

[0013] Step 5: During the training phase, a numerical distillation loss for latent variables is constructed, and an amortized latent variable predictor is trained to replace the RootFind numerical solution. During the inference phase, the amortized predictor is used by default to generate latent variables, and fixed-point iterative correction is performed based on the predicted latent variables to construct a lightweight and fast inference path.

[0014] Step 6: Divide the complete point cloud and reassemble the complete denoised point cloud using a cache reuse inference strategy.

[0015] Furthermore,

[0016] Step 1: Obtain the point cloud to be denoised and construct the initial point cloud features. The specific steps are as follows:

[0017] Step 1.1: Obtain noisy point cloud As shown in equation (1):

[0018] (1)

[0019] in, Indicates the first A three-dimensional point, This indicates the number of points in the point cloud;

[0020] Step 1.2: Map the point coordinates to initial features using the point feature embedding function, as shown in equation (2):

[0021] (2)

[0022] in, Represents the point feature embedding function. Indicates the initial number of feature channels. This represents the initial point cloud features of the input reversible flow backbone.

[0023] Furthermore,

[0024] Step 2: Construct the shared graph context. The specific steps are as follows:

[0025] Step 2.1: For each point in the point cloud Search for it in the input geometric space The nearest neighbor points are then removed, and the center itself is removed to obtain the neighborhood set, as shown in equation (3):

[0026] (3)

[0027] in, Point The corresponding neighborhood index set;

[0028] Step 2.2: Calculate points Its neighboring points Euclidean distance between And calculate the average scale of the neighborhood distance of the point, as shown in Equation (4):

[0029] (4)

[0030] in, Point The local neighborhood scale;

[0031] Step 2.3: Generate normalized edge weights based on neighborhood distances, as shown in equation (5):

[0032] (5)

[0033] in, Point With neighboring points Normalized graph edge weights between them;

[0034] Step 2.4: Combine the neighborhood index set and edge weights into a shared graph context according to equation (6):

[0035] (6)

[0036] in, This represents a shared graph context; this shared graph context is reused in multiple subsequent enhanced reversible flow modules to avoid redundant graph construction.

[0037] Furthermore,

[0038] Step 3: Construct a lightweight bi-frequency graph conditional representation and generate staged injection features. The specific steps are as follows:

[0039] Step 3.1: Extract initial local graph features based on input point cloud and shared neighborhood relationships. As shown in equation (7):

[0040] (7)

[0041] in, This represents a local feature extraction function;

[0042] Step 3.2: Perform low-frequency structure aggregation on the initial local map features to obtain low-frequency structure features, as shown in Equation (8):

[0043] (8)

[0044] in, Point The low-frequency structural features are used to characterize the smooth structural trends of local surfaces;

[0045] Step 3.3: Construct high-frequency detail features based on the differences between the central features and the low-frequency structural features, as shown in Equation (9):

[0046] (9)

[0047] in, Point High-frequency detail features are used to characterize local high-frequency information such as edges, curvature changes, and noise disturbances;

[0048] Step 3.4: Generate channel-level gating weights based on neighborhood distance statistics, as shown in equations (10), (11), and (12):

[0049] (10)

[0050] (11)

[0051] (12)

[0052] in, and Representing points respectively The mean and variance of the neighborhood distance. This refers to a lightweight multilayer perceptron. Indicates channel-level gating weights;

[0053] Step 3.5: Utilize gated weights to modulate high-frequency detail features As shown in equation (13):

[0054] (13)

[0055] in, This represents channel-by-channel multiplication;

[0056] Step 3.6: Initial local map features Low-frequency structural characteristics and high-frequency detail features The fusion yields a shared dual-frequency conditional representation. As shown in equation (14):

[0057] (14)

[0058] in, This indicates a feature concatenation operation. Represents the feature fusion function;

[0059] Step 3.7: Using shared dual-frequency map conditions This represents the initial state, and the conditional features are updated stage by stage through residual edge convolution, as shown in Equation (15):

[0060] (15)

[0061] in, Indicates the first The input condition state at each stage, Indicates the first Residual edge convolution operation in each stage;

[0062] Step 3.8: Perform stage adaptation on the conditional states of each stage to generate the injection condition features of the corresponding enhanced reversible flow module, as shown in Equations (16) and (17):

[0063] (16)

[0064] (17)

[0065] in, Indicates the first Feature adaptation function for each stage Indicates the first Each stage undergoes a stage adaptation function. The intermediate stage representation obtained later. Indicates the first Adaptive convolution function for each stage, This represents the stage weight prediction function. Indicates the first Learnable scaling parameters for each stage Indicates the first Injection condition characteristics of an enhanced reversible flow module.

[0066] Furthermore,

[0067] Step 4: Construct a graph residual conditional enhanced reversible flow model and perform a reversible transformation. The specific steps are as follows:

[0068] Step 4.1: Add the staged injection conditional features to the current point cloud features to obtain the conditionally modulated input features. As shown in equation (18):

[0069] (18)

[0070] in, Indicates the first Midpoint of the reversible flow stage Input features, This indicates the corresponding staged injection condition features;

[0071] Step 4.2: Perform neighborhood weighted aggregation on the conditionally modulated input features based on the shared graph context to obtain local structural reference features, as shown in Equation (19):

[0072] (19)

[0073] in, Point In the The neighborhood weighted mean characteristics of each stage;

[0074] Step 4.3: Calculate the graph residual of the center point feature relative to the local structural reference feature, as shown in Equation (20):

[0075] (20)

[0076] in, Point In the Residual characteristics of the graph at each stage;

[0077] Step 4.4: Embed the graph residual into the Lipschitz branch of the implicit invertible block to obtain the graph-conditional Lipschitz transformation function, as shown in equation (21):

[0078] (twenty one)

[0079] in, Indicates the first The graphical conditional Lipschitz transform function for each stage. Indicates the original Lipschitz branch. Represents the projection function of the graph residual. This represents the scaling factor of the graph residual branch. Represents the hidden variables in an implicitly invertible block. Indicates a shared graph context;

[0080] Step 4.5: Perform a forward invertible transformation according to the graph-conditional Lipschitz transform function to map the noisy features to the latent representation, as shown in equations (22) and (23):

[0081] (twenty two)

[0082] (twenty three)

[0083] in, Indicates the first Hidden variables in the forward transformation of each stage Indicates the first Output characteristics after each stage of forward transformation;

[0084] Step 4.6: Perform the inverse reversible transformation according to the graph-conditional Lipschitz transform function to recover the latent representation into denoised features, as shown in equations (24) and (25):

[0085] (twenty four)

[0086] (25)

[0087] in, Indicates the first Hidden variables in the inverse transformation of each stage Indicates the first Output characteristics of an enhanced reversible flow module;

[0088] Step 4.7: Repeat steps 4.1 to 4.6 in sequence. An enhanced reversible flow module is used to obtain the final denoising features. As shown in equation (26):

[0089] (26)

[0090] in, Indicates the first Individual graph residual conditionalization enhanced reversible flow module This indicates a module concatenation operation. This represents the initial point cloud features before being input into the first enhanced reversible flow module. Indicates a shared graph context. Indicates the number of stages. A sequence representing the conditional features of all stages;

[0091] Furthermore,

[0092] Step 5: Perform inference path alignment, residual distillation, and obtain a fast inference path. The specific steps are as follows:

[0093] Step 5.1: During the training phase, the teacher's latent variables are obtained by exact implicit solution, and the forward and backward latent variables are predicted by the amortized predictor, as shown in equations (27) and (28):

[0094] (27)

[0095] (28)

[0096] in, and They represent the first Forward and backward amortization predictors for each stage. This represents the residual scaling factor. and These represent the positive and negative latent variables obtained from the prediction, respectively;

[0097] Step 5.2: Construct the latent variable numerical distillation loss, as shown in equation (29):

[0098] (29)

[0099] in, This indicates that the gradient operator is stopped. and These represent the positive and negative teacher latent variables obtained through precise solution, respectively;

[0100] Step 5.3: Construct the implicit equation residual loss, as shown in equation (30):

[0101] (30)

[0102] in, This is used to constrain the latent variables in the amortization forecast to satisfy the implicit invertible transformation equation.

[0103] Step 5.4: Explicitly enable amortized fast paths for denoising and reconstruction during the training phase, and construct the deployment path alignment loss as shown in Equation (31):

[0104] (31)

[0105] in, This represents the denoised point cloud obtained through the amortized fast path. This represents the denoised point cloud obtained by precisely solving the path. Indicates clean point clouds. Indicates geometric reconstruction loss;

[0106] Step 5.5: Construct the total loss As shown in equation (32):

[0107] (32)

[0108] in, This represents the basic geometric denoising loss. These are the loss weighting coefficients;

[0109] Step 5.6: During the inference phase, the amortized predictor is used by default to generate latent variables instead of the exact RootFind solution; when further improvement in accuracy is required, a small amount of fixed-point correction is performed on the predicted latent variables, as shown in Equation (33):

[0110] (33)

[0111] in, This indicates the number of iterations for fixed-point correction.

[0112] Furthermore,

[0113] Step 6: Reconstruct the complete denoised point cloud using a cache reuse inference strategy. The specific steps are as follows:

[0114] Step 6.1: Divide the complete point cloud into multiple overlapping local blocks, and cache the best source information for each original point during the local block construction stage, as shown in Equations (34) and (35):

[0115] (34)

[0116] (35)

[0117] in, Indicates containing the first Local block geometry of an original point Indicates the first In the local block, the first The selection weights corresponding to each original point Indicates the best local block number in the cache. This indicates the local index of the point within the optimal local block;

[0118] Step 6.2: Perform steps 1 to 5 on each local block to obtain the denoising result of each local block, as shown in equation (36):

[0119] (36)

[0120] in, Indicates the first A noisy local block, Indicates the first A local denoising block;

[0121] Step 6.3: Based on the optimal local block number and local index of the cache, directly read the final denoising result corresponding to each original point, as shown in Equation (37):

[0122] (37)

[0123] in, Indicates the first The final denoised block corresponding to each original point Indicates the first The local index in each denoised local block is: point;

[0124] Step 6.4: After outputting the complete denoised point cloud, it is shown in equation (38):

[0125] (38)

[0126] in, This represents the denoised point cloud that was finally recovered.

[0127] This invention also provides an efficient graph-conditionally reversible flow system for scalable point cloud denoising, comprising the following units:

[0128] An acquisition unit is used to acquire noisy point cloud data to be denoised, and to construct initial features from the noisy point cloud data to obtain initial point cloud features.

[0129] The shared graph context construction unit is used to perform nearest neighbor search on the noisy point cloud data, and generate a neighborhood index and normalized edge weights based on the distance between the point and its neighboring points to obtain the shared graph context.

[0130] A lightweight dual-frequency graph conditional modeling unit is used to perform low-frequency structure modeling and high-frequency detail modeling on the initial point cloud features based on the shared graph context, and generate staged graph conditional injection features.

[0131] The graph residual conditional reversible flow unit is used to perform graph conditional reversible transformation on point cloud features based on the shared graph context and the staged graph conditional injection features to obtain denoised point cloud features.

[0132] The inference path aligned residual distillation unit is used to distill the latent variable solution process in the reversible flow during the training phase and generate predicted latent variables to replace the exact implicit solution during the inference phase.

[0133] The cache reuse inference unit is used to divide large-scale point clouds into local blocks, cache the best source local block number and local index, and reorganize the complete denoised point cloud data based on the cache results;

[0134] Furthermore, the shared graph context construction unit includes:

[0135] The neighborhood search subunit is used to perform a K-nearest neighbor search on each point in the noisy point cloud data to obtain the neighborhood index set corresponding to each point.

[0136] The distance calculation subunit is used to calculate the Euclidean distance between each point and its neighboring points, and to calculate the local neighborhood scale corresponding to each point;

[0137] An edge weight generation subunit is used to generate normalized edge weights based on the Euclidean distance and the local neighborhood scale.

[0138] The graph context generation subunit is used to combine the neighborhood index set and the normalized edge weights into a shared graph context, and to provide the shared graph context to the subsequent graph residual conditional reversible flow unit for reuse.

[0139] Furthermore, the lightweight dual-frequency graph conditional modeling unit includes:

[0140] The initial local feature extraction subunit is used to extract initial local map features based on noisy point cloud data and nearest neighbor relationships;

[0141] A low-frequency structure modeling subunit is used to perform neighborhood aggregation on the initial local graph features to obtain low-frequency structural features that represent the local smooth surface structure.

[0142] The high-frequency detail modeling subunit is used to obtain high-frequency detail features representing local detail residuals based on the difference between the initial local map features and the low-frequency structural features.

[0143] A gated modulation subunit is used to generate gated weights based on neighborhood distance statistics and to adaptively modulate the high-frequency detail features using the gated weights.

[0144] The dual-frequency fusion subunit is used to fuse the initial local map features, the low-frequency structural features, and the modulated high-frequency detail features to obtain a shared dual-frequency map conditional representation;

[0145] A staged injection feature generation subunit is used to perform staged residual updates and feature adaptations on the shared dual-frequency graph conditional representation to generate staged graph conditional injection features corresponding to multiple reversible flow stages.

[0146] Furthermore, the graph residual conditional reversible flow unit includes:

[0147] The conditional injection subunit is used to add the graph conditional injection features of the corresponding stage to the current point cloud features to obtain conditionally modulated point cloud features.

[0148] The neighborhood aggregation subunit is used to perform neighborhood weighted aggregation on the conditionally modulated point cloud features based on the neighborhood index and normalized edge weight in the shared graph context to obtain local structural reference features.

[0149] The graph residual projection subunit is used to calculate graph residual features based on the local structural reference features and center point features, and to project the graph residual features onto the reversible flow transformation space.

[0150] An implicit reversible transformation subunit is used to embed the graph residual features into the Lipschitz subnetwork and perform forward and inverse reversible transformations.

[0151] The denoising feature output subunit is used to cascade the results of reversible transformations from multiple stages to obtain the final denoised point cloud features.

[0152] Furthermore, the inference path aligned residual distillation unit includes:

[0153] The teacher latent variable solving subunit is used to obtain the positive and negative teacher latent variables through precise implicit solving during the training phase.

[0154] The amortized latent variable prediction subunit is used to predict positive and negative latent variables based on the current input features;

[0155] The latent variable numerical distillation subunit is used to constrain the predicted positive and negative latent variables to be close to their corresponding teacher latent variables.

[0156] Implicit equation residual constraint sub-unit, used to constrain the predicted implicit variables to satisfy the implicit invertible transformation equation in the graph condition invertible flow unit;

[0157] Deploy path supervision subunits to constrain the denoised point cloud obtained based on predicted latent variables to be consistent with the denoised point cloud obtained based on exact implicit solution, and to make it close to clean point cloud data.

[0158] Furthermore, the cache reuse inference unit includes:

[0159] Point cloud segmentation subunits are used to divide a complete noisy point cloud into multiple overlapping local blocks;

[0160] The source cache subunit is used to cache the best source local block number and the local index of the point in the best source local block for each original point during the local block construction phase.

[0161] The local block denoising subunit is used to call the graph residual conditional reversible flow unit to denoise each local block, resulting in multiple denoised local blocks.

[0162] The index reading subunit is used to read the denoising result corresponding to each original point from the corresponding denoising local block according to the optimal source local block number and the local index;

[0163] The point cloud reconstruction subunit is used to reconstruct the complete denoised point cloud data based on the read denoising results;

[0164] Compared with existing technologies, the beneficial results of this invention are as follows: By introducing a graph residual conditionalization mechanism and a lightweight dual-frequency graph conditional modeling module into the reversible flow backbone, this invention enables local neighborhood structure, low-frequency surface structure, and high-frequency detail residual information to jointly participate in point cloud latent space modeling, thereby improving geometric consistency and detail preservation capabilities during point cloud denoising. Simultaneously, by using inference path alignment residual distillation and cache reuse inference strategies, redundant computations in implicit solving and local block reassembly processes are reduced, lowering memory usage and inference latency while maintaining competitive denoising accuracy. Therefore, this invention can better balance point cloud denoising quality, geometric detail preservation, and inference efficiency, making it suitable for efficient denoising processing of large-scale or densely sampled point clouds. Attached Figure Description

[0165] Figure 1 This is a schematic flowchart of the method of the present invention;

[0166] Figure 2 This is a schematic diagram of the overall model of the method of the present invention;

[0167] Figure 3 This is a schematic diagram of the system of the present invention;

[0168] Figure 4 It is a noisy cloud;

[0169] Figure 5 This is the point cloud after denoising using the method of this invention. Detailed Implementation

[0170] The following examples illustrate in detail the specific implementation of the efficient graph-conditional reversible flow method for scalable point cloud denoising according to the present invention.

[0171] This invention presents an efficient graph-conditional reversible flow method for scalable point cloud denoising. An example is a denoising task using point clouds of industrial parts acquired by a 3D scanner. Due to factors such as sensor accuracy, surface reflection, uneven sampling density, and environmental interference during actual scanning, the acquired point clouds typically contain random noise and local geometric perturbations. To verify the applicability of this invention in large-scale or densely sampled point cloud scenarios, this embodiment selects a noisy point cloud with 50,000 points as the object to be processed, with a noise intensity set to 3%. Figure 4 As shown, the input point cloud exhibits significant local surface disturbances; after processing by the method of this invention, the result is as follows: Figure 5 The denoised point cloud is shown. In this embodiment, the overall process of the method of the present invention is as follows: Figure 1 As shown, the overall structure of the model is as follows: Figure 2 As shown, the system structure is as follows Figure 3As shown. Specifically, it includes the following steps:

[0172] Step 1: Obtain the point cloud to be denoised and construct the initial point cloud features. The specific steps are as follows:

[0173] Step 1.1: Obtain noisy point cloud As shown in equation (1):

[0174] (1)

[0175] in, Indicates the first A three-dimensional point, This represents the number of points in the point cloud; in this embodiment, =50000;

[0176] Step 1.2: Map the point coordinates to initial features using the point feature embedding function, as shown in equation (2):

[0177] (2)

[0178] in, Represents the point feature embedding function. Indicates the initial number of feature channels. This represents the initial point cloud features of the input reversible flow backbone; in this embodiment, the initial feature channel number is set to... =64;

[0179] Step 2: Construct the shared graph context. The specific steps are as follows:

[0180] Step 2.1: For each point in the point cloud Search for it in the input geometric space The nearest neighbor points are then removed, and the center itself is removed to obtain the neighborhood set, as shown in equation (3):

[0181] (3)

[0182] in, Point The corresponding neighborhood index set; in this embodiment, ;

[0183] Step 2.2: Calculate points Its neighboring points Euclidean distance between And calculate the average scale of the neighborhood distance of the point, as shown in Equation (4):

[0184] (4)

[0185] in, Point The local neighborhood scale;

[0186] Step 2.3: Generate normalized edge weights based on neighborhood distances, as shown in equation (5):

[0187] (5)

[0188] in, Point With neighboring points Normalized graph edge weights between them;

[0189] Step 2.4: Combine the neighborhood index set and edge weights into a shared graph context according to equation (6):

[0190] (6)

[0191] in, This represents a shared graph context; this shared graph context is reused in multiple subsequent enhanced reversible flow modules to avoid redundant graph construction.

[0192] Step 3: Construct a lightweight bi-frequency graph conditional representation and generate staged injection features. The specific steps are as follows:

[0193] Step 3.1: Extract initial local graph features based on input point cloud and shared neighborhood relationships. As shown in equation (7):

[0194] (7)

[0195] in, This represents a local feature extraction function;

[0196] Step 3.2: Perform low-frequency structure aggregation on the initial local map features to obtain low-frequency structure features, as shown in Equation (8):

[0197] (8)

[0198] in, Point The low-frequency structural features are used to characterize the smooth structural trends of local surfaces;

[0199] Step 3.3: Construct high-frequency detail features based on the differences between the central features and the low-frequency structural features, as shown in Equation (9):

[0200] (9)

[0201] in, Point High-frequency detail features are used to characterize local high-frequency information such as edges, curvature changes, and noise disturbances;

[0202] Step 3.4: Generate channel-level gating weights based on neighborhood distance statistics, as shown in equations (10), (11), and (12):

[0203] (10)

[0204] (11)

[0205] (12)

[0206] in, and Representing points respectively The mean and variance of the neighborhood distance. This refers to a lightweight multilayer perceptron. Indicates channel-level gating weights;

[0207] Step 3.5: Utilize gated weights to modulate high-frequency detail features As shown in equation (13):

[0208] (13)

[0209] in, This represents channel-by-channel multiplication;

[0210] Step 3.6: Initial local map features Low-frequency structural characteristics and high-frequency detail features The fusion yields a shared dual-frequency conditional representation. As shown in equation (14):

[0211] (14)

[0212] in, This indicates a feature concatenation operation. Represents the feature fusion function;

[0213] Step 3.7: Using shared dual-frequency map conditions This represents the initial state, and the conditional features are updated stage by stage through residual edge convolution, as shown in Equation (15):

[0214] (15)

[0215] in, Indicates the first The input condition state at each stage, Indicates the first Residual edge convolution operation in each stage;

[0216] Step 3.8: Perform stage adaptation on the conditional states of each stage to generate the injection condition features of the corresponding enhanced reversible flow module, as shown in Equations (16) and (17):

[0217] (16)

[0218] (17)

[0219] in, Indicates the first Feature adaptation function for each stage Indicates the first Each stage undergoes a stage adaptation function. The intermediate stage representation obtained later. Indicates the first Adaptive convolution function for each stage, This represents the stage weight prediction function. Indicates the first Learnable scaling parameters for each stage Indicates the first Injection condition characteristics of an enhanced reversible flow module;

[0220] Step 4: Construct a graph residual conditional enhanced reversible flow model and perform a reversible transformation. The specific steps are as follows:

[0221] Step 4.1: Add the staged injection conditional features to the current point cloud features to obtain the conditionally modulated input features. As shown in equation (18):

[0222] (18)

[0223] in, Indicates the first Midpoint of the reversible flow stage Input features, This indicates the corresponding staged injection condition features;

[0224] Step 4.2: Perform neighborhood weighted aggregation on the conditionally modulated input features based on the shared graph context to obtain local structural reference features, as shown in Equation (19):

[0225] (19)

[0226] in, Point In the The neighborhood weighted mean characteristics of each stage;

[0227] Step 4.3: Calculate the graph residual of the center point feature relative to the local structural reference feature, as shown in Equation (20):

[0228] (20)

[0229] in, Point In the Residual characteristics of the graph at each stage;

[0230] Step 4.4: Embed the graph residual into the Lipschitz branch of the implicit invertible block to obtain the graph-conditional Lipschitz transformation function, as shown in equation (21):

[0231] (twenty one)

[0232] in, Indicates the first The graphical conditional Lipschitz transform function for each stage. Indicates the original Lipschitz branch. Represents the projection function of the graph residual. This represents the scaling factor of the graph residual branch. Represents the implicit variables in an implicitly invertible block; This represents a shared graph context; in this embodiment, ;

[0233] Step 4.5: Perform a forward invertible transformation according to the graph-conditional Lipschitz transform function to map the noisy features to the latent representation, as shown in equations (22) and (23):

[0234] (twenty two)

[0235] (twenty three)

[0236] in, Indicates the first Hidden variables in the forward transformation of each stage Indicates the first Output characteristics after each stage of forward transformation;

[0237] Step 4.6: Perform the inverse reversible transformation according to the graph-conditional Lipschitz transform function to recover the latent representation into denoised features, as shown in equations (24) and (25):

[0238] (twenty four)

[0239] (25)

[0240] in, Indicates the first Hidden variables in the inverse transformation of each stage Indicates the first Output characteristics of an enhanced reversible flow module;

[0241] Step 4.7: Repeat steps 4.1 to 4.6 in sequence. An enhanced reversible flow module is used to obtain the final denoising features. As shown in equation (26):

[0242] (26)

[0243] in, Indicates the first Individual graph residual conditional enhancement reversible flow module; This indicates a module concatenation operation. This represents the initial point cloud features before being input into the first enhanced reversible flow module. Indicates a shared graph context. Indicates the number of stages. A sequence representing the conditional features of all stages;

[0244] Step 5: Perform inference path alignment, residual distillation, and obtain a fast inference path. The specific steps are as follows:

[0245] Step 5.1: During the training phase, the teacher's latent variables are obtained by exact implicit solution, and the forward and backward latent variables are predicted by the amortized predictor, as shown in equations (27) and (28):

[0246] (27)

[0247] (28)

[0248] in, and They represent the first Forward and backward amortization predictors for each stage. This represents the residual scaling factor. and These represent the positive and negative latent variables obtained from the prediction, respectively;

[0249] Step 5.2: Construct the latent variable numerical distillation loss, as shown in equation (29):

[0250] (29)

[0251] in, This indicates that the gradient operator is stopped. and These represent the positive and negative teacher latent variables obtained through precise solution, respectively;

[0252] Step 5.3: Construct the implicit equation residual loss, as shown in equation (30):

[0253] (30)

[0254] in, This is used to constrain the latent variables in the amortization forecast to satisfy the implicit invertible transformation equation.

[0255] Step 5.4: Explicitly enable amortized fast paths for denoising and reconstruction during the training phase, and construct the deployment path alignment loss as shown in Equation (31):

[0256] (31)

[0257] in, This represents the denoised point cloud obtained through the amortized fast path. This represents the denoised point cloud obtained by precisely solving the path. Indicates clean point clouds. Indicates geometric reconstruction loss;

[0258] Step 5.5: Construct the total loss As shown in equation (32):

[0259] (32)

[0260] in, This represents the basic geometric denoising loss. These are the loss weighting coefficients; in this embodiment, ;

[0261] Step 5.6: During the inference phase, the amortized predictor is used by default to generate latent variables instead of the exact RootFind solution; when further improvement in accuracy is required, a small amount of fixed-point correction is performed on the predicted latent variables, as shown in Equation (33):

[0262] (33)

[0263] in, Indicates the number of iterations for fixed-point correction;

[0264] Step 6: Reconstruct the complete denoised point cloud using a cache reuse inference strategy. The specific steps are as follows:

[0265] Step 6.1: Divide the complete point cloud into multiple overlapping local blocks, and cache the best source information for each original point during the local block construction stage, as shown in Equations (34) and (35):

[0266] (34)

[0267] (35)

[0268] in, Indicates containing the first Local block geometry of an original point Indicates the first In the local block, the first The selection weights corresponding to each original point Indicates the best local block number in the cache. This indicates the local index of the point within the optimal local block;

[0269] Step 6.2: Perform steps 1 to 5 on each local block to obtain the denoising result of each local block, as shown in equation (36):

[0270] (36)

[0271] in, Indicates the first A noisy local block, Indicates the first A local denoising block;

[0272] Step 6.3: Based on the optimal local block number and local index of the cache, directly read the final denoising result corresponding to each original point, as shown in Equation (37):

[0273] (37)

[0274] in, Indicates the first The final denoised block corresponding to each original point Indicates the first The local index in each denoised local block is: point;

[0275] Step 6.4: After outputting the complete denoised point cloud, it is shown in equation (38):

[0276] (38)

[0277] in, This represents the denoised point cloud that was finally recovered.

[0278] Table 1 compares the differences in runtime overhead between the method of this invention and existing point cloud denoising methods. The comparison methods include ScoreDenoise, PDFlow, IterativePFN, PD-LTS, StraightPCF, P2P-Bridge, ASDN, and 3DMambaIPF. This table is compiled under the same test conditions. The test input is a high-point-count point cloud scene, specifically 50k point clouds with 3% noise. Evaluation metrics include model parameter count, floating-point computation, GPU memory usage, and single inference time. Lower parameter count, floating-point computation, GPU memory usage, and inference time indicate lower runtime overhead.

[0279] Table 1 compares the operating costs of this method with existing methods. ;

[0280] As shown in Table 1, the inference time of the method of this invention is 2.56s, which is the lowest among all the compared methods. Compared with the reversible flow denoising method PD-LTS, which has the closest structure, PD-LTS has a memory usage of 20130MB and an inference time of 8.18s, while the method of this invention has a memory usage of 5412MB and an inference time of 2.56s, representing a reduction of approximately 73.1% in memory usage and approximately 68.7% in inference time. This indicates that the present invention significantly reduces the memory requirements and inference latency in the high-point-count point cloud denoising process while maintaining the graph-conditional reversible flow modeling capability.

[0281] Furthermore, compared to existing methods such as ScoreDenoise, PDFlow, IterativePFN, StraightPCF, P2P-Bridge, ASDN, and 3DMambaIPF, while the method of this invention is not the lowest in all individual metrics—for example, ASDN and 3DMambaIPF have lower memory usage, and PDFlow has lower floating-point operations—this invention has a significant advantage in inference time, with a floating-point computation of only 13.12G, significantly lower than IterativePFN, StraightPCF, P2P-Bridge, and ASDN. Therefore, this invention does not simply pursue the minimum number of model parameters, but rather achieves a better overall balance between point cloud denoising quality, computational complexity, memory usage, and inference speed.

[0282] In summary, this invention effectively reduces redundant computation and implicit solution overhead in high-point-count point cloud denoising by employing graph residual conditionalization, lightweight dual-frequency graph conditional modeling, inference path-aligned residual distillation, and cache reuse strategies. Compared to existing technologies, especially reversible flow point cloud denoising methods, this invention can significantly reduce memory usage and shorten inference time in large-scale or densely sampled point cloud scenarios, demonstrating better scalability and practical application value.

[0283] The embodiments described in this specification are merely examples of implementations of the inventive concept. The scope of protection of this invention should not be considered as limited to the specific forms described in the embodiments. The scope of protection of this invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. An efficient graph-conditionally reversible flow method for scalable point cloud denoising, comprising the following steps: Step 1: Obtain noisy point cloud Initial point cloud features are generated through point feature embedding; Step 2: Construct a global shared graph context based on the point cloud geometric space. The global shared graph context consists of a neighborhood index set and edge weights, which can be reused in the subsequent reversible flow module to avoid repeated graph construction. Step 3: Based on the shared graph context, perform high- and low-frequency decomposition on the initial point cloud features, use neighborhood distance statistics to generate channel gating weights to adaptively suppress high-frequency noise components, and generate staged injection condition features corresponding to each reversible flow module through multi-stage residual edge convolutional layer adaptation. Step 4: Modulate point cloud features using staged injection conditional features, calculate local geometric graph residuals based on shared graph context, embed graph residuals into Lipschitz-constrained reversible branches to construct graph conditional reversible transformation functions, and stack multiple sets of enhanced reversible flow modules through forward and inverse pairwise reversible transformations to output point cloud denoising features. Step 5: During the training phase, a numerical distillation loss for latent variables is constructed, and an amortized latent variable predictor is trained to replace the RootFind numerical solution. During the inference phase, the amortized predictor is used by default to generate latent variables, and fixed-point iterative correction is performed based on the predicted latent variables to construct a lightweight and fast inference path. Step 6: Divide the complete point cloud and reassemble the complete denoised point cloud using a cache reuse inference strategy.

2. The efficient graph-conditionally reversible flow method for scalable point cloud denoising according to claim 1, characterized in that, Step 1 is described in detail as follows: Step 1.1: Obtain noisy point cloud ; Step 1.2: Map the point coordinates to initial features using the point feature embedding function.

3. The efficient graph-conditionally reversible flow method for scalable point cloud denoising according to claim 1, characterized in that, Step 2 is described in detail below: Step 2.1: For each point in the point cloud Search for it in the input geometric space Find the nearest neighbor and remove the center point itself to obtain the neighborhood set. ; Step 2.2: Calculate points Its neighboring points Euclidean distance between And calculate the average scale of the neighborhood distance of that point; Step 2.3: Generate normalized edge weights based on neighborhood distance; ； in, Point With neighboring points Normalized graph edge weights between them Point The local neighborhood scale; Step 2.4: Combine the neighborhood index set and edge weights to form a shared graph context. : 。 4. The efficient graph-conditionally reversible flow method for scalable point cloud denoising according to claim 1, characterized in that, Step 3 is as follows: Step 3.1: Extract initial local graph features based on input point cloud and shared neighborhood relationships. ; Step 3.2: Perform low-frequency structure aggregation on the initial local map features to obtain low-frequency structure features. ; Step 3.3: Construct high-frequency detail features based on the differences between central features and low-frequency structural features. ; Step 3.4: Generate channel-level gating weights based on neighborhood distance statistics. , ； in, and Representing points respectively The mean and variance of the neighborhood distance. This refers to a lightweight multilayer perceptron. Step 3.5: Utilize channel-level gating weights Modulation high-frequency detail features ; Step 3.6: Initial local map features Low-frequency structural characteristics and high-frequency detail features The fusion yields a shared dual-frequency conditional representation. ; Step 3.7: Using shared dual-frequency map conditions This represents the initial state, and the conditional features are updated stage by stage through residual edge convolution: ； in, Indicates the first The input condition state at each stage, Indicates the first Residual edge convolution operation in each stage; Step 3.8: Perform stage adaptation for the conditional states of each stage to generate the injection condition features of the corresponding enhanced reversible flow module: ； in, Indicates the first Feature adaptation function for each stage Indicates the first Each stage undergoes a stage adaptation function. The intermediate stage representation obtained later. Indicates the first Adaptive convolution function for each stage, This represents the stage weight prediction function. Indicates the first Learnable scaling parameters for each stage Indicates the first Injection condition characteristics of an enhanced reversible flow module.

5. The efficient graph-conditionally reversible flow method for scalable point cloud denoising according to claim 1, characterized in that, Step 4 is as follows: Step 4.1: Add the staged injection conditional features to the current point cloud features to obtain the conditionally modulated input features. ; Step 4.2: Perform neighborhood-weighted aggregation on the conditionally modulated input features based on the shared graph context to obtain local structural reference features. ; Step 4.3: Calculate the graphical residual of the center point feature relative to the local structural reference feature. ; Step 4.4: Embed the graph residual into the Lipschitz branch of the implicit invertible block to obtain the graph-conditional Lipschitz transformation function: ； in, Indicates the first The graphical conditional Lipschitz transform function for each stage. Indicates the original Lipschitz branch. Represents the projection function of the graph residual. This represents the scaling factor of the graph residual branch. Represents the implicit variables in an implicitly invertible block; Step 4.5: Perform a forward invertible transformation according to the graph-conditional Lipschitz transform function to map the noisy features to the latent representation: ； ； in, Indicates the first Hidden variables in the forward transformation of each stage Indicates the first Output characteristics after each stage of forward transformation; Step 4.6: Perform an inverse reversible transformation based on the graph-conditional Lipschitz transform function to recover the latent representation into denoised features: ； ； in, Indicates the first Hidden variables in the inverse transformation of each stage Indicates the first Output characteristics of an enhanced reversible flow module; Step 4.7: Repeat steps 4.1 to 4.6 in sequence. An enhanced reversible flow module is used to obtain the final denoising features. : ； in, Indicates the first Individual graph residual conditionalization enhanced reversible flow module This indicates a module concatenation operation. This represents the initial point cloud features before being input into the first enhanced reversible flow module. Indicates a shared graph context. Indicates the number of stages. A sequence representing the conditional characteristics of all stages.

6. The efficient graph-conditionally reversible flow method for scalable point cloud denoising according to claim 1, characterized in that, Step 5 is described in detail below: Step 5.1: During the training phase, implicitly solve for the teacher's latent variables and use an amortized predictor to predict the forward and backward latent variables. ； ； in, and They represent the first Forward and backward amortization predictors for each stage. This represents the residual scaling factor. and These represent the positive and negative latent variables obtained from the prediction, respectively; Step 5.2: Construct the latent variable numerical distillation loss: ； in, This indicates that the gradient operator is stopped. and These represent the positive and negative teacher latent variables obtained through precise solution, respectively; Step 5.3: Construct the implicit equation residual loss: ； in, This is used to constrain the latent variables in the amortization forecast to satisfy the implicit invertible transformation equation. Step 5.4: Explicitly enable amortized fast path for denoising and reconstruction during the training phase, and construct the deployment path alignment loss: ； in, This represents the denoised point cloud obtained through the amortized fast path. This represents the denoised point cloud obtained by precisely solving the path. Indicates clean point clouds. Indicates geometric reconstruction loss; Step 5.5: Construct the total loss : ； in, This represents the basic geometric denoising loss. These are the loss weighting coefficients; Step 5.6: During the inference phase, the amortized predictor is used by default to generate latent variables instead of the exact RootFind solution; to further improve accuracy, fixed-point correction is performed based on the predicted latent variables: ； in, This indicates the number of iterations for fixed-point correction.

7. The efficient graph-conditionally reversible flow method for scalable point cloud denoising according to claim 1, characterized in that, Step 6 is as follows: Step 6.1: Divide the complete point cloud into multiple overlapping local blocks, and cache the best source information for each original point during the local block construction phase: ； ； in, Indicates containing the first Local block geometry of an original point Indicates the first In the local block, the first The selection weights corresponding to each original point Indicates the best local block number in the cache. This indicates the local index of the point within the optimal local block; Step 6.2: Perform steps 1 to 5 on each local block to obtain the denoising result for each local block: Step 6.3: Based on the optimal local block number and local index of the cache, directly read the final denoising result corresponding to each original point: ； in, Indicates the first The final denoised block corresponding to each original point Indicates the first The local index in each denoised local block is: point; Step 6.4: Output the complete denoised point cloud.

8. An efficient graph-conditionally reversible flow system for scalable point cloud denoising, characterized in that, Includes the following units: An acquisition unit is used to acquire noisy point cloud data to be denoised, and to construct initial features from the noisy point cloud data to obtain initial point cloud features. The shared graph context construction unit is used to perform nearest neighbor search on the noisy point cloud data, and generate a neighborhood index and normalized edge weights based on the distance between the point and its neighboring points to obtain the shared graph context. A lightweight dual-frequency graph conditional modeling unit is used to perform low-frequency structure modeling and high-frequency detail modeling on the initial point cloud features based on the shared graph context, and generate staged graph conditional injection features. The graph residual conditional reversible flow unit is used to perform graph conditional reversible transformation on point cloud features based on the shared graph context and the staged graph conditional injection features to obtain denoised point cloud features. The inference path aligned residual distillation unit is used to distill the latent variable solution process in the reversible flow during the training phase and generate predicted latent variables to replace the exact implicit solution during the inference phase. The cache reuse inference unit is used to divide large-scale point clouds into local blocks, cache the best source local block number and local index, and reorganize the complete denoised point cloud data based on the cache results.

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