Point cloud denoising method based on density and meta learning parameter optimization
By using a density- and meta-learning parameter optimization method, multi-scale hybrid sampling and density adaptive filtering are employed to solve the problem that existing denoising methods are unable to preserve geometric features in multi-scale noise environments, thus achieving efficient and accurate point cloud denoising processing.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- WUXI WEIFU HIGH TECH CO LTD
- Filing Date
- 2026-01-16
- Publication Date
- 2026-05-01
AI Technical Summary
Existing point cloud denoising methods are difficult to effectively remove multi-scale noise while preserving geometric features, and they are computationally complex and inefficient, failing to meet the high-precision requirements of industrial inspection and reverse engineering.
We employ a density- and meta-learning-based parameter optimization method. We acquire sample point cloud datasets through multi-scale hybrid sampling, combine meta-learning and gradient descent to optimize neighborhood parameters, design a density adaptive filter, and use Gaussian kernel density estimation and quartile range analysis for denoising.
It achieves efficient denoising in multi-scale noise environments, preserves the integrity of point cloud geometric features, reduces computational complexity and manual parameter tuning costs, adapts to different density distributions, and improves the accuracy and efficiency of point cloud processing.
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Figure CN121961908A_ABST
Abstract
Description
A Point Cloud Denoising Method Based on Density and Meta-Learning Parameter Optimization Technical Field
[0001] This invention relates to the field of 3D point cloud processing technology, and more specifically, to a point cloud denoising method based on density and meta-learning parameter optimization. Background Technology
[0002] With the industrial breakthroughs in 3D scanning technologies such as LiDAR, structured light scanning, and photogrammetry, 3D point clouds, as the core data carriers that carry the 3D geometric shape and topological relationship of objects, have become a key link connecting the physical world and digital models. Their quality directly determines the accuracy of subsequent point cloud registration, segmentation, feature extraction, and model reconstruction, thereby affecting the reliability of end applications.
[0003] However, noise is inevitably introduced throughout the entire point cloud acquisition and generation process, from the perspectives of sensors, environment, and the characteristics of the objects themselves. In addition, during the post-processing of point cloud data, the interpolation approximation during resampling and the registration deviation during multi-view stitching will further aggravate the noise distribution. Especially in the processing of large-scale industrial point clouds (such as automobile body point clouds) with millions or even tens of millions of data points, the noise from different perspectives will also superimpose, increasing the difficulty of subsequent denoising.
[0004] Based on their characteristics, noise can be divided into large-scale noise (drift points, isolated points) and small-scale noise (mixed points). This type of noise can lead to point cloud feature degradation and structural distortion, severely limiting measurement accuracy and reconstruction quality.
[0005] Existing point cloud denoising methods have significant limitations: traditional spatial domain filtering (such as statistical filtering and radius filtering) relies on manual parameter tuning, resulting in low efficiency and difficulty in adapting to multi-scale and non-uniformly distributed noise; geometric feature-driven methods are susceptible to noise interference and have high computational complexity; deep learning methods have weak generalization ability, high training costs, and demanding hardware requirements. Furthermore, existing methods struggle to effectively preserve point cloud geometric features while removing multi-scale noise, failing to meet the demands of high-precision scenarios such as industrial inspection and reverse engineering. Therefore, there is an urgent need for a point cloud denoising method that requires no manual parameter tuning, is robust to multi-scale noise, and preserves geometric features. Summary of the Invention
[0006] To overcome the aforementioned shortcomings in the existing technology, this invention provides a point cloud denoising method based on density and meta-learning parameter optimization. By integrating meta-learning and gradient descent parameter optimization, the optimal denoising parameters are generated for the point cloud to guide adaptive density estimation and noise removal while maintaining the integrity of geometric features.
[0007] As a first aspect of the present invention, a point cloud denoising method based on density and meta-learning parameter optimization is provided, comprising the following steps: Step S1: Obtaining an original point cloud dataset and a historical point cloud dataset, and extracting a sample point cloud dataset containing global structure and local details from the original point cloud dataset; Step S2: Learning meta-parameters based on the historical point cloud dataset to generate an optimal initial value for a neighborhood parameter k; Step S3: Starting from the optimal initial value of the neighborhood parameter k, iteratively adjusting the neighborhood parameter k to obtain the current iterative value of the neighborhood parameter k; Step S4: Calculating the value of each sample point in the sample point cloud dataset based on the current iterative value of the neighborhood parameter k. The local density value of the cloud is calculated, and the sample point cloud dataset is denoised based on the local density value of each sample point cloud in the sample point cloud dataset to obtain the current denoised point cloud dataset; Step S5: Calculate the comprehensive score value of the current denoised point cloud dataset; If the comprehensive score value of the current denoised point cloud dataset reaches a preset threshold, it means that the current iteration value of the neighborhood parameter k is the optimal iteration value, and the current denoised point cloud dataset is output; If the comprehensive score value of the current denoised point cloud dataset does not reach the preset threshold, return to step S3 to continue iteratively adjusting the neighborhood parameter k until the comprehensive score value of the current denoised point cloud dataset reaches the preset threshold.
[0008] Further, the step of extracting a sample point cloud dataset containing global structure and local details from the original point cloud dataset includes: performing global random sampling, voxel downsampling, and local random sampling on the original point cloud dataset in sequence to extract a global sample subset S1, a mesoscopic sample subset S2, and a local sample subset S3 in sequence, and combining the global sample subset S1, the mesoscopic sample subset S2, and the local sample subset S3 to form the sample point cloud dataset S.
[0009] Further, step S2 includes: Step S21: For each historical point cloud C in the historical point cloud dataset... i Using the current time meta-parameter θ t Using the current initial value of the neighborhood parameter k, perform T steps of gradient descent optimization to obtain the optimized initial value of the neighborhood parameter k. : Where GD represents the gradient descent optimization process; Step S22: Calculate the meta-parameter θ at the current time. t meta-objective function ,in, It is all the historical point clouds C in the historical point cloud dataset. i The initial value of the optimization of the neighborhood parameter k Evaluation function value under Average value: Where N is the number of historical point clouds in the historical point cloud dataset; For each historical point cloud C i The initial value of the optimization of the neighborhood parameter k The evaluation function value is given below; Step S23: Calculate the meta-objective function using the central difference method. Meta-parameters at the current time gradient : ;in,, The perturbation value; Step S24: Obtain the gradient Then, the meta-learning rate η is used to update the meta-parameters θ at the current time step. t until the trained meta-parameters θ are obtained. * ; ;in, For the next time step, use the trained meta-parameters θ; Step S25: Use the trained meta-parameters θ * The optimal initial value k0 is used as the neighborhood parameter k.
[0010] Further, step S3 includes: Step S31: For the current iteration value k of the neighborhood parameter k t The gradient is estimated using the finite difference method; if the current iteration value k t If the value is greater than 1, the gradient is estimated using the central difference method. : If the current iteration value k t When the value equals 1, the gradient is estimated using the one-sided difference method. : Where Δk is the difference step size, To evaluate the function value Regarding the current iteration value k t The gradient; L is the evaluation function; Step S32: Obtain the gradient Then, the momentum method is used to update the neighborhood parameter k: ; ; where v t V is the momentum term at time t; t+1 Let α be the momentum term at time t+1; α be the learning rate; β be the momentum coefficient; k t Let k be the iteration value of the neighborhood parameter k at time t, that is, the current iteration value of the neighborhood parameter k; t+1 This is the iteration value of the neighborhood parameter k at time t+1.
[0011] Further, step S4 includes: Step S41: For each sample point cloud S in the sample point cloud dataset S i Calculate the distance between it and its k nearest neighbor point clouds, and then calculate S for each point cloud. iLocal density value : Where σ is the adaptive bandwidth parameter, and d ij Let S be the point cloud of the i-th sample. i The distance between it and its j-th nearest neighbor sample point cloud; Step S42: Calculate the first quartile Q1 and the third quartile Q3 of the local density values of all sample point clouds in the sample point cloud dataset S to obtain the quartile range IQR: ; IQR = Q3 - Q1; where m is the number of sample point clouds in the sample point cloud dataset S; percentile is the percentile; Step S43: Set the density threshold for: Where r is an adjustable parameter; median is the median; Step S44: Retain the local density values in the sample point cloud dataset S. Above the density threshold Sample point cloud S i To form the current denoised point cloud dataset P': .
[0012] Furthermore, the calculation of the comprehensive score value of the current denoised point cloud dataset also includes: the calculation formula of the comprehensive score value L(k) of the current denoised point cloud dataset P' is as follows: L(k)=w1×D(k) + w2×G(k); where w1 and w2 are both weight coefficients, D(k) is the density uniformity index, and G(k) is the geometric integrity index; Where b is the number of denoised point clouds in the current denoised point cloud dataset P', and μ and σ are the mean and standard deviation of the local density values of all denoised point clouds in the current denoised point cloud dataset P', respectively. ;in, S represents any one of the sample point clouds in the sample point cloud dataset S. i The minimum distance between the current denoised point cloud dataset P' and all denoised point clouds, where I is an indicator function; if If the value is 0, then the indicator function I takes the value of 1; otherwise, if If the value is greater than 0, then the value of the indicator function I is 0.
[0013] The point cloud denoising method provided by this invention based on density and meta-learning parameter optimization has the following advantages: First, multi-scale hybrid sampling is used to extract feature point clouds, and the initial values of neighborhood parameters are generated by the meta-learning optimizer and the parameters are optimized by combining the momentum-accelerated gradient descent algorithm. Second, a density adaptive filter is designed to fuse Gaussian kernel density estimation and quartile range analysis to achieve multi-scale noise removal. Attached Figure Description
[0014] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the following detailed description to explain the invention, but do not constitute a limitation thereof.
[0015] Figure 1 is a flowchart of the point cloud denoising method based on density and meta-learning parameter optimization provided by the present invention.
[0016] Figure 2 is a flowchart of a specific implementation of the point cloud denoising method based on density and meta-learning parameter optimization provided by the present invention.
[0017] Figure 3 shows the original point cloud dataset of the dragon model provided by this invention.
[0018] Figures 4(a) to 4(f) are point cloud datasets of metal parts provided by the present invention. Among them, Figure 4(a) is laptop shell part 1; Figure 4(b) is laptop shell part 2; Figure 4(c) is laptop shell part 3; Figure 4(d) is metal part 1; Figure 4(e) is metal part 2; and Figure 4(f) is metal part 3.
[0019] Figures 5(a) to 5(c) show the point cloud datasets of the dragon model provided by this invention after adding random noise. Among them, Figure 5(a) shows 10% random noise; Figure 5(b) shows 30% random noise; and Figure 5(c) shows 50% random noise.
[0020] Figures 6(a) to 6(c) show the point cloud datasets of the dragon model provided by this invention after adding Gaussian noise. Among them, Figure 6(a) shows 10% Gaussian noise; Figure 6(b) shows 30% Gaussian noise; and Figure 6(c) shows 50% Gaussian noise.
[0021] Figure 7 shows the results of denoising the dragon model point cloud datasets in Figures 5(a) to 5(c) using four methods. Groups A, B, and C represent the denoising results of point cloud datasets with 10%, 30%, and 50% random noise, respectively. In each group, from left to right, they correspond to the denoising results of three traditional methods and the method of this invention.
[0022] Figure 8 shows the results of denoising the dragon model point cloud datasets in Figures 6(a) to 6(c) using four methods. Groups A, B, and C represent the denoising results of point cloud datasets with 10%, 30%, and 50% Gaussian noise, respectively. In each group, from left to right, they correspond to the denoising results of three traditional methods and the method of this invention.
[0023] Figure 9 shows the result of manually denoised point cloud. Among them, (a) is laptop shell part 1, (b) is laptop shell part 2, and (c) is laptop shell part 3.
[0024] Figure 10 shows the results of denoising three point cloud datasets of laptop casing parts using four methods. (a), (b), (c), and (d) correspond to the denoising results of the point cloud dataset of laptop casing part 1 using the four methods; (e), (f), (g), and (h) correspond to the denoising results of the point cloud dataset of laptop casing part 2 using the four methods; and (i), (j), (k), and (l) correspond to the denoising results of the point cloud dataset of laptop casing part 3 using the four methods.
[0025] Figure 11 shows the results of artificially denoised point cloud. Among them, (a) is metal part 1, (b) is metal part 2, and (c) is metal part 3.
[0026] Figure 12 shows the results of denoising three metal part point cloud datasets using four methods. Among them, (a), (b), (c), and (d) correspond to the denoising results of the point cloud dataset of metal part 1 using the four methods; (e), (f), (g), and (h) correspond to the denoising results of the point cloud dataset of metal part 2 using the four methods; and (i), (j), (k), and (l) correspond to the denoising results of the point cloud dataset of metal part 3 using the four methods. Detailed Implementation
[0027] To further illustrate the technical means and effects adopted by the present invention to achieve its intended purpose, the following, in conjunction with the accompanying drawings and preferred embodiments, details the specific implementation, structure, features, and effects of a point cloud denoising method based on density and meta-learning parameter optimization proposed according to the present invention. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the protection scope of the present invention.
[0028] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate for the embodiments of the invention described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.
[0029] This embodiment provides a point cloud denoising method based on density and meta-learning parameter optimization, as shown in Figure 1. Please also refer to Figure 2. The point cloud denoising method based on density and meta-learning parameter optimization includes the following steps: Step S1, multi-scale hybrid sampling: acquire the original point cloud dataset and the historical point cloud dataset, and extract a sample point cloud dataset containing global structure and local details from the original point cloud dataset; preferably, the step of extracting the sample point cloud dataset containing global structure and local details from the original point cloud dataset includes: performing global random sampling, voxel downsampling and local random sampling on the original point cloud dataset in sequence to extract a global sample subset S1, a mesoscale sample subset S2 and a local sample subset S3 in sequence, and combining the global sample subset S1, the mesoscale sample subset S2 and the local sample subset S3 to form the sample point cloud dataset S.
[0030] Specifically, the original point cloud dataset is first subjected to global random sampling to preserve the overall distribution characteristics of the point cloud. Then, voxel downsampling is used to downsample the geometric structure at the mesoscale, reducing redundant data in high-density areas. Finally, the remaining original point cloud is subjected to local random sampling, focusing on preserving high-frequency detail areas such as sharp edges and holes. This strategy effectively reduces the dimensionality of the point cloud data, improves subsequent processing efficiency, and effectively preserves geometric features at different scales, providing high-quality sample point clouds for subsequent meta-learning parameter optimization and denoising.
[0031] The core objective of global random sampling is to fully preserve the overall spatial distribution characteristics of the point cloud, avoiding the impact of data distribution distortion on global parameter optimization in subsequent processing. Specifically, for the original point cloud dataset P={P1,P2,P3,…,P…} n R1·m points are uniformly and randomly selected from the point cloud to form a global sample subset S1. The key advantage of this method is that by controlling the number and randomness of samples, it avoids global structural redundancy and distortion caused by oversampling while ensuring that the macroscopic distribution characteristics of the point cloud (such as overall shape and spatial pose) are not lost. The mathematical expression for global random sampling is: Where r1 is the global sampling ratio coefficient, m is the total number of samples in the sample point cloud, and i j The index variable is a globally random sampled variable used to select the point cloud at the corresponding location from the original point cloud dataset. Uniform(1,n) is a uniform distribution function, representing i j The points follow a uniform distribution in the interval [1, n], where n is the total number of original point clouds in the original point cloud dataset.
[0032] Voxel downsampling can be viewed as a coarse-grained representation of the original point cloud, capturing its mesoscopic geometric features. The remaining original point cloud is divided into a 3D grid of size v, with one representative point retained within each grid, forming a mesoscopic sample subset S2. This method effectively reduces point cloud density while preserving the main geometric structure, making it particularly suitable for processing high-density point cloud regions. The mathematical expression for voxel downsampling is: Where v is the voxel size, Voxel downsampling.
[0033] In the local random sampling portion, m - |S1| - |S2| points are randomly extracted from the remaining original point cloud to form a local sample subset S3. This sampling method is mainly used to supplement local details that may be lost in mesoscale sampling, especially in geometrically complex regions. The final sample point cloud dataset S is the union of the three subsets, i.e., S = S1∪S2∪S3. The multi-scale sampling strategy, by mixing the proportions of different scale sampling, can effectively preserve the global structure and local detail features of the point cloud while reducing computational cost. The mathematical expression for the local sample subset S3 is: ; where j k This is an index variable for local random sampling, used to select the point cloud at the corresponding location from the remaining original point cloud.
[0034] Step S2, Meta-parameter optimization: Meta-parameters are learned based on the historical point cloud dataset to generate the optimal initial value of the neighborhood parameter k; wherein, to avoid manual parameter tuning, a hierarchical meta-learning framework is designed to generate the optimal initial value k0 of the neighborhood parameter k through experience extraction across datasets.
[0035] Preferably, step S2 includes: Step S21: Learning meta-parameters θ using a historical point cloud dataset. For each historical point cloud C in the historical point cloud dataset... i Using the current time meta-parameter θ t Using the current initial value of the neighborhood parameter k, perform T steps of gradient descent optimization to obtain the optimized initial value of the neighborhood parameter k. : Where GD represents the gradient descent optimization process; Step S22: Calculate the meta-parameter θ at the current time. t meta-objective function ,in, It is all the historical point clouds C in the historical point cloud dataset. i The initial value of the optimization of the neighborhood parameter k Evaluation function value under Average value: Where N is the number of historical point clouds in the historical point cloud dataset; For each historical point cloud C i The initial value of the optimization of the neighborhood parameter k The evaluation function value is given below; Step S23: In order to update the meta-parameter θ, the meta-objective function needs to be calculated. about gradient Since directly calculating this gradient is difficult, the central difference method is used to calculate the meta-objective function. Meta-parameters at the current time gradient : ;in, The perturbation value is set to 0.001; Step S24: Obtain the gradient. Then, the meta-learning rate η is used to update the meta-parameters θ at the current time step. t until the trained meta-parameters θ are obtained. * ; ;in, For the next time step, use the trained meta-parameters θ; Step S25: Use the trained meta-parameters θ * As the optimal initial value k0 for the neighborhood parameter k, convergence can be achieved quickly with a small number of iterations.
[0036] Step S3, Gradient Descent Optimization: A momentum-accelerated gradient descent algorithm is employed, with the evaluation function as the optimization objective. Starting from the optimal initial value of the neighborhood parameter k, the neighborhood parameter k is iteratively adjusted to obtain its current iterative value, avoiding manual parameter tuning. The core of this gradient descent optimization is defining an evaluation function that can measure the denoising effect. The optimization process starts with the optimal initial value k0 of the neighborhood parameter k. In each iteration, the evaluation function is calculated. We calculate the gradient with respect to the neighborhood parameter k and use this gradient to update the neighborhood parameter k. To improve the robustness of the optimization, we introduce momentum to accelerate convergence and reduce oscillations.
[0037] Preferably, step S3 includes: step S31: defining an evaluation function that can measure the noise reduction effect. For the current iteration value k of the neighborhood parameter k t The gradient is estimated using the finite difference method; if the current iteration value k t If the value is greater than 1, the gradient is estimated using the central difference method. : If the current iteration value k t Since the value is 1, and two-sided differencing is not possible, the gradient is estimated using one-sided differencing. : Where Δk is the difference step size, which is usually set to 1; To evaluate the function value Regarding the current iteration value k t The gradient; L is the evaluation function; Step S32: Obtain the gradient Then, the momentum method is used to update the neighborhood parameter k: ; ; where v t V is the momentum term at time t; t+1 Let α be the momentum term at time t+1; α be the learning rate; β be the momentum coefficient; k t Let k be the iteration value of the neighborhood parameter k at time t, that is, the current iteration value of the neighborhood parameter k; t+1 Let be the iteration value of the neighborhood parameter k at time t+1. The momentum term accumulates historical gradient information, accelerating convergence and reducing oscillations during parameter updates. This gradient descent-based parameter optimization automatically adapts to the characteristics of different point cloud data, providing the optimal neighborhood parameter k for subsequent density calculations and denoising.
[0038] Step S4, density adaptive denoising: Calculate the local density value of each sample point cloud in the sample point cloud dataset based on the current iteration value of the neighborhood parameter k, and denoise the sample point cloud dataset based on the local density value of each sample point cloud in the sample point cloud dataset to obtain the current denoised point cloud dataset; preferably, step S4 includes: Step S41: For each sample point cloud S in the sample point cloud dataset S... i Calculate the distance between it and its k nearest neighbor point clouds, and then calculate S for each point cloud. i Local density value In order to calculate the point cloud S i Local density Using a Gaussian kernel function, it can smoothly represent the local distribution of point clouds: Where σ is the adaptive bandwidth parameter, set as the average distance of the k nearest neighbors; d ij Let S be the point cloud of the i-th sample. i The distance between it and its j-th nearest neighbor sample point cloud; this method allows the density estimation to be automatically adjusted according to the density of the point cloud distribution, improving the algorithm's adaptability to regions with different densities.
[0039] Step S42: After obtaining the density values of all points, a suitable threshold needs to be determined to distinguish between inliers and noise. Traditional fixed threshold methods cannot adapt to the non-uniformity of point cloud density; therefore, this invention employs an adaptive thresholding method based on IQR. First, the first quartile Q1 and the third quartile Q3 of the local density values of all sample point clouds in the sample point cloud dataset S are calculated to obtain the quartile range IQR: ; IQR = Q3 - Q1; where m is the number of sample point clouds in the sample point cloud dataset S; percentile is the percentile; Step S43: Set the density threshold for: Where r is an adjustable parameter, set to 1.5 in the experiment; median is the median; Step S44: Retain the local density values in the sample point cloud dataset S. Above the density threshold Sample point cloud S i This is used to form the current denoised point cloud dataset P', achieving noise removal and geometric feature preservation: .
[0040] Step S5, Closed-loop evaluation and feedback: The comprehensive score of the current denoised point cloud dataset is calculated using an evaluation function. If the comprehensive score of the current denoised point cloud dataset reaches a preset threshold, it indicates that the current iteration value of the neighborhood parameter k is the optimal iteration value, and the current denoised point cloud dataset is output. If the comprehensive score of the current denoised point cloud dataset does not reach the preset threshold, the process returns to step S3 to continue iteratively adjusting the neighborhood parameter k until the comprehensive score of the current denoised point cloud dataset reaches the preset threshold. The evaluation function comprehensively considers the density uniformity and geometric integrity of the denoised point cloud.
[0041] Preferably, the calculation of the comprehensive score of the current denoised point cloud dataset further includes: the calculation formula for the comprehensive score L(k) of the current denoised point cloud dataset P' is as follows: L(k) = w1 × D(k) + w2 × G(k); where w1 and w2 are weight coefficients, controlling the importance of the two indicators respectively. In the experiment, w1 = 0.75 and w2 = 0.25 are set, indicating a greater focus on density uniformity; D(k) is the density uniformity index, and G(k) is the geometric integrity index; the density uniformity index measures the consistency of the density distribution of the point cloud after denoising. First, the density values of all points are standardized, and then their standard deviation is calculated: Where b is the number of denoised point clouds in the current denoised point cloud dataset P', and μ and σ are the mean and standard deviation of the local density values of all denoised point clouds in the current denoised point cloud dataset P', respectively. A lower standard deviation indicates a more uniform density distribution. The geometric integrity index measures the degree to which the original geometric structure of the point cloud is preserved during the denoising process. Geometric integrity is evaluated by calculating the nearest neighbor distance between the sample point cloud and the denoised point cloud. ;in, S represents any one of the sample point clouds in the sample point cloud dataset S. i The minimum distance between the point cloud S and all denoised point clouds in the current denoised point cloud dataset P', specifically, the minimum distance between the point cloud S and P'.i and The minimum Euclidean distance among all denoised point clouds. I is an indicator function, whose value is determined by... The size determines; if the sample point cloud S i If a point is not mistakenly removed during the denoising process and remains intact in the current denoised point cloud dataset P', then... If the value is 0, then the indicator function I takes the value of 1; conversely, if the sample point cloud S... i If the filter is removed due to noise misjudgment or over-filtering, then If the value is greater than 0, then the value of the indicator function I is 0.
[0042] Specifically, the density uniformity index is calculated by the standard deviation of the local density values after standardization. The lower the standard deviation, the more uniform the density distribution. The geometric integrity index is obtained by calculating the nearest neighbor distance between the sample point cloud and the denoised point cloud, reflecting the degree of preservation of the original geometric structure.
[0043] The point cloud denoising method based on density and meta-learning parameter optimization provided by this invention will be described in detail below with specific implementation examples.
[0044] (1) The dataset was set up to verify the performance of the proposed algorithm. All experiments were conducted on the PyCharm development platform using Python 3.9. The Dragon model from the Stanford University public point cloud dataset and structured light point clouds from six industrial scenarios were selected as the experimental dataset, as shown in Figure 3 and Figures 4(a) to 4(f). Figures 4(a), 4(b), and 4(c) are line structured light point clouds, and Figures 4(d), 4(e), and 4(f) are surface structured light point clouds. The number of point clouds is shown in Table 1. In the dataset, Figures 5(a) to 5(c) show the Dragon model with random noise added based on 10%, 30%, and 50% of its own point cloud quantity to simulate large-scale noise in actual point clouds; Figures 6(a) to 6(c) show the Dragon model with Gaussian noise added based on 10%, 30%, and 50% of its own point cloud quantity to simulate small-scale noise in actual point clouds. Since the structured light point clouds of industrial parts themselves have noise, no additional processing was performed.
[0045] Table 1. Number of point clouds in the experimental dataset
[0046] (2) Evaluation Metrics: The key challenge in point cloud denoising lies in balancing the two core issues of noise retention and feature loss. In traditional denoising methods, one type relies on fixed judgment thresholds or single screening logic. When faced with point cloud data with uneven density distribution, it is easy to mistakenly delete effective geometric feature points in low-density areas, thereby destroying the structural integrity of the point cloud model. Another type of method relies on specific geometric models for fitting, and its applicability is limited to structured scenes. When dealing with point clouds with irregular surface morphology, it is difficult to adapt to complex geometric shapes, ultimately resulting in a low retention rate of effective points. Both types of methods struggle to achieve an effective balance between noise removal effect and the integrity of the original geometric features of the model.
[0047] To address the core requirements of point cloud denoising, this invention selects geometric integrity (recall), geometric shape consistency (bevel distance), and processing time as key evaluation metrics. The geometric integrity metric quantifies the completeness of geometric feature preservation by calculating the nearest distance from valid points in the sample point cloud to the denoised point cloud. Whether this distance is below a set minimum threshold determines whether valid points have been successfully preserved, ultimately yielding the retention rate of valid points in the denoised point cloud. The geometric shape consistency metric is calculated bidirectionally: first, the Euclidean distance from each point in the sample point cloud to the nearest point in the denoised point cloud is calculated; then, the Euclidean distance from each point in the denoised point cloud to the nearest point in the sample point cloud is calculated. The average of these two distances is then taken to quantify the geometric shape consistency between the denoised point cloud and the sample point cloud.
[0048] (3) Standard Point Cloud Denoising Experiment To fully verify the performance of the proposed algorithm and highlight its innovative advantages, the experiment selected three classic methods in the field of point cloud denoising: Method I (denoising method based on RANSAC), Method II (radius filtering method), and Method III (SOR statistical filtering method) to compare and verify with the method in this paper. The core basis for selecting these three methods is as follows: First, they cover the mainstream technical paths in this field and can form a multi-dimensional comparison benchmark. RANSAC, as a representative method based on robust geometric model fitting, is widely used in structured scenarios and can specifically test the ability of the algorithm in this paper to handle irregular geometric structures and small-scale noise; radius filtering determines outliers by counting the number of points in the neighborhood of a fixed radius, which is a typical local density screening method; the neighborhood distribution statistical mechanism of the SOR algorithm and the density discrimination logic of the algorithm in this paper have the same methodological origin, and can accurately compare the parameter adaptive performance under a unified theoretical framework, avoiding evaluation bias caused by differences in principles. Secondly, the three methods have inherent limitations such as poor adaptability to irregular structures, strong density sensitivity, and excessive reliance on manual parameter adjustment. These limitations complement the innovative direction of meta-learning parameter optimization in this paper, and can fully verify the improvement effect of the algorithm from multiple dimensions.
[0049] To simulate typical noise interference during point cloud acquisition, the experiment uses the Dragon model from the Stanford University public dataset as the research object. Point clouds with different proportions of random noise and Gaussian noise were denoised using the three traditional methods mentioned above and the algorithm presented in this paper, respectively. The visualization results are shown in Figures 7-8, and the quantitative data are listed in Table 2.
[0050] In random noise scenarios with a noise ratio of 10% to 50%, traditional methods suffer from significant performance degradation due to inherent limitations. Method I relies on geometric model fitting and has poor adaptability to irregular structures; Method II is constrained by a fixed radius threshold and is prone to erroneously deleting low-density valid points under high noise conditions; while Method III outperforms the first two, its chamfer distance remains relatively high in some cases. In contrast, the algorithm presented in this paper exhibits outstanding advantages: the recall rate after denoising using the dragon model remains consistently above 0.987 across the entire noise ratio range, and the chamfer distance is consistently at the lowest level. Compared with Methods I and II, its chamfer distance is reduced by a maximum of 80.9%; compared with Method III, the reduction exceeds 22.7%, and it can completely preserve geometric features in high-noise environments with minimal shape deviation.
[0051] In Gaussian noise scenarios, traditional methods are more susceptible to noise diffusion characteristics. While Methods I and III can eliminate some noise, under 30% Gaussian noise, the chamfer distances of the dragon model reach 0.228 and 0.113, respectively, indicating poor shape consistency. In contrast, the algorithm presented in this paper demonstrates superior Gaussian noise handling capabilities: compared to Method II, the recall rate is improved by 71.6%; compared to Methods I and II, the maximum reduction in chamfer distance reaches 67.1%. Even under 50% high Gaussian noise conditions, it can still preserve the original surface morphology of the dragon model without significant oversmoothing.
[0052] In terms of time consumption, traditional methods typically have shorter processing times per cycle due to their simpler computational logic. While the algorithm in this paper takes slightly longer per cycle, it eliminates the time cost of manually adjusting neighborhood parameters and thresholds required by traditional methods. Furthermore, the algorithm reduces the amount of data through multi-scale hybrid sampling, ultimately achieving higher overall efficiency in engineering applications.
[0053] Table 2 Comparison data of random noise and Gaussian noise removal experiments in the model
[0054] (4) Denoising Experiment of Line Structured Light Point Cloud for Industrial Parts: To accurately verify the small-scale noise processing performance of line structured light point clouds, three types of aluminum alloy casing parts for laptops were selected as test objects in the comparative experiment. During the line structured light acquisition process, these parts are prone to edge artifact noise due to uneven laser reflection, which is a typical industrial scenario for small-scale noise processing. The experiment used the results of manual fine denoising as verification data, as shown in Figure 9. After registering the denoising results of each method with the manually denoised point cloud, the core evaluation indicators such as geometric integrity index and geometric shape consistency index were obtained.
[0055] The quantitative analysis results in Table 3 fully demonstrate that the proposed algorithm exhibits significant advantages in point cloud denoising for industrial parts. Specifically, the algorithm significantly outperforms the comparative methods in geometric integrity metrics across all test cases: in the test scenario of laptop part 3, its recall rate reaches 0.991, an improvement of approximately 4.1% compared to the SOR method, indicating that the algorithm can more comprehensively retain effective point cloud information and effectively avoid the loss of geometric features. Regarding geometric shape consistency metrics, the algorithm achieves the minimum value in all test samples: taking laptop part 1 as an example, its chamfer distance is only 0.037, a reduction of 34.7% compared to the SOR method, reflecting higher geometric consistency between the denoised point cloud and the real surface.
[0056] The visualization results shown in Figure 10 further demonstrate the advantages of the algorithm: traditional methods tend to over-smooth or blur features in the edges and hole areas of parts, while the algorithm proposed in this paper effectively suppresses small-scale noise while accurately preserving the sharp features of the part structure. Furthermore, although the algorithm's single computation time is slightly longer than that of traditional methods, the meta-learning-driven adaptive parameter optimization eliminates the tedious manual parameter tuning process of traditional methods, significantly reducing the cost of human intervention and maintaining a high level of overall engineering application efficiency, thus possessing practical industrial promotion value.
[0057] Table 3. Comparison of experimental data on noise reduction of structured light point clouds for three types of laptop parts.
[0058] (5) Denoising Experiment of Regional Structured Light Point Cloud for Metal Parts Considering the characteristics of regional structured light systems with small-scale noise and large-scale noise, three types of metal parts were selected for denoising tests in the comparative experiment. In the experiment, the results of artificial denoising were used as the benchmark, as shown in Figure 11. Finally, the denoising results of each method were combined with the artificially denoised point cloud for quantitative calculation to obtain the corresponding evaluation index.
[0059] The data in Table 4 show that, in terms of geometric integrity metrics (recall), the proposed algorithm significantly outperforms the other three methods, demonstrating its clear advantage in preserving valid point clouds. Regarding the chamfer distance metric for measuring geometric consistency, the proposed algorithm shows a significant reduction compared to other methods: a 31.7% reduction compared to the SOR method, a 42.3% reduction compared to the radius filtering method, and a 51.2% reduction compared to the RANSAC method. This result proves that the proposed algorithm can better preserve the geometric topology of the point cloud while removing noise. From a visual comparison, as shown in Figure 12, the RANSAC method, due to its reliance on geometric model fitting, leads to a large number of erroneous deletions when processing irregular metal surfaces; the radius filtering method, constrained by a fixed threshold, excessively removes valid points in low-density regions; although the SOR method can eliminate some noise, feature loss still occurs in complex structures. In contrast, the proposed algorithm achieves the optimal balance between noise removal and feature preservation through a density-adaptive filtering mechanism.
[0060] Table 4 Comparison of experimental data on denoising of structured light point clouds of three types of metal parts
[0061] In summary, the point cloud denoising method based on density and meta-learning parameter optimization provided by this invention firstly extracts feature point clouds using multi-scale hybrid sampling, inputs them into a meta-learning optimizer to generate initial values of neighborhood parameters, and combines a momentum-accelerated gradient descent algorithm to achieve parameter optimization. Secondly, it designs a density adaptive filter that integrates Gaussian kernel density estimation and quartile range analysis to achieve multi-scale noise removal.
[0062] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes, and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.
Claims
1. A point cloud denoising method based on density and meta-learning parameter optimization, characterized in that, The process includes the following steps: Step S1: Obtain the original point cloud dataset and the historical point cloud dataset, and extract a sample point cloud dataset containing global structure and local details from the original point cloud dataset; Step S2: Learn meta-parameters based on the historical point cloud dataset to generate the optimal initial value of the neighborhood parameter k; Step S3: Starting from the optimal initial value of the neighborhood parameter k, iteratively adjust the neighborhood parameter k to obtain the current iterative value of the neighborhood parameter k; Step S4: Calculate the local density value of each sample point cloud in the sample point cloud dataset based on the current iterative value of the neighborhood parameter k, and denoise the sample point cloud dataset based on the local density value of each sample point cloud in the sample point cloud dataset to obtain the current denoised point cloud dataset; Step S5: Calculate the comprehensive score value of the current denoised point cloud dataset. If the comprehensive score of the current denoised point cloud dataset reaches a preset threshold, it means that the current iteration value of the neighborhood parameter k is the optimal iteration value, and the current denoised point cloud dataset is output. If the overall score of the current denoised point cloud dataset does not reach the preset threshold, the process returns to step S3 to continue iteratively adjusting the neighborhood parameter k until the overall score of the current denoised point cloud dataset reaches the preset threshold.
2. The point cloud denoising method based on density and meta-learning parameter optimization according to claim 1, characterized in that, The step of extracting a sample point cloud dataset containing global structure and local details from the original point cloud dataset includes: performing global random sampling, voxel downsampling, and local random sampling on the original point cloud dataset in sequence to extract a global sample subset S1, a mesoscopic sample subset S2, and a local sample subset S3 in sequence, and combining the global sample subset S1, the mesoscopic sample subset S2, and the local sample subset S3 to form the sample point cloud dataset S.
3. The point cloud denoising method based on density and meta-learning parameter optimization according to claim 1, characterized in that, Step S2 includes: Step S21: For each historical point cloud C in the historical point cloud dataset i Using the current time meta-parameter θ t Using the current initial value of the neighborhood parameter k, perform T steps of gradient descent optimization to obtain the optimized initial value of the neighborhood parameter k. ： Where GD represents the gradient descent optimization process; Step S22: Calculate the meta-parameter θ at the current time. t meta-objective function ,in, It is all the historical point clouds C in the historical point cloud dataset. i The initial value of the optimized neighborhood parameter k Evaluation function value under Average value: Where N is the number of historical point clouds in the historical point cloud dataset; For each historical point cloud C i The initial value of the optimized neighborhood parameter k The evaluation function value is given below; Step S23: Calculate the meta-objective function using the central difference method. Meta-parameters at the current time gradient ： ;in, The perturbation value; Step S24: Obtain the gradient Then, the meta-learning rate η is used to update the meta-parameters θ at the current time step. t until the trained meta-parameters θ are obtained. * ; ;in, For the next time step, use the trained meta-parameters θ; Step S25: Use the trained meta-parameters θ * The optimal initial value k0 is used as the neighborhood parameter k.
4. The point cloud denoising method based on density and meta-learning parameter optimization according to claim 1, characterized in that, Step S3 includes: Step S31: For the current iteration value k of the neighborhood parameter k t The gradient is estimated using the finite difference method; if the current iteration value k t If the value is greater than 1, the gradient is estimated using the central difference method. ： If the current iteration value k t When the value equals 1, the gradient is estimated using the one-sided difference method. ： Where Δk is the difference step size, To evaluate the function value Regarding the current iteration value k t The gradient; L is the evaluation function; Step S32: Obtain the gradient Then, the momentum method is used to update the neighborhood parameter k: ； ; where v t V is the momentum term at time t; t+1 Let α be the momentum term at time t+1; α be the learning rate; β be the momentum coefficient; k t Let k be the iteration value of the neighborhood parameter k at time t, that is, the current iteration value of the neighborhood parameter k; t+1 This is the iteration value of the neighborhood parameter k at time t+1.
5. The point cloud denoising method based on density and meta-learning parameter optimization according to claim 1, characterized in that, Step S4 includes: Step S41: For each sample point cloud S in the sample point cloud dataset S i Calculate the distance between it and its k nearest neighbor point clouds, and then calculate S for each point cloud. i Local density value ： Where σ is the adaptive bandwidth parameter, and d ij Let S be the point cloud of the i-th sample. i The distance between it and its j-th nearest neighbor sample point cloud; Step S42: Calculate the first quartile Q1 and the third quartile Q3 of the local density values of all sample point clouds in the sample point cloud dataset S to obtain the quartile range IQR: ； IQR = Q3 - Q1; where m is the number of sample point clouds in the sample point cloud dataset S; percentile is the percentile; Step S43: Set the density threshold for: Where r is an adjustable parameter; median is the median; Step S44: Retain the local density values in the sample point cloud dataset S. Above the density threshold Sample point cloud S i To form the current denoised point cloud dataset P': 。 6. The point cloud denoising method based on density and meta-learning parameter optimization according to claim 5, characterized in that, The calculation of the comprehensive score of the current denoised point cloud dataset also includes: the calculation formula of the comprehensive score L(k) of the current denoised point cloud dataset P' is as follows: L(k)=w1×D(k) + w2×G(k); where w1 and w2 are both weight coefficients, D(k) is the density uniformity index, and G(k) is the geometric integrity index. Where b is the number of denoised point clouds in the current denoised point cloud dataset P', and μ and σ are the mean and standard deviation of the local density values of all denoised point clouds in the current denoised point cloud dataset P', respectively. ;in, S represents any one of the sample point clouds in the sample point cloud dataset S. i The minimum distance between the current denoised point cloud dataset P' and all denoised point clouds, where I is an indicator function; if If the value is 0, then the indicator function I takes the value of 1; otherwise, if If the value is greater than 0, then the value of the indicator function I is 0.