Three-dimensional vision measurement system error compensation method based on spatial adaptive weighted RBF (Radial Basis Function) residual neural network

Abstract

The invention discloses a three-dimensional vision measurement system error compensation method based on a spatial adaptive weighted RBF residual neural network, and particularly provides a spatial adaptive residual learning framework SAW-RFramework, in the first stage, global rigid body errors are eliminated based on a Kabsch algorithm, and point cloud rigid alignment is realized; in the second stage, a thin-plate spline kernel RBF interpolator is used for modeling a spatial smoothing error field, and position-related systematic deviation is captured; and in the third stage, a partition weighted residual neural network is adopted, and an improved residual compensation network is proposed for residual high-fluctuation nonlinear residual after RBF modeling: a regional importance coefficient is calculated based on a mean value and a variance of the residual in a self-adaptive three-dimensional grid, so that network training focuses on a high-error and high-fluctuation region. According to the method, the problems of insufficient global spatial modeling capability, low boundary region compensation precision, poor generalization capability and the like of an existing method can be solved; high-precision error compensation of the three-dimensional vision measurement system is realized, the measurement result reaches submillimeter precision, and the application reliability in robot control, man-machine interaction and precision manufacturing is improved.

Description

Technical Field

[0001] This invention relates to error correction and accuracy compensation technology for optical motion capture systems, belonging to the fields of computer vision, 3D measurement and human-computer interaction, and particularly to an error compensation method for 3D vision measurement systems based on spatial adaptive weighted RBF residual neural networks. Background Technology

[0002] Optical motion capture systems acquire two-dimensional images of reflective markers in space using multi-view cameras and reconstruct three-dimensional coordinates using triangulation principles. Due to their advantages of being non-contact, high-speed, and high-precision, they have been widely applied in fields such as robot calibration, virtual reality interaction, biomechanical analysis, and film and animation. However, in practical applications, their accuracy is still affected by various factors: camera lens distortion, installation deviations, lighting variations, occlusion, and the instability of calculation methods can all lead to systematic biases and local nonlinear errors across the entire domain. Existing technologies mainly employ three types of methods for correction: first, rigid body registration methods, which can eliminate overall translation and rotational biases but cannot handle complex distortions; second, interpolation fitting methods based on polynomials or radial basis functions (RBF), which can achieve global smooth compensation but lack accuracy at boundaries and in areas with high local errors; and third, neural network methods, which, while capable of fitting nonlinear residuals, rely on a large amount of training data and suffer from overfitting and weak generalization capabilities.

[0003] Therefore, existing solutions struggle to balance global accuracy with local compensation capabilities, failing to meet the demands of sub-millimeter level high-precision applications. This has become a major bottleneck for the further promotion of motion capture technology. Summary of the Invention

[0004] To address the aforementioned shortcomings, this invention provides an error compensation method for 3D vision measurement systems based on a spatially adaptive weighted RBF residual neural network. This method solves problems such as insufficient global spatial modeling capabilities, low accuracy in boundary region compensation, and poor generalization ability of existing methods. It achieves high-precision error compensation for optical motion capture systems, enabling measurement results to reach sub-millimeter level accuracy and improving the reliability of applications in robot control, human-computer interaction, and precision manufacturing.

[0005] The technical solution adopted by the present invention to achieve the above objectives is as follows:

[0006] An error compensation method for a 3D vision measurement system based on a spatially adaptive weighted RBF residual neural network captures the non-uniformity of the anatomical spatial error distribution between the center and the boundary, and compensates for it by mesh weight equalization to eliminate boundary drift; including the following steps:

[0007] In the application scenario, the paired point clouds of the target object are acquired simultaneously by the motion capture camera and the laser tracker;

[0008] Global rigid body error correction: The Kabsch algorithm is used to perform rigid body registration of paired point clouds in the motion capture camera coordinate system and the laser tracker coordinate system to eliminate systematic rotation and translation errors; the points in the motion capture camera coordinate system are then... Points registered after transformation to the laser tracker coordinate system ;

[0009] Global error modeling based on thin plate spline (TPS) radial basis function: Using the collected calibration point data, a 3D TPS-RBF interpolation function is constructed to smooth and initially compensate for the global spatial error, obtaining arbitrary registration spatial points. On the prediction error ;

[0010] Spatial adaptive grid weight calculation: The entire workspace is divided into several adaptive grids. The weights are determined based on the mean and variance of the error distribution within the grid. Normalization and clipping are used to ensure a reasonable weight distribution, resulting in the spatial adaptive weights after grid partitioning. ;

[0011] Residual Neural Network Compensation: A lightweight residual neural network is constructed to perform secondary modeling of the residuals after RBF compensation; spatially adaptive weights are introduced during training. This improves the model's learning ability in high-error regions and ensures accuracy in boundary and non-uniformly distributed regions.

[0012] Comprehensive compensation output: The rigid body registration, RBF fitting, and weighted residual network are sequentially fused to obtain the final high-precision compensation result coordinates. ,in .

[0013] The global rigid body error correction specifically includes:

[0014] Define the marker point cloud in the motion capture camera coordinate system Simultaneously, the corresponding real-world point cloud in the laser tracker coordinate system. ;

[0015] First, the centroids of the two sets of data are centered to obtain their respective mean points: ;

[0016] Then, with the goal of minimizing the mean square error between the two sets of points, the Kabsch rigid body registration algorithm is used to construct the covariance matrix and perform SVD decomposition to solve for the optimal rotation matrix R and translation vector t.

[0017]

[0018]

[0019] in, Represents the centered covariance matrix. The matrix obtained from singular value decomposition is minimized as follows: ;

[0020] Ultimately, After conversion to the laser tracker coordinate system for registration According to this formula, we can obtain the same result as... The optimal rigid body alignment state.

[0021] The global error modeling based on the radial basis function of thin plate spline (TPS) includes:

[0022] Motion capture point cloud after rigid body registration and alignment With reference point cloud Based on this, define the residual vector Used for subsequent error modeling and compensation.

[0023] To capture the anatomical spatial error distribution, radial basis function interpolation is employed, primarily using the Thin-PlateSpline (TPS) kernel. The RBF Interpolator in SciPy is used to fit and predict the spatial error mapping, calculating the prediction error at any registered spatial point f. ;

[0024]

[0025] in The points to be predicted are the rigid body registration points in the coordinate system of the laser tracker. For the interpolation coefficient vector, the parameters and This is the global affine component, used to correct overall offset and linear trend; TPS kernel. It is the radial basis function representation of a thin-plate spline in a two-dimensional plane in a general form in 3D space.

[0026] The process of dividing the entire workspace into several adaptive grids includes:

[0027] To capture the non-uniformity of the spatial distribution of errors and prioritize training regions with larger or unstable errors, the registered point cloud... Divided into three-dimensional space One grid cell;

[0028]

[0029] Where N is the total number of samples. It is the target number of points per square. These represent the upper and lower limits of the number of grid cells, respectively.

[0030] The process of determining weights based on the mean and variance of the error distribution within the grid, and ensuring a reasonable weight distribution through normalization and pruning, includes: calculating weights based on inverse-variance.

[0031]

[0032] in The sampling weights in the weighted loss are used to highlight regions with large errors or instability. Represents each cell Mean of the error magnitude at the midpoint This represents the standard deviation and the mean of the global standard deviation. ; Represents the global mean error;

[0033]

[0034] in For the normalized spatial adaptive weights, This indicates that the weights will be clipped to... Within the range, This represents the weight of sample j during traversal.

[0035] The residual neural network structure includes:

[0036] Input layer coordinates after rigid body registration and RBF interpolation prediction For input: ; Due to prediction error Calculated using the formula;

[0037] The hidden layers are fully connected layers with a topology set to [256, 256, 256, 128], and each layer includes normalized BatchNorm and SiLU activation;

[0038] Add Dropout to the intermediate layer to prevent overfitting;

[0039] The output layer is linearly mapped to the residual correction term. .

[0040] The structure of each residual block is as follows:

[0041]

[0042] in This represents the nonlinear transformation after passing through a linear layer, BatchNorm, and activation function.

[0043] The residual neural network is trained using a weighted Huber loss (Smooth L1 Loss) combined with weights obtained from spatial grid partitioning. To ensure consistency in the overall scale of losses:

[0044]

[0045] in, To introduce a residual neural network, ResidualCompensation Neural Net, to learn and compensate for the residuals after RBF interpolation, It is a real location point cloud , This is the output of the neural network.

[0046] The final corrected coordinates are .

[0047] The training process employs the AdamW optimizer and the ReduceLROnPlateau learning rate scheduling strategy to dynamically adjust the learning rate during training, and uses an early stopping mechanism to avoid overfitting.

[0048] The present invention has the following beneficial effects and advantages:

[0049] 1. Improved global accuracy: Combining RBF and residual network can achieve sub-millimeter level error compensation, which is significantly better than single methods.

[0050] 2. Strong local compensation capability: The spatial adaptive weighting mechanism effectively improves the compensation accuracy of boundaries and complex areas.

[0051] 3. Good model generalization: It exhibits high accuracy on different types of motion capture devices and has the potential for cross-device application.

[0052] 4. Improved numerical stability: By hierarchical modeling and weight pruning, the ill-conditioned problem of RBF under large-scale samples is reduced.

[0053] 5. Strong feasibility for engineering applications: The method has high computational efficiency and can be deployed in offline and near real-time scenarios, meeting the application needs of industrial robots, precision measurement, human-computer interaction and other applications. Attached Figure Description

[0054] Figure 1 This is a schematic diagram of the measurement system of the present invention.

[0055] Figure 2 This is a 3D registration visualization diagram of the present invention.

[0056] Figure 3 This is a schematic diagram of the captured area partitioning of the present invention.

[0057] Figure 4 This is a diagram of the error compensation framework of the present invention. Detailed Implementation

[0058] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of the invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0059] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. The invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0060] Key technical points and areas to be protected in this invention:

[0061] (1) Hierarchical residual compensation framework: rigid body registration → RBF interpolation → residual neural network.

[0062] (2) Spatial adaptive grid weighting mechanism: The learning weights of the network are adjusted by error statistics to improve local accuracy.

[0063] (3) Composite modeling method: RBF handles global low-frequency errors, and residual network handles local high-frequency errors. The two complement each other.

[0064] This invention proposes a spatially adaptive residual learning framework (SAW-R² Framework) that enables a two-stage error decoupling mechanism: the first stage uses the Kabsch algorithm to eliminate global rigid body errors (calibration bias / system noise) and achieve rigid alignment of point clouds; the second stage uses a thin plate spline kernel RBF interpolator to model the spatial smoothing error field and capture position-related systematic biases; the third stage uses a partitioned weighted residual neural network to improve the residual compensation network for the high-fluctuation nonlinear residuals (such as label drift) after RBF modeling: the regional importance coefficient is calculated based on the mean and variance of the residuals in the adaptive 3D grid, so that the network training focuses on high-error, high-fluctuation regions.

[0065] Phase 1:

[0066] Use a motion capture camera to collect data from marker points on the experimental platform. At the same time, the laser tracker will correspond to the point cloud of the real location. Records. For example... Figure 1As shown, the paired point clouds of the target object, synchronously acquired by a motion capture camera and a laser tracker, form the basic data for the compensation system of this invention. To eliminate the spatial offset and orientation difference between the two, the Kabsch rigid body registration algorithm is used to solve for the optimal rotation matrix R and translation vector t, thereby minimizing the mean square error between the two sets of points. First, the centroids of the two sets of data are centered. Then, the covariance matrix is ​​constructed and SVD decomposition is performed to determine the rotation matrix and translation vector.

[0067]

[0068]

[0069] Here Represents the centered covariance matrix. The matrix obtained from singular value decomposition. Let these represent the rotation matrix and translation vector, respectively. After conversion to registration You can get the same as The optimal rigid body alignment state minimizes the mean square error. .like Figure 2 The image shown is a visualization of the three-dimensional registration of this invention. The left image is the point cloud collected by the motion capture camera, and the right image is the point cloud after registration.

[0070] Phase Two:

[0071] Motion capture point cloud after rigid body registration and alignment With reference point cloud Based on this, define the residual vector This is used for subsequent error modeling and compensation. To capture the anatomical spatial error distribution, this paper uses radial basis function interpolation, mainly the Thin-Plate Spline (TPS) kernel function, and utilizes the RBF Interpolator in SciPy to fit and predict the spatial error mapping.

[0072]

[0073] in The point to be predicted (the point after rigid body registration). For the interpolation coefficient vector, the parameters and This is the global affine component, used to correct overall offset and linear trends. (TPS kernel) It is a radial basis function representation of a thin-plate spline in a two-dimensional plane in 3D space, possessing the advantages of analytical closed-form solutions and smooth minimum bending energy characteristics. The coefficients of the model are determined by solving the linear system. Then it can be used at any registration space point. Upper prediction error .

[0074] Phase Three:

[0075] To capture the non-uniformity of the spatial distribution of errors and prioritize training regions with larger or unstable errors, we propose to perform a process of training the registered point cloud... Divided into three-dimensional space The system uses a grid of cells and calculates the mean and standard deviation of the error for each cell to construct sample weights. The number of grid cells is adaptively divided.

[0076]

[0077] Where N is the total number of samples (number of rigid body registration points). It is the target number of points per square. These are the upper and lower limits for the number of grid cells, respectively, and the weights are then calculated based on inverse-variance:

[0078]

[0079] in The sampling weights in the weighted loss are used to highlight regions with large errors or instability. Represents each cell Mean of the error magnitude at the midpoint This represents the standard deviation and the mean of the global standard deviation. ; Represents the global mean error;

[0080]

[0081] in For the normalized spatial adaptive weights, This indicates that the weights will be clipped to... Within the range; This represents the weight of sample j during traversal.

[0082] like Figure 3 This is a calculated zoning outline. After completing RBF interpolation prediction... Subsequently, this paper further introduces a residual compensation neural network to learn and compensate for the residuals after RBF interpolation, thereby improving the overall compensation accuracy. This structure can be described as follows:

[0083]

[0084]

[0085] in It is the residual correction term of the neural network output, and the input data is... The final corrected coordinates are The entire network structure is as follows: Figure 4 The input layer contains the coordinates after rigid body registration. and RBF interpolation prediction The input consists of 6 dimensions. The hidden layers are fully connected layers with a topology set to [256, 256, 256, 128]. Each layer includes BatchNorm and SiLU (Swish) activations. Dropout (0.2) is added to the intermediate layers to prevent overfitting. The output layer is linearly mapped as follows: It directly predicts the error correction amount. Each residual block has the following structure:

[0086]

[0087] in This represents a non-linear transformation after passing through a linear layer, BatchNorm, and activation function. This type of structure helps solve the vanishing gradient problem in deep network training, improving model stability and expressive power.

[0088] The network training uses a weighted Huber loss (Smooth L1 Loss), combined with weights obtained from spatial grid partitioning. Ultimately, by dividing by Ensure consistency in the scale of overall losses.

[0089]

[0090] The AdamW optimizer and ReduceLROnPlateau learning rate scheduling strategy are used to dynamically adjust the learning rate during training, and an early stopping mechanism is used to avoid overfitting.

[0091] The motion capture error compensation method proposed in this invention takes layered modeling as its core, which not only improves the numerical stability of error modeling, but also significantly improves the compensation accuracy in boundary and high error regions, achieving sub-millimeter level accuracy of the motion capture system in a large spatial range.

[0092] The embodiments described above will help those skilled in the art to further understand the present invention, but do not limit the present invention in any way. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention. These all fall within the protection scope of the present invention.

Claims

1. An error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network, characterized in that, The following steps are used to capture the non-uniformity of the anatomical spatial error distribution between the center and the boundary, and to compensate for it with mesh weight equalization to eliminate boundary drift; including the following steps: In the application scenario, the paired point clouds of the target object are acquired simultaneously by the motion capture camera and the laser tracker; Global rigid body error correction: The Kabsch algorithm is used to perform rigid body registration of paired point clouds in the motion capture camera coordinate system and the laser tracker coordinate system to eliminate systematic rotation and translation errors; the points in the motion capture camera coordinate system are then... Points registered after transformation to the laser tracker coordinate system ; Global error modeling based on thin plate spline (TPS) radial basis function: Using the collected calibration point data, a 3D TPS-RBF interpolation function is constructed to smooth and initially compensate for the global spatial error, obtaining arbitrary registration spatial points. On the prediction error ; Spatial adaptive grid weight calculation: The entire workspace is divided into several adaptive grids. The weights are determined based on the mean and variance of the error distribution within the grid. Normalization and clipping are used to ensure a reasonable weight distribution, resulting in the spatial adaptive weights after grid partitioning. ; Residual Neural Network Compensation: A lightweight residual neural network is constructed to perform secondary modeling of the residuals after RBF compensation; spatially adaptive weights are introduced during training. This improves the model's learning ability in high-error regions and ensures accuracy in boundary and non-uniformly distributed regions. Comprehensive compensation output: The rigid body registration, RBF fitting, and weighted residual network are sequentially fused to obtain the final high-precision compensation result coordinates. ,in .

2. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 1, characterized in that, The global rigid body error correction specifically includes: Define the marker point cloud in the motion capture camera coordinate system Simultaneously, the corresponding real-world point cloud in the laser tracker coordinate system. ; First, the centroids of the two sets of data are centered to obtain their respective mean points: ; Then, with the goal of minimizing the mean square error between the two sets of points, the Kabsch rigid body registration algorithm is used to construct the covariance matrix and perform SVD decomposition to solve for the optimal rotation matrix R and translation vector t. in, Represents the centered covariance matrix. The matrix obtained from singular value decomposition is minimized as follows: ; Ultimately, After conversion to the laser tracker coordinate system for registration According to this formula, we can obtain the same result as... The optimal rigid body alignment state.

3. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 1, characterized in that, The global error modeling based on the radial basis function of thin plate spline (TPS) includes: Motion capture point cloud after rigid body registration and alignment With reference point cloud Based on this, define the residual vector Used for subsequent error modeling and compensation. To capture the anatomical spatial error distribution, radial basis function interpolation is employed, primarily using the Thin-PlateSpline (TPS) kernel. The RBF Interpolator in SciPy is used to fit and predict the spatial error mapping, calculating the prediction error at any registered spatial point f. ; in The points to be predicted are the rigid body registration points in the coordinate system of the laser tracker. For the interpolation coefficient vector, the parameters and This is the global affine component, used to correct overall offset and linear trend; TPS kernel. It is the radial basis function representation of a thin-plate spline in a two-dimensional plane in a general form in 3D space.

4. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 1, characterized in that, The process of dividing the entire workspace into several adaptive grids includes: To capture the non-uniformity of the spatial distribution of errors and prioritize training regions with larger or unstable errors, the registered point cloud... Divided into three-dimensional space One grid cell; Where N is the total number of samples. It is the target number of points per square. These represent the upper and lower limits of the number of grid cells, respectively.

5. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 4, characterized in that, The process of determining weights based on the mean and variance of the error distribution within the grid, and ensuring a reasonable weight distribution through normalization and pruning, includes: calculating weights based on inverse-variance. in The sampling weights in the weighted loss are used to highlight regions with large errors or instability. Represents each cell Mean of the error magnitude at the midpoint This represents the standard deviation and the mean of the global standard deviation. ; Represents the global mean error; in For the normalized spatial adaptive weights, This indicates that the weights will be clipped to... Within the range, This represents the weight of sample j during traversal.

6. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 1, characterized in that, The residual neural network structure includes: Input layer coordinates after rigid body registration and RBF interpolation prediction For input: ; Due to prediction error Calculated using the formula; The hidden layers are fully connected layers with a topology set to [256, 256, 256, 128], and each layer includes normalized BatchNorm and SiLU activation; Add Dropout to the intermediate layer to prevent overfitting; The output layer is linearly mapped to the residual correction term. .

7. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 6, characterized in that, The structure of each residual block is as follows: in This represents the nonlinear transformation after passing through a linear layer, BatchNorm, and activation function.

8. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 6, characterized in that, The residual neural network is trained using a weighted Huber loss (Smooth L1 Loss) combined with weights obtained from spatial grid partitioning. To ensure consistency in the overall scale of losses: in, To introduce a residual neural network, ResidualCompensation Neural Net, to learn and compensate for the residuals after RBF interpolation, It is a real location point cloud , This is the output of the neural network.

9. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 4, characterized in that, The final corrected coordinates are .

10. The error compensation method for a three-dimensional vision measurement system based on a spatially adaptive weighted RBF residual neural network according to claim 4, characterized in that, The training process employs the AdamW optimizer and the ReduceLROnPlateau learning rate scheduling strategy to dynamically adjust the learning rate during training, and uses an early stopping mechanism to avoid overfitting.

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