Method and device for quickly calibrating microscopic CT (Computed Tomography) system based on forest ball array

By utilizing a forest ball array-based micro-CT system, high-precision industrial CT scanning and advanced image processing algorithms are employed to solve the problems of slow calibration speed and unstable accuracy in micro-CT systems, achieving rapid and accurate calibration results suitable for precision manufacturing.

CN120847148APending Publication Date: 2025-10-28ZHEJIANG INSTITUTE OF QUALITY SCIENCES
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Patent Information

Application Number
CN202510964704.9
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-07-14
Publication Date
2025-10-28

AI Technical Summary

Technical Problem

Existing calibration methods for micro-CT systems suffer from slow speed and unstable accuracy, making it difficult to meet real-time detection requirements, especially in complex noise environments, and they also lack robustness.

Method used

A forest ball array-based micro-CT system was adopted, and three-dimensional image data was acquired by a high-precision industrial CT scanner. Image preprocessing was performed by combining anisotropic diffusion filtering and morphological-watershed hybrid segmentation algorithms. Point cloud data was optimized by normal vector estimation and dynamic error compensation model. Finally, the coordinates of the sphere center were quickly extracted by a robust sphere fitting algorithm.

Benefits of technology

It enables rapid calibration of the micro-CT system, improving calibration speed and accuracy, and maintains stability under complex noise and temperature variation scenarios, making it suitable for precision manufacturing.

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Abstract

According to the technical scheme, system hardware is composed of a micro-focus ray source, a flat panel detector, a motion platform and a multi-ball standard part (forest ball array), and high-precision data acquisition and processing are achieved in combination with a multi-physics field sensing module and a parallel computing unit. The method comprises the steps of optimizing CT image preprocessing by using an adaptive denoising and hybrid segmentation algorithm, improving the point cloud precision by using a weighted covariance matrix and a dynamic error compensation model, and rapidly extracting a sphere center coordinate through a robust sphere fitting algorithm. In addition, a thermal-mechanical coupling compensation and spinor theory error transfer mechanism is introduced, and the environment temperature and mechanical motion errors are effectively restrained. According to the method, the calibration time is remarkably shortened, the positioning precision is improved to the micron level, the stability of the system in a complex noise and temperature change scene is enhanced, and the method is suitable for efficient microscopic CT system calibration in the precision manufacturing field.
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Description

Technical Field

[0001] This invention relates to the field of precision measurement technology in industrial CT, specifically to a rapid calibration method and apparatus for a micro-CT system based on a forest ball array. Background Technology

[0002] In the field of precision manufacturing, micro-CT systems require calibration of equipment accuracy using the geometric parameters (such as center coordinates and spacing) of a standard spherical array (forest sphere).

[0003] Traditional methods rely on the sphere fitting modules of commercial software (such as VGSTUDIO MAX), but face two major bottlenecks: firstly, speed limitations, as global point cloud processing is time-consuming and difficult to meet real-time detection requirements; secondly, accuracy fluctuations, as fitting results are easily affected by outliers in complex noisy scenarios, leading to cumulative errors in the sphere center coordinates. Tools like VGSTUDIO MAX use generalized least squares or random sampling (RANSAC) to fit the sphere, requiring traversal of the entire point cloud, resulting in high computational redundancy; and they lack robustness to low-resolution or partially missing point clouds. Summary of the Invention

[0004] To address the problems mentioned in the background section, the present invention aims to provide a rapid calibration method and apparatus for a micro-CT system based on a forest ball array, which has the advantages of fast calibration speed and good calibration effect, and solves the problems of insufficient calibration methods for existing micro-CT systems.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a rapid calibration method for a micro-CT system based on a forest ball array, comprising the following steps: Step 1: Use a high-precision industrial CT scanner to acquire 3D image data of the forest ball array and import the measured 3D image data of the forest ball; Step 2: After scanning the forest sphere array with micro-CT, the CT data is preprocessed. The CT data is preprocessed and the spheres are quickly segmented. Anisotropic diffusion filtering and the three-dimensional Perona-Malik equation are applied to the CT images for denoising and enhancement. The morphology-watershed hybrid segmentation algorithm is used to quickly segment the spheres. Step 3: Surface measurement. The surface of the segmented sphere is measured using a surface feature extraction algorithm based on normal vector estimation. Step 4: Point cloud optimization, which optimizes the point cloud data using a dynamic error compensation model; Step 5: Sphere fitting. Use a robust sphere fitting algorithm to fit the spheres and measure the distance between their centers. Measure the distance between the centers of two specified spheres in sequence and compare it with the standard to obtain the error. Step 6: Measure the distance and obtain the error, analyze the error of the measured sphere center distance, perform error analysis on the measurement results, and evaluate the calibration accuracy; Thus, a rapid calibration method for micro-CT systems has been achieved.

[0006] As a preferred embodiment of the present invention, step 1 is specifically implemented according to the following process: Using a high-precision industrial CT scanner and setting appropriate scanning parameters, three-dimensional image data of the forest ball array were acquired.

[0007] As a preferred embodiment of the present invention, step 2 is specifically implemented according to the following process: Anisotropic diffusion filtering achieves image denoising and enhancement through the three-dimensional Perona-Malik equation. Details of the three-dimensional Perona-Malik equation implementation are as follows:

[0008]

[0009] Morphological-watershed hybrid segmentation is employed: First, distance transformation is calculated to generate a distance map.

[0010] Next, a tagging function is generated to avoid over-segmentation: .

[0011] As a preferred embodiment of the present invention, the surface measurement principle in step 3 is as follows: For a point pi in a point cloud, its normal vector It can be obtained by calculating the eigenvector corresponding to the smallest eigenvalue of the covariance matrix of its neighboring points. Let Ni be the set of neighboring points of pi, and the covariance matrix Ci is calculated as follows: .

[0012] As a preferred embodiment of the present invention, the dynamic error compensation model in step 4 is as follows: The point cloud data is optimized using a dynamic error compensation model, including thermo-mechanical coupling compensation and an error propagation equation based on spinor theory.

[0013] Secondly, there is the kinematic transmission error, based on the error transmission equation of spinor theory:

[0014] Where J is the joint variable and K is the geometric error parameter.

[0015] As a preferred embodiment of the present invention, the robust sphere fitting algorithm in step 5 is as follows: First, a coarse fit is performed, and initial parameters are calculated by randomly sampling four points to satisfy geometric constraints:

[0016] Then, fine optimization is performed using a weighted least squares objective function to improve fitting accuracy:

[0017] Then, the center coordinates and radius of each sphere are extracted from the fitting results, and the distance between the centers of the two spheres is calculated using the Euclidean distance formula:

[0018] The calculated distance is compared with the standard distance to analyze the error.

[0019] In a preferred embodiment of the present invention, the multi-ball standard (ball stick, ball plate, forest ball) consists of 27 balls, with a fixed spacing between the balls and the center-to-center distance can be obtained through calibration. The multi-ball standard is made of ruby. The supporting rods are made of carbon fiber reinforced material with low X-ray absorption.

[0020] In a preferred embodiment of the present invention, the multi-sphere standard is placed in the measurement space of the CT scanner, and measurements are performed according to the operating instructions of the CT scanner, using the set voltage and current parameters and the step scanning mode. Specifically, the scanning voltage is set to 150V, the current to 100A, the number of projections to 1800, and the integration time to 500ms, to ensure high-quality image data is obtained.

[0021] Compared with the prior art, the present invention has the following beneficial effects: 1. This invention employs a system hardware consisting of a microfocus X-ray source, a flat panel detector, a motion platform, and multi-sphere standard components (forest sphere array). Combined with a multiphysics sensing module and a parallel computing unit, it achieves high-precision data acquisition and processing. The method includes optimizing CT image preprocessing using adaptive denoising and hybrid segmentation algorithms, improving point cloud accuracy using a weighted covariance matrix and dynamic error compensation model, and rapidly extracting sphere center coordinates through a robust sphere fitting algorithm. Furthermore, it introduces a thermo-mechanical coupling compensation and spinor theory error propagation mechanism to effectively suppress environmental temperature and mechanical motion errors. This invention significantly shortens calibration time, improves positioning accuracy to the micrometer level, and enhances system stability under complex noise and temperature variation scenarios. It is suitable for high-efficiency micro-CT system calibration in precision manufacturing fields, and the device boasts advantages of fast calibration speed and excellent calibration results.

[0022] 2. This invention uses a high-precision industrial CT scanner to accurately capture the geometry and spatial distribution of forest ball arrays, laying the foundation for subsequent calibration processing. Attached Figure Description

[0023] Figure 1 This is a flowchart of the steps of the method of the present invention; Figure 2 This is a schematic diagram of the three-dimensional image data acquisition for the forest sphere array; Figure 3 This involves the implementation details of anisotropic diffusion filtering and the three-dimensional Perona-Malik equations; Figure 4 This is a flowchart of the morphology-watershed hybrid segmentation algorithm; Figure 5 This is a flowchart of a robust sphere fitting algorithm. Detailed Implementation

[0024] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] like Figures 1 to 5 As shown, a rapid calibration method for a forest ball array-based micro-CT system includes the following steps: Step 1: Use a high-precision industrial CT scanner to acquire 3D image data of the forest ball array and import the measured 3D image data of the forest ball; Step 2: After scanning the forest sphere array with micro-CT, the CT data is preprocessed. The CT data is preprocessed and the spheres are quickly segmented. Anisotropic diffusion filtering and the three-dimensional Perona-Malik equation are applied to the CT images for denoising and enhancement. The morphology-watershed hybrid segmentation algorithm is used to quickly segment the spheres. Step 3: Surface measurement. The surface of the segmented sphere is measured using a surface feature extraction algorithm based on normal vector estimation. Step 4: Point cloud optimization, which optimizes the point cloud data using a dynamic error compensation model; Step 5: Sphere fitting. Use a robust sphere fitting algorithm to fit the spheres and measure the distance between their centers. Measure the distance between the centers of two specified spheres in sequence and compare it with the standard to obtain the error. Step 6: Measure the distance and obtain the error, analyze the error of the measured sphere center distance, perform error analysis on the measurement results, and evaluate the calibration accuracy; Thus, a rapid calibration method for micro-CT systems has been achieved.

[0026] refer to Figure 1 Step 1 is implemented according to the following process: Using a high-precision industrial CT scanner and setting appropriate scanning parameters, three-dimensional image data of the forest ball array were acquired.

[0027] As a technical optimization of the present invention, a high-precision industrial CT scanner can accurately capture the geometry and spatial distribution of the forest ball array, laying the foundation for subsequent calibration processing.

[0028] refer to Figure 4 Step 2 is implemented according to the following process: Anisotropic diffusion filtering achieves image denoising and enhancement through the three-dimensional Perona-Malik equation. Details of the three-dimensional Perona-Malik equation implementation are as follows:

[0029]

[0030] Morphological-watershed hybrid segmentation is employed: First, distance transformation is calculated to generate a distance map.

[0031] Next, a tagging function is generated to avoid over-segmentation: .

[0032] As a technical optimization of this invention, a morphological-watershed hybrid segmentation algorithm is used to quickly segment the sphere. First, a distance transformation correction is performed, using Euclidean distance transformation combined with morphological closing operations to eliminate internal holes and generate a distance map.

[0033] refer to Figure 1 The principle of surface measurement in step 3 is as follows: For a point pi in a point cloud, its normal vector It can be obtained by calculating the eigenvector corresponding to the smallest eigenvalue of the covariance matrix of its neighboring points. Let Ni be the set of neighboring points of pi, and the covariance matrix Ci is calculated as follows: .

[0034] As a technical optimization of this invention, the surface of the segmented sphere is measured using a surface feature extraction algorithm based on normal vector estimation. By calculating the normal vector of each point in the point cloud, the local features and orientation of the surface are determined. The normal vector can provide important information about the surface tilt and orientation, which is helpful for the subsequent sphere fitting process.

[0035] refer to Figure 3 The dynamic error compensation model in step 4 is shown below: The point cloud data is optimized using a dynamic error compensation model, including thermo-mechanical coupling compensation and an error propagation equation based on spinor theory.

[0036] Secondly, there is the kinematic transmission error, based on the error transmission equation of spinor theory:

[0037] Where J is the joint variable and K is the geometric error parameter.

[0038] As a technical optimization of this invention, point cloud data is optimized using a dynamic error compensation model. This model includes thermo-mechanical coupling compensation and an error propagation equation based on spinor theory. Thermo-mechanical coupling compensation considers the influence of ambient temperature changes on the mechanical structure, and corrects measurement errors caused by temperature changes by calculating the displacement compensation amount.

[0039] refer to Figure 1 The robust sphere fitting algorithm in step 5: First, a coarse fit is performed, and initial parameters are calculated by randomly sampling four points to satisfy geometric constraints:

[0040] Then, fine optimization is performed using a weighted least squares objective function to improve fitting accuracy:

[0041] Then, the center coordinates and radius of each sphere are extracted from the fitting results, and the distance between the centers of the two spheres is calculated using the Euclidean distance formula:

[0042] The calculated distance is compared with the standard distance to analyze the error.

[0043] As a technical optimization of this invention, a robust sphere fitting algorithm is used for sphere fitting. First, a coarse fitting is performed by randomly sampling four points p1, p2, p3, and p4 to calculate initial parameters, satisfying geometric constraints, and initially determining parameters such as the center and radius of the sphere.

[0044] refer to Figure 1 The composition of the system hardware; The CT detection platform consists of a microfocal light source, a flat panel detector, and a motion platform. The multi-ball standard (ball stick, ball plate, forest ball) is composed of 27 balls. The spacing between the balls is fixed and the center-to-center distance can be obtained through calibration. The multi-ball standard is made of ruby, and the round rod supporting the balls is made of carbon fiber reinforced material with low X-ray absorption capacity.

[0045] As a technical optimization of this invention, the forest ball array is composed of multiple uniformly sized and regularly distributed spheres arranged in a specific array structure in three-dimensional space, providing abundant reference point information for calibration. A high-precision industrial CT scanner can accurately capture the geometry and spatial distribution of the forest ball array, laying the foundation for subsequent calibration processing.

[0046] refer to Figure 1 The multi-sphere standard was placed in the measurement space of the CT scanner, and measurements were performed according to the operating instructions of the CT scanner, using the set voltage and current parameters and step scan mode. Specifically, the scanning voltage was set to 150V, the current to 100A, the number of projections to 1800, and the integration time to 500ms to ensure high-quality image data.

[0047] As a technical optimization of this invention, the scanning voltage is 150V, the current is 100A, and the number of projections is 1800 to reduce reconstruction artifacts; the integration time is 500ms to balance the signal-to-noise ratio and scanning efficiency. A closed-loop feedback system is used to achieve high-precision linkage between the rotation axis and the translation axis, with a position repeatability accuracy of ≤1 micrometer to avoid imaging blurring caused by mechanical vibration.

[0048] Working principle and usage of this invention: In use, this invention constructs a calibration system consisting of a forest ball array standard component, a multiphysics field sensing module, and a parallel computing unit, achieving micron-level precision calibration through the following innovations: Standard parts modules: bat, paddle, forest ball; Data acquisition module: microfocus X-ray source, flat panel detector, motion platform; Calculation modules include: data processing module, surface measurement module, point cloud optimization module, sphere fitting module, and error analysis module.

[0049] A high-precision industrial CT scanner was used to acquire 3D image data of the forest sphere array using specific parameters. The scanning voltage was 150V, the current was 100A, and the number of projections was 1800 to reduce reconstruction artifacts; the integration time was 500ms to balance the signal-to-noise ratio and scanning efficiency. A closed-loop feedback system was used to achieve high-precision linkage between the rotation and translation axes, with a positional repeatability accuracy of ≤1 micrometer to avoid image blurring caused by mechanical vibration. The forest sphere array consists of multiple uniformly sized, regularly distributed spheres arranged in a specific array structure in 3D space, providing rich reference point information for calibration. The high-precision industrial CT scanner accurately captured the geometry and spatial distribution of the forest sphere array, laying the foundation for subsequent calibration processing.

[0050] Next, CT data preprocessing and rapid sphere segmentation were performed. Anisotropic diffusion filtering and the three-dimensional Perona-Malik equation were then applied to denoise and enhance the CT images. Anisotropic diffusion filtering effectively removes noise while preserving image edge information, while the three-dimensional Perona-Malik equation further enhances the image's detail, making the sphere's outline clearer.

[0051]

[0052] where g Let K be the diffusion coefficient and K be the gradient threshold. To adapt to the non-uniform noise in CT data, an adaptive threshold K= is proposed. ( (where N is the noise standard deviation and N is the number of neighboring pixels). To dynamically suppress noise while preserving edges, a morphological-watershed hybrid segmentation algorithm is used for fast sphere segmentation. First, a distance transformation correction is performed, using Euclidean distance transformation combined with morphological closing operations to eliminate internal holes and generate a distance map.

[0053] Then a tagging function is generated to avoid over-segmentation:

[0054] This accurately separates each sphere from the complex background, where D(p) is the distance map. It is 0.8 times the radius of the sphere. Next, surface measurement is performed on the segmented sphere using a surface feature extraction algorithm based on normal vector estimation. By calculating the normal vector of each point in the point cloud, the local features and orientation of the surface are determined. The normal vector provides important information about the surface tilt and orientation, which is helpful in the subsequent sphere fitting process. For a point p in the point cloud... i Its normal vector It can be obtained by calculating the eigenvector corresponding to the smallest eigenvalue of the covariance matrix of its neighboring points. Let p i The neighborhood set of N is i Covariance matrix C i The eigenvalue decomposition can be expressed as:

[0055] The eigenvector corresponding to the smallest eigenvalue is the normal vector. To improve noise resistance, robust statistical weights are introduced. Reconstruct the weighted covariance matrix:

[0056] Next, point cloud optimization is performed using a dynamic error compensation model. This model includes thermo-mechanical coupling compensation and an error propagation equation based on spinor theory. Thermo-mechanical coupling compensation considers the impact of ambient temperature changes on the mechanical structure, correcting measurement errors caused by temperature variations by calculating displacement compensation. The dynamic error compensation model, including thermo-mechanical coupling compensation and an error propagation equation based on spinor theory, optimizes the point cloud data.

[0057] in, L is the coefficient of thermal expansion of the material, L0 is the reference length of the material, and T is the real-time temperature. t is the thermal conductivity coefficient, and t is time.

[0058] The error propagation equation based on spinor theory is used to describe the kinematic propagation error.

[0059] Where J is the joint variable and K is the geometric error parameter. For joint error, This represents the attitude angle error. This equation allows for the precise analysis and compensation of geometric errors during mechanical motion, thereby improving the accuracy of point cloud data.

[0060] Next, a sphere fitting is performed and the distance between the sphere's centers is measured. A robust sphere fitting algorithm is then used for sphere fitting. First, a coarse fit is performed by randomly sampling four points p1, p2, p3, and p4 to calculate initial parameters that satisfy geometric constraints, thus preliminarily determining the sphere's center and radius.

[0061] If the four points are coplanar, i.e., satisfying det[p2-p1, p3-p1, p4-p1], then resampling is performed to avoid ill-conditioned solutions.

[0062] Subsequent optimization was performed using a weighted least squares objective function to improve fitting accuracy and make the description of the sphere's surface more accurate. The residual function was defined as follows:

[0063]

[0064] Weight From point cloud confidence Identify and suppress the influence of outliers.

[0065] Next, the center-to-center distances of the two designated spheres are measured sequentially and compared with a standard to obtain the error. Using the precise sphere fitting results, the center-to-center distances between each sphere are calculated and compared with the known standard center-to-center distances to determine the system's errors.

[0066] Then, error analysis of the measured sphere center distance is performed to evaluate the calibration accuracy. Through statistical analysis and model correction, the sources and distribution patterns of errors are investigated in depth, further improving the accuracy and stability of the calibration. This analytical process is of great significance for continuously improving calibration methods and enhancing the imaging quality of micro-CT systems.

[0067] Furthermore, in practical implementation, a forest sphere material is selected, the current (V), voltage (A) are adjusted, the number of projections is fixed at 1800, the integration time is 500ms, and the signal-to-noise ratio (SNR) is ≥40dB. Then, the forest sphere array is adjusted to a suitable position, which allows for a complete and clear scan of the forest sphere's location, and scanning is performed according to the preset parameters.

[0068] After obtaining the 3D image data of the forest ball, PyCharm imports the original CT image data I0 and iteratively applies the 3D Perona-Malik equation. ,parameter t=0.15, iteration count N=10, gradient K value adaptively adjusted (see appendix) Figure 3 ).

[0069] First, morphological watershed segmentation is performed. Then, a Euclidean distance transform is applied to the binarized image, with a kernel size of 1.2 times the sphere diameter. (Based on conditional...) and Define the top marker. Watershed segmentation: Output independent spherical regions with an oversegmentation rate of <2%.

[0070] Then, surface measurement and point cloud optimization are performed. For the segmented point cloud, each point p... i Select a neighborhood N centered on the center i Calculate the weighted covariance matrix: Based on the temperature field distribution Calculate displacement compensation The analytical geometric error is determined by the Jacobian matrix K (formula: ), to compensate for sensitive directional errors.

[0071] Then, robust spherical fitting is performed. First, a coarse fit is conducted: four points are randomly sampled, and a coplanarity test is performed (condition: det[p2-p1, p3-p1, p4-p1] < 10). -6Kd accelerates resampling. Next, fine optimization is performed: the Levenberg-Marquardt algorithm is used to iteratively optimize the objective function.

[0072] Weight Convergence condition: residual rate of change < 1e-6.

[0073] Finally, measure the center distance between adjacent spheres. , and standard value Comparison, error Output the statistical results.

[0074] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0075] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A rapid calibration method for a micro-CT system based on a forest ball array, characterized in that: Includes the following steps: Step 1: Use a high-precision industrial CT scanner to acquire 3D image data of the forest ball array and import the measured 3D image data of the forest ball; Step 2: After scanning the forest sphere array with micro-CT, the CT data is preprocessed. The CT data is preprocessed and the spheres are quickly segmented. Anisotropic diffusion filtering and the three-dimensional Perona-Malik equation are applied to the CT images for denoising and enhancement. The morphology-watershed hybrid segmentation algorithm is used to quickly segment the spheres. Step 3: Surface measurement. The surface of the segmented sphere is measured using a surface feature extraction algorithm based on normal vector estimation. Step 4: Point cloud optimization, which optimizes the point cloud data using a dynamic error compensation model; Step 5: Sphere fitting. Use a robust sphere fitting algorithm to fit the spheres and measure the distance between their centers. Measure the distance between the centers of two specified spheres in sequence and compare it with the standard to obtain the error. Step 6: Measure the distance and obtain the error, analyze the error of the measured sphere center distance, perform error analysis on the measurement results, and evaluate the calibration accuracy; Thus, a rapid calibration method for micro-CT systems has been achieved.

2. The rapid calibration method for a micro-CT system based on a forest ball array according to claim 1, characterized in that: Step 1 is implemented according to the following process: Using a high-precision industrial CT scanner and setting appropriate scanning parameters, three-dimensional image data of the forest ball array were acquired.

3. The rapid calibration method for a forest ball array-based micro-CT system according to claim 2, characterized in that: Step 2 is implemented according to the following process: Anisotropic diffusion filtering achieves image denoising and enhancement through the three-dimensional Perona-Malik equation. Details of the three-dimensional Perona-Malik equation implementation are as follows: Morphological-watershed hybrid segmentation is employed: First, distance transformation is calculated to generate a distance map. Next, a tagging function is generated to avoid over-segmentation:

4. The rapid calibration method for a forest ball array-based micro-CT system according to claim 3, characterized in that: The principle of surface measurement in step 3 is as follows: For a point pi in a point cloud, its normal vector It can be obtained by calculating the eigenvector corresponding to the smallest eigenvalue of the covariance matrix of its neighboring points. Let Ni be the set of neighboring points of pi, and the covariance matrix Ci is calculated as follows:

5. The rapid calibration method for a forest ball array-based micro-CT system according to claim 4, characterized in that: The dynamic error compensation model in step 4 is as follows: The point cloud data is optimized using a dynamic error compensation model, including thermo-mechanical coupling compensation and an error propagation equation based on spinor theory. Secondly, there is the kinematic transmission error, based on the error transmission equation of spinor theory: Where J is the joint variable and K is the geometric error parameter.

6. The rapid calibration method for a forest ball array-based micro-CT system according to claim 5, characterized in that: The robust sphere fitting algorithm in step 5 is as follows: First, a coarse fit is performed, and initial parameters are calculated by randomly sampling four points to satisfy geometric constraints: Then, fine optimization is performed using a weighted least squares objective function to improve fitting accuracy: Then, the center coordinates and radius of each sphere are extracted from the fitting results, and the distance between the centers of the two spheres is calculated using the Euclidean distance formula: The calculated distance is compared with the standard distance to analyze the error.

7. The rapid calibration device for a micro-CT system based on a forest ball array according to claim 6, characterized in that: The multi-ball standard (ball stick, ball plate, forest ball) consists of 27 balls. The spacing between the balls is fixed and the center-to-center distance can be obtained by calibration. The multi-ball standard is made of ruby, and the round rod supporting the balls is made of carbon fiber reinforced material with low X-ray absorption.

8. The rapid calibration device for a micro-CT system based on a forest ball array according to claim 7, characterized in that: The multi-sphere standard is placed in the measurement space of the CT measuring machine, and the measurement is performed according to the operating instructions of the CT measuring machine. The set voltage and current parameters and step scanning mode are used, specifically: the scanning voltage is set to 150V, the current is 100A, the number of projections is 1800, and the integration time is 500ms, so as to ensure that high-quality image data is obtained.