Industrial ct system geometry parameter sphere calibration method for multi-carriage switching

Abstract

The application discloses a multi-carrier platform switching-oriented industrial CT system geometric parameter sphere calibration method and belongs to the technical field of industrial CT systems.The method establishes a mathematical mapping relationship between the direction vectors of the X and Y directions of a carrier platform and a virtual rotating shaft and key geometric parameters of a system, and incorporates the relationship into a nonlinear optimization model.Through acquisition of projection data of a multi-sphere phantom under different carrier platform states, a residual function between projection position predicted values and measured values is constructed, the least square method is used to simultaneously optimize the direction vectors and the geometric parameters, and finally dynamic compensation and accurate correction of mechanical deviation caused by carrier platform replacement are realized.The application effectively solves the multi-carrier platform adaptation problem, significantly improves the imaging quality, geometric consistency and measurement accuracy of the CT system under different carrier platform configurations, and has good robustness and engineering application value.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of industrial CT system, and particularly relates to a geometric parameter sphere calibration method for industrial CT system switching of multiple loading tables. BACKGROUND

[0002] As an important technical means in the field of non-destructive testing, industrial CT has been widely used in the fields of manufacturing precision part detection, aerospace key component flaw detection, automobile industry part quality screening, etc. due to its high-precision imaging capability of internal structure of an object. In actual production detection scenarios, due to the significant differences in size specifications, shape structures and weight levels of objects to be detected, and the imaging needs for specific angles in part of the detection requirements, the CT system often needs to replace the special fixture to adapt to the detection object, and replace the corresponding specification loading table to meet the bearing and positioning requirements.

[0003] However, different loading tables have inherent differences in structure design and installation and debugging process, and after replacement, the mechanical deviation that cannot be ignored is easily introduced. Such deviation mainly embodies two core dimensions: one is the spatial position offset of the loading table rotating shaft, and the other is the angle deviation of the rotating shaft direction vector. The above mechanical deviation will directly cause the key geometric parameters of the CT system to deviate from the ideal value, including the numerical deviation of the distance from the ray source to the loading table rotating center (SOD), the distance from the ray source to the detector plane (SDD), the offset of the detector center relative to the system reference axis, and the change of the inclination angle of the detector plane around each axis. The mismatch of these geometric parameters will introduce obvious artifacts in the CT image reconstruction process, not only reducing the image spatial resolution, but also causing the deviation of key detection results such as size measurement and defect judgment, seriously affecting the detection reliability.

[0004] The existing CT system geometric parameter calibration method has certain limitations: the design premise usually assumes that the geometric position and rotating direction of the loading table are in an ideal state, and does not establish a mechanical deviation compensation mechanism for the loading table replacement scene. For example, the traditional calibration method depends on the preset reference of the fixed loading table, or only optimizes the parameters of a single loading table. When the loading table is replaced, the mismatch between the original calibration parameters and the actual system state is highlighted, and the whole process of calibration needs to be re-performed, which not only increases the operation complexity, but also is difficult to ensure the consistency of the imaging quality after the switching of different loading tables.

[0005] Therefore, aiming at the actual demand of multi-carrier platform switching in industrial production, developing a kind of geometric parameter calibration method which can accurately quantify the mechanical deviation of the carrier platform and realize the adaptation of multiple carrier platforms based on the deviation characteristics is the key to solve the current CT system detection bottleneck. By establishing the correlation model of mechanical deviation and geometric parameters, the active correction of the deviation is realized, which can provide technical and method support for the imaging quality improvement and measurement accuracy guarantee of the CT system in the multi-carrier platform scene, and has important engineering application value. SUMMARY

[0006] The purpose of the present application is to provide a kind of geometric parameter calibration method of industrial CT system for multi-carrier platform switching, by establishing the mapping relationship between the direction vector of carrier platform and the geometric parameters of system, and incorporating into nonlinear optimization model, the dynamic compensation and accurate correction of mechanical deviation caused by carrier platform replacement are realized, so as to guarantee the imaging quality and measurement accuracy of system in the multi-carrier platform scene.

[0007] To achieve the above purpose, the technical scheme adopted by the present application is: a kind of geometric parameter calibration method of industrial CT system for multi-carrier platform switching, comprising the following steps:

[0008] Step S1, establish coordinate system and direction vector model, the coordinate system includes global coordinate system and detector coordinate system, define the X direction direction vector of carrier platform, Y direction direction vector and virtual rotation axis direction vector;

[0009] Step S2, construct geometric parameter calculation model, based on carrier platform direction vector and position parameter calculation: the distance SOD of ray source to carrier platform center, the distance SDD of ray source to detector plane, and the horizontal physical offset of detector center dx, the vertical physical offset of detector center dz, establish the mapping relationship between carrier platform direction vector and geometric parameters;

[0010] Step S3, obtain multi-sphere array phantom projection data and process, rotate carrier platform to collect projection data at multiple angles, and extract the center projection coordinates of each small ball from each projection image;

[0011] Step S4, according to the distribution characteristics of the center projection, the initial rotation radius r of the small ball around the rotation axis of the carrier platform, the initial offset z0 of the small ball array relative to the rotation axis of the carrier platform and the initial phase angle φ0 of the carrier platform rotation are calculated, the three direction vectors of the carrier platform are set as approximately orthogonal unit vectors, which are used as the initial reference values for subsequent nonlinear optimization solution;

[0012] Step S5: Predict the projected coordinates of the center of the small ball. Based on the coordinate system and direction vector model established in step S1 and the geometric parameters calculated in step S2, construct the center coordinate model, define the detector plane attitude, clarify the position of the ray source point and the detector center point in the global coordinate system, and then calculate the predicted projected coordinates.

[0013] Step S6: Construct and solve the optimization model. Based on the projected coordinates predicted in step S5 and the actual projected coordinates extracted in step S3, construct the fitting objective function and use the nonlinear least squares method to optimize and solve the parameters to be optimized. The parameters to be optimized include the detector attitude parameters, phantom parameters and stage direction vector components.

[0014] Step S7: Based on the optimized direction vector parameters, calculate the final distance SOD from the X-ray source to the center of the stage, the distance SDD from the X-ray source to the detector plane, the horizontal physical offset dx of the detector center, and the vertical physical offset dz of the detector center, and apply them to the image reconstruction process of the CT system.

[0015] Further, in step S1, the global coordinate system takes the center of the stage plane as the origin, the longitudinal direction of the stage plane as the x-axis direction in the global coordinate system, the transverse direction of the stage plane as the y-axis direction in the global coordinate system, and the direction perpendicular to the stage plane as the z-axis direction of the rotation axis in the global coordinate system.

[0016] The detector coordinate system takes the principal point of the detector plane as its origin, the direction parallel to the x-axis of the global coordinate system as the u-axis direction, and the direction parallel to the z-axis of the global coordinate system as the v-axis direction.

[0017] Furthermore, in step S2, the formula for calculating the geometric parameters based on the stage orientation vector and position parameters is as follows:

[0018] ,

[0019] ,

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] In the formula, S, O, and D represent the origins of the X-ray source, stage, and detector in the global coordinate system, respectively, and S', O', and D' represent the actual positions of the origins of the X-ray source, stage, and detector, respectively. , , These are the X, Y direction vectors of the stage and the virtual rotation axis, respectively. s The perpendicular line from the X-ray source S to the detector plane and the virtual rotation axis The intersection, The actual location of the radiation source to the intersection point O s The vector, Let be the vector from the actual position of the X-ray source to the actual position of the detector. , These represent the offsets of the stage in the X and Y directions, respectively. From the ray source S to the intersection point O s The component in the z-direction.

[0025] Further, the implementation process of step S5 includes: first, defining the detector plane attitude through the Euler angle rotation matrix to obtain the detector plane normal vector and the horizontal and vertical axis direction vectors; then, defining the positions of the ray source point and the detector center point in the global coordinate system; next, calculating the intersection parameters of the ray connecting the ray source point and the center of the small ball with the detector plane; finally, based on the intersection parameters, the detector center coordinates and the detector axial direction vector, calculating the predicted projection horizontal and vertical coordinates.

[0026] Furthermore, in step S5, the first The first projection angle The formula for the coordinates of the center of each small ball is:

[0027] ,

[0028] ,

[0029] In the formula, This represents the average projected radius of the sphere. For the first The projected radius of each small sphere. Indicates the rotation angle of the i-th projection. Indicates the distance between the balls. This represents the initial offset of the ball array along the Z-axis.

[0030] Furthermore, in step S5, the Euler angle rotation matrix is ​​used to rotate in xyz order. Define the orientation of the detector plane, and calculate the normal vector of the detector plane and the direction vectors of the coordinate axes within the plane:

[0031] , , , ,

[0032] In the formula, Let be a rotation matrix. Here is the Euler angle rotation matrix. Let be the tilt angle of the detector about its horizontal axis. Let be the angle of rotation of the detector about its normal direction. Let be the tilt angle of the detector about its vertical axis. Let u be the normal vector of the detector plane, and let v be the direction vectors of the horizontal and vertical axes in the detector plane, respectively. , , is the standard basis vector of the world coordinate system.

[0033] Further, in step S5, the intersection parameters are calculated using the following formula:

[0034] ,

[0035] The x-coordinate of the intersection point in the detector's plane coordinate system y-axis They are respectively:

[0036] ,

[0037] ,

[0038] In the formula, Here, C represents the intersection parameters, C is the position of the detector center point in the global coordinate system, and S is the position of the ray source point in the global coordinate system. For the first The first projection angle The coordinates of the point of each small ball. The normal vector of the detector plane. and These are the direction vectors of the horizontal and vertical axes in the detector plane, respectively. , These are the x-coordinate and y-coordinate of the detector center in its own plane coordinate system, respectively.

[0039] Furthermore, in step S6, the formula for the fitted objective function is:

[0040] ,

[0041] In the formula, x is the parameter to be optimized. and These are the actual measured projected coordinates. and For the predicted projected coordinates, For the number of projection angles, The number of balls.

[0042] Furthermore, in step S6, the expression for the parameter x to be optimized is:

[0043] x=[ψ,θ,φ, r, z0, φ0, , , , , , , , , ] T

[0044] In the formula, ψ, θ, and φ are the detector attitude parameters. , , Let X be the three components of the direction vector of the stage in the X direction. , , These are the three components of the Y-direction vector of the stage. , , These are the three components of the direction vector of the virtual rotation axis of the stage.

[0045] Furthermore, in step S3, the method for extracting the projection coordinates of the center of the small ball from the projection image includes: performing binarization processing on the projection image, and then using connected component analysis to locate and calculate the center coordinates of the projection regions of each small ball.

[0046] The beneficial effects of the above scheme are as follows:

[0047] 1. This invention improves the calibration accuracy and reconstructed image quality of industrial CT systems. Traditional methods use the stage as an ideal reference, failing to correct its inherent mechanical deviations. This invention establishes a precise mathematical mapping between the stage orientation vector and the system's geometric parameters, enabling it to actively sense and dynamically compensate for the actual spatial attitude deviations of the stage. Experimental results show that after calibration using this method, the edges of spheres in the reconstructed images are clear, the contours are distinct, the background is uniform, and artifacts caused by geometric mismatch are suppressed, thus laying a reliable foundation for high-precision dimensional measurement and defect analysis.

[0048] 2. This invention enables multi-stage adaptation capabilities for industrial CT systems, enhancing the practicality of the equipment. This method addresses application scenarios with frequent stage switching by establishing a unique set of orientation vector parameters for each stage. In actual production, after changing stages, operators do not need to perform cumbersome mechanical adjustments or manual measurements; they can quickly restore the system to its optimal imaging state simply by calling the corresponding parameter set. This effectively solves the system performance fluctuation problem caused by differences in stage structure and installation, meeting the urgent needs of modern intelligent manufacturing production lines for inspection flexibility and efficiency.

[0049] 3. This method improves the robustness of the calibration process and the stability of the results. By incorporating the stage orientation vector and traditional geometric parameters into a unified optimization model for a one-time solution, the risk of error propagation and accumulation in step-by-step calibration is avoided. Experimental data demonstrates that even under disturbances such as stage offset, the optimization algorithm can still converge stably and obtain physically reasonable parameter results. This strong anti-interference capability ensures the reliability of calibration results under different working conditions and reduces reliance on operator experience.

[0050] 4. This invention optimizes the overall cost of engineering applications while ensuring high performance. Based on a universal multi-sphere array phantom, this method eliminates the need for custom-designed, high-cost precision phantoms for each stage, inheriting the low-cost advantage of sphere calibration methods. Through advanced algorithm design, it reduces the reliance on extreme mechanical precision of the equipment, thus solving high-value engineering problems with relatively low hardware and software investment. This low-investment, high-return calibration effect is particularly suitable for large-scale application in industrial settings where frequent tooling and fixture changes are required. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the geometry of a CT system under ideal conditions.

[0052] Figure 2 This is a schematic diagram of the geometric structure of the deviation CT system in an embodiment of the present invention;

[0053] Figure 3 This is a schematic diagram of the detector tilt state in an embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram of the stage coordinate system and direction vector model in an embodiment of the present invention;

[0055] Figure 5 This is a schematic diagram of the phantom structure in an embodiment of the present invention;

[0056] Figure 6 This is a comparison diagram of the effects before and after initial state geometric parameter calibration in an embodiment of the present invention;

[0057] Figure 7 This is a comparison diagram of the geometric parameter calibration effect before and after in the X-direction offset state in an embodiment of the present invention;

[0058] Figure 8 This is a comparison diagram of the geometric parameter calibration effect before and after in the Y-direction offset state in an embodiment of the present invention;

[0059] Figure 9 These are the reconstructed images before and after calibration in the initial state in this embodiment of the invention;

[0060] Figure 10 These are the reconstructed images before and after calibration under the X-direction offset state in this embodiment of the invention;

[0061] Figure 11 These are the reconstructed images before and after calibration in the Y-direction offset state in this embodiment of the invention. Detailed Implementation

[0062] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0063] It should be noted that, unless otherwise specified, 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 application pertains.

[0064] A method for sphere calibration of geometric parameters in industrial CT systems with multi-stage switching includes the following steps:

[0065] Step S1: Establish a coordinate system and direction vector model. The coordinate system includes the global coordinate system and the detector coordinate system. Define the X-direction direction vector, Y-direction direction vector, and virtual rotation axis direction vector of the stage.

[0066] Step S2: Construct a geometric parameter calculation model and calculate the following based on the stage direction vector and position parameters: distance SOD from the X-ray source to the center of the stage, distance SDD from the X-ray source to the detector plane, horizontal physical offset dx of the detector center, and vertical physical offset dz of the detector center. Establish the mapping relationship between the stage direction vector and the geometric parameters.

[0067] Step S3: Acquire and process the projection data of the multi-sphere array phantom. Rotate the stage to collect projection data from multiple angles and extract the projection coordinates of the center of each sphere from each projection image.

[0068] Step S4: Based on the distribution characteristics of the sphere center projection, calculate the initial rotation radius r of the sphere around the rotation axis of the stage, the initial offset z0 of the sphere array relative to the rotation axis of the stage, and the initial phase angle φ0 of the stage rotation. Set the three direction vectors of the stage as approximately orthogonal unit vectors as the initial reference values ​​for subsequent nonlinear optimization solutions.

[0069] Step S5: Predict the projected coordinates of the center of the small ball. Based on the coordinate system and direction vector model established in step S1 and the geometric parameters calculated in step S2, construct the center coordinate model, define the detector plane attitude, clarify the position of the ray source point and the detector center point in the global coordinate system, and then calculate the predicted projected coordinates.

[0070] Step S6: Construct and solve the optimization model. Based on the projected coordinates predicted in step S5 and the actual projected coordinates extracted in step S3, construct the fitting objective function and use the nonlinear least squares method to optimize and solve the parameters to be optimized. The parameters to be optimized include the detector attitude parameters, phantom parameters and stage direction vector components.

[0071] Step S7: Based on the optimized direction vector parameters, calculate the final distance SOD from the X-ray source to the center of the stage, the distance SDD from the X-ray source to the detector plane, the horizontal physical offset dx of the detector center, and the vertical physical offset dz of the detector center, and apply them to the image reconstruction process of the CT system.

[0072] The implementation process of each step of the present invention will be described in detail below.

[0073] This embodiment is based on an industrial cone-beam CT system for calibration. The core components of the system include an X-ray source, a detector, a replaceable stage, and a multi-sphere array phantom. The X-ray source is an X-ray source, and the detector is a flat panel detector.

[0074] In this embodiment, the specific structure of the multi-sphere array mold is as follows: six steel spheres, each with a diameter of 4mm, are evenly arranged vertically, with a spacing of 34mm between adjacent spheres. All the spheres are fixed to an acrylic plate, and the structure is as follows. Figure 5 As shown. The mold body adapts to the load-bearing and positioning requirements of the platform, ensuring that the mold body can still be stably installed and rotate synchronously with the platform after switching platforms.

[0075] like Figure 1 For the ideal geometry of a CT system, the X-ray source and detector are located on opposite sides of the stage. The X-ray source, the center of the stage plane, and the center of the detector plane are collinear. The rotation axis of the stage plane is parallel to the plane of the detector plane.

[0076] However, after the CT system is configured with a stage and a phantom fixture is installed, mechanical deviations occur in the system. This manifests as translation and rotation of the positions of the X-ray source, stage, and flat panel detector in an ideal CT system. These changes in the position or orientation of the components lead to deviations in the system's geometric structure.

[0077] like Figure 2 , Figure 3 As shown, S, O, and D represent the origins of the X-ray source, stage, and detector, respectively, while S', O', and D' represent the actual positions of the X-ray source, stage, and detector origin, respectively. The geometric parameters involved are: the x-coordinate of the detector center's offset in its own plane coordinate system. ,like Figure 3 (a); The offset ordinate of the detector center in its own planar coordinate system ,like Figure 3(a); The tilt angle ψ of the detector about its horizontal axis (u-axis), such as Figure 3 (b); The rotation angle θ of the detector about its normal direction, such as Figure 3 (c); The tilt angle φ of the detector about its vertical axis (v-axis), such as Figure 3 (d). The distance from the X-ray source to the center of the stage (SOD), and the distance from the X-ray source to the detector plane (SDD), such as... Figure 4 .

[0078] Step S1: Establish coordinate system and direction vector model

[0079] The global coordinate system has its origin at the center of the stage plane. The vertical direction of the stage plane is the x-axis of the global coordinate system, the horizontal direction of the stage plane is the y-axis of the global coordinate system, and the direction perpendicular to the stage plane is the z-axis of the global coordinate system.

[0080] The detector coordinate system takes the principal point of the detector plane as its origin. The direction parallel to the x-axis of the global coordinate system is the u-axis direction in the detector coordinate system, and the direction parallel to the z-axis of the global coordinate system is the v-axis direction in the detector coordinate system.

[0081] Define the direction vector of the stage's spatial attitude: the direction vector of the stage in the X direction is denoted as... The direction vector of the stage in the Y direction is denoted as The direction vector of the virtual rotation axis of the stage is denoted as At the same time, the offset of the stage in the X direction should be clearly defined. Y-direction offset The horizontal physical offset dx and vertical physical offset dz of the detector center lay the foundation for subsequent geometric parameter mapping, such as... Figure 4 As shown.

[0082] Step S2: Construct geometric parameter mapping relationship

[0083] Based on the coordinate system and direction vector definition established in step S1, the mapping relationship between the stage direction vector and the core geometric parameters is constructed through the following formula, thereby realizing the quantitative correlation between mechanical deviation and geometric parameters.

[0084] ,

[0085] ,

[0086] ,

[0087] ,

[0088] ,

[0089] ,

[0090] In the formula, S, O, and D represent the origins of the X-ray source, stage, and detector in the global coordinate system, respectively, and S', O', and D' represent the actual positions of the origins of the X-ray source, stage, and detector, respectively. , , These are the X, Y direction vectors of the stage and the virtual rotation axis, respectively. s The perpendicular line from the X-ray source S to the detector plane and the virtual rotation axis The intersection, The actual location of the radiation source to the intersection point O s The vector, Let be the vector from the actual position of the X-ray source to the actual position of the detector. , These represent the offsets of the stage in the X and Y directions, respectively. From the ray source S to the intersection point O s The component in the z-direction.

[0091] The coordinates of the detector center in its own plane coordinate system and Numerically, they are equal to dx and dz respectively, that is: The mechanical deviation of the stage can be converted into calculable geometric parameter deviation values ​​using the above formula.

[0092] Step S3: Obtain projection data of the multi-sphere array phantom and extract the projection coordinates of the sphere centers.

[0093] Fix the multi-sphere array phantom at the center of the stage to be calibrated, ensuring a stable connection between the phantom and the stage to prevent relative displacement during rotation. Control the stage to rotate around a virtual rotation axis, uniformly collecting projection data during rotation. Set the number of data collections to 120, with an angular interval of 3 degrees between each collection, covering the entire 360-degree rotation range to ensure complete phantom projection information is obtained.

[0094] Each acquired projection image is preprocessed: first, it is binarized to distinguish the projection area of ​​the steel ball from the background area; then, the projection area of ​​each steel ball is identified by connected component analysis, and the geometric center of each area is calculated. This center is the projection coordinate of the center of the corresponding steel ball. Finally, the u and v two-dimensional projection coordinate dataset of the six steel balls under all projection angles is obtained.

[0095] Step S4: Initial parameter estimation

[0096] Based on the distribution characteristics of the sphere center projection coordinates extracted in step S3, the initial rotation radius r of the small ball around the rotation axis of the stage is calculated; according to the position distribution of different steel ball projections in the v-axis direction, the initial vertical offset z0 of the small ball array relative to the rotation axis of the stage is estimated; by analyzing the phase change law of the projection coordinates of the same steel ball at different angles, the initial phase angle φ0 of the stage rotation is obtained.

[0097] At the same time, the three directional vectors of the stage , , Set as an approximately orthogonal unit vector; this setting provides a reasonable initial reference value for subsequent nonlinear optimization.

[0098] Step S5: Predict the projected coordinates of the center of the small ball.

[0099] (1) Modeling the coordinates of the center point of the ball

[0100] Based on the initial parameters and the rotation law of the stage, the first... The first projection angle The formula for the coordinates of the center of each small ball is:

[0101] ,

[0102] ,

[0103] In the formula, This represents the average projected radius of the sphere. For the first The projected radius of each small sphere. Indicates the rotation angle of the i-th projection. Indicates the distance between the balls. This represents the initial offset of the ball array along the Z-axis.

[0104] (2) Detector attitude definition

[0105] Euler angle rotation matrix by rotating in xyz order Define the orientation of the detector plane, and calculate the normal vector of the detector plane and the direction vectors of the coordinate axes within the plane:

[0106] , , , ,

[0107] In the formula, Let be a rotation matrix. Here is the Euler angle rotation matrix. Let be the tilt angle of the detector about its horizontal axis. Let be the angle of rotation of the detector about its normal direction. Let be the tilt angle of the detector about its vertical axis. Let be the normal vector of the detector plane, and u and v be the direction vectors of the horizontal and vertical axes in the detector plane, respectively. , , is the standard basis vector of the world coordinate system.

[0108] The positions of the ray source point S and the detector center point C in the global coordinate system are defined as follows:

[0109] , ,

[0110] SOD, SDD, dx, and dz are calculated from step S2, where ODD = SDD - SOD.

[0111] (3) Prediction of projection position

[0112] For the center point of the k-th ball under the i-th projection angle The steps to calculate its projected coordinates are as follows:

[0113] Calculate the ray Intersection parameters with the detector plane :

[0114] ,

[0115] Calculate the x-coordinate of the intersection point in the detector's plane coordinate system. y-axis :

[0116] ,

[0117] ,

[0118] In the formula, C represents the position of the detector center point in the global coordinate system, and S represents the position of the ray source point in the global coordinate system. For the first The first projection angle The coordinates of the point of each small ball. The normal vector of the detector plane. and These are the direction vectors of the horizontal and vertical axes in the detector plane, respectively. , These are the x-coordinate and y-coordinate of the detector center in its own plane coordinate system, respectively.

[0119] Step S6: Construct and solve the optimization model

[0120] Construct a fitting objective function to minimize the residual between the predicted and measured projected coordinates, as shown in the following formula:

[0121] ,

[0122] In the formula, x is the parameter to be optimized. and These are the actual measured projected coordinates. and For the predicted projected coordinates, For the number of projection angles, The number of balls.

[0123] The specific expression for the parameter x to be optimized is:

[0124] x=[ψ,θ,φ, r, z0, φ0, , , , , , , , , ] T

[0125] In the formula, ψ, θ, and φ are the detector attitude parameters. , , Let X be the three components of the direction vector of the stage in the X direction. , , These are the three components of the Y-direction vector of the stage. , , The three components of the virtual rotation axis direction vector of the stage are T, which indicates that the set of parameters is a column vector.

[0126] The 15 parameters to be optimized are iteratively solved using the nonlinear least squares method. During the iteration process, the parameter values ​​are continuously adjusted until the objective function value converges to the preset threshold, thus obtaining the optimal parameter combination.

[0127] Step S7: Parameter Update and Application

[0128] Based on the latest values ​​of the direction vector parameters obtained from step S6, the final corrected system geometric parameters, including SOD, SDD, dx, and dz, are recalculated using the geometric parameter calculation model from step S2.

[0129] These precisely calibrated geometric parameters are updated into the image reconstruction process of the industrial CT system to complete the calibration of the geometric parameters of the current stage. When using this stage for scanning in the future, data reconstruction can be carried out based on these calibration parameters to obtain CT images with low geometric distortion, few artifacts and high resolution.

[0130] When it is necessary to switch to a stage of other specifications, repeat steps S1 to S7 above. There is no need to change the model or adjust the calibration logic. The new stage can be quickly and accurately calibrated by simply optimizing the stage orientation vector and associated parameters.

[0131] Experimental verification and effect description

[0132] To verify the effectiveness of the present invention, scanning experiments were conducted in three different states on the same stage, as detailed below:

[0133] (1) Initial state: The stage is in the initial installation position;

[0134] (2) X-direction offset state: The stage moves slightly along the X-direction of the global coordinate system;

[0135] (3) Y-direction offset state: The stage moves slightly along the Y-direction of the global coordinate system.

[0136] Each experiment collected 120 projected images to ensure consistency in the number of images collected and the angle distribution, thereby ensuring the comparability of the experimental results.

[0137] The geometric parameters of three sets of experimental data were calibrated using the method of this invention. The effects before and after calibration are compared below. Figures 6 to 8 As shown in the figure, (a) and (b) represent the effects before and after calibration, respectively. The comparison results show that after calibration, the projection points of the sphere center are more concentrated and more evenly distributed in all three sets of data, which are in high agreement with the projection positions predicted by the geometric model. This fully verifies the stability and adaptability of the method under different displacement conditions of the stage, and demonstrates its technical potential for multi-stage adaptation.

[0138] Calibration result data analysis

[0139] Table 1 shows the parameter values ​​of SOD, SDD, dx, dz, and the three directional vectors of the stage, calculated after calibration by the method of this invention under three states.

[0140] Table 1. Calibrated direction vectors and calculated SOD, SDD, dx, and dz

[0141]

[0142] As shown in Table 1, the values ​​of dx and dz are relatively small in the initial state, indicating that the detector center offset is within the normal range. When the stage is offset along the X direction, dx increases significantly to 16.75 mm, while SOD and SDD remain relatively stable, indicating that the present invention effectively compensates for the influence of lateral offset on geometric parameters by dynamically adjusting the direction vector. Under the Y-direction offset state, the SOD value increases to 799.64 mm, an increase of approximately 52 mm compared to the initial state, and the components of the direction vector change accordingly, proving that the present method can accurately correct the geometric parameter mismatch problem caused by longitudinal offset.

[0143] It is worth noting the direction vectors in the three states. The Z-axis component remains close to 1, indicating that the rotation axis of the stage remains stable. In contrast, and The differences observed under various states further validate that this method can effectively compensate for the geometric deviation of the system by dynamically correcting these two directional vectors when mechanical offset occurs in the X and Y directions.

[0144] Experimental Results and Analysis

[0145] This section verifies the effectiveness of this method under different stage conditions by using CT image reconstruction results. Figures 9 to 11 As shown in the figure, (a) represents the reconstructed image before calibration, and (b) represents the reconstructed image after calibration.

[0146] Initial state reconstruction effect: After calibration using this method, the initial state CT reconstructed image is as follows: Figure 9 As shown, the reconstructed image has a uniform background with no obvious artifacts, and the edges of the sphere are clear and the contours are continuous. This indicates that the geometric parameters calibrated by this method can accurately reflect the geometric structure of the actual system, laying the foundation for high-precision reconstruction.

[0147] Reconstruction effect under X-direction offset state: The reconstruction effect before and after calibration by the method of this invention under the X-direction offset state of the stage is as follows: Figure 10 As shown in the figure, the comparison reveals that even after a small displacement of the stage along the X-direction, the image calibrated and reconstructed using this method still exhibits excellent quality. Artifacts in the image are significantly reduced, proving that this method can successfully correct for the effects of X-direction stage displacement.

[0148] Reconstruction effect under Y-direction offset state: The reconstructed images before and after calibration are shown below when the stage is offset in the Y-direction. Figure 11 As shown in the figure. The results show that when the stage is offset along the Y direction, the proposed method successfully corrects the resulting geometric mismatch, and the spherical outline and details of the reconstructed image remain clear. This further verifies the effectiveness and stability of the proposed method under stage offset conditions.

[0149] In summary, the method of this invention, by introducing stage orientation vector modeling, can stably and accurately calibrate the system's geometric parameters under different stage offset conditions, effectively correcting projection position errors caused by mechanical deviations, thereby ensuring geometric consistency and high precision in CT image reconstruction. Compared with existing sphere calibration methods, this method has better adaptability and robustness in complex mechanical environments, providing a reliable geometric correction scheme for high-precision industrial CT inspection, and meeting the accurate inspection requirements in multi-stage switching scenarios.

[0150] Finally, it should be noted that any parts of this invention not described in detail are prior art. Those skilled in the art will understand that the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A method for sphere calibration of geometric parameters in an industrial CT system with multi-stage switching, characterized in that, Includes the following steps: Step S1: Establish a coordinate system and direction vector model. The coordinate system includes the global coordinate system and the detector coordinate system. Define the X-direction direction vector, Y-direction direction vector, and virtual rotation axis direction vector of the stage. Step S2: Construct a geometric parameter calculation model and calculate the following based on the stage direction vector and position parameters: distance SOD from the X-ray source to the center of the stage, distance SDD from the X-ray source to the detector plane, horizontal physical offset dx of the detector center, and vertical physical offset dz of the detector center. Establish the mapping relationship between the stage direction vector and the geometric parameters. Step S3: Acquire and process the projection data of the multi-sphere array phantom. Rotate the stage to collect projection data from multiple angles and extract the projection coordinates of the center of each sphere from each projection image. Step S4: Based on the distribution characteristics of the sphere center projection, calculate the initial rotation radius r of the sphere around the rotation axis of the stage, the initial offset z0 of the sphere array relative to the rotation axis of the stage, and the initial phase angle φ0 of the stage rotation. Set the three direction vectors of the stage as approximately orthogonal unit vectors as the initial reference values ​​for subsequent nonlinear optimization solutions. Step S5: Predict the projected coordinates of the center of the small ball. Based on the coordinate system and direction vector model established in step S1 and the geometric parameters calculated in step S2, construct the center coordinate model, define the detector plane attitude, clarify the position of the ray source point and the detector center point in the global coordinate system, and then calculate the predicted projected coordinates. Step S6: Construct and solve the optimization model. Based on the projected coordinates predicted in step S5 and the actual projected coordinates extracted in step S3, construct the fitting objective function and use the nonlinear least squares method to optimize and solve the parameters to be optimized. The parameters to be optimized include the detector attitude parameters, phantom parameters and stage direction vector components. Step S7: Based on the optimized direction vector parameters, calculate the final distance SOD from the X-ray source to the stage center, the distance SDD from the X-ray source to the detector plane, the horizontal physical offset dx of the detector center, and the vertical physical offset dz of the detector center, and apply them to the image reconstruction process of the CT system. In step S2, the formula for calculating the geometric parameters based on the stage orientation vector and position parameters is as follows: , , ， ， ， ， In the formula, S , O , D Let these represent the origins of the X-ray source, stage, and detector in the global coordinate system, respectively. S' , O' , D' These represent the actual locations of the origins of the X-ray source, stage, and detector, respectively. , , These are the X and Y direction vectors of the stage and the virtual rotation axis, respectively. O s As a radiation source S The perpendicular line to the detector plane and the virtual rotation axis The intersection, The actual location of the radiation source to the intersection point O s The vector, Let be the vector from the actual position of the X-ray source to the actual position of the detector. , These are the offsets of the stage in the X and Y directions, respectively. As a radiation source S to the intersection O s The component in the z-direction.

2. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 1, characterized in that, In step S1, the global coordinate system takes the center of the stage plane as the origin, the longitudinal direction of the stage plane as the x-axis direction, the transverse direction of the stage plane as the y-axis direction, and the direction perpendicular to the stage plane as the z-axis direction of the rotation axis of the global coordinate system. The detector coordinate system takes the principal point of the detector plane as its origin, the direction parallel to the x-axis of the global coordinate system as the u-axis direction, and the direction parallel to the z-axis of the global coordinate system as the v-axis direction.

3. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 1, characterized in that, The implementation process of step S5 includes: First, defining the detector plane attitude through the Euler angle rotation matrix to obtain the detector plane normal vector and the horizontal and vertical axis direction vectors; then, defining the positions of the ray source point and the detector center point in the global coordinate system; next, calculating the intersection parameters of the ray connecting the ray source point and the center of the small ball with the detector plane; finally, based on the intersection parameters, the detector center coordinates and the detector axial direction vector, calculating the predicted projection horizontal and vertical coordinates.

4. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 3, characterized in that, In step S5, the first The first projection angle The formula for the coordinates of the center of each small ball is: ， ， In the formula, This represents the average projected radius of the sphere. For the first The projected radius of each small sphere. Indicates the rotation angle of the i-th projection. Indicates the distance between the balls. This represents the initial offset of the ball array along the Z-axis.

5. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 3, characterized in that, In step S5, the Euler angle rotation matrix is ​​used to rotate the axes in the xyz order. Define the orientation of the detector plane, and calculate the normal vector of the detector plane and the direction vectors of the coordinate axes within the plane: , , , , In the formula, Let be a rotation matrix. Here is the Euler angle rotation matrix. Let be the tilt angle of the detector about its horizontal axis. Let be the angle of rotation of the detector about its normal direction. Let be the tilt angle of the detector about its vertical axis. Let be the normal vector of the detector plane, and u and v be the direction vectors of the horizontal and vertical axes in the detector plane, respectively. , , is the standard basis vector of the world coordinate system.

6. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 3, characterized in that, The intersection parameters are calculated using the following formula: , The x-coordinate of the intersection point in the detector's plane coordinate system y-axis They are respectively: ， ， In the formula, Here, C represents the intersection parameters, C is the position of the detector center point in the global coordinate system, and S is the position of the ray source point in the global coordinate system. For the first The first projection angle The coordinates of the point of each small ball. The normal vector of the detector plane. and These are the direction vectors of the horizontal and vertical axes in the detector plane, respectively. , These are the x-coordinate and y-coordinate of the detector center in its own plane coordinate system, respectively.

7. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 1, characterized in that, In step S6, the formula for the fitted objective function is: , In the formula, x is the parameter to be optimized. and These are the actual measured projected coordinates. and For the predicted projected coordinates, For the number of projection angles, The number of balls.

8. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 7, characterized in that, In step S6, the expression for the parameter x to be optimized is: x=[ ψ , θ , φ , r , z 0, φ 0, , , , , , , , , ] T In the formula, ψ, θ, and φ are the detector attitude parameters. , , Let X be the three components of the direction vector of the stage in the X direction. , , These are the three components of the Y-direction vector of the stage. , , These are the three components of the direction vector of the virtual rotation axis of the stage.

9. The method for sphere calibration of geometric parameters of an industrial CT system with multi-stage switching as described in claim 1, characterized in that, In step S3, the method for extracting the projection coordinates of the center of the small ball from the projection image includes: performing binarization processing on the projection image, and then using connected component analysis to locate and calculate the center coordinates of the projection area of ​​each small ball.

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