Phantom and calibration method for geometric correction of cone-beam CT systems with general trajectories

Abstract

The present invention discloses a phantom and calibration method suitable for geometric correction of a general trajectory cone beam CT system. The calibration method includes: constructing the back projection line of the small ball at different angles based on the projection data of the small ball and introducing the virtual intersection of auxiliary parameters; constructing the objective function of the intersection of the back projection line according to the virtual intersection; expanding the objective function to obtain the sum objective function of N small balls; finding the optimal solution of the sum objective function through the optimization algorithm to obtain the initial three-dimensional coordinates of the center of mass of the N small balls; aligning and averaging the initial three-dimensional coordinate values ​​of the N small balls based on the rigid motion registration algorithm of singular value decomposition to obtain accurate three-dimensional coordinate values ​​as the reference value of any trajectory geometry calibration method. The present invention aims to accurately obtain high-precision spatial parameters of the phantom without relying on mechanical processing accuracy, and thus provide a calibration phantom for geometric correction of general trajectory cone beam CT systems, especially high-resolution cone beam CT systems.

Description

Technical Field

[0001] The present invention relates to the technical field of computer tomography image processing, and in particular to a phantom and a calibration method suitable for geometric correction of a general trajectory cone beam CT system. Background Art

[0002] The cone-beam CT (Computerized Tomography) system uses rays to scan objects at different angles, and expresses the density and thickness changes of the object's fault layer in the form of computer tomography images. The reconstruction of the tomography image can obtain the internal image information of the object being tested. It has characteristics that cannot be replaced by other non-destructive testing methods and has broad application prospects in the field of industrial non-destructive testing.

[0003] The reconstruction algorithm of the cone-beam CT system has strict requirements on the geometric structure of the imaging, which is called the ideal geometric structure. However, in actual situations, the actual geometric structure will deviate from the ideal geometric structure due to installation errors and processing errors. In this case, if the ideal geometric structure is continued to be used for image reconstruction, geometric artifacts will be generated in the reconstructed image, affecting the image quality. The geometric trajectory of a general cone-beam CT system is a circular trajectory. There are many methods to achieve the correction of geometric parameters for such a system. However, with the improvement of the resolution of the cone-beam CT system, the standard circular trajectory is difficult to guarantee. In addition, there are many other special scanning requirements that require the scanning trajectory to be not a circular trajectory, which requires high-precision geometric correction for the general trajectory cone-beam CT system. To achieve high-precision geometric correction of a general trajectory cone-beam CT system, it is necessary to develop a high-precision geometric phantom. The existing methods require high-precision manufacturing equipment to process the phantom, which is very inconvenient in actual use. This patent introduces a low-cost phantom production and high-precision calibration method. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to address the deficiencies of the prior art and provide a phantom and calibration method for geometric correction of a CT system with a general trajectory. A multi-ball correction phantom that does not require precision machining is used, and in a CT system equipped with a turntable with higher circularity and concentricity, a geometric correction algorithm based on the degree of convergence of back-projection lines and a rigid motion registration algorithm based on singular value decomposition are used to solve the three-dimensional coordinates of the center of mass of each small ball, so that a manually processed phantom can also meet the accuracy requirements for the phantom in the geometric correction of a CT system with a general trajectory.

[0005] Technical solution: The phantom adapted for geometric correction of a CT system of a general trajectory of the present invention comprises the following steps for preparation:

[0006] S1: Use a material with a low X-ray absorption coefficient to make a calibration phantom, and use a material with a high X-ray absorption coefficient to make N round balls;

[0007] S2: Setting a small ball mounting hole in the calibration phantom, embedding the small balls in the mounting hole and sealing the holes, so that the small balls are regularly arranged after being fixed;

[0008] S3: Scan the calibration phantom using a cone-beam CT system equipped with a turntable with high circularity and high concentricity, and acquire projection data of the sphere through a detector.

[0009] Furthermore, the calibration phantom is made of plexiglass or low-density rigid material as the main body material, and the shape of the calibration phantom includes but is not limited to a cylinder; the arrangement pattern of the small balls in the calibration phantom includes but is not limited to a spiral type and a linear type; the small balls are made of metal material, and the size of the small balls is inversely proportional to the resolution of the cone-beam CT system, and the number of the small balls N is ≥ 5. A system with a high resolution selects a smaller small ball, and a system with a low resolution selects a larger small ball.

[0010] The calibration method applied to the phantom suitable for geometric correction of a general trajectory cone-beam CT system comprises the following steps:

[0011] S4: constructing the back-projection line of any small ball at different angles based on the projection data of the small ball, and introducing the auxiliary parameter virtual intersection point based on the back-projection line;

[0012] S5: constructing the objective function of the intersection degree of the back-projection lines according to the virtual intersection points;

[0013] S6: Expand the objective function to obtain the sum objective function of N balls;

[0014] S7: Find the optimal solution of the total objective function through the optimization algorithm. When the total objective function reaches the minimum value, the initial three-dimensional coordinates of the center of mass of the N small balls are obtained;

[0015] S8: The rigid motion registration algorithm based on singular value decomposition is used to register and average the initial three-dimensional coordinate values ​​of N balls to obtain accurate three-dimensional coordinate values;

[0016] S9: The precise three-dimensional coordinates of the ball are used as the reference values ​​for the arbitrary trajectory geometry calibration method.

[0017] Furthermore, the cone beam CT system used to calibrate the ball parameters in S3 is a standard circular trajectory system, and the geometric parameters of the system are represented by a vector v = (SDD, u c ,v c ,η,θ,φ), SDD is the distance from the ray source to the detector, (u c ,v c ) is the projection coordinate of the ray source, and (η, θ, φ) is the Euler angle of the detector in three directions.

[0018] Furthermore, the objective function of a single ball in S5 is:

[0019]

[0020] B i,j is the virtual intersection coordinate of the back-projection lines at the i-th and j-th angles, For all virtual intersection points B i,j is the mean of the coordinates, ‖·‖2 represents the second norm, and M is the number of projection angles.

[0021] Furthermore, the objective function in S5 is expressed as a function of the vector v, and the specific process is as follows:

[0022] S501. In an ideal circular trajectory cone beam CT system, a standard right-handed coordinate system XYZ is defined, wherein the Z axis is along the direction of the rotation axis, the X axis is defined as a straight line passing through the focus of the radiation source and perpendicular to the Z axis, and an ω-α-β coordinate system is defined based on the detector plane, wherein α represents the horizontal axis of the detector, β represents the vertical axis of the detector, ω represents the axis perpendicular to the detector plane, and the projection coordinate of the radiation source focus passing through the Z axis on the detector is expressed as P c =(u c ,v c ), the distance from the ray source to the projection point is assumed to be SDD, and the distance from the ray source to the rotation axis is SRD;

[0023] S502, ball projection point (p u ,p v ) is represented in the XYZ coordinate system as follows

[0024]

[0025] Among them, R θ , R φ and R η They represent the rotation matrix represented by three Euler angles. These three Euler angles represent the orientation of the detector in the XYZ coordinate system. T is a translation vector, R θ , R φ , R η and T are represented as follows:

[0026]

[0027] When a virtual detector plane is introduced, SRD and SDD are considered equal, and the above equation (2) is simplified to

[0028]

[0029] S503, the coordinates of the ray source at the initial angle are expressed as O0 = (SDD, 0, 0). If the coordinates of a small ball are known to be P k , then we have the equation of the line l0: After rotating around the rotation axis by an angle of β, the corresponding O β and χ β , the corresponding straight line equation is expressed as l β : When a cone-beam CT system is accurately geometrically calibrated, the lines l0 and l β They must intersect, and the intersection point is the coordinate of the ball;

[0030] S504, define a straight line l at any two angles i , l j The virtual intersection point B i,j is the midpoint of the perpendicular line segment between the two straight lines. Since the straight line is a parametric equation composed of vector v, B i,j Written as B i,j (v)

[0031]

[0032] in, It's all B i,j The average value of (v).

[0033] Furthermore, the objective function is expanded in S5 to obtain the objective function of N small balls as follows:

[0034]

[0035] Furthermore, the calibration phantom with N small balls is placed in a cone-beam CT system with a standard circular trajectory for scanning, and the corresponding projection data is obtained. The simplex simulated annealing method is used to optimize and solve the sum objective function described in S7 to obtain the minimum value of the sum objective function. The multiple virtual intersection points corresponding to the minimum value are B k,i,j , then the three-dimensional coordinates of the center of mass of the N balls are N represents the following:

[0036]

[0037] Further, the S8 includes

[0038] S801, place the calibration phantom in a cone beam CT system at a random position for T scans, and perform the above steps to obtain T different small ball space coordinates B m_k , m = 1, 2, ..., T, if the measurement error is not considered, the relationship between the coordinates of the ball measured for the first time and the mth time can be expressed as:

[0039] B 1_k =R m B m_k +T m (8)

[0040] Among them, R and T represent the rotation transformation and translation transformation between two measurements, respectively. Therefore, R is obtained by minimizing the objective function m and T m :

[0041]

[0042] S802, the minimization solution process is as follows: Minimizing the above formula (9) can get T m

[0043]

[0044] make Substituting (10) into (9) yields

[0045]

[0046] S803, use SVD decomposition method to solve the minimum value of equation (11), let matrix X = [s m_1 s m_2 …s m_K ], S=XY T , perform SVD decomposition on the matrix S to obtain S = UΣV T , then R m =VU T , substituting it into equation (10) to obtain T m , after obtaining R m and T m Then the coordinates of the ball measured multiple times are transformed into the coordinate system of the first measurement;

[0047] S804, the final accurately calibrated ball coordinates are expressed as

[0048] Beneficial effect: Compared with the prior art, the advantages of the present invention are as follows: the phantom and calibration method for geometric correction of a CT system with a general trajectory provided by the present invention adopt a multi-ball correction phantom that does not require precision processing, and in a CT system equipped with a turntable with higher circularity and concentricity, a geometric correction algorithm based on the degree of convergence of back-projection lines and a rigid motion registration algorithm based on singular value decomposition are used to solve the three-dimensional coordinates of the center of mass of each small ball, so that a manually processed phantom can also meet the accuracy requirements of the phantom in the geometric correction of a CT system with a general trajectory.

[0049] The present invention aims to accurately obtain high-precision spatial parameters of the phantom without relying on mechanical processing accuracy, and thus provide a calibration phantom for geometric correction of general trajectory cone-beam CT systems, especially high-resolution cone-beam CT systems. The advantage of using a correlation algorithm to calculate three-dimensional coordinates is that the accuracy requirements when machining and correcting the phantom can be reduced as much as possible while ensuring the accuracy of the coordinates, and the robustness has been verified under noise conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic structural diagram of the correction phantom of the present invention;

[0051] Figure 2 It is the geometric relationship diagram of the circular trajectory cone beam CT system;

[0052] Figure 3 It is a schematic diagram of the angle relationship between the detector coordinate system and the space right-hand coordinate system XYZ;

[0053] Figure 4 It is a schematic diagram of virtual intersection;

[0054] Figure 5 It is a simulation projection diagram of the calibration phantom. DETAILED DESCRIPTION

[0055] The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the protection scope of the present invention is not limited to the embodiments.

[0056] 1. Preparation of calibration phantom

[0057] Figure 1 The figure is a schematic diagram of the three-dimensional structure of the calibration phantom and the projection results. The calibration phantom is mainly composed of a plexiglass cylinder, in which N metal balls are spirally inlaid, N ≥ 5. The size of the balls is inversely proportional to the resolution of the cone-beam CT system. A system with a high resolution selects smaller balls, and a system with a low resolution selects larger balls. The calibration phantom is scanned using a cone-beam CT system equipped with a turntable with high circularity and high concentricity, and the projection data of the balls is obtained through the detector. There are two main reasons for designing the metal balls to be spirally distributed: (1) to avoid overlapping of adjacent balls in the projection image, which makes it impossible to extract the projection coordinates of the center of mass; (2) to ensure that the relative position of the ball projection in the V-axis direction in the image does not change, so as to avoid confusion of the projection coordinates of the center of mass of each ball.

[0058] 2. Calculation of three-dimensional coordinates in the phantom space

[0059] Most non-circular orbit offline correction algorithms require the spatial three-dimensional coordinates and projection coordinates of the center of mass of each metal ball to be known in order to solve the system geometric parameters. Among them, there are many methods to calculate the projection coordinates, and this application adopts the regional growing method. For the spatial three-dimensional coordinates, the projection data obtained by multiple scans of the phantom under circular orbit CT is selected here. First, the initial three-dimensional coordinates of each group of data are calculated through a geometric correction algorithm based on the degree of convergence of the back projection lines, and then the rigid motion registration algorithm based on singular value decomposition is used to improve the calculation accuracy of each group of initial coordinate values. The advantage of using a related algorithm to calculate the three-dimensional coordinates is that it can reduce the accuracy requirements when processing and correcting the phantom as much as possible while ensuring the accuracy of the coordinates.

[0060] like Figure 2 As shown in the figure, the cone-beam CT system used to calibrate the parameters of the ball is a standard circular trajectory system, and the following seven geometric parameters are used to describe the system structure: the distance SRD from the ray source to the rotation axis, the distance SDD from the ray source to the detector, the ray source projection coordinates (u c ,v c ), the Euler angles (η, θ, φ) in the three directions of the detector. Among them, the parameter SRD only affects the system magnification and does not affect the quality of the reconstructed image. Therefore, a virtual detector plane parallel to the detector can be introduced at the rotation axis to eliminate SRD. Finally, the geometric parameters of circular orbit CT are simplified to 6: SDD, u c ,v c ,η,θ,φ.

[0061] Taking a single metal ball as an example, in a precisely corrected circular orbit CT system, all back-projection lines at each angle should intersect at the center of mass of the ball. However, in a system that has not undergone geometric correction, these back-projection lines often cannot intersect at one point. Based on the above principles, the geometric correction algorithm constructs an objective function model that measures the intersection of back-projection lines, and uses an optimization algorithm to obtain the geometric parameters when the back-projection lines at all angles reach the maximum degree of convergence.

[0062] Assume that in an uncorrected CT system, the two back-projection lines at the i-th and j-th angles are O i P i and O j P j (i≠j), then the two straight lines do not intersect. Figure 3 As shown, in order to establish a continuous objective function, it is assumed that the midpoint B of the line segment perpendicular to the two back-projection lines is i,j is the virtual intersection point. Obviously, when the two back-projection lines intersect, this virtual intersection point is the real intersection point, that is, the center of mass of the metal ball. Therefore, the objective function can be defined as:

[0063]

[0064] Among them, B i,j is the virtual intersection coordinate of the back-projection lines at the i-th and j-th angles, For all virtual intersection points B i,j is the mean of the coordinates, ‖·‖2 represents the second norm, and M is the number of projection angles.

[0065] like Figure 4 As shown, a standard right-handed coordinate system XYZ is defined in an ideal circular trajectory cone beam CT system, where the Z axis is along the rotation axis, the X axis is defined as a straight line passing through the focus of the radiation source and perpendicular to the Z axis, and an ω-α-β coordinate system is defined based on the detector plane, where α represents the horizontal axis of the detector, β represents the vertical axis of the detector, and ω represents the axis perpendicular to the detector plane. The projection coordinate of the radiation source focus passing through the Z axis on the detector is expressed as P c =(u c ,v c ), the distance from the ray source to the projection point is assumed to be SDD, and the distance from the ray source to the rotation axis is SRD.

[0066] The projection point of the ball (p u ,p v ) is represented in the XYZ coordinate system as follows

[0067]

[0068] Among them, / 0, / φ and / 2 represent the rotation matrix represented by three Euler angles. These three Euler angles represent the orientation of the detector in the XYZ coordinate system. T is a translation vector, / 0, / φ , / η and T are represented as follows:

[0069]

[0070] When a virtual detector plane is introduced, SRD and SDD are considered equal, and the above equation (2) is simplified to

[0071]

[0072] The coordinates of the ray source at the initial angle are expressed as O0 = (SDD, 0, 0). If the coordinates of a small ball are known to be P k , then we have the equation of the line L0: After rotating around the rotation axis by an angle of β, the corresponding O β and χ β , the corresponding straight line equation is expressed as L β : When a cone-beam CT system is accurately geometrically calibrated, the lines l0 and lβ They must intersect, and the point of intersection is the coordinates of the ball.

[0073] Define a straight line l between any two angles i , l j The virtual intersection point B i,j is the midpoint of the perpendicular line segment between the two straight lines. Since the straight line is a parametric equation composed of vector v, B i,j Written as B i,j (v)

[0074]

[0075] in, It's all B i,j The average value of (v).

[0076] The calibration phantom with N small balls is placed in a cone beam CT system with a standard circular trajectory for scanning, and the corresponding projection data is obtained. The simplex simulated annealing method is used to optimize and solve the sum objective function described in S7 to obtain the minimum value of the sum objective function. The multiple virtual intersection points corresponding to the minimum value are B k,i,j , then the three-dimensional coordinates of the center of mass of the N balls are N represents the following:

[0077]

[0078] Place the calibration phantom in a random position in the cone-beam CT system for T scans, and perform the above steps to obtain T different sphere spatial coordinates B m_k , m = 1, 2, ..., T, if the measurement error is not considered, the relationship between the coordinates of the ball measured for the first time and the mth time can be expressed as:

[0079] B 1_k =R m B m_k +T m (8).

[0080] Among them, R and T represent the rotation transformation and translation transformation between two measurements, respectively. Therefore, R can be obtained by minimizing the objective function m and T m ;

[0081]

[0082] The minimization solution process is as follows: Minimizing the above formula (9) can get T m

[0083]

[0084] make Substituting (10) into (9) yields

[0085]

[0086] Use SVD decomposition method to solve the minimum value of equation (11), let matrix X = [s m_1 s m_2 …s m_ v ], S=XY T , perform SVD decomposition on the matrix S to obtain S = UΣV T , then R m =VU T , substituting it into equation (10) to obtain i m , after obtaining R m and T m Then the coordinates of the ball measured multiple times are transformed into the coordinate system of the first measurement;

[0087] The final accurately calibrated ball coordinates are expressed as

[0088] 3. Experimental results and analysis

[0089] The algorithm's calculation accuracy for correcting the three-dimensional coordinates of the phantom space and the system's geometric parameters was tested through simulation experiments, and the robustness of the algorithm was verified under noisy conditions.

[0090] The accuracy test of the calculation of the three-dimensional coordinates of the calibration model space: First, the accuracy of the algorithm for calculating the three-dimensional coordinates of the center of mass of each ball in the calibration model under the ideal condition without noise is tested. The calibration model used in this group of simulation experiments contains 8 metal balls with known three-dimensional coordinates of the center of mass. The simulation projection diagram under the circular orbit is generated in the Matlab environment using the Astra Toolbox simulation module. The specific orthographic projection parameters and simulation projection diagram are shown in Table 1 and Figure 5 shown.

[0091] Table 1 Orthographic projection parameters

[0092]

[0093] By moving and rotating the phantom and performing multiple simulation projections, the registration results of the three-dimensional coordinates of the center of mass of each ball can be calculated, and the comparison with the preset value is shown in Table 2. As can be seen from Table 2, under ideal conditions, the average error between the calculated value of the three-dimensional coordinates of each metal ball and the preset value is about 0.2 pixels, indicating that the algorithm has a high calculation accuracy for the three-dimensional coordinates of the metal ball.

[0094] Table 2 Calculation results of the three-dimensional coordinates of the center of mass of the metal ball under ideal conditions (unit: pixel)

[0095]

[0096]

[0097] In order to verify the robustness of the algorithm under noise conditions, Gaussian noise with a standard deviation of 50% pixel size is added to the horizontal and vertical coordinates of the projection of the centroid of each ball. When the orthographic projection parameters remain unchanged, the registration results of the three-dimensional coordinates of the centroid of each ball under noise conditions are calculated, as shown in Table 3. As can be seen from Table 3, under noise conditions, the absolute error between the calculated value and the preset value of the three-dimensional coordinates of each metal ball increases, but the calculation accuracy of most balls can still be maintained at the sub-pixel level, which proves that the algorithm has good robustness under noise conditions.

[0098] Table 3 Calculation results of the 3D coordinates of the ball's center of mass under noise conditions (unit: pixel)

[0099]

[0100]

[0101] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes in form and details may be made without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A calibration method applicable to geometric correction of a general trajectory cone-beam CT system, characterized by: The preparation of the model includes the following steps: S1: Use a material with a low X-ray absorption coefficient to make a calibration phantom, and use a material with a high X-ray absorption coefficient to make N round balls; S2: Setting a small ball mounting hole in the calibration phantom, embedding the small balls in the mounting hole and sealing the holes, so that the small balls are regularly arranged after being fixed; S3: Scanning the calibration phantom using a cone-beam CT system equipped with a turntable having high circularity and high concentricity, and acquiring projection data of the sphere through a detector; The calibration method includes the following steps: S4: constructing the back-projection line of any small ball at different angles based on the projection data of the small ball, and introducing the auxiliary parameter virtual intersection point based on the back-projection line; S5: constructing the objective function of the intersection degree of the back-projection lines according to the virtual intersection points; S6: Expand the objective function to obtain the sum objective function of N balls; S7: Find the optimal solution of the total objective function through the optimization algorithm. When the total objective function reaches the minimum value, the initial three-dimensional coordinates of the center of mass of the N small balls are obtained; S8: The rigid motion registration algorithm based on singular value decomposition is used to register and average the initial three-dimensional coordinate values ​​of N balls to obtain accurate three-dimensional coordinate values; S9: Using the precise three-dimensional coordinates of the ball as the reference value for the arbitrary trajectory geometry calibration method; The S8 includes: S801, place the calibration phantom in a cone beam CT system at a random position for T scans, and perform the above steps to obtain T different small ball spatial coordinates , , if the measurement error is not considered, the relationship between the coordinates of the ball measured for the first time and the mth time can be expressed as: (8) in, and Represent the rotation transformation and translation transformation between two measurements, respectively, so by minimizing the objective function and : (9); S802, the minimization solution process is as follows: , we minimize the above formula (9) and get : (10)， make , substituting (10) into (9) we obtain (11); S803, use SVD decomposition method to solve the minimum value of equation (11), let the matrix , , , perform SVD decomposition on the matrix S to obtain ,So , substituting it into equation (10) we get , after obtaining and Then the coordinates of the ball measured multiple times are transformed into the coordinate system of the first measurement; S804, the final accurately calibrated ball coordinates are expressed as .

2. The calibration method for geometric correction of a cone-beam CT system according to claim 1, characterized in that: The correction phantom is made of plexiglass or low-density rigid material as the main body, and the shape of the correction phantom includes but is not limited to a cylinder; the arrangement pattern of the small balls in the correction phantom includes but is not limited to a spiral type and a linear type; the small balls are made of metal, and the size of the small balls is inversely proportional to the resolution of the cone-beam CT system, and the number of the small balls N is ≥5.

3. The calibration method for geometric correction of a general trajectory cone-beam CT system according to claim 1, characterized in that: The cone-beam CT system used to calibrate the ball parameters in S3 is a standard circular trajectory system, and the geometric parameters of the system are expressed as vectors , is the distance from the radiation source to the detector, is the projection coordinate of the ray source, are the Euler angles of the detector in three directions.

4. The calibration method for geometric correction of a general trajectory cone-beam CT system according to claim 3, characterized in that: The objective function of a single ball in S5 is: （1）， is the virtual intersection coordinate of the back-projection lines at the i-th and j-th angles, For all virtual intersections The mean of the coordinates, represents the second norm, and M is the number of projection angles.

5. The calibration method for geometric correction of a general trajectory cone-beam CT system according to claim 4, characterized in that: The objective function in S5 is expressed as a vector The specific process is as follows: S501. Define a standard right-handed coordinate system in an ideal circular trajectory cone-beam CT system ,in The axis is along the direction of rotation, The axis is defined as a straight line passing through the focus of the ray source and intersecting the Z axis perpendicularly, and a Coordinate system, where represents the horizontal axis of the detector, represents the vertical axis of the detector, represents the axis perpendicular to the detector plane through which the source focus passes The projection coordinates of the axis on the detector are expressed as , the distance from the ray source to the projection point is assumed to be SDD, and the distance from the ray source to the rotation axis is SRD; S502, small ball projection point exist The coordinate system is represented as follows: （2）， Among them , and They represent the rotation matrices represented by three Euler angles. These three Euler angles represent the rotation of the detector in the coordinate system. The direction in which T is a translation vector, , , and T are represented as follows: （3）， When a virtual detector plane is introduced, SRD and SDD are considered equal, and the above equation (2) is simplified to （4）； S503, the coordinates of the ray source at the initial angle are expressed as , if the coordinates of a small ball are known to be , then we have the equation of the line , when rotated around the axis of rotation After the angle, we get the corresponding and , then the corresponding straight line equation is expressed as ; When a cone-beam CT system is accurately geometrically calibrated, the straight line and They must intersect, and the intersection point is the coordinate of the ball; S504, define a straight line at any two angles and The virtual intersection of is the midpoint of the perpendicular line segment between the two lines, because the line is composed of vectors The parametric equation is formed, so Written , （5）， in, is all The average value of .

6. The calibration method for geometric correction of a general trajectory cone-beam CT system according to claim 5, characterized in that: In S5, the objective function is expanded to obtain the objective function of N small balls: （6）。 7. The calibration method for geometric correction of a general trajectory cone-beam CT system according to claim 6, characterized in that: The calibration phantom with N small balls is placed in a cone-beam CT system with a standard circular trajectory for scanning, and the corresponding projection data is obtained. The simplex simulated annealing method is used to optimize and solve the sum objective function described in S7 to obtain the minimum value of the sum objective function. The multiple virtual intersection points corresponding to the minimum value are , then the three-dimensional coordinates of the center of mass of the N balls are , It is expressed as follows: （7）。

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