Projection-by-projection geometric calibration method of X-ray imaging system

Abstract

The invention discloses a projection-by-projection geometric calibration method for an X-ray imaging system, which comprises the following steps of: 1) selecting a plurality of coordinate points as a group of voxel points in a three-dimensional space, and scanning a die body containing the voxel points by using a cone beam imaging system to obtain a projection image; acquiring a group of projection points corresponding to the group of voxel points on the projection image; calculating to obtain a projection matrix based on the coordinates of the group of voxel points and the coordinates of the corresponding projection points; 2) calculating by using the projection matrix to obtain a group of vectors (,...), and determining the geometric attitude of the cone beam imaging system; the spatial position of a radiation source is represented, the spatial position of a fixed reference point on a detector plane is represented, the unit vector along the row direction on the detector plane is represented, and the unit vector along the column direction on the detector plane is represented. According to the method, the angle-by-angle and all-parameter solution of the imaging system can be realized.

Description

Technical Field

[0001] This invention belongs to the field of non-destructive testing technology of X-ray computed tomography (CT), and relates to a method for projective geometric calibration of an X-ray imaging system, which is mainly used to calculate the geometric parameters of an arbitrary cone-beam imaging system. Background Technology

[0002] With the development of computed tomography (CT) technology, cone-beam imaging systems, consisting of X-ray sources and flat panel detectors, have been widely used. The spatial positions of the X-ray source and the flat panel detector, as well as the orientation of the flat panel detector, are referred to as the geometric state of the imaging system, and acquiring this geometric state is called geometric calibration. High-precision geometric calibration is crucial for ensuring high-quality imaging. Therefore, as imaging resolution continues to improve, the requirements for the installation, calibration, and standardization accuracy of various components of the CT system are also increasing.

[0003] In recent years, cone-beam imaging systems with greater flexibility, such as computed tomography (CL) and robotic arm-based CT imaging systems, have gained development and attention due to their advantages in detecting large, flat objects (such as PCB boards) or achieving complex trajectory scans. However, the scan trajectories of these systems (such as the arbitrary path of a robotic arm) are more complex, and their geometric parameters often change dynamically with the accumulation of motion errors in the mechanical mechanism, which poses a greater challenge to the geometric calibration of the equipment.

[0004] In the modeling of cone-beam imaging systems, to simplify calculations, the focal point of the X-ray source is usually abstracted as a point, and the flat panel detector is abstracted as a plane. The geometric calibration of a cone-beam imaging system essentially involves determining the coordinates of the X-ray source focal point, the detector plane coordinates, and the orientation for each projected image. Geometric calibration methods for CT systems based on traditional circular scanning trajectories are relatively mature and can be mainly categorized into three types.

[0005] 1) Analytical method based on precision calibration phantom: This method utilizes a phantom with precisely known geometric features (such as a small ball array) to calculate system parameters through one or more projections. It offers fast calculation speed, allowing all parameters to be obtained in a single operation, but requires high precision in phantom machining and positioning.

[0006] 2) Parameter-based optimization methods: These methods use system geometric parameters and phantom characteristic parameters as optimization variables, establish an objective function (such as projection and reprojection errors), and solve it using optimization algorithms. These methods are convenient and do not depend on specific phantoms. However, they are computationally intensive, may get trapped in local optima, and typically can only optimize a few parameters at a time.

[0007] 3) Feature point-based scanning trajectory method: Based on the scanning trajectory of feature points, specific parameters of the device (such as detector offset, rotation, etc.) are calculated. This method is widely used in practical engineering and is simple in process, but it is difficult to handle parameters that change dynamically with the scanning angle.

[0008] Currently, there is relatively little research on the geometric calibration of CT systems with higher degrees of freedom or special structures, such as robotic arm CT systems and cone-beam scanning (CBS) systems. For robotic arm CT systems, existing methods cannot yet calculate all parameters per projection angle; for CBS systems, existing methods mostly focus on obtaining specific parameters (such as the projection coordinates of the X-ray source focus and the tilt angle of the central X-ray). In summary, a stable, universal, angle-by-angle, and full-parameter calibration method is still lacking for cone-beam scanning systems with arbitrary trajectories. Summary of the Invention

[0009] To address the problems existing in the prior art, the purpose of this invention is to provide a method for projective geometric calibration of an X-ray imaging system.

[0010] This invention calculates the three-dimensional spatial coordinates of the X-ray source and detector, and the spatial attitude of the detector, under the current projection by using multiple feature points with known three-dimensional spatial coordinates and the two-dimensional coordinates of each feature point on a certain projected image. To accurately describe and calibrate the geometric state of the cone-beam imaging system at any given time, this invention includes the following main components.

[0011] 1. Geometric description of a vector-based cone-beam imaging system Cone-beam imaging systems, such as Figure 1 As shown, where the vector This indicates the spatial position of the ray source focus (equivalent to a point source) in the coordinate system. );vector This represents the spatial position of a fixed reference point on the detector plane (usually taken as a corner point of the detector plane). );vector This represents a unit vector along its "row" direction (usually the pixel row direction) on the detector plane; vector This represents a unit vector along its "column" direction (usually the pixel column direction) on the detector plane. and The length usually corresponds to the pixel size of the detector.

[0012] vector , , , The position of the X-ray source, the position and orientation of the detector plane are fully defined, completely independent of the specific scanning trajectory. Therefore, any component displacement, orientation deflection, or trajectory deviation that may occur during the scanning process can be detected through vector sequences. , , , , (Where N is the number of projection angles) The scanning process of the CT system is accurately modeled to achieve calibration and correction.

[0013] 2. Calculate the projection matrix A corresponding to the projected image of feature points based on multiple sets of known spatial coordinates. exist Figure 1 In the hypothetical space, voxel points Projected onto the detector as a point Then the voxel points and projection points have the following relationship: (1) in for The projection matrix, Let be the homogeneous coordinates in three-dimensional space. Let be the homogeneous coordinates of the detector plane; This describes the correspondence between voxel coordinates, projected point coordinates, and the projection matrix. `w` is the coefficient of the homogeneous coordinates, defaulting to 1. Calculating the projection matrix A only requires multiple sets of [...]. That's all; in practical applications, The center of the characteristic sphere can be used to represent it, and the spatial coordinates of the sphere center can be calibrated using the three-coordinate method or other methods; The coordinates of the center of the circle are obtained by fitting the projection image. Expanding formula (1) yields: (2) When the position and orientation of the X-ray source and detector remain unchanged, the projection matrix is ​​also fixed. The projection matrix can be calculated using multiple sets of known voxel-projection point correspondences. That is, on a single projected image, the projection matrix is ​​calculated based on the three-dimensional spatial coordinates of multiple sets of feature points and the coordinates of the corresponding feature points on the detector plane.

[0014] voxel points and projection point Matching can be done in various ways, including but not limited to: 1) Use small balls of different materials or densities to differentiate them based on differences in projected grayscale; 2) Use small balls of different radii to differentiate them based on the size of their projected radii; 3) Arrange the balls in a specific way and distinguish them based on their positions in the projection; 4) Identify and depict the trajectory of the ball at various projection angles, and design algorithms or use manual methods to distinguish them.

[0015] The specific method is as follows: The projection matrix is ​​obtained by formula (3). Perform a one-dimensional expansion, the result of which is .

[0016] (3) Given the first Spatial coordinates of feature points The corresponding coordinates in the projected image are Construct the first one using formula (4) The matrix related to the group of feature points and projection points : (4) in All parameters are known. A corresponding value can be calculated for each voxel-projection coordinate pair. A matrix can be constructed using six or more voxel-projection coordinate pairs. : (5) Finally, based on the relationship: The projection matrix can be calculated using SVD decomposition. .

[0017] 3. Vector decomposition of the projection matrix Next, the transformation from the projection matrix to a vector describing the geometric state of the imaging system can be achieved through iterative optimization or analytical calculation, ultimately yielding... , , , Equal vectors. Iterative optimization methods use the vector to be calculated as the optimization variable, iteratively solving for the vector parameters through gradient descent or Newton's method. Analytical calculations require constructing a specific transformation matrix, whose elements consist of the geometric relationships between several direction vectors defined in the system. The transformation matrix can be divided into two substructures with clear mathematical relationships. Based on the geometric constraints inherent in the two substructures, the core direction vector of the system can be solved by specific combinations of row vectors within them. This solution process includes a normalization step based on the overall properties of the substructures and a criterion: when the substructure does not satisfy specific internal geometric conditions, the entire solution process will terminate, and the system will be determined to have no solution.

[0018] The matrix construction, partitioning, and vector calculation processes involved in the method can all be implemented using mathematical tools and programming techniques known in the art. The specific operational rules are obvious to those skilled in the art after understanding the technical principles described in this invention, or can be determined through a limited number of conventional experiments.

[0019] 4. Calculation of geometric parameters for each projection For a sequence of multiple projections, repeating steps 1-3 for each projected image to calculate geometric parameters yields a vector sequence describing the motion trajectory and attitude of the imaging system relative to the phantom. Therefore, this invention is a projection-by-projection geometric calibration method, and the overall calculation process is as follows: Figure 2 As shown.

[0020] The technical solution of this invention is as follows: A method for projective geometric calibration of an X-ray imaging system, comprising the following steps: 1) Select multiple coordinate points in three-dimensional space as a set of voxel points, and use a cone-beam imaging system to scan the phantom containing voxel points to obtain a projection image; obtain a set of projection points corresponding to the set of voxel points on the projection image; calculate the projection matrix A based on the coordinates of the set of voxel points and their corresponding projection point coordinates. 2) A set of vectors is calculated using the projection matrix A. , , , ), based on this set of vectors ( , , , Determine the geometric orientation of the cone-beam imaging system; wherein, vector The vector represents the spatial position of the X-ray source in a cone-beam imaging system. The vector represents the spatial position of a fixed reference point on the detector plane in a cone-beam imaging system. This represents the unit vector along the "row" direction on the detector plane in a cone-beam imaging system. This represents the unit vector along its "column" direction on the detector plane.

[0021] Preferably, the method for calculating the projection matrix A is as follows: Let the voxel points in space be... Projected onto the detector as a point Then there is a relationship between voxel points and projection points. And perform a one-dimensional expansion on the projection matrix A to obtain the expanded result. Based on the known spatial coordinates of each voxel and their corresponding coordinates in the projected image, construct the correlation matrix between the voxel and the projected point. Using SVD The projection matrix is ​​obtained by solving the problem. .

[0022] Preferably, a set of vectors is calculated using the projection matrix A through iterative optimization. , , , The method is as follows: the vector to be calculated is used as the optimization variable, and a set of vectors is calculated iteratively through gradient descent or Newton's method. , , , ).

[0023] Preferably, a set of vectors is calculated using the projection matrix A through analytical calculation. , , , The method is as follows: select several vectors from the projection matrix A, and construct a transformation matrix based on the geometric relationship between the selected vectors; divide the transformation matrix into two mathematically related substructures; based on the combination operation between the row vectors within the two substructures, solve for a set of vectors ( , , , ).

[0024] Preferably, the cone-beam imaging system scans the phantom containing voxel points at N different angles to obtain N projected images of the phantom; N projection matrices are calculated using these N projected images, and then a vector sequence consisting of N sets of vectors is calculated based on these N projection matrices. , , , };in,( , , , () represents a set of vectors corresponding to the i-th projection degree. According to the vector sequence { , , , The scanning process of the cone-beam imaging system is modeled to obtain the geometric model of the cone-beam imaging system.

[0025] Preferably, the voxel point is the center of the steel ball, and its corresponding projection point is the center of the circle after the steel ball is projected.

[0026] The present invention also provides a geometric modeling method for an X-ray imaging system, the steps of which include: 1) Select multiple coordinate points in three-dimensional space as a set of voxel points, and use a cone-beam imaging system to scan the phantom containing voxel points at N different angles to obtain N projection images of the phantom; obtain a set of projection points corresponding to the set of voxel points on each projection image; calculate a projection matrix based on the coordinates of the set of voxel points and the coordinates of the corresponding projection points on each projection image. 2) Calculate N projection matrices using the N projected images, and then calculate a vector sequence consisting of N sets of vectors based on these N projection matrices. , , , };in,( , , , () represents a set of vectors corresponding to the i-th projection degree. According to the vector sequence { , , , The scanning process of the cone-beam imaging system is modeled to obtain the geometric model of the cone-beam imaging system.

[0027] In summary, this invention proposes a method for calibrating high-degree-of-freedom CT geometry angle-by-angle projection. This method precisely decomposes the projection matrix into four vectors describing the geometric state of the system at any given time: the ray source position vector... Detector reference point position vector Detector horizontal direction vector and vertical direction vector It can achieve the calibration of cone-beam systems with arbitrary trajectories.

[0028] The calibration results can be directly used for high-quality analytical or iterative reconstruction; they can also be based on multiple sets of data calculated from the projection sequence. , The vector directly reflects the spatial trajectory of the X-ray source and detector during the scanning process. This invention provides a foundation for high-quality imaging, mechanical system debugging, and error source localization in cone-beam imaging equipment.

[0029] The advantages of this invention are as follows: This invention can be used in cone-beam scanning systems based on X-ray sources and flat panel detectors with arbitrary trajectories. Only one projection image is needed to calibrate the geometric state of the imaging system corresponding to the projection. It is a stable and universal calibration method that can solve for each angle and all parameters. Attached Figure Description

[0030] Figure 1 This is a structural diagram of a cone-beam imaging system.

[0031] Figure 2 The flowchart shows the geometric calibration process for each projection.

[0032] Figure 3 This is a schematic diagram of the calibration phantom.

[0033] Figure 4 CT projection image of the calibration phantom. Detailed Implementation

[0034] The present invention will now be described in further detail with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0035] Taking the geometric calibration of a projection image from a CT imaging system as an example, the input, core algorithm, and output of each step are continuously described.

[0036] The calibration phantom used, such as Figure 3 As shown, the model consists of multiple spirally arranged metal spheres, where the three-dimensional coordinates of the center of each sphere are known. The center point is the feature point required by the algorithm. The coordinates of the centers of the metal spheres are represented as follows: .

[0037] Using CT imaging systems Figure 2 The phantom shown is scanned to obtain a series of projected images. One of the projected images is shown below. Figure 4 As shown.

[0038] The metal spheres in the phantom are represented as circles or ellipses in the projection. Next, a circle or ellipse detection algorithm (such as Hough transform, edge detection, etc.) is used to fit the projection. Figure 3 The center of the projection of all metal spheres in the projection ,in The coordinates of the center of the circle on the projection diagram are two-dimensional coordinates.

[0039] Coordinates of the center of each metal sphere Find the coordinates of its corresponding projection center. Multiple sets of feature point-projection point coordinate pairs are established, and a matrix is ​​constructed. .in, For matrix SVD decomposition can be obtained ,in Will The projection matrix can be obtained by reordering. .

[0040] The projection matrix can then be decomposed analytically or through optimization. First, the projection matrix is ​​constructed as a specific transformation matrix. Then, the transformation matrix is ​​divided into two substructures with a clear mathematical relationship. Based on specific combinations of row vectors within these two substructures, the core direction vector of the system can be solved, yielding the system's geometric state parameters describing the projection. , , , .

[0041] Using the methods described above, a projection matrix can be calculated for each projected image. This can be further decomposed into a geometric state that describes the cone-beam imaging system at a certain moment. , , , Four vectors; on a motion trajectory, multiple sets of continuous projected images can be calculated. , , , This allows us to describe the geometric state of the cone-beam imaging system throughout its motion.

[0042] Although specific embodiments of the invention have been disclosed for illustrative purposes to aid in understanding and implementing the invention, those skilled in the art will understand that various substitutions, variations, and modifications are possible without departing from the spirit and scope of the invention and the appended claims. Therefore, the invention should not be limited to the content disclosed in the preferred embodiments, and the scope of protection claimed by the invention is defined by the claims.

Claims

1. A method for calibrating the geometry of an X-ray imaging system on a projection-by-projection basis, comprising the steps of: 1) selecting a plurality of coordinate points in a three-dimensional space as a set of voxels, scanning a phantom containing the voxels using a cone-beam imaging system to obtain a projection image; obtaining a set of projection points corresponding to the set of voxels on the projection image; calculating a projection matrix A based on the coordinates of the set of voxels and the coordinates of the projection points corresponding thereto; 2) A set of vectors is calculated using the projection matrix A. , , , ), based on this set of vectors ( , , , Determine the geometric orientation of the cone-beam imaging system; wherein, vector The vector represents the spatial position of the X-ray source in a cone-beam imaging system. The vector represents the spatial position of a fixed reference point on the detector plane in a cone-beam imaging system. This represents the unit vector along the "row" direction on the detector plane in a cone-beam imaging system. This represents the unit vector along its "column" direction on the detector plane.

2. The method of claim 1, wherein, The method for calculating the projection matrix A is as follows: Let the voxel points in space be... Projected onto the detector as a point Then there is a relationship between voxel points and projection points. And perform a one-dimensional expansion on the projection matrix A to obtain the expanded result. Based on the known spatial coordinates of each voxel and their corresponding coordinates in the projected image, construct the correlation matrix between the voxel and the projected point. Using SVD The projection matrix is ​​obtained by solving the problem. .

3. The method of claim 1, wherein, A set of vectors (x) is calculated by using the projection matrix A in an iterative optimization manner , , , , and the method is as follows: taking the vector to be calculated as an optimization variable, a set of vectors (x) is calculated by using gradient descent or Newton method iteration , , , .

4. The method of claim 1, wherein, A set of vectors (x1, x2, x3, x4) is calculated by using the projection matrix A in a way of analytical calculation , , , ), and the method is as follows: selecting several vectors from the projection matrix A, and constructing a conversion matrix according to the geometric relationship between the selected vectors; dividing the conversion matrix into two substructures with mathematical correlation; and inversely calculating a set of vectors (x1, x2, x3, x4) based on the combination operation between the internal row vectors of the two substructures , , , ).

5. The method according to claim 1 or 2 or 3, characterized in that, The cone beam imaging system is used to scan a phantom containing voxels at N different angles to obtain N projection images of the phantom; the N projection matrices are calculated using the N projection images, and then a vector sequence composed of N groups of vectors is calculated according to the N projection matrices 、 、 、 }; wherein, ( 、 、 、 ) is a group of vectors corresponding to the i th projection degree, ; the scanning process of the cone beam imaging system is modeled according to the vector sequence { 、 、 、 } to obtain a geometric model of the cone beam imaging system.

6. The method according to claim 1 or 2 or 3, characterized in that, the voxels are the centers of characteristic spheres, and the projection points corresponding thereto are the centers of the projections of the characteristic spheres.

7. A method for modeling the geometry of an X-ray imaging system, comprising the steps of: 1) selecting a plurality of coordinate points in a three-dimensional space as a set of voxels, scanning a phantom containing the voxels using a cone-beam imaging system at N different angles to obtain N projection images of the phantom; obtaining a set of projection points corresponding to the set of voxels on each of the projection images; calculating a projection matrix based on the coordinates of the set of voxels and the coordinates of the projection points corresponding thereto on each of the projection images; 2) using the N projection images to calculate N projection matrices, and then using the N projection matrices to calculate a vector sequence composed of N groups of vectors , , , }; wherein ( , , , ) is a group of vectors corresponding to the i-th projection degree, ; using the vector sequence { , , , } to complete modeling of a scanning process of the cone beam imaging system, to obtain a geometric model of the cone beam imaging system.

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