A central axis calibration method for horizontal CT systems

Abstract

The present invention belongs to the field of horizontal industrial CT and discloses a method for calibrating the central axis of a horizontal CT system. The present invention designs a cylindrical calibration block composed of evenly distributed carbon fiber plates and ceramic balls embedded therein for a horizontal CT system. After performing a CT scan on the calibration block, the projection of the calibration block on the detector can be obtained. The present invention proposes a method for calibrating the central axis of a horizontal CT system, which detects projections containing several circles and determines the position of the balls in a single projection through the center of the circle. The present invention designs a method for analyzing the elliptical motion trajectory of the balls, which performs a comprehensive analysis on the 360 projections obtained by CT scanning to obtain the elliptical motion trajectory of each ball. A straight line is fitted using the center points of each ellipse, i.e., the rotation center of the horizontal CT, thereby measuring the deviation distance between the central axis of the horizontal CT rotating disk and the center of the radiation source beam to improve the quality of the reconstructed image.

Description

Technical Field

[0001] The present invention belongs to the field of horizontal industrial CT and relates to a central axis calibration method for a horizontal CT system, which can calculate the central position of a rotating disk of the horizontal CT. Background Art

[0002] For horizontal industrial CT, the object to be detected is fixed by a clamp and located at the center of the rotating disk, while the radiation source and detector are located on both sides of the rotating disk. The central axis of the rotating disk is parallel to the ground. How to ensure that the center of the beam of the radiation source coincides with the axis is crucial to ensure the quality of CT reconstructed images. In the field of vertical CT, patent CN117890399A reports a CT calibration and calibration method based on a metal wire phantom. It designs a phantom containing 4 mutually parallel metal wires, obtains projections through rotation scanning, and then uses the geometric symmetry relationship between two projections with an angle difference of 180 degrees to calculate the offset angle and deflection torsion angle of the detector, thereby realizing CT calibration and calibration. However, this method adopts a planar fan beam scanning method, which extracts the metal wire projections row by row on the detector, and is not suitable for the cone beam scanning structure of horizontal CT. Patent CN117805149A describes a calibration method for a nuclear fuel rod weld CT inspection system. This method deploys a three-dimensional slide between the X-ray source and detector, with a small metal ball placed on the slide. The system is calibrated by moving the ball and calculating the source axis distance and source offset distance using the movement distance and projected image coordinates. However, this method requires moving the ball, making it unsuitable for horizontal CT systems where the object being inspected is secured by a clamp.

[0003] In order to accurately calibrate the beam center of the ray source and the central axis of the rotating disk, the key difficulty lies in accurately measuring the central axis position of the disk. The present invention proposes a central axis calibration method for a horizontal CT system, which provides a solution for measuring the central axis of the horizontal CT rotating disk. Specifically, the present invention adopts the following method: Figure 1 The cylindrical body made of carbon fiber sheet shown here serves as the calibration block, with several ceramic spheres embedded in its surface from top to bottom. First, a CT scan of the calibration block is performed to obtain projections from 360 viewing angles. The embedded spheres in each projection are circular. Then, each projection containing a circle is grayscale processed and circularity detected using the Hough circle transform. By summing the center points detected in all projections, several ellipses are obtained. These are the motion trajectories of the spheres embedded in the calibration block. Each sphere has an elliptical trajectory, and a straight line is fitted from the center of each ellipse. This line represents the position of the central axis of the horizontal CT rotating disk. After measuring the disk's central axis, the error between the central axis of the horizontal CT rotating disk and the center of the X-ray source beam can be analyzed by comparing it with the horizontal coordinate u0 where the beam center falls on the detector plane, thereby achieving calibration. Summary of the Invention

[0004] The present invention provides a method for analyzing the central axis of a horizontal CT rotating disk. A 360-degree CT scan is performed on a carbon fiber calibration block to obtain circular projections of the embedded ceramic spheres. The center points detected in all projections are combined to obtain the elliptical motion trajectory of each ceramic sphere. A straight line is fitted to the center of each ellipse to determine the position of the rotation center. By comparing the deviation between the rotating disk's central axis and the beam center with the center of the X-ray source beam, calibration is achieved.

[0005] The technical solution of the present invention:

[0006] A method for calibrating the central axis of a horizontal CT system includes the following steps:

[0007] Step 1: Scanning of the calibration block

[0008] like Figure 1 As shown, the calibration block is a cylindrical body made of carbon fiber plate, with multiple ceramic balls embedded in it; the inner diameter of the cylindrical calibration block is 1.4 cm, the outer diameter is 2 cm, and the height is 9 cm. The diameter of the small ball embedded in the calibration block is 3 mm. The distribution of the ceramic balls is such that only one is embedded at the same height, so that the circle can be detected and distinguished according to the height. When the horizontal CT is working, the calibration block is fixed by a clamp. In order to prevent the clamp from being blocked during the CT scanning process, a certain margin is left at the tail of the calibration block, that is, the ceramic ball at the bottom of the calibration block is required to have a distance from the bottom edge of the calibration block; after the horizontal CT cone beam scans at all angles, 360 projections of the calibration block are obtained. The projection of the ceramic ball on the detector plane of the horizontal CT is a circle, and the projection needs to be detected as a circle;

[0009] Step 2: Circle detection in calibration block projection

[0010] (1) Preprocessing of the projection image: In order to distinguish the projection of the ceramic ball from the background and reduce the interference of the background that does not contain circles on the circle detection, the upper and lower edges of the projection are cropped before the circle detection is formally performed on the projection; then the grayscale value range of the projection is adjusted, and the grayscale value of any point in the projection is recorded as p, and the minimum grayscale value in the projection is p min , the maximum gray value in the projection is p max , normalize the grayscale value of the projection to between 0 and 1, as shown in formula (1); then scale the normalized grayscale value of the projection to between 0 and 255 to generate a standard grayscale image p gray , as shown in formula (2);

[0011]

[0012]

[0013] (2) Circle detection: The gradient-based Hough circle detection method is used to detect the grayscale image p gray Perform preliminary circle detection; the circle passes through its center (x c ,y c ) and radius r, as shown in formula (3), so the Hough circle detection method is used to convert the circle equation shown in formula (3) into the horizontal coordinate x of the center of the circle. c , the vertical coordinate y of the center of the circle c and radius r; transform the circle into parameter space through Hough transform, and search for potential circles in the projection in this parameter space;

[0014]

[0015] For a fixed radius r, the horizontal coordinate x at the center of the circle c , the vertical coordinate y of the center of the circle c and the parameter space composed of radius r to record the possible center (x c ,y c ), ultimately detecting all circles in the projection; each circle actually detected by the Hough circle detection method contains the coordinates of the circle center and the radius. Note that the detection results at this point are preliminary, and there may be overlap between circles, which requires de-overlapping to ensure that each circle in the result is independent and non-overlapping. Traverse each pair of circles, and if the distance between the centers of the two circles is less than the sum of their radii, the two circles are considered overlapping; after the traversal is complete, delete all circles marked as overlapping;

[0016] The above Hough circle detection method is a preliminary circle detection, and the circle obtained does not completely match the real circle in the projection. The level set method is then used to further optimize the circle edge, and the circle edge in the projection is accurately located through iterative optimization. First, for any pixel (x, y) in the projection, the level set function is initialized. , as shown in formula (4):

[0017]

[0018] Get the points on the circle boundary =0, point inside the circle <0, points outside the circle >0;

[0019] Then, the level set function Perform iterative optimization to make the detected circular edge match the circular edge in the projection; the steps of each iteration are as follows: calculate The horizontal and vertical gradients of are as shown in Equations (5) and (6):

[0020]

[0021]

[0022] Calculate the magnitude of the gradient and normalize it, as shown in Equations (7), (8), and (9):

[0023]

[0024]

[0025]

[0026] The divergence k is obtained by calculating the second-order derivatives in the horizontal and vertical directions, as shown in formula (10):

[0027]

[0028] The Laplace operator detects the grayscale image p by calculating the second-order derivative of the pixel point gray The area with large intensity changes is shown in formula (11), where is the projection gray value;

[0029]

[0030] Define edge strength driver As shown in formula (12), the second-order gradient of the projection is calculated using the Laplace operator to detect the edge; the absolute value of the Laplace result is taken and Gaussian smoothing is applied to reduce the influence of noise;

[0031]

[0032] The term is driven by the divergence k and the edge strength Update the level set function , gradually Converges to the target edge, as shown in Equation (13), where To update the step size, control the level set function the speed of evolution;

[0033]

[0034] After multiple iterations, the level set function Converge to the target edge; finally obtain the edge through threshold segmentation, and output a binary edge mask mask, as shown in formula (14); Points less than zero represent the interior or boundary points of the circle, and the remaining points represent the exterior of the circle; finally, the level set method allows Converge so that it accurately fits the edge of the circle; at this point, the projected circle detection process is completed;

[0035]

[0036] Step 3: Obtain the elliptical trajectory of the ball

[0037] After detecting the projected circle, the position of the ceramic ball in a single projection is determined by the center of the circle, and the motion trajectory of each ceramic ball is obtained by integrating all the projections; since the heights of the ceramic balls in the calibration block are different, the motion trajectories of each ceramic ball under the illumination of a point light source are separate ellipses; in order to determine the elliptical motion trajectory of the ceramic ball, the 360 collected projections are layered; the 360 projections are integrated and divided into multiple layers according to the height; each circle is assigned to a different layer according to the vertical coordinate of the center of each circle; when assigning each circle, all layers are traversed; if the vertical coordinate of a circle is within the range of a certain layer and the layer has not yet been assigned a circle, it is saved directly. If there is already a circle in the layer during traversal, the current vertical coordinate of the center of the circle is compared with the vertical coordinate of the existing center of the circle, and the circle closest to the center of the layer is selected for saving; after multiple rounds of sorting, all circles will be assigned to layers of different heights; at this point, the elliptical motion trajectory of each ceramic ball is obtained;

[0038] Step 4: Error Analysis of the Rotating Disc's Center Axis

[0039] The error analysis between the beam center and the rotation axis is performed on the projection plane. The central beam of the ray source is perpendicular to the detector plane. The coordinates of the intersection of the beam center and the detector plane are marked as (u0, v0). The rotation center axis is fitted using the elliptical motion trajectory of the ceramic ball embedded in the calibration block. After comparing it with u0, the deviation between the rotation center and the beam center is obtained.

[0040] According to the elliptical motion trajectory obtained in step 3, the center coordinates of each ellipse are determined, and a vertical line is fitted using the horizontal coordinates of the center of each ellipse; the deviation between the center point of each ellipse and the fitted vertical line is calculated, and the mean and standard deviation of the deviation are calculated. Points with excessive deviation from the vertical line are selected for plotting. The fitting result of the central axis of the rotating disk is as follows: Figure 2As shown in the figure, the original data points of each ellipse are shown in blue, and the fitted elliptical trajectory is drawn in red. Normal points with small deviations are shown in orange, and the fitted vertical line is shown in purple dashed lines. The center points of the elliptical trajectory are evenly distributed on both sides of the fitted vertical line, and each center point deviates slightly from the fitted rotation axis.

[0041] Effects and benefits of the present invention: The present invention is aimed at a horizontal CT system, and designs a cylindrical calibration block with embedded ceramic balls, as well as a central axis calibration method. First, a circular detection method for the projection domain is proposed to determine the position of the balls in each projection. Then, a method for analyzing the elliptical motion trajectory of the balls is designed, and the 360 projections obtained by CT scanning are comprehensively analyzed to obtain the elliptical motion trajectory of each ball. Finally, a straight line is fitted using the center points of each ellipse, which is the rotation center of the horizontal CT, so as to measure the deviation distance between the central axis of the horizontal CT rotating disk and the center of the radiation source beam, thereby realizing system calibration. Compared with the existing horizontal CT rotation center calibration method, the calibration block designed by the present invention has a lower cost, the proposed method has a fast detection speed, and the central axis of the rotating disk is analyzed from the projection domain, and the result is more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a diagram of the circular detection result based on the cylindrical calibration block of the present invention.

[0043] Figure 2 This is a diagram of the central axis fitting result based on the cylindrical calibration block of the present invention. DETAILED DESCRIPTION

[0044] The specific implementation of the present invention is further described below in conjunction with the accompanying drawings and technical solutions.

[0045] First, the calibration block was fixed on the clamp and CT scanned. After full-angle cone-beam scanning of the horizontal CT, 360 projections of the calibration block were obtained.

[0046] The projections are then grayscale processed, converting the input matrix data into a grayscale image (i.e., an 8-bit grayscale image). To reduce the probability of multiple circle detections in non-interested areas, the projections are cropped at the upper and lower edges. Circle detection is then performed on the grayscale-processed projections using the gradient-based Hough circle detection method. After detection, the circles undergo de-overlapping processing, and the level set method is used to optimize and detect the circular edges. Through iterative optimization, the circular edges in the image are precisely located. Finally, the 360 collected projections are layered, and each circle is assigned to a corresponding layer based on the vertical coordinate of the circle center to obtain the elliptical motion trajectory of each ball. A vertical line is fitted using the horizontal coordinate of each ellipse center for error calibration of the rotation center.

[0047] For example, the intersection of the source beam center and the detector plane is denoted as (u0, v0). Assume u0 is 1529 and v0 is 1273. The cylindrical calibration block used contains nine small balls, and after CT scanning, nine elliptical motion trajectories are obtained. Fitting the rotation axis yields x = 1531.16, meaning the rotation axis is located at x = 1531.16. Therefore, u0 is offset by 2.16 pixels. If the detector pixel size is 0.1 mm, meaning each pixel on the detector is 0.1 mm in size, the resulting projection domain error is a 0.216 mm offset between the rotation axis and the beam center.

Claims

1. A central axis calibration method for a horizontal CT system, characterized in that: Here are the steps: Step 1: Scanning of the calibration block The calibration block is a cylindrical body made of carbon fiber board with multiple ceramic balls embedded inside. The ceramic balls are distributed so that only one is embedded at a given height. When the horizontal CT scan is in operation, the calibration block is fixed by a clamp. To prevent the clamp from obstructing the CT scan, a distance must be left between the lowest ceramic ball in the calibration block and the bottom edge of the calibration block. After a full-angle cone-beam scan of the horizontal CT scan, 360 projections of the calibration block are obtained. The projection of the ceramic ball on the detector plane of the horizontal CT scan is circular, so the projection needs to be tested for circularity. Step 2: Circle detection in calibration block projection (1) Preprocessing of the projection image: In order to distinguish the projection of the ceramic ball from the background, the upper and lower edges of the projection are first cropped; then the grayscale value range of the projection is adjusted, and the grayscale value of any point in the projection is recorded as p, and the minimum grayscale value in the projection is p min , the maximum gray value in the projection is p max , normalize the projected grayscale value to between 0 and 1, as shown in formula (1); Then scale the normalized projection grayscale value to between 0 and 255 to generate a standard grayscale image p gray , as shown in formula (2); , ,(2)Circle detection: The gradient-based Hough circle detection method is used to detect the grayscale image p gray Perform preliminary circle detection; the circle passes through its center (x c ,y c ) and radius r, as shown in formula (3), so the Hough circle detection method is used to convert the circle equation shown in formula (3) into the horizontal coordinate x of the center of the circle. c , the vertical coordinate y of the center of the circle c and radius r; transform the circle into parameter space through Hough transform, and search for potential circles in the projection in this parameter space; , for a fixed radius r, at the center of the circle, the horizontal coordinate x c , the vertical coordinate y of the center of the circle c and the parameter space composed of radius r to record the possible center (x c ,y c ), and finally all the circles in the projection are detected; then each pair of circles is traversed, and if the distance between the centers of the two circles is less than the sum of the radii of the two circles, the two circles are considered to overlap; after the traversal is completed, all circles marked as overlapping are deleted; The above Hough circle detection method is a preliminary circle detection, and the circle obtained does not completely match the real circle in the projection. The level set method is then used to further optimize the circle edge, and the circle edge in the projection is accurately located through iterative optimization. First, for any pixel (x, y) in the projection, the level set function is initialized. , as shown in formula (4): , get the points on the circle boundary =0, point inside the circle <0, points outside the circle >0; Then, the level set function Perform iterative optimization to make the detected circular edge match the edge of the circle in the projection; The steps of each iteration are as follows: calculate The horizontal and vertical gradients of are as shown in Equations (5) and (6): , , calculate the gradient and normalize it, as shown in equations (7), (8), and (9): , , , the divergence k is obtained by calculating the second-order derivatives in the horizontal and vertical directions, as shown in formula (10): , the Laplace operator detects the grayscale image p by calculating the second-order derivative of the pixel point gray The area with large intensity changes is shown in formula (11), where is the projection gray value; , defining the edge strength driving term As shown in formula (12), the second-order gradient of the projection is calculated using the Laplace operator to detect the edge; the absolute value of the Laplace result is taken and Gaussian smoothing is applied to reduce the influence of noise; , driven by the divergence k and edge strength Update the level set function , gradually Converges to the target edge, as shown in Equation (13), where To update the step size, control the level set function the speed of evolution; , after multiple iterations, the level set function Converge to the target edge; finally obtain the edge through threshold segmentation, and output a binary edge mask mask, as shown in formula (14); Points less than zero represent the interior or boundary points of the circle, and the remaining points represent the exterior of the circle; finally, the level set method allows Converge so that it accurately fits the edge of the circle; at this point, the projected circle detection process is completed; , Step 3: Get the elliptical motion trajectory of the ball After detecting the projected circle, the position of the ceramic ball in a single projection is determined by the center of the circle, and the motion trajectory of each ceramic ball is obtained by integrating all the projections; since the heights of the ceramic balls in the calibration block are different, the motion trajectories of each ceramic ball under the illumination of a point light source are separate ellipses; in order to determine the elliptical motion trajectory of the ceramic ball, the 360 collected projections are layered; the 360 projections are integrated and divided into multiple layers according to the height; each circle is assigned to a different layer according to the vertical coordinate of the center of each circle; when assigning each circle, all layers are traversed; if the vertical coordinate of a circle is within the range of a certain layer and the layer has not yet been assigned a circle, it is saved directly. If there is already a circle in the layer during traversal, the current vertical coordinate of the center of the circle is compared with the vertical coordinate of the existing center of the circle, and the circle closest to the center of the layer is selected for saving; after multiple rounds of sorting, all circles will be assigned to layers of different heights; at this point, the elliptical motion trajectory of each ceramic ball is obtained; Step 4: Error Analysis of the Rotating Disc's Center Axis The error analysis between the beam center and the rotation axis is performed on the projection plane. The central beam of the ray source is perpendicular to the detector plane. The coordinates of the intersection of the beam center and the detector plane are marked as (u0, v0). The rotation center axis is fitted using the elliptical motion trajectory of the ceramic ball embedded in the calibration block. After comparing it with u0, the deviation between the rotation center and the beam center is obtained. According to the elliptical motion trajectories obtained in step 3, the center coordinates of each ellipse are determined, and a vertical line is fitted using the horizontal coordinates of the center of each ellipse; the deviation between the center point of each ellipse and the fitted vertical line is calculated, and the mean and standard deviation of the deviation are calculated, and points with excessive deviation from the vertical line are screened out for drawing display.

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