CN114820927A - Industrial CT three-dimensional image reconstruction method based on data rearrangement and conjugate rays - Google Patents
Industrial CT three-dimensional image reconstruction method based on data rearrangement and conjugate rays Download PDFInfo
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- CN114820927A CN114820927A CN202210426807.6A CN202210426807A CN114820927A CN 114820927 A CN114820927 A CN 114820927A CN 202210426807 A CN202210426807 A CN 202210426807A CN 114820927 A CN114820927 A CN 114820927A
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Abstract
The invention discloses an industrial CT three-dimensional image reconstruction method based on data rearrangement and conjugate rays. The method comprises the steps of firstly, obtaining projection data of a measured sample through industrial cone beam CT circular orbit scanning; then, the projection data are rearranged by a method of converting the plane detector into a cylindrical surface detector, and the precision of the projection data is improved by adopting four-adjacent-point bilinear interpolation; secondly, cosine weighting is carried out on the rearranged projection data, a three-dimensional empirical weighting function is constructed by adopting a method based on conjugate rays, and secondary weighting is carried out; and then, filtering the weighted projection data by adopting a one-dimensional slope filter, and obtaining a reconstruction result by back projection. The method has stronger robustness, and can eliminate the reconstruction artifact of the projection data with larger cone angle, thereby improving the accuracy of industrial CT measurement.
Description
Technical Field
The invention relates to an industrial CT three-dimensional image reconstruction method based on data rearrangement and conjugate rays, in particular to an industrial cone beam CT circular orbit three-dimensional image approximate reconstruction method.
Background
Industrial CT is an industrial application of a computed tomography technology, and uses high-energy X-rays to penetrate a detected workpiece to obtain projection data, and then obtains a two-dimensional image or a three-dimensional image of the workpiece through a reconstruction algorithm. The industrial CT can clearly, accurately and visually display the size, position, shape, composition, material and defect conditions of the internal structure of the detected workpiece under the conditions of non-contact and no damage, and is not influenced by the material, shape and object surface of the workpiece. Industrial CT has the advantages of fast detection speed, high spatial and density resolution, etc., and thus is widely used in the field of industrial nondestructive detection.
Currently, industrial CT mainly uses cone beam X-ray, and during scanning, the scanning path of the X-ray source is in a circular orbit relative to the detected workpiece. The scanning mode has the advantages of high scanning speed and high radiation utilization rate, can simplify the hardware structure of industrial CT, and simultaneously improves the reconstruction speed. However, circular orbit scanning cannot satisfy Tuy conditions for cone beam CT reconstruction, and therefore accurate reconstruction of three-dimensional images cannot be achieved, and only approximate reconstruction can be achieved through an algorithm.
For industrial cone-beam CT circular orbit scanning, there are currently improved three-dimensional Radon inverse transforms, improved Grangeat algorithms, and FDK algorithms. The improved three-dimensional Radon inverse transformation and the improved Grangeat algorithm are both suitable for accurate reconstruction of three-dimensional images before improvement, and the algorithm is suitable for approximate reconstruction through an interpolation method after improvement, and the two algorithms are complex and complicated in processing mode of projection data and need to interpolate missing data of Radon transformation; the FDK algorithm is accurate for reconstructing the central plane of the detected workpiece, and the error of the reconstruction result of the penetrating plane is gradually increased along with the increase of the cone angle of the X-ray, so that a more obvious artifact phenomenon is generated finally.
Disclosure of Invention
The invention provides an industrial CT three-dimensional image reconstruction method based on data rearrangement and conjugate rays aiming at the defects of the existing industrial CT reconstruction algorithm. Firstly, scanning an industrial cone beam CT circular track to obtain projection data of a measured sample; then, the projection data are rearranged by a method of converting the plane detector into a cylindrical surface detector, and the precision of the projection data is improved by adopting four-adjacent-point bilinear interpolation; secondly, cosine weighting is carried out on the rearranged projection data, a three-dimensional empirical weighting function is constructed by adopting a method based on conjugate rays, and secondary weighting is carried out; and then, filtering the weighted projection data by adopting a one-dimensional slope filter, and obtaining a reconstruction result by back projection. The method has stronger robustness, and can eliminate the reconstruction artifact of the projection data with larger cone angle, thereby improving the accuracy of industrial CT measurement.
The technical scheme adopted by the invention is that the industrial CT three-dimensional image reconstruction method based on data rearrangement and conjugate rays is implemented according to the following steps:
step 1: detecting a workpiece by adopting a circular track scanning mode on conical beam X-rays of industrial CT to obtain projection data of a planar detector under different scanning angles;
step 2: performing position-to-analog conversion on the planar detector in the step 1 to obtain a virtual planar detector smaller than the real detector, transferring projection data on the real detector to the virtual planar detector, converting the three-dimensional cone-beam X-rays in the step 1 into a plurality of two-dimensional virtual cone-beam X-ray sources, and further converting the virtual planar detector into a virtual cylindrical detector;
and step 3: adopting four-neighborhood bilinear interpolation to the projection data on the virtual plane detector in the step 2, and filling the virtual cylindrical surface detector in the step 2 with the projection data after interpolation;
and 4, step 4: pre-weighting the projection data obtained in the step (3) by adopting a cosine function of an X-ray incident angle;
and 5: constructing a three-dimensional empirical weighting function by adopting a conjugate ray-based method, and carrying out secondary weighting on the data pre-weighted in the step 4;
step 6: adopting fast Fourier transform to realize convolution operation of the one-dimensional slope filter and the data subjected to secondary weighting in the step 5, thereby achieving the filtering effect;
and 7: carrying out back projection operation on the data filtered in the step 6 to obtain a value of a reconstruction point;
and 8: and (4) operating all points needing to be reconstructed according to the steps 4 to 7, and finally obtaining a three-dimensional reconstruction result.
The invention has the beneficial effects that: the reconstruction operation process is simplified by adopting a data rearrangement method, different contribution values are set for each X ray passing through the reconstruction point by utilizing the theory and the empirical method of conjugate rays, and the reconstruction of the industrial CT three-dimensional image is finally realized. The method has high reconstruction efficiency, can eliminate the reconstruction artifact of a larger cone angle, and improves the accuracy of industrial CT measurement; meanwhile, the method has stronger robustness and can be suitable for reconstruction of projections of workpieces with various shapes.
Drawings
FIG. 1 is a flow chart of the steps of the method of the present invention.
FIG. 2 is a schematic view of an industrial CT scan of the method of the present invention.
Fig. 3 is a schematic view of a virtual flat panel detector of the method of the invention.
FIG. 4 is a schematic view of the detector plane coordinate system after the rotation of the rotary stage according to the method of the present invention.
Figure 5 is a schematic view of a virtual cylinder detector of the method of the present invention.
FIG. 6 is a schematic illustration of interpolation of virtual screen detector projection data according to the method of the present invention.
FIG. 7 is a schematic representation of the conjugate rays of the method of the present invention.
FIG. 8 is a pictorial view of a standard ball panel for the method of the present invention.
FIG. 9 is a three-dimensional reconstruction of a standard sphere plate after an industrial CT scan according to the method of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the method of the present invention comprises the steps of:
step 1: detecting a workpiece by adopting a circular track scanning mode on conical beam X-rays of industrial CT to obtain projection data of a planar detector under different scanning angles;
as shown in fig. 2, the X-ray source emits a cone beam of X-rays to penetrate the workpiece to be detected, and the flat panel detector senses the intensity attenuation of the X-rays to obtain a projection data map. And then the rotating platform rotates clockwise, and 1 projection data picture can be acquired by the flat panel detector every time the rotating platform rotates 1 degree. During the measurement, the rotating platform rotates for 1 circle, a flat panel detector can obtain 360 projection data images in total, and the cone beam X-ray presents a circular scanning track relative to the rotating platform. Meanwhile, a scan object coordinate system is established in the coordinate system shown in fig. 1.
And 2, step: performing position-to-analog conversion on the planar detector in the step 1 to obtain a virtual planar detector smaller than the real detector, transferring projection data on the real detector to the virtual planar detector, converting the three-dimensional cone-beam X-rays in the step 1 into a plurality of two-dimensional virtual cone-beam X-ray sources, and further converting the virtual planar detector into a virtual cylindrical detector;
as shown in fig. 3, taking the X-ray source S as the location center, performing location transformation on the real planar detector to make it coincide with the central plane of the rotating table in step 1, and obtaining the virtual planar detector. And establishing a space rectangular coordinate system by using the center O of the virtual plane detector, and transferring the projection data on the real detector to the virtual plane detector. As shown in FIG. 4, when the rotation stage rotates clockwise, let a be the horizontal direction of the virtual flat panel detector, b be the direction of the connecting line between the X-ray source S and the center O of the virtual flat panel detector, c be the vertical direction of the virtual flat panel detector, and coincide with the z direction of the scanning object coordinate system,
for an angle of the virtual plane detector rotating counterclockwise relative to the rotation stage, which is equal to an angle of the rotation stage rotating clockwise, the conversion relationship between the coordinate system of the virtual plane detector and the scanned object is
Then, a virtual planar detector parameter space is established
And the virtual cylindrical detector parameter space (s, c, theta)
Wherein, R is the distance from the X-ray source S to the center O of the virtual plane detector. As shown in fig. 5, the coordinate transformation rearranges the projection points on the virtual plane detector to form a curve on the same horizontal plane, and then connects the curve to form a curved surface, thereby finally transforming the virtual plane detector into a virtual cylindrical surface detector. In the virtual cylindrical surface detector, S is a direction perpendicular to a connecting line of the X-ray source S 'and the center O of the virtual cylindrical surface detector, t is a connecting line direction of the X-ray source S' and the center O of the virtual cylindrical surface detector, and theta is an included angle formed by counterclockwise rotation of the S direction relative to the X direction of a scanning object coordinate system.
And step 3: adopting four-neighborhood bilinear interpolation to the projection data on the virtual plane detector in the step 2, and then filling the virtual cylindrical surface detector in the step 2 with the projection data after interpolation;
as shown in FIG. 6, P is the projection on the virtual flat panel detector, and its projection data is set as
The projection data of the adjacent detector unit at the lower left of the point is
Projection data of top left adjacent detector unitsIs composed of
Projection data of the lower right adjacent detector unit is
Projection data of the upper right adjacent detector unit is
Calculating p and p 11 Coordinate difference of (2)
u＝a-a 0 (5)
v＝c-c 0 (6)
Then pair
Using four-neighbor bilinear interpolation, having
Filling the virtual cylindrical surface detector in the step 2 with the interpolated projection data, and enabling the number of filling points of the curve on each height to be an integer power of 2, wherein the filling relation is
In the formula, the projection data after filling the virtual cylindrical surface detector is obtained.
And 4, step 4: pre-weighting the projection data obtained in the step 3 by adopting a cosine function of an X-ray incident angle;
the coordinate of the reconstruction point of the detected workpiece is set as (x, y, z), and the value of c in the coordinate of the projection point on the virtual cylindrical surface detector can be calculated by the similarity relation of the triangles
Then, the pre-weighted cosine function of the projection data by the cone beam X-ray is equivalent to a pre-weighted factor reconstructed under the imaging geometry of the parallel sector, the included angle between the connecting line of the X-ray source S ' and the center O of the virtual cylindrical surface detector and the projection point P from the X-ray source S ' to the virtual cylindrical surface detector is set as alpha, the projection of P on the circular orbit plane is set as P ', and the value of S ' P ' is calculated firstly
Then calculating the value of S' P
Finally, according to the ratio of S ' P ' to S ' P, the cosine function is calculated
Pre-weighting the projection data obtained in step 3 by using a cosine function cos alpha, having
p 1 (s,c,θ)＝p 0 (s,c,θ)cosα (13)
And 5: constructing a three-dimensional empirical weighting function by adopting a conjugate ray-based method, and carrying out secondary weighting on the data subjected to pre-weighting in the step 4;
as shown in FIG. 7, A is a reconstruction point on the detected workpiece, the projection of the ray emitted by the X-ray source S 'and passing through A on the plane of the circular scanning track is a straight line l, and the intersection point of the straight line l and the circular scanning track different from S' is S C ', S' A and S C ' A ' are conjugate rays, and the included angle between S ' A and l is alpha, and S is C Angle between' A and l is alpha C P toThe distance of the circular scanning track plane being d, alpha C Can be considered as a function of alpha. In order to make the reconstruction result have higher confidence, the smaller cone angle ray in the conjugate ray is given a larger weight. This weighting process first requires the definition of conjugate rays S' A and S C Degree of difference between' A
Then, an empirical three-dimensional weighting function for alpha is constructed according to the S-shaped curve property of the sigmoid function image
Then, in order to increase the weight difference between conjugate rays as the distance d from P to the circular orbit plane increases, an empirical constant k larger than 0 is set, and finally a three-dimensional weighting function of S' a is obtained
Using a three-dimensional weighting function w 3D (α, d) Secondary weighting of the projection data obtained in step 4, having
p 2 (s,c,θ)＝p 1 (s,c,θ)w 3D (α,d) (17)
Step 6: performing convolution operation on the data subjected to secondary weighting in the step 5 by using a one-dimensional slope filter by adopting fast Fourier transform, thereby achieving the filtering effect;
performing convolution operation on the projection data obtained in the step 4 by using a one-dimensional ramp filter
p 3 (s,c,θ)＝p 2 (s,c,θ)*h(s) (18)
Where h(s) is a one-dimensional ramp filter, for p 2 The filtering of(s) is performed along the s direction, the actual filtering path beingA curve of the virtual cylinder detector at the same height. The convolution operation can be implemented by fast Fourier transform, i.e. by fast Fourier transform, p is transformed 2 (s) conversion to P 2 (ω) converting H(s) to H (ω) satisfying
H(ω)＝|ω| (19)
Then, P is added 2 Multiplying (omega) by H (omega) to obtain P 3 (ω), then to P 3 (omega) carrying out inverse fast Fourier transform to obtain p 3 (s) of the reaction mixture. In order to eliminate signal aliasing caused by the periodicity of Fourier transform and reduce the artifact of image reconstruction, zero filling is used for multiplying the length of a filter before convolution operation, and the multiplication coefficient is 2 or 4.
And 7: carrying out back projection operation on the data filtered in the step 6 to obtain a value of a reconstruction point;
carrying out back projection operation on the data filtered in the step 6 according to the following formula
Wherein f (x, y, z) is the value of the reconstruction point. For the back projection operation, combining the property that the operation among all projections does not have correlation, using the cluster technology to perform projection angle parallel, distributing the projections under different angles to different nodes in the cluster, and after the calculation is finished, accumulating the calculation results of all the calculation nodes by the control node and outputting the accumulated calculation results.
And 8: and (4) operating all points needing to be reconstructed according to the steps 4 to 7, and finally obtaining a three-dimensional reconstruction result.
Fig. 8 is a real object diagram of a standard sphere plate, after the detected workpiece is scanned by the method in step 1 to obtain projection data, the number and positions of reconstruction points are determined, and all the reconstruction points are reconstructed according to steps 4 to 7 to obtain voxel data. In the process of reconstruction, a method of a normal memory is adopted to store other intermediate variables only related to the projection angle and the trigonometric function, and simultaneously, each thread of the computer is enabled to respectively complete the reconstruction task of a series of points in the corresponding z direction, thereby reducing repeated operation. After all the voxel data are obtained, trilinear interpolation is used to improve the resolution, and finally, a three-dimensional reconstruction result of a standard sphere plate is obtained, as shown in fig. 9. Therefore, the reconstruction of the industrial CT three-dimensional image is realized.
The above description is only a preferred embodiment of the method of the present invention, but the scope of the method of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the method of the present invention are included in the scope of the method of the present invention. Therefore, the protection scope of the method of the present invention shall be subject to the protection scope of the claims.
Claims (7)
1. An industrial CT three-dimensional image reconstruction method based on data rearrangement and conjugate rays is characterized by comprising the following steps:
step 1: detecting a workpiece by adopting a circular track scanning mode on conical beam X-rays of industrial CT to obtain projection data of a planar detector under different scanning angles;
step 2: performing position-to-analog conversion on the plane detector in the step (1) to obtain a virtual plane detector smaller than the real detector, transferring projection data on the real detector to the virtual plane detector, converting the three-dimensional cone-beam X-rays in the step (1) into a plurality of two-dimensional virtual cone-beam X-ray sources, and further converting the virtual plane detector into a virtual cylindrical surface detector;
and step 3: adopting four-neighborhood bilinear interpolation to the projection data on the virtual plane detector in the step 2, and filling the virtual cylindrical surface detector in the step 2 with the projection data after interpolation;
and 4, step 4: pre-weighting the projection data obtained in the step (3) by adopting a cosine function of an X-ray incident angle;
and 5: constructing a three-dimensional empirical weighting function by adopting a conjugate ray-based method, and carrying out secondary weighting on the data subjected to pre-weighting in the step 4;
step 6: adopting fast Fourier transform to realize convolution operation of the one-dimensional slope filter and the data subjected to secondary weighting in the step 5, thereby achieving the filtering effect;
and 7: carrying out back projection operation on the data filtered in the step 6 to obtain a value of a reconstruction point;
and 8: operating all points to be reconstructed according to the steps 4 to 7 to finally obtain a three-dimensional reconstruction result;
therefore, the reconstruction of the industrial CT three-dimensional image is realized.
2. The industrial CT three-dimensional image reconstruction method according to claim 1, wherein the process of converting the real detector into the virtual detector in the step 2 is as follows:
and (3) performing similarity transformation on the real plane detector by taking the X-ray source as a similarity center to ensure that the real plane detector is superposed with the central plane of the rotating table to obtain the virtual plane detector. Transferring projection data on a real detector to a virtual flat detector
Then, a conversion relation between the virtual plane detector and the virtual cylindrical surface detector is established
3. The industrial CT three-dimensional image reconstruction method according to claim 1, wherein the filling process of the virtual cylindrical detector in the step 3 is as follows:
let the projection of a point on the virtual flat detector be
The projection of the adjacent point at the lower left of the point is
Projection of the upper left adjacent point is
The projection of the adjacent point at the lower right is
Projection of the upper right neighboring point is
Calculating p and p 11 Difference of (2)
u＝a-a 0
v＝c-c 0
To pair
Using four-neighbor bilinear interpolation, having
By using
Filling the virtual cylindrical surface detector, and making the number of filling points of each height be an integer power of 2, wherein the filling relation is
4. The industrial CT three-dimensional image reconstruction method according to claim 1, wherein the cosine weighting process in the step 4 is as follows:
calculating the height of the projection point on the virtual cylindrical surface detector according to the similarity relation of the triangles
Setting the included angle between the central connecting line of the X-ray source S 'and the virtual cylindrical surface detector and the projection point P from S' to the virtual cylindrical surface detector as alpha, the projection of P on the circular orbit plane as P ', firstly calculating S' P ', then calculating S' P, and finally calculating cosine function
The interpolated projection data are pre-weighted by cos alpha, as
p 1 (s,c,θ)＝p 0 (s,c,θ)cosα
5. The industrial CT three-dimensional image reconstruction method according to claim 1, wherein the secondary weighting process in the step 5 is as follows:
let A be the reconstruction point, projection of S 'A on the orbit plane be l, and intersection point of l and the orbit different from S' be S C ', the included angle between the S' A and the L is alpha, S C The angle between A and l is alpha C And P is at a distance d from the plane of the track. Definition of S' A and S C Degree of variance of' A
Then, the function is constructed
Then, a constant k larger than 0 is set, and finally a three-dimensional weighting function is obtained
Finally, use w 3D (α, d) quadratic weighting of the pre-weighted projection data
p 2 (s,c,θ)＝p 1 (s,c,θ)w 3D (α,d)
6. The industrial CT three-dimensional image reconstruction method according to claim 1, wherein the filtering process in the step 6 is as follows:
performing convolution operation on the twice-weighted projection data by using a one-dimensional slope filter h(s) comprising
p 3 (s,c,θ)＝p 2 (s,c,θ)*h(s)
Before convolution operation, the length of the filter is multiplied by zero filling, the multiplication coefficient is 2 or 4, and the convolution operation is realized by fast Fourier transform and inverse fast Fourier transform.
7. The industrial CT three-dimensional image reconstruction method according to claim 1, wherein the back projection process in the step 7 is as follows:
and carrying out back projection operation on the filtered data, combining the property that the operation among all projections does not have correlation, carrying out projection angle parallelism by using a cluster technology, distributing the projections at different angles to different nodes in a cluster, and accumulating the calculation results of all the calculation nodes by the control node after the calculation is finished and then outputting the accumulated calculation results.
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