WO2018126335A1

WO2018126335A1 - Method for evaluating and correcting geometric parameters of cone-beam ct system based on glomerulus motif

Info

Publication number: WO2018126335A1
Application number: PCT/CN2017/000025
Authority: WO
Inventors: 罗守华; 沈涛; 李光; 顾宁
Original assignee: 苏州海斯菲德信息科技有限公司; 东南大学
Priority date: 2017-01-03
Filing date: 2017-01-03
Publication date: 2018-07-12

Abstract

Disclosed is a method for evaluating and correcting geometric parameters of a cone-beam CT system based on a glomerulus motif. The method uses a geometric model, a correction motif, a defined back projection ray convergence degree evaluation index and a geometric parameter solving algorithm to provide a convergence degree evaluation index of a virtual intersecting point of back projection rays, wherein the index can effectively evaluate the reconstruction quality under a current geometric parameter. By means of calculating an evaluation index of geometric parameters and in conjunction with an optimization method, the geometric parameters of a cone-beam CT system can be calculated with high precision, a motif scanning mode is flexible, calculation is convenient, and the requirements of many kinds of cone-beam CT systems for geometric correction precision can be met.

Description

Geometric Parameter Evaluation and Correction Method of Cone Beam CT System Based on Small Ball Model

Technical field

The invention belongs to the technical field of image processing, and in particular relates to a method for evaluating and correcting geometric parameters of a cone beam CT system.

Background technique

X-ray computed tomography (hereinafter referred to as CT) system plays an important role in imaging technology and industrial non-destructive testing. The geometric position parameters of the CT system have a very large impact on the imaging quality. Errors in geometric parameters can result in reduced spatial resolution of the system, image artifacts, and even rendering of reconstructed images. The main components of the cone beam CT system include the X-ray source, the stage and the detector. For the cone beam projection, the FDK algorithm and its improved algorithm are generally used. The standard FDK algorithm requires that the ray source, the rotating shaft and the flat panel detector in the cone beam CT system satisfy a strict spatial positional relationship. The positional relationship is described as follows: the line of the ray source focus and the detector center is perpendicular to the detector plane. And the wire passes through the rotating shaft while requiring the axis of rotation to be parallel to the edge of the flat detector in the vertical direction. The relationship of the above Cartesian coordinate system can be expressed by six parameters, which are D, θ, φ, η, u _c , v _{c , respectively} . Where D represents the distance from the source to the axis of rotation, and the point (u _c , v _c ) represents the projection point of the source along the line passing through it and perpendicular to the z-axis. In order to be able to express the directional deflection of the detector plane, it is necessary to introduce three further two orthogonal intermediate variables α, β, ω, which are angle deflection parameters in each dimension. In the actual cone beam CT system, the ray source, the rotating shaft and the detector usually cannot satisfy the above spatial positional relationship, that is, there is a certain error between their actual spatial position and the ideal spatial position. If this error is not corrected, The projected image is still reconstructed using the standard FDK algorithm, and the reconstructed image is degraded. This degradation is called geometric artifact. Therefore, to obtain a good reconstructed image, the cone beam CT system must be geometrically corrected.

Many correction methods have emerged in the development of the past two decades. The overall can be divided into two categories, offline and online calibration methods. The so-called offline calibration algorithm relies on the scanning of specific phantoms to calculate the geometric parameters. The modalities used in most methods are composed of metal spheres. The two-ball-based correction algorithm proposed by Noo has proven to be convenient and efficient for use in conventional Micro-CT systems because of its simple phantom. However, this method is theoretically incomplete, assuming that the axis of rotation is parallel to the plane of the detector. In addition, the calibration accuracy of the method depends on the shape of the fitted ellipse. When the ellipse becomes flat, the accuracy of the calibration will decrease, and in the high-resolution CT, the correction accuracy is not high and the robustness is low. The online calculation method is more to iteratively reconstruct the image, and obtain the geometric parameters by evaluating the image quality. The accuracy of such calibration will be directly related to the signal-to-noise ratio of the system, and the calculation amount is large.

Patent CN105023251A proposes a geometric correction method for a high-resolution cone-beam CT system. The method establishes a model by scanning a single metal ball phantom, and solves the optimization problem to obtain a solution of geometric parameters. However, this method can only be scanned with a single ball, and the acquisition of the centroid of the projection is inaccurate in the case of a large noise. At the same time, the evaluation function established by the model only has a good effect under the fan beam, and the accuracy of the geometric parameters cannot be effectively evaluated in the case of cone beam.

Summary of the invention

In order to overcome the problems existing in the prior art, the present invention firstly proposes a geometric parameter evaluation method for a cone beam CT system based on a small ball phantom, and further uses the evaluation method to propose a geometric parameter correction algorithm for a cone beam CT system; The method is simple and easy to operate, and has high robustness, and is suitable for various cone beam CT systems.

The technical solution of the present invention solves the above technical problem: a geometric parameter evaluation method of a cone beam CT system based on a small ball phantom, the method comprising the following steps:

(1) The cone beam CT system obtains a plurality of projection images by scanning the ball phantoms at various angles;

(2) Solving the position of the center of mass of the ball projection on the detector, and solving the method of centroid of the small ball is solved by iterative method;

(3) determining the back projection ray passing through the centroid of the small sphere in the geometric space by the six geometric parameters of the cone beam CT;

(4) Calculate the "virtual intersection point" between the two pairs of back projection rays

(5) Calculate the degree of convergence of the "virtual intersection" as an indicator for evaluating the geometric parameters. The indicator is in pixels. If the index is greater than one pixel, it indicates that the geometric parameters of the system have large errors, which will cause observable degradation of the reconstructed image.

The evaluation index unit of the geometric parameter in the present invention is a pixel. Under ideal conditions, the index under the correct geometric parameter calculation is 0. The lower the index, the closer the geometric parameter is to the ideal value. When the evaluation index is greater than 1, it indicates that the geometric parameters of the system have large errors, which will make the reconstructed image. Produces observable degradation.

A method for correcting geometric parameters of a cone beam CT system based on a small ball phantom, the method comprising the following steps:

(1) According to the existing six geometric parameters or randomly set parameters of the existing system as the initial value;

(2) Using the optimization method to solve the six geometric parameters when the aforementioned index is the smallest;

(3) The CT image is corrected by the six geometric parameters obtained by the solution.

Further, the foregoing method for correcting a geometric parameter of a cone-beam CT system based on a ball phantom, the method uses a single or multiple ball phantoms to simultaneously scan, and the optimization methods include, but are not limited to, an ant colony algorithm, a particle swarm algorithm, Simulated annealing algorithm, etc.

Advantageous Effects: Compared with the prior art, the present invention has the following advantages:

(1) Using a small ball mold body, the production is simple, and the number of small balls can be arbitrarily selected; the prior art generally adopts multiple small balls, and Moreover, there is a certain limitation on the relative position of the small ball. In the method proposed by the present invention, the number of small ball phantoms can be arbitrarily selected, and a single small ball can satisfy the high-precision calculation requirement, and the more the number of small balls, the evaluation The more accurate the indicator, the stronger the anti-noise ability; the more accurate results can be obtained when used for calibration;

(2) The evaluation index has high reliability and numerical value; the degree of convergence of the virtual focus directly reflects the reconstruction of a point in the reconstruction space. Once the index value is greater than 1 pixel, it can directly indicate that the reconstructed image has observable degradation. The larger, the worse the reconstruction quality;

(3) The scanning method is flexible and can be adjusted as needed; the off-line scanning method in the prior art needs to collect a 360-degree complete projection image of the phantom; and the method proposed by the invention can collect the projection image in any angle range. Through the relationship between the virtual intersection points of each back projection ray, the evaluation index is calculated, and the scope of application is wider and expandable;

(4) High robustness, used in all kinds of cone beam CT systems; Scientifically evaluate the accuracy of geometric parameters, and use the optimized method to solve geometric parameters, theoretically complete, without various assumptions to approximate, and there is no error Disadvantages of analytic methods such as propagation.

DRAWINGS

1 is a spatial geometric relationship of a cone beam CT system of the present invention.

Figure 2 shows the inverse projection ray relationship under ideal geometric parameters.

Figure 3 shows the inverse projection ray relationship under the wrong geometric parameters.

4 is a schematic view of a "dummy focus" of a back projection ray of the present invention.

FIG. 5 is a simulation experiment error analysis of an embodiment of the present invention.

detailed description

The present invention will be further described by way of embodiments with reference to the accompanying drawings.

The phantom used in the model of this embodiment is a circular microsphere 1 with a large absorption coefficient. In order to construct the objective function on which the optimization algorithm is based, it is first assumed that the centroid of the microsphere is I, which is in a Cartesian coordinate system (x). The coordinates in , y, z) are (I _x , I _y , I _z )'. By rotating the gantry 2, we can obtain the projection coordinates of the centroid point on the detector plane 3 at different scanning angles. It is P _i =(P _ix ,P _iy ,P _iz )', i∈[1,N] (N is the number of scanning angles, i is the scanning angle index), and the coordinates of the point O _i are assumed to be (O _ix , O _iy , O _iz )', we can get the back projection line O _i P _{i for} each scan angle; when a cone beam CT system is accurately corrected, then all these back projection lines should theoretically be handed over to one point, and This point should be the centroid I of the microsphere, as shown in Figure 2. But in reality, in an uncorrected system, these back-projection lines do not intersect at a point in space, and their spatial relationship can be visually represented as the state shown in Figure 3.

Suppose that the two back-projection lines in an uncorrected system are O _i P _i and O _j P _j (i∈[1,N],j∈[1,N],i≠j), respectively, they are not Intersect, so there is no intersection between the two lines. Here, the present application proposes a definition of "virtual intersection point", that is, a midpoint M _ij of a line segment A _i A _j perpendicular to the two lines is assumed to be a virtual intersection of the two back projection lines, as shown in FIG. When the two lines intersect, this virtual intersection is the real intersection.

This formula is the evaluation index of the geometric parameters proposed by the present invention, wherein

Is the mean of all M _i,j , and ||V|| ₂ represents the l2 norm of the vector V. In theory, when the geometric parameters of the system are accurately corrected, the indicator will reach a minimum of zero.

As shown in Fig. 3, it is assumed that the coordinates of points A _i and A _j in the Cartesian coordinate system (x, y, z) are (x _i , y _i , z _i ) and (x _j , y _j , z _j ) . Since point A _i is on line i, point A _j is on line j, and vector A _i A _j is perpendicular to line i and line j at the same time, so the following equation holds:

Here the vector (a _i , b _i , c _i )' and the vector (a _j , b _j , c _j )' are the unit direction vectors of the straight lines O _i P _i and O _j P _j , respectively, the parameter _mi and the parameter m _j It is the parameter in the parameter equation of the above two lines. By solving the above equations, we can get the analytical expression of the parameter:

among them

τ = (a _i , b _i , c _i )·(a _j , b _j , c _j )'. Thus we can get the coordinates of the points A _i and A _j and get the virtual intersection M _{i of the} lines i and j _{, j}

M _i,j =(A _i +A _j )/2

Assuming that the projection coordinates of the microsphere centroid on the detector at scan angle i are (u _i , v _i ), the coordinates of this projection point in space (ω _i , α _i , β _i ) can be expressed as

The coordinates of this point in the Cartesian coordinate system (x, y, z) can be expressed as

Now, we can establish the equation of the line with the geometric parameters as parameters, so that we can get the direction vector of the line i represented by the geometric parameters. Combined with the above equations, the index proposed by the present invention can be transformed into the parameter with the geometric parameter as the parameter. function

The computational complexity of this index is O(N ² ). In order to simplify the computational complexity, we only need to calculate the virtual intersection point of the back projection line whose scan angle is about 45 degrees, so that the computational complexity of the index becomes O ( N). Although the computational complexity is significantly reduced, higher geometric correction accuracy can still be obtained during the experiment. As shown in Fig. 5, the simulation method for further calculating geometric parameters using this index has extremely high precision.

The evaluation index Ct is a vector value function, which contains six real variables corresponding to six important geometric parameters D, θ, φ, η, u _c , v _c . Where D represents the distance from the source to the axis of rotation, and the point (u _c , v _c ) represents the projection point of the source along the line passing through it and perpendicular to the z-axis. In order to be able to express the directional deflection of the detector plane, it is necessary to introduce three further two orthogonal intermediate variables α, β, ω, which are angle deflection parameters in each dimension. The vector can also be viewed as a point in a six-dimensional European space, and each point can be represented as. Because of the existence of noise and error, the objective function is generally not a convex function. Therefore, we use the optimization method such as simulated annealing to solve the minimum value of the index, and obtain the optimal solution of the geometric parameters.

The cone beam CT system detector geometric correction method of the embodiment includes the following steps:

In the first step, the metal ball is fixed on the stage of the CT system, and the metal ball is scanned by X-rays of 30 kV/200 μA. The angular interval and the scanning range can be freely selected according to requirements, and a projection image of N small balls is obtained.

In the second step, the projection image is binarized to obtain a small ball after the background is removed.

In the third step, the centered projection image is centered. Since the object is black in the processed projected image, it is measured that the center of mass of the black area in the projected image is the projection center. Taking the measurement of the abscissa as an example, the specific method is to first make nXSum=0, nCount=0, where nXSum represents the X coordinate of all black pixels, and nCount represents black. The number of pixels, where n indicates that the data is represented by an int type, and it is sequentially determined whether the point in the image after binarization is 0. If 0, nXSum is added to the abscissa of the point, and the number of black pixels is nCount Add 1 and after all the points of the whole image have been judged, nXSum divided by nCount is the projection center of the object of the image.

The fourth step is to calculate the geometric parameter evaluation index value under the current geometric parameters.

In the fifth step, the simulated annealing-simplex joint algorithm is used to iteratively calculate the index value, and the geometric parameter value under the minimum index value is solved until the iterative termination condition is satisfied, and the optimal solution of the geometric parameter is obtained.

In the sixth step, the projected image is geometrically corrected using the optimal solution of the obtained geometric parameters.

The above embodiments are only for explaining the technical idea of the present invention, and the scope of protection of the present invention is not limited thereto. Any modification made based on the technical idea according to the technical idea of the present invention falls within the protection scope of the present invention. Inside.

Claims

A method for evaluating a geometric parameter of a cone beam CT system based on a small ball phantom, characterized in that the method comprises the following steps:

(1) The cone beam CT system obtains a plurality of projection images by scanning the ball phantoms at various angles;

(2) Solving the position of the center of mass of the small ball projection on the detector;

(3) determining the back projection ray passing through the centroid of the small sphere in the geometric space by the six geometric parameters of the cone beam CT;

(4) Calculating the "virtual intersection point" between the two pairs of back projection rays;

(5) Calculate the degree of convergence of the "virtual intersection point", that is, the standard deviation of the space coordinates as an indicator for evaluating the geometric parameters.
The method for evaluating geometric parameters of a cone-beam CT system based on a small ball phantom according to claim 1, wherein the "virtual focus" between the back projection rays is two disjoint spaces in the space of the present application. The midpoint of the shortest line segment formed by two points on the back projection ray.
The method for evaluating geometric parameters of a cone-beam CT system based on a small ball phantom according to claim 1, wherein the evaluation index unit of the geometric parameter is a pixel.
A method for correcting geometric parameters of a cone beam CT system based on a small ball phantom, characterized in that the method comprises the following steps:

(1) According to the existing six geometric parameters or randomly set parameters of the existing system as the initial value;

(2) using the optimization method to solve the six geometric parameters when the index under claim 1 is minimum;

(3) The CT image is corrected by the six geometric parameters obtained by the solution.
The method for correcting geometric parameters of a cone-beam CT system based on a small ball phantom according to claim 4, wherein the method uses one or more small ball phantoms to simultaneously scan, and can be corrected by different systems and different precisions. Determine the number of phantoms.
The method for correcting geometric parameters of a cone-beam CT system based on a small ball phantom according to claim 4, wherein the optimization method is an ant colony algorithm, a particle swarm algorithm or a simulated annealing algorithm.