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CN101936720B - Method for calibrating detector torsion angle applied to cone-beam XCT system - Google Patents

Method for calibrating detector torsion angle applied to cone-beam XCT system Download PDF

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CN101936720B
CN101936720B CN2010102419806A CN201010241980A CN101936720B CN 101936720 B CN101936720 B CN 101936720B CN 2010102419806 A CN2010102419806 A CN 2010102419806A CN 201010241980 A CN201010241980 A CN 201010241980A CN 101936720 B CN101936720 B CN 101936720B
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coordinate
image
detector
objective body
axle
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CN101936720A (en
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杨民
刘永瞻
高海东
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Beihang University
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Abstract

The invention discloses a method for calibrating a detector torsion angle applied to a cone-beam XCT system. In the calibration method, a spherical object is adopted to rotate around a z shaft by a circle in a cone-beam ray field, and the track of the projected mass center of the object in an imaging coordinate system xdodzd is an approximate ellipse; and the track of the projected mass center is fitted into an elliptic equation of xd2+azd2+bxdzd+cxd+ezd+f=0 by using the least square fitting method, wherein an included angle between a long axis of the ellipse and an xd axis is the detector torsion angle Xi. The detector torsion angle Xi is represented by the included angle between the long axis of the ellipse and the xd axis, so the calibration method has the advantages of low calculated quantity in the calibrating process, difficult occurrence of false solution, and high repeatability precision.

Description

A kind of scaling method that is applicable to the detector torsion angle of cone-beam XCT system
Technical field
The present invention relates to a kind of cone-beam XCT (X-ray Computed Tomography) system, more particularly say, be meant the detector torsion angle scaling method of a kind of cone-beam XCT system.
Background technology
In the last few years, the develop rapidly of Along with computer technology and the appearance of planar array detector, cone-beam XCT (Cone-beam X-ray Computed Tomography) becomes the research focus in NDT (Non-destructive Testing) field day by day.In numerous CT reconstruction algorithm, consider operand and Project Realization difficulty, the algorithm of FDK (Feldkamp-Davis-Kress) type is the most practical, also is the main flow in the practical engineering application always.The scanning theory of cone-beam XCT system is as shown in Figure 1; Be that testee 4 on 2 pairs of multiple degrees of freedom objective tables 3 of cone-beam x-ray of sending of radiographic source 1 carries out transillumination; Testee 4 rotates around axis under the drive of multiple degrees of freedom objective table 3; Planar array detector 5 is gathered the DR projection (DR-Digital Radiography, ray digital imaging) of testee 4 under different visual angles, and the image reconstruction unit in the last PC utilizes these two-dimentional DR projection sequence to carry out three-dimensional reconstruction.
Shown in Figure 1A, the FDK reconstruction algorithm is in the coordinate system xyz of radiographic source and detector structure (be also referred to as and rebuild coordinate system), to carry out, and the imaging coordinate system of detector 5 is x do dz d, the FDK reconstruction algorithm requires the relation of these two coordinate systems to be in theory: o dz dAxle is parallel to oz axle, o dx dAxle is parallel to the ox axle.Yet in the cone-beam XCT of reality system installs, exist mechanical alignment error inevitably, cause o dz dAxle is not parallel to oz axle, o dx dAxle is not parallel to the ox axle, is equivalent to coordinate system x do dz dRotated certain angle around the y axle, this angle is the torsion angle ξ of detector.The existence of torsion angle ξ has influenced the precision of two-dimentional DR projection sequence reconstructed image, causes the generation of pseudo-shadow, thereby influences the resolving power of reconstructed image and effectively detecting of reconstructed image details.
Summary of the invention
The objective of the invention is to propose a kind of scaling method to detector torsion angle ξ in the cone-beam XCT scanning system, this demarcation adopted spherical objective body in the cone-beam x-ray field after the z axle rotates a circle, it is at imaging coordinate system x do dz dIn DR projected centroids track be a sub-elliptical, and utilize least square fitting method that the track fitting of DR projected centroids is x d 2+ az d 2+ bx dz d+ cx d+ ez dThe elliptic equation of+f=0; In DR projected centroids elliptical orbit, its transverse and x dThe angle of axle is detector torsion angle ξ; In the present invention in order to realize that spherical objective body around the rotation of z axle, designed eccentric slide holder, and spherical imageable target body (testee) is installed on this off-centre slide holder, and eccentric slide holder is installed on the multiple degrees of freedom objective table; When the multiple degrees of freedom objective table when axis revolves three-sixth turn, detector will collect the DR projection sequence of spherical objective body under different visual angles.
A kind of scaling method that is applicable to the detector torsion angle of cone-beam XCT system of the present invention, concrete steps are following:
The first step: adjust spherical objective body and be imaged on the position in the detector
Multiple degrees of freedom objective table 3 is placed the optional position between radiographic source 1 and the planar array detector 5; Vertical sleeve 6 of eccentric slide holder inserts in the center pit of multiple degrees of freedom objective table 3; A spherical objective body 10 is fixed on the column of slide block 9; Regulate the height of elevating lever 7 on axis through holding out against screw 61, and the position of moving slider 9 on horizontal guide rod 8; Adjusting spherical objective body, to be imaged on position in the detector be to guarantee spherical objective body 10 by cone-beam x-ray 2 irradiations, and the imaging of spherical objective body can be gathered by detector 5 imaging surfaces;
Second step: the adjustment anglec of rotation
Start multiple degrees of freedom objective table 3, and multiple degrees of freedom objective table 3 is rotated in 360 degree scopes around axis, under the anglec of rotation of every interval 5 degree～15 degree, planar array detector 5 collects the DR projected image of spherical objective body 10;
The 3rd step: obtain bianry image
The every width of cloth DR projected image that in Flame Image Process and visualization, second step was obtained carries out Threshold Segmentation to be handled, thereby obtains two-value DR image; In said two-value DR image, the projection value of spherical objective body is designated as 1, and all the other regional projection values are designated as 0;
The 4th step: ask DR projected centroids coordinate (x D-i, z D-i)
In image reconstruction unit, the every width of cloth two-value DR image that obtains in the 3rd step is carried out DR projected centroids coordinate and ask for, be i.e. DR projected centroids coordinate (x D-i, z D-i) in
Figure BSA00000212390500021
Figure BSA00000212390500022
M representes the length of DR projection;
N representes the height of DR projection;
F (x d, z d) two-dimensional function of expression two-value DR image, wherein, x dExpression imaging coordinate system x do dz dFollowing x dCoordinate variable on the axle, z dExpression imaging coordinate system x do dz dFollowing z dCoordinate variable on the axle;
x D-iRepresent that spherical objective body projected centroids is at x in the i width of cloth two-value DR image dCoordinate on the axle;
z D-iRepresent that spherical objective body projected centroids is at z in the i width of cloth two-value DR image dCoordinate on the axle;
The 5th step: match DR projected centroids track
In image reconstruction unit, utilize least square fitting method to carry out track fitting, be about to all DR projected centroids point coordinate (x each center-of-mass coordinate that obtains in the 4th step D-i, z D-i) fit to x d 2+ az d 2+ bx dz d+ cx d+ ez dThe elliptic equation of+f=0 can access all DR projected centroids point coordinate (x according to this elliptic equation D-i, z D-i) elliptical orbit that forms, the slope of said elliptical orbit does Thereby obtain torsion angle ξ=arctg (k) that planar array detector produces when mounted according to this elliptical orbit slope;
x dExpression imaging coordinate system x do dz dFollowing x dCoordinate variable on the axle;
z dExpression imaging coordinate system x do dz dFollowing z dCoordinate variable on the axle;
A representes variable z in the elliptic equation dThe quadratic term coefficient;
B representes variable x in the elliptic equation dz dThe quadratic term coefficient;
C representes variable x in the elliptic equation dOnce coefficient;
E representes variable z in the elliptic equation dOnce coefficient;
F representes the constant term of elliptic equation.
The advantage of scaling method of the present invention:
1) through spherical objective body is installed on the eccentric slide holder, the multiple degrees of freedom objective table drives eccentric slide holder and rotates a circle around the z axle, and spherical objective body is at imaging coordinate system x do dz dThe middle projected footprint that forms sub-elliptical.Through spherical objective body moving on slide holder, the shape of scalable sub-elliptical track helps obtaining best elliptical orbit.
2) utilize least square method pairing approximation elliptical orbit to carry out the elliptic equation x that match obtains d 2+ az d 2+ bx dz d+ cx d+ ez d+ f=0 can satisfy the minimum principle of error, thereby has guaranteed the precision of calibration result.
3) utilize long axis of ellipse and x dThe angle of axle characterizes the torsion angle ξ of detector, makes that calculated amount is few in the calibration process, is not prone to vacation and separates, and repeatable accuracy is high.
4) scaling method of the present invention is realized easily, and principle is simple, only need spherical objective body be revolved three-sixth turn between radiographic source and detector and get final product.
Description of drawings
Fig. 1 is the scanning theory figure of cone-beam XCT system.
Figure 1A is the detector torsion angle machinery alignment error synoptic diagram that occurs when cone-beam XCT system is installed.
Fig. 2 is the structural drawing of eccentric slide holder of the present invention.
Fig. 2 A is the structural drawing of horizontal guide rod in the eccentric slide holder of the present invention.
Fig. 2 B is the structural drawing of slide block in the eccentric slide holder of the present invention.
Fig. 3 puts synoptic diagram with the position that eccentric sliding support of the present invention is placed in the cone-beam XCT system.
Fig. 4 is the figure as a result that 24 width of cloth DR images of spherical objective body is synthesized a width of cloth DR image.
Fig. 4 A is the oval synoptic diagram that match obtains.
Fig. 4 B is the partial enlarged drawing of Fig. 4 A.
Fig. 5 is the CT reconstructed image before not demarcating.
Fig. 5 A adopts the calibrated CT reconstructed image of the inventive method.
Embodiment
To combine accompanying drawing and embodiment that the present invention is done further detailed description below.
A kind of scaling method that is applicable to the detector torsion angle of cone-beam XCT system that the present invention proposes; Be that the detector torsion angle ξ to cone-beam XCT system demarcates before dispatching from the factory; Or cone-beam XCT system is after a period of time uses, and detector torsion angle ξ is carried out timing and a kind of comparatively easy, the easy-operating scaling method that adopts.One cover cone-beam XCT system generally is made up of hardware components and software section, and wherein, hardware components comprises: radiographic source, multiple degrees of freedom objective table, controller, PC, planar array detector; Software section comprises: CT control module, image reconstruction unit, Flame Image Process and visualization.
Referring to shown in Figure 3, the present invention is to the imaging coordinate system x of planar array detector 5 do dz dProducing certain anglec of rotation ξ around the y axle demarcates; Be employed on the axis direction to go up and down, can spherical imageable target body 10 (testee) be installed with the eccentric slide holder (shown in Fig. 2, Fig. 2 A, Fig. 2 B) that multiple degrees of freedom objective table 3 rotates on the sense of rotation, make projection that spherical imageable target body 10 become under the irradiation of cone-beam x-ray 2 by planar array detector 5 collections.
In the present invention; At first design eccentric slide holder shown in Fig. 2, Fig. 2 A, Fig. 2 B; By vertical sleeve 6, elevating lever 7, laterally guide rod 8 and slide block 9 are formed, the base of slide block 9 is installed on the slideway 81 of horizontal guide rod 8, and spherical objective body 10 is installed on the column of slide block 9; Elevating lever 7 is fixed tightly on vertical sleeve 6 through holding out against screw 61, and holds out against screw 61 and regulate the height of elevating lever 7 on the axis direction of multiple degrees of freedom objective table 3 through loosening, tighten.The effect of this off-centre slide holder is the rotation center that spherical objective body 10 is departed from multiple degrees of freedom objective table 3 under the condition of rotating.
A kind of scaling method that is applicable to the detector torsion angle of cone-beam XCT system of the present invention, concrete steps are following:
The first step: adjust spherical objective body and be imaged on the position in the detector
Multiple degrees of freedom objective table 3 is placed the optional position between radiographic source 1 and the planar array detector 5; Vertical sleeve 6 of eccentric slide holder is inserted in the center pit of multiple degrees of freedom objective table 3; A spherical objective body 10 is fixed on the column of slide block 9; Regulate the height of elevating lever 7 through holding out against screw 61, and the position of moving slider 9 on horizontal guide rod 8, make spherical objective body 10 be imaged on the correct position of detector 5 imaging surfaces.As shown in Figure 3.
In the present invention; Spherical objective body is imaged on the position in the detector as long as guarantee that measured object (spherical objective body 10) can be by cone-beam x-ray 2 irradiations; Do not do requirement for the concrete distance of multiple degrees of freedom objective table 3 between radiographic source 1 and planar array detector 5; This has just reduced in the cone-beam XCT system requirement to the exact position, thereby makes calibration process simple, and is easy to operate.
Second step: the adjustment anglec of rotation
Start multiple degrees of freedom objective table 3 and in 360 degree scopes, rotate, certain angle (5 degree～15 degree) detector 5 in every interval will collect the DR image of spherical objective body;
In the present invention, at interval certain angle carries out the DR IMAQ of spherical objective body, is in order to obtain spherical objective body 10 under the driving of multiple degrees of freedom objective table 3, and the DR image sequence of the diverse location in the journey is spent in rotation 360, and is as shown in Figure 4.In order to see elliptical orbit clearly, the inventor amplifies amplification and the track that Fig. 4 has carried out under planimetric coordinates, shown in Fig. 4 A and Fig. 4 B.
The 3rd step: obtain bianry image
The every width of cloth DR image that in Flame Image Process and visualization, second step was obtained carries out Threshold Segmentation, is converted into bianry image, and in the two-value DR image that obtains, the projection value of spherical objective body is 1, and all the other regional projection values are 0.
In the present invention, Threshold Segmentation is a kind of image processing algorithm commonly used.
The 4th step: ask DR projected centroids coordinate (x D-i, z D-i)
In image reconstruction unit to the center-of-mass coordinate (x of spherical objective body projection in every width of cloth two-value DR image of obtaining in the 3rd step D-i, z D-i), shown in formula:
x d - i = 1 MN Σ x d = 1 M Σ z d = 1 N x d × f ( x d , z d )
z d - i = 1 MN Σ x d = 1 M Σ z d = 1 N z d × f ( x d , z d )
M representes the length of DR projection;
N representes the height of DR projection;
F (x d, z d) two-dimensional function of expression two-value DR image, wherein, x dExpression imaging coordinate system x do dz dFollowing x dCoordinate variable on the axle, z dExpression imaging coordinate system x do dz dFollowing z dCoordinate variable on the axle.
x D-iRepresent that spherical objective body projected centroids is at x in the i width of cloth two-value DR image dCoordinate on the axle;
z D-iRepresent that spherical objective body projected centroids is at z in the i width of cloth two-value DR image dCoordinate on the axle.
The 5th step: match DR projected centroids track
In image reconstruction unit, each center-of-mass coordinate that obtains in the 4th step is utilized least square fitting method, with all projected centroids point coordinate (x D-i, z D-i) fit to an elliptic equation:
x d 2+az d 2+bx dz d+cx d+ez d+f＝0
This oval slope expression formula is:
k = a - 1 - ( 1 - a ) 2 + b 2 b
According to the transverse slope, obtain the torsion angle ξ=arctg (k) of detector.
In the present invention, when fitted ellipse, adopt the nonlinear least square fitting method.
Elliptic equation is:
x d 2+az d 2+bx dz d+cx d+ez d+f＝0 (1)
In the formula (1):
x dExpression imaging coordinate system x do dz dFollowing x dCoordinate variable on the axle;
z dExpression imaging coordinate system x do dz dFollowing z dCoordinate variable on the axle;
A representes variable z in the elliptic equation dThe quadratic term coefficient;
B representes variable x in the elliptic equation dz dThe quadratic term coefficient;
C representes variable x in the elliptic equation dOnce coefficient;
E representes variable z in the elliptic equation dOnce coefficient;
F representes the constant term of elliptic equation.
Get functional relation by formula (1):
z d ( x d , a , b , c , e , f ) = 1 2 a [ - bx d - e ± ( b 2 - 4 a ) x d 2 + ( 2 be - 4 ac ) x d - e 2 - 4 af ] - - - ( 2 )
z d(x d, a, b, c, e, f) expression is based on the variable z of elliptic equation (1) dAbout x d, a, b, c, e, f function.
Set up error function:
Q = Σ i = 1 n [ z d - i - z d ( x d - i , a , b , c , e , f ) ] 2 - - - ( 3 )
In the formula (3):
N representes the number of spherical objective body DR projected centroids;
Q represents error function;
x D-iRepresent that spherical objective body projected centroids is at x in the i width of cloth two-value DR image dCoordinate on the axle;
z D-iRepresent that spherical objective body projected centroids is at z in the i width of cloth two-value DR image dCoordinate on the axle.
Ask the non-linear least square that satisfies formula (3) to separate, can obtain the value of parameter a, b, c, e and f.The slope expression formula of transverse is so:
k = tgξ = a - 1 - ( 1 - a ) 2 + b 2 b - - - ( 4 )
Examples of implementation
In order to verify the validity of measuring method of the present invention; The inventor has designed eccentric slide holder; With external diameter is that the steel ball of 8mm is installed on the slide block 9 of eccentric slide holder; And vertical sleeve 6 of eccentric slide holder is inserted in the center pit of multiple degrees of freedom objective table 3, thus, 3 rotations of multiple degrees of freedom objective table drive spherical objective body 10 and rotate synchronously.
The main hardware of the 160kV cone-beam XCT system that selects for use disposes as follows:
(1) radiographic source: the German YXLON product MG165/2.25X-of company radiographic source, focal spot size 0.2mm;
(2) eccentric slide holder: by vertical sleeve 6, elevating lever 7, laterally guide rod 8 and slide block 9 constitute;
(3) planar array detector: U.S. Varian company produces PaxScan2520 type amorphous silicon planar array detector, imaging area 200 * 250mm 2, visit elemental size 0.127mm.
The steel ball that the multiple degrees of freedom objective table drives on the eccentric slide holder rotates in 360 degree scopes; Every interval 15 degree detectors are gathered a width of cloth DR image; Gather 24 width of cloth images altogether; Fig. 4 can find out that for this 24 width of cloth DR image being synthesized the result of a width of cloth DR image all steel ball projections are distributed on the elliptical orbit.Step above utilizing is extracted the center-of-mass coordinate of each steel ball projection, fits to an elliptic equation then, thereby draws this long axis of ellipse slope, shown in Fig. 4 A, Fig. 4 B.
The Design Theory torsion angle of this equipment detector when assembling is 0 degree, yet in the system of reality installs, has mechanical alignment error inevitably, causes reconstructed image pseudo-shadow to occur.Pair cross-section is that the rectangular parallelepiped organic glass test specimen of 10mm * 10mm carries out CT scan in this system, and Fig. 5 is not for carrying out the reconstructed image that the detector torsion angle is proofreaied and correct, and distortion has taken place image, and four angle moulds of rectangular cross section are stuck with paste unclear.The measuring method of utilizing the present invention to propose, the torsion angle that records this system detector are 0.4586 degree, in the correction parameter with this value input reconstruction algorithm, obtain the reconstructed image shown in Fig. 5 A, and image edge clear is coincide better with true form.

Claims (2)

1. scaling method that is applicable to the detector torsion angle of cone-beam XCT system is characterized in that including following demarcating steps:
The first step: adjust spherical objective body and be imaged on the position in the detector
Multiple degrees of freedom objective table (3) is placed the optional position between radiographic source (1) and the planar array detector (5); Vertical sleeve (6) of eccentric slide holder inserts in the center pit of multiple degrees of freedom objective table (3); A spherical objective body (10) is fixed on the column of slide block (9); Regulate the height of elevating lever (7) on axis through holding out against screw (61), and the position of moving slider (9) on horizontal guide rod (8); Adjusting spherical objective body, to be imaged on position in the detector be to guarantee spherical objective body (10) by cone-beam x-ray (2) irradiation, and the imaging of spherical objective body can be gathered by detector (5) imaging surface;
Second step: the adjustment anglec of rotation
Start multiple degrees of freedom objective table (3), and multiple degrees of freedom objective table (3) is rotated in 360 degree scopes around axis, under the anglec of rotation of every interval 5 degree～15 degree, planar array detector (5) collects the DR projected image of spherical objective body (10);
The 3rd step: obtain bianry image
The every width of cloth DR projected image that in Flame Image Process and visualization, second step was obtained carries out Threshold Segmentation to be handled, thereby obtains two-value DR image; In said two-value DR image, the projection value of spherical objective body is designated as 1, and all the other regional projection values are designated as 0;
The 4th step: ask DR projected centroids coordinate (x D-i, z D-i)
In image reconstruction unit, the every width of cloth two-value DR image that obtains in the 3rd step is carried out DR projected centroids coordinate and ask for, be i.e. DR projected centroids coordinate (x D-i, z D-i) in x d - i = 1 MN Σ x d = 1 M Σ z d = 1 N x d × f ( x d , z d ) , z d - i = 1 MN Σ x d = 1 M Σ z d = 1 N z d × f ( x d , z d ) ;
M representes the length of DR projection;
N representes the height of DR projection;
F (x d, z d) two-dimensional function of expression two-value DR image, wherein, x dExpression imaging coordinate system x do dz dFollowing x dCoordinate variable on the axle, z dExpression imaging coordinate system x do dz dFollowing z dCoordinate variable on the axle;
x D-iRepresent that spherical objective body projected centroids is at x in the i width of cloth two-value DR image dCoordinate on the axle;
z D-iRepresent that spherical objective body projected centroids is at z in the i width of cloth two-value DR image dCoordinate on the axle;
The 5th step: match DR projected centroids track
In image reconstruction unit, utilize least square fitting method to carry out track fitting, be about to all DR projected centroids point coordinate (x each center-of-mass coordinate that obtains in the 4th step D-i, z D-i) fit to x d 2+ az d 2+ bx dz d+ cx d+ ez dThe elliptic equation of+f=0 can access all DR projected centroids point coordinate (x according to this elliptic equation D-i, z D-i) elliptical orbit that forms, the slope expression formula of said transverse does
Figure FSB00000621601100021
Thereby obtain torsion angle ξ=arctg (k) that planar array detector produces when mounted according to this elliptical orbit slope;
x dExpression imaging coordinate system x do dz dFollowing x dCoordinate variable on the axle;
z dExpression imaging coordinate system x do dz dFollowing z dCoordinate variable on the axle;
A representes variable z in the elliptic equation dThe quadratic term coefficient;
B representes variable x in the elliptic equation dz dThe quadratic term coefficient;
C representes variable x in the elliptic equation dOnce coefficient;
E representes variable z in the elliptic equation dOnce coefficient;
F representes the constant term of elliptic equation.
2. the scaling method that is applicable to the detector torsion angle of cone-beam XCT system according to claim 1; It is characterized in that: eccentric slide holder is made up of vertical sleeve (6), elevating lever (7), horizontal guide rod (8) and slide block (9); The base of slide block (9) is installed on the slideway (81) of horizontal guide rod (8); Spherical objective body (10) is installed on the column of slide block (9); Elevating lever (7) is fixed tightly on vertical sleeve (6) through holding out against screw (61), and holds out against screw (61) and regulate the height of elevating lever (7) on the axis direction of multiple degrees of freedom objective table (3) through loosening, tighten.
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