CN103549971B - A kind of method determining geometric calibration parameter in C-arm computed tomography (SPECT) system - Google Patents

Abstract

The invention discloses a kind of method determining geometric calibration parameter in C-arm computed tomography (SPECT) system, specifically directly determine C-arm with helix die body? in CT system, 9 geometric calibration parameters, belong to medical imaging field.The method utilizes the geometrical property of helix, and it is converted to a series of parallelogram dexterously.Then obtain the intersection point of these diagonal of a parallelogram, be used for determining the projection of die body coordinate system coordinate axes, be finally integrated in corresponding calibration algorithm.The present invention is based on the helix die body of extensive use, do not need additional processing to demarcate die body, and be a kind of method of parsing, make full use of the information of index point on helix die body, there is higher robustness and accuracy.

Description

A kind of method determining geometric calibration parameter in C-arm computed tomography (SPECT) system

Technical field

The present invention relates to a kind of off-line calibration method in C-arm fault imaging (C-armCT) system, more particularly, it relates to a kind of method directly determining geometric calibration parameter in C-armCT system based on helix die body, belongs to medical imaging field.

Background technology

Being integrated with C-arm fault imaging (C-armCT) system of flat panel detector, building the faultage image of object by obtaining a series of two-dimensional x-ray data for projection duplicate removal.C-arm imaging system is primarily of x-ray source, and flat panel detector, C-arm framework forms.For traditional CT, the advantages such as C-armCT has conveniently moving, low price, especially its opening Design, can be widely used in the preoperative planning in interventional therapy, in art detect and outcome evaluation in.

But in actual applications, because machine-building, the impact of the factor such as the system integration and gravity sag, the actual track of C-armCT system can depart from predetermined trajectory.These irregular deviations can reduce image resolution ratio, or cause occurring serious artifact in reconstruction image, affect doctor and judge.

At present for this problem, helix die body, owing to having 3 good dimension space information, is widely used in actual geometric calibration.This die body main body is the columniform resin of hollow, and be embedded with above by the evenly distributed a series of little steel ball of helix, these little steel balls are index point.The method that researcher adopts, mostly based on projection matrix, namely utilizes the corresponding relation of 2 dimension information of 3 dimension space information of index point on die body and projected image to carry out calibration system.But the method does not describe particularly to imaging system, as x-ray source position, the inclination of detector and the anglec of rotation, source is to the distance etc. of detector, and when system departs from larger, obtaining reconstructed image quality in this approach may be undesirable.

Other researcher can obtain the concrete calibrating parameters of system, but now helix die body is no longer applicable, needs to design special demarcation die body, increases additional workload like this.

Summary of the invention

The object of the invention is to solve the problem, proposing a kind of method directly determining geometric calibration parameter in C-arm computed tomography (SPECT) system based on helix die body.The method utilizes conventional helix die body, obtains whole 9 geometric calibration parameters of imaging system, have higher robustness and accuracy with analytic method.

The present invention utilizes the geometrical property of helix, and by the index point on helix by the classification of different sorting techniques, for each group, every four index points define a parallelogram.When not considering subpoint overlap, the subpoint of these four index points determines a tetragon.The cornerwise intersection point of tetragon that this projection obtains is the projection of cornerwise intersection point of parallelogram.Concrete technical scheme is as follows:

The first step, is placed on helix die body on C-arm articles holding table, with C-arm scanning, obtains data for projection.

Second step, determines the projected position of index point on flat panel detector on helix.

3rd step, utilizes the geometrical property of helix, determines die body coordinate system z-axis, and x-axis and two are parallel to the projection of y-axis.

4th step, determines the projection of die body coordinate origin on flat panel detector.

5th step, obtains intermediate parameters: a, b, c;

6th step, 9 geometric calibration parameters of system are obtained: the anglec of rotation (3 parameters: the angle of pitch of detector by intermediate parameters, deflection angle, inclination angle), x-ray source to detector distance (1 parameter), x-ray source position (3 parameters: x direction, y direction, z direction), die body coordinate origin projection on the detector (2 parameters: horizontal direction and vertical direction).

The invention has the advantages that:

(1) the method can obtain whole 9 geometric calibration parameters of system, thus can describe this imaging system particularly, has directive significance to machine-building.And obtain independently geometric calibration parameter, provided probability for the later stage is integrated in corresponding algorithm for reconstructing;

(2) the method is based on the helix die body of extensive use, does not need additional processing to demarcate die body;

(3) the method is a kind of analytic method, not based on mathematics reduction.And make full use of the information of index point on helix die body, ensure that robustness and the accuracy of method.

Accompanying drawing explanation

Fig. 1 is helix die body schematic diagram.

Fig. 2 is the flow chart determining geometric calibration parameter.

Fig. 3 is the schematic diagram determining that coordinate system z-axis projects.

In figure:

Detailed description of the invention

Below in conjunction with drawings and Examples, the present invention is described in further detail.

The present invention is a kind of method determining geometric calibration parameter in C-arm computed tomography (SPECT) system, as shown in Figure 2, comprises following step:

The first step, is placed on helix die body on the articles holding table in C-arm computed tomography (SPECT) system, with C-arm scanning, obtains the projected image of helix die body on flat panel detector.

Helix die body as shown in Figure 1, in the present invention, die body inlays the resin part of little steel ball (i.e. index point) with general little consistent, the present invention adopts helical pipe to instead of conventional hollow cylindrical, this reduces the resin manufactured required for die body, thus reduce the cost (adopting the processing method of rapid shaping) manufacturing this die body.The arrangement of little steel ball is consistent with general zigzag shape die body, can not affect the versatility of this method like this.

The placement of helix die body will ensure that the central shaft of helix is probably consistent with the direction of C-arm system rotating shaft.With C-arm continuous sweep one week, angular range setting was according to the difference of type, and the difference of the scope of application adjusts.Meet the half that the minimum angles scope of carrying out fault imaging requirement is 180 °+maximum fan-angle.

Finally, obtain x-ray and penetrate the projected image of helix die body on flat panel detector.

Second step, determines the projected position of index point on flat panel detector on helix.

In order to determine index point projection position on the detector, first obtaining the border of index point by the method for canny border detection, then adopting on the ellipse fitting algorithm determination projected image based on singular value decomposition and indicate dot center.The present invention adopts oval center as projection centre, and according to pertinent literature, the error between both can be ignored.

3rd step, utilizes the geometrical property of helix, determines die body coordinate system z-axis, projection that x-axis and two are parallel to the axle of y-axis.

On helix, the arrangement of index point meets radius is R, and pitch is the helix equation of 2 π h, and l index point position is defined as follows:

r _l＝(Rsinψ _l，Rcosψ _l，hψ _l)

ψ _l＝l×Δψ(l＝-N ₁，-N ₁+1，...，N ₂-1，N ₂)

Wherein: Δ ψ is the angle intervals of index point on helix, provided by equation Δ ψ=π/N.The value of N is integer, and in theory, the span of N can from 1 to infinity.But in actual applications, when helical length keeps fixing, along with the increase of N value, the quantity of index point is also along with increasing, and the now projection of index point may occur overlap on projection images, is unfavorable for post-processed.When N value is too little, index point number is very few, can affect arithmetic accuracy.So in actual applications, the span of N is 3≤N≤18 is more rational.

Parameter N ₁and N ₂value be integer, choosing with choosing of the total length of helix axis and reference point of they is relevant.The length supposing the helix axis that evenly distributed index point is formed is L, so N ₁+ N ₂=L/ (h Δ ψ)-1.Generally choose to be positioned in the middle part of helix or close to the index point at middle part as reference point, the angle of this parameter point is 0, i.e. ψ ₀=0.After the chosen position of the total length and reference point that provide helix axis, N can be determined ₁and N ₂value.

(1) determine the method that coordinate system z-axis projects, as shown in Figure 3, choose 4 index points from helix, form parallelogram as follows:

$P_k^z=\left\{r_A{r}_B{r}_C{r}_{D_k}\right|{\mathrm{\ψ}}_A={\mathrm{\ψ}}_k,{\mathrm{\ψ}}_B={\mathrm{\ψ}}_k+2\mathrm{\π},{\mathrm{\ψ}}_C={\mathrm{\ψ}}_k+3\mathrm{\π},{\mathrm{\ψ}}_D={\mathrm{\ψ}}_k+\mathrm{\π},$

k∈[-N ₁，N ₂-3N]}，

Wherein, r _a, r _b, r _c, r _dbeing 4 index points in helix, is also 4 summits forming this parallelogram; ψ _a, ψ _b, ψ _c, ψ _dbe respectively a r _a, r _b, r _c, r _dangle position in helix; K is the index value of this parallelogram, ψ _k=k × Δ ψ.

Parallelogram cornerwise intersection point is:

${r_I^z}_k=(\mathrm{0,0},h({\mathrm{\ψ}}_k+3\mathrm{\π}/2)).$

Parallelogram on the detector be projected as tetragon diagonal intersection point being projected as on the detector because diagonal intersection point in z-axis, so the diagonal intersection point obtained that projects on the projection z ' of z-axis, from newly choosing parallelogram, obtaining the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, determining the projection z ' axle of die body coordinate system z-axis.

Fig. 3 is the schematic diagram determining that coordinate system z-axis projects, wherein p _a, p _b, p _c, p _dbe respectively a r _a, r _b, r _c, r _dsubpoint on the detector.In the nonoverlapping situation of subpoint, these 4 subpoints determine a tetragon, and the cornerwise intersection point of this tetragon is p _i.P _iwith r _iit is one-to-one relationship.In figure 3, the angle intervals of setting helix is π/6(, parallelogram four summit r _a, r _b, r _c, r _dthe angle parameter in helix be respectively:

ψ _a=-2 π/3, ψ _b=4 ψ/3, ψ _c=7 ψ/3, ψ _d=π/3, now parallelogram cornerwise intersecting point coordinate is cornerwise intersection point in z-axis, therefore project the tetragon obtained the diagonal intersection point projection z ' that determines z-axis visiting a point on device.Same, a series of projection quadrilateral can be obtained thus determine the projection of z-axis.

(2) determine that coordinate system x-axis projects.Choose 4 index points from helix, form parallelogram as follows:

$P_i^x=\left\{r_A{r}_B{r}_C{r}_{D_i}\right|{\mathrm{\ψ}}_A={\mathrm{\ψ}}_i,{\mathrm{\ψ}}_B={\mathrm{\ψ}}_i+2\mathrm{\π},{\mathrm{\ψ}}_C=-{\mathrm{\ψ}}_i,{\mathrm{\ψ}}_D=-{\mathrm{\ψ}}_i-2\mathrm{\π},$

i∈[max(-N ₁，-N ₂，-N+1)，min(N ₂-2N，N ₁-2N)]，i≠0}

Wherein, r _a, r _b, r _c, r _dbeing 4 index points in helix, is also 4 summits forming this parallelogram; ψ _a, ψ _b, ψ _c, ψ _dbe respectively a r _a, r _b, r _c, r _dangle position in helix; I is the index value of this parallelogram, ψ _i=i × Δ ψ.Parallelogram cornerwise intersection point is:

${r_I^x}_i=(R\cos {\mathrm{\ψ}}_i,\mathrm{0,0})$

With ask z-axis to project similar, determine a point in x-axis, obtain the cornerwise intersection point of corresponding projection quadrilateral, choosing parallelogram, obtain the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, the projection of x-axis on the projection x ' axle determination detector determining die body coordinate system x-axis.

(3) two projections being parallel to y-axis are determined.Choose 8 index points from helix, form two parallelogrames with

$P_{j1}^y=\left\{r_A{r}_B{r}_C{r}_{D_{j1}}\right|{\mathrm{\ψ}}_A={\mathrm{\ψ}}_{j1},{\mathrm{\ψ}}_B={\mathrm{\ψ}}_{j1}+2\mathrm{\π},{\mathrm{\ψ}}_C=-{\mathrm{\ψ}}_{j1}+\mathrm{\π},{\mathrm{\π}}_D=-{\mathrm{\ψ}}_{j1}-\mathrm{\π},$

$j1\∈[\max (-N_1,N-N_2,-\frac{N}{2}+1),\min (N_1-N,N_2-2N)],j1\≠\frac{N}{2}\},$

$P_{j2}^y=\left\{r_A{r}_B{r}_C{r}_{D_{j2}}\right|{\mathrm{\ψ}}_A={\mathrm{\ψ}}_{j2},{\mathrm{\ψ}}_B={\mathrm{\ψ}}_{j2}+2\mathrm{\π},{\mathrm{\ψ}}_C=-{\mathrm{\ψ}}_{j2}+\mathrm{\π},{\mathrm{\π}}_D=-{\mathrm{\ψ}}_{j2}-\mathrm{\π},$

$j2\∈[\max (2N-N_1,N-N_2),\min (N_1-N,N_2,\frac{N}{2}-1)],j2\≠-\frac{N}{2}\},$

$P_j^y=P_{j1}^y\∪P_{j2}^y.$

Wherein, r _a, r _b, r _c, r _dbeing 4 index points in helix, is also 4 summits forming this parallelogram; ψ _a, ψ _b, ψ _c, ψ _dbe respectively a r _a, r _b, r _c, r _dangle position in helix; J1, j2 are the index values of this parallelogram,

ψ _j1＝j1×Δψ,ψ _j2＝j2×Δψ。

The intersection point of two parallelogrames is:

${r_I^y}_{j1}=(0,R\sin {\mathrm{\ψ}}_{j1},\mathrm{\πh}/2)$

${r_I^y}_{j2}=(0,R\sin {\mathrm{\ψ}}_{j2},-\mathrm{\πh}/2)$

To each intersection point , their subpoint is used for determining two projections being parallel to the axle of y-axis.

With ask z-axis to project similar, the y ' axial projection of first parallel y-axis: determine a point in y-axis, obtain the cornerwise intersection point of corresponding projection quadrilateral, choosing parallelogram, obtain the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, the projection of y-axis on the projection y ' axle determination detector determining die body coordinate system y-axis;

Y ' ' the axial projection of second parallel y-axis: determine a point in y-axis, obtain the cornerwise intersection point of corresponding projection quadrilateral, choosing parallelogram, obtain the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, the projection of y-axis on the projection y ' ' axle determination detector determining die body coordinate system y-axis;

4th step, determines the projection of die body coordinate origin on flat panel detector;

Penetrate is some the projection of die body coordinate origin on flat panel detector; The projection on the detector of die body coordinate origin is determined by the intersection point that x-axis projects and z-axis projects.

Pretreatment is carried out to the coordinate of all subpoints, the coordinate of subpoint is deducted and penetrates point coordinates.

5th step, acquisition intermediate parameters a, b, c;

A _x, a _y, a _zrepresent the projection of a at x, y, z axle respectively; b _x, b _y, b _zrepresent the projection of b at x, y, z axle respectively; c _x, c _y, c _zrepresent the projection of c at x, y, z axle respectively;

To point wherein:

${u_I^z}_k=\frac{a_z({\mathrm{\ψ}}_k+3\mathrm{\π}/2)h}{c_z({\mathrm{\ψ}}_k+3\mathrm{\π}/2)h+1}$

${v_I^z}_k=\frac{b_z({\mathrm{\ψ}}_k+3\mathrm{\π}/2)h}{c_z({\mathrm{\ψ}}_k+3\mathrm{\π}/2)h+1}$

Wherein: represent corresponding coordinate figure on the detector.

Be unknown number be a _z, b _z, c _zsystem of linear equations.When k >=2, above-mentioned formula has 3 unknown quantitys, the overdetermined linear system of 2k linear equation, can easily via the Optimization Method such as based on singular value decomposition.

Same, for point wherein:

${u_I^x}_i=\frac{a_{x}R\cos {\mathrm{\ψ}}_i}{c_{x}R\cos {\mathrm{\ψ}}_i+1}$

${v_I^x}_i=\frac{b_{x}R\cos {\mathrm{\ψ}}_i}{c_{x}R\cos {\mathrm{\ψ}}_i+1}$

Wherein, represent corresponding coordinate figure on the detector.

A _x, b _x, c _xcan be obtained by above-mentioned equation group;

Same, for point wherein:

${u_I^y}_{j1}=\frac{a_{y}R\sin {\mathrm{\ψ}}_{j1}+a_z(\mathrm{\π}/2)h}{c_{y}R\sin {\mathrm{\ψ}}_{j1}+c_z(\mathrm{\π}/2)h+1}$

${v_I^y}_{j1}=\frac{b_{y}R\sin {\mathrm{\ψ}}_{j1}+b_z(\mathrm{\π}/2)h}{c_{y}R\sin {\mathrm{\ψ}}_{j1}+c_z(\mathrm{\π}/2)h+1}$

${u_I^y}_{j2}=\frac{a_{y}R\sin {\mathrm{\ψ}}_{j2}+a_z(\mathrm{\π}/2)h}{c_{y}R\sin {\mathrm{\ψ}}_{j2}+c_z(\mathrm{\π}/2)h+1}$

${v_I^y}_{j2}=\frac{b_{y}R\sin {\mathrm{\ψ}}_{j2}+b_z(\mathrm{\π}/2)h}{c_{y}R\sin {\mathrm{\ψ}}_{j2}+c_z(\mathrm{\π}/2)h+1}$

Wherein: represent corresponding coordinate figure on the detector; represent corresponding coordinate figure on the detector;

A _y, b _y, c _ycan be obtained by above-mentioned equation group.

6th step, obtains 9 geometric calibration parameters of C-arm computed tomography (SPECT) system by intermediate parameters;

Geometric calibration parameter comprise the anglec of rotation of detector, x-ray source to the position of detector distance, x-ray source, initial point projection on the detector;

The anglec of rotation of detector comprises the angle of pitch, deflection angle, inclination angle,

The position of x-ray source comprise x-ray source respectively in x direction, y direction, z direction position;

The projection on the detector of die body coordinate origin comprises horizontal direction projection and vertical direction projection.

By 9 calibrating parameters obtained above, C-arm computed tomography (SPECT) system is described, has directive function to machine-building.Most C-arm algorithm for reconstructing rebuilds image according to projection matrix, and when vibrating larger, this kind of method is no longer applicable.Obtain independently geometric calibration parameter, can by this independently geometric parameter be integrated in corresponding algorithm for reconstructing, obtain the picture quality more excellent compared with projection matrix.

Intermediate parameters can list of references (C.Mennessier to the transformational relation of 9 geometric calibration parameters, R.Clackdoyle, andF.Noo, " Directdeterminationofgeometricalignmentparametersforcone-beamscanners, " PhysMedBiol, vol.54, no.6, pp.1633-60, Mar21,2009.)

To in Numerical Validation experiment of the present invention, when interpolation is equivalent to the Gaussian noise of 10% detector pixel size, the average of measured 9 geometric calibration parameter errors: position <0.02mm, angle <0.003 °; The variance of error: position <0.3mm, angle <0.1 °.Can find out that the inventive method has higher robustness and accuracy.

Claims (3)

1. determine a method for geometric calibration parameter in C-arm computed tomography (SPECT) system, comprise following step:

The first step, is placed on helix die body on the articles holding table in C-arm computed tomography (SPECT) system, with C-arm scanning, obtains the projected image of helix die body on flat panel detector;

Second step, determines the projected position of index point on flat panel detector on helix;

3rd step, utilizes the geometrical property of helix, determines die body coordinate system z-axis, projection that x-axis and two are parallel to the axle of y-axis;

On helix, the arrangement of index point meets radius is R, and pitch is the helix equation of 2 π h, and l index point position is:

r _l＝(Rsinψ _l,Rcosψ _l,hψ _l)

ψ _l＝l×Δψ(l＝-N ₁,-N ₁+1,…,N ₂-1,N ₂)

Wherein: Δ ψ is the angle intervals of index point on helix, and Δ ψ=π/N, N represents integer; N ₁and N ₂value be integer, suppose that the length of the helix axis that evenly distributed index point is formed is L, then N ₁+ N ₂=L/ (h Δ ψ)-1;

(1) determine the method that coordinate system z-axis projects, choose 4 index points from helix, form parallelogram as follows:

$P_k^z=\left\{r_A{r}_B{r}_C{r}_{D_k}\right|{\mathrm{\&psi;}}_A={\mathrm{\&psi;}}_k,{\mathrm{\&psi;}}_B={\mathrm{\&psi;}}_k+2\mathrm{\&pi;},{\mathrm{\&psi;}}_C={\mathrm{\&psi;}}_k+3\mathrm{\&pi;},{\mathrm{\&psi;}}_D={\mathrm{\&psi;}}_k+\mathrm{\&pi;},$

k∈[-N ₁,N ₂-3N]},

Wherein, r _a, r _b, r _c, r _dbeing 4 index points in helix, is also 4 summits forming this parallelogram; ψ _a, ψ _b, ψ _c, ψ _dbe respectively a r _a, r _b, r _c, r _dangle position in helix; K is the index value of this parallelogram, ψ _k=k × Δ ψ;

Parallelogram cornerwise intersection point is:

$r_{I_k}^z=(0,0,h({\mathrm{\&psi;}}_k+3\mathrm{\&pi;}/2\left)\right)$

Parallelogram on the detector be projected as tetragon diagonal intersection point being projected as on the detector because diagonal intersection point in z-axis, so the diagonal intersection point obtained that projects on the projection z ' of z-axis, again choose parallelogram, obtain the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, determine the projection z ' axle of die body coordinate system z-axis;

(2) determine that coordinate system x-axis projects, choose 4 index points from helix, form parallelogram as follows:

$P_i^x=\left\{r_A{r}_B{r}_C{r}_{D_i}\right|{\mathrm{\&psi;}}_A={\mathrm{\&psi;}}_i,{\mathrm{\&psi;}}_B={\mathrm{\&psi;}}_i+2\mathrm{\&pi;},{\mathrm{\&psi;}}_C=-{\mathrm{\&psi;}}_i,{\mathrm{\&psi;}}_D=-{\mathrm{\&psi;}}_i-2\mathrm{\&pi;},$

i∈[max(-N ₁,-N ₂,-N+1),min(N ₂-2N,N ₁-2N)],i≠0}

Wherein, r _a, r _b, r _c, r _dbeing 4 index points in helix, is also 4 summits forming this parallelogram; ψ _a, ψ _b, ψ _c, ψ _dbe respectively a r _a, r _b, r _c, r _dangle position in helix; I is the index value of this parallelogram, ψ _i=i × Δ ψ; Parallelogram cornerwise intersection point is:

$r_{I_i}^x=(R{\mathrm{cos\&psi;}}_i,0,0)$

Wherein, determine a point in x-axis, obtain the cornerwise intersection point of corresponding projection quadrilateral, choosing parallelogram, obtain the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, the projection of x-axis on the projection x ' axle determination detector determining die body coordinate system x-axis;

(3) determine two projections being parallel to y-axis, choose 8 index points from helix, form two parallelogrames with

$P_{j1}^y=\left\{r_A{r}_B{r}_C{r}_{D_{j1}}\right|{\mathrm{\&psi;}}_A={\mathrm{\&psi;}}_{j1},{\mathrm{\&psi;}}_B={\mathrm{\&psi;}}_{j1}+2\mathrm{\&pi;},{\mathrm{\&psi;}}_C=-{\mathrm{\&psi;}}_{j1}+\mathrm{\&pi;},{\mathrm{\&psi;}}_D=-{\mathrm{\&psi;}}_{j1}-\mathrm{\&pi;},$

$j1\&Element;\&lsqb;max\left(-N_1,N-N_2,-\frac{N}{2}+1\right),min\left(N_1-N,N_2-2N\right)\&rsqb;,j1\&NotEqual;\frac{N}{2}\},$

$P_{j2}^y=\left\{r_A{r}_B{r}_C{r}_{D_{j2}}\right|{\mathrm{\&psi;}}_A={\mathrm{\&psi;}}_{j2},{\mathrm{\&psi;}}_B={\mathrm{\&psi;}}_{j2}-2\mathrm{\&pi;},{\mathrm{\&psi;}}_C=-{\mathrm{\&psi;}}_{j2}-\mathrm{\&pi;},{\mathrm{\&psi;}}_D=-{\mathrm{\&psi;}}_{j2}+\mathrm{\&pi;},$

$j2\&Element;\&lsqb;max\left(2N-N_1,N-N_2\right),min\left(N_1-N,N_2,\frac{N}{2}-1\right)\&rsqb;,j2\&NotEqual;-\frac{N}{2}\},$

Wherein, r _a, r _b, r _c, r _dbeing 4 index points in helix, is also 4 summits forming this parallelogram; ψ _a, ψ _b, ψ _c, ψ _dbe respectively a r _a, r _b, r _c, r _dangle position in helix; J1, j2 are the index values of this parallelogram,

ψ _j1＝j1×Δψ,ψ _j2＝j2×Δψ；

The intersection point of two parallelogrames is:

$r_{I_{j1}}^y=(0,R{\mathrm{sin\&psi;}}_{j1},\mathrm{\&pi;}h/2)$

$r_{I_{j2}}^y=(0,R{\mathrm{sin\&psi;}}_{j2},-\mathrm{\&pi;}h/2)$

Y ' the axial projection of first parallel y-axis: determine a point in y-axis, obtain the cornerwise intersection point of corresponding projection quadrilateral, choose parallelogram again, obtain the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, the projection of y-axis on the projection y ' axle determination detector determining die body coordinate system y-axis;

The y of second parallel y-axis " axial projection: determine a point in y-axis, obtain the cornerwise intersection point of corresponding projection quadrilateral, choose parallelogram again, obtain the projection on the detector of diagonal of a parallelogram intersection point, according to two projected diagonal intersection points, determine the projection y of die body coordinate system y-axis " projection of y-axis on axle determination detector;

4th step, determines the projection of die body coordinate origin on flat panel detector;

Penetrate is some the projection of die body coordinate origin on flat panel detector; The projection on the detector of die body coordinate origin is determined by the intersection point that x-axis projects and z-axis projects;

Pretreatment is carried out to the coordinate of all subpoints, the coordinate of subpoint is deducted and penetrates point coordinates;

5th step, acquisition intermediate parameters a, b, c;

A _x, a _y, a _zrepresent the projection of a at x, y, z axle respectively; b _x, b _y, b _zrepresent the projection of b at x, y, z axle respectively; c _x, c _y, c _zrepresent the projection of c at x, y, z axle respectively;

To point wherein:

$u_{I_k}^z=\frac{a_z({\mathrm{\&psi;}}_k+3\mathrm{\&pi;}/2)h}{c_z({\mathrm{\&psi;}}_k+3\mathrm{\&pi;}/2)h+1}$

$v_{I_k}^z=\frac{b_z({\mathrm{\&psi;}}_k+3\mathrm{\&pi;}/2)h}{c_z({\mathrm{\&psi;}}_k+3\mathrm{\&pi;}/2)h+1}$

Wherein: represent corresponding coordinate figure on the detector;

When k>=2, a _z, b _z, c _zobtained by above-mentioned equation group;

Same, for point wherein:

$u_{I_i}^x=\frac{a_x{\mathrm{Rcos\&psi;}}_i}{c_x{\mathrm{Rcos\&psi;}}_1+1}$

$v_{I_i}^x=\frac{b_x{\mathrm{Rcos\&psi;}}_i}{c_x{\mathrm{Rcos\&psi;}}_i+1}$

Wherein, represent corresponding coordinate figure on the detector;

When i>=2, a _x, b _x, c _xobtained by above-mentioned equation group;

Same, for point wherein:

$u_{I_{j1}}^y=\frac{a_{y}R{\mathrm{sin\&psi;}}_{j1}+a_z(\mathrm{\&pi;}/2)h}{c_{y}R{\mathrm{sin\&psi;}}_{j1}+c_z(\mathrm{\&pi;}/2)h+1}$

$v_{I_{j1}}^y=\frac{b_{y}R{\mathrm{sin\&psi;}}_{j1}+b_z\left(\mathrm{\&pi;}/2\right)h}{c_{y}R{\mathrm{sin\&psi;}}_{j1}+c_z\left(\mathrm{\&pi;}/2\right)h+1}$

$u_{I_{j2}}^y=\frac{a_{y}R{\mathrm{sin\&psi;}}_{j2}-a_z(\mathrm{\&pi;}/2)h}{c_{y}R{\mathrm{sin\&psi;}}_{j2}-c_z(\mathrm{\&pi;}/2)h+1}$

$v_{I_{j2}}^y=\frac{b_{y}R{\mathrm{sin\&psi;}}_{j2}-b_z\left(\mathrm{\&pi;}/2\right)h}{c_{y}R{\mathrm{sin\&psi;}}_{j2}-c_z\left(\mathrm{\&pi;}/2\right)h+1}$

Wherein: represent corresponding coordinate figure on the detector; represent corresponding coordinate figure on the detector;

A _y, b _y, c _yobtained by above-mentioned equation group;

6th step, obtains 9 geometric calibration parameters of C-arm computed tomography (SPECT) system by intermediate parameters;

Geometric calibration parameter comprise the anglec of rotation of detector, x-ray source to the position of detector distance, x-ray source, initial point projection on the detector;

The anglec of rotation of detector comprises the angle of pitch of detector, deflection angle, inclination angle,

The position of x-ray source comprise x-ray source respectively in x direction, y direction, z direction position;

The projection on the detector of die body coordinate origin comprises horizontal direction projection and vertical direction projection;

By 9 calibrating parameters obtained above, C-arm computed tomography (SPECT) system is described.

2. a kind of method determining geometric calibration parameter in C-arm computed tomography (SPECT) system according to claim 1, described helix die body adopts helical pipe, and little steel ball is arranged in helical pipe.

3. a kind of method determining geometric calibration parameter in C-arm computed tomography (SPECT) system according to claim 1, in second step, first obtain the border of index point by the method for canny border detection, then adopt on the ellipse fitting algorithm determination projected image based on singular value decomposition and indicate dot center.