CN117582243A - Calibration system and space positioning method of C-arm X-ray machine - Google Patents
Calibration system and space positioning method of C-arm X-ray machine Download PDFInfo
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- CN117582243A CN117582243A CN202410080331.4A CN202410080331A CN117582243A CN 117582243 A CN117582243 A CN 117582243A CN 202410080331 A CN202410080331 A CN 202410080331A CN 117582243 A CN117582243 A CN 117582243A
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- 238000000034 method Methods 0.000 title claims abstract description 27
- 230000003287 optical effect Effects 0.000 claims abstract description 35
- 238000013178 mathematical model Methods 0.000 claims abstract description 34
- 238000003384 imaging method Methods 0.000 claims abstract description 27
- 239000000523 sample Substances 0.000 claims abstract description 15
- 239000011159 matrix material Substances 0.000 claims description 21
- 238000006243 chemical reaction Methods 0.000 claims description 10
- 239000003550 marker Substances 0.000 claims description 6
- 230000008030 elimination Effects 0.000 claims description 5
- 238000003379 elimination reaction Methods 0.000 claims description 5
- 238000004364 calculation method Methods 0.000 abstract description 9
- 230000008569 process Effects 0.000 abstract description 7
- 239000008188 pellet Substances 0.000 description 9
- 230000009466 transformation Effects 0.000 description 5
- 230000004044 response Effects 0.000 description 4
- 238000010586 diagram Methods 0.000 description 3
- 238000013507 mapping Methods 0.000 description 3
- 239000011324 bead Substances 0.000 description 2
- 238000001514 detection method Methods 0.000 description 2
- 238000001356 surgical procedure Methods 0.000 description 2
- 241001422033 Thestylus Species 0.000 description 1
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
- A61B6/58—Testing, adjusting or calibrating apparatus or devices for radiation diagnosis
- A61B6/582—Calibration
- A61B6/583—Calibration using calibration phantoms
- A61B6/584—Calibration using calibration phantoms determining position of components of the apparatus or device using images of the phantom
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
- A61B6/00—Apparatus for radiation diagnosis, e.g. combined with radiation therapy equipment
- A61B6/44—Constructional features of apparatus for radiation diagnosis
- A61B6/4429—Constructional features of apparatus for radiation diagnosis related to the mounting of source units and detector units
- A61B6/4435—Constructional features of apparatus for radiation diagnosis related to the mounting of source units and detector units the source unit and the detector unit being coupled by a rigid structure
- A61B6/4441—Constructional features of apparatus for radiation diagnosis related to the mounting of source units and detector units the source unit and the detector unit being coupled by a rigid structure the rigid structure being a C-arm or U-arm
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
- G06T7/85—Stereo camera calibration
Abstract
The invention discloses a calibration system and a space positioning method of a C-arm X-ray machine, which relate to the technical field of medical appliances, wherein the calibration system comprises: the X-ray machine comprises a C-shaped arm X-ray machine, optical tracking equipment, a calibration plate, a three-coordinate probe and n targets which can be developed under X-rays, wherein n is more than or equal to 6; the target point is arranged on a calibration plate, the calibration plate is fixed on the operating table through a supporting device, and the calibration plate is perpendicular to the optical axis of the C-shaped arm X-ray machine and is positioned under the imaging view field of the C-shaped arm X-ray machine; the three-coordinate probe is used for acquiring the three-dimensional space coordinates of each target point relative to a basic coordinate system of the optical tracking equipment; the C-arm X-ray machine is used for shooting X-ray images of targets on the calibration plate so as to acquire coordinates of each target on the X-ray images. According to the invention, the mathematical model parameters of the C-arm X-ray machine under the current gesture can be calculated by shooting only one X-ray film with 3D characteristics, so that the model parameter calculation process is greatly simplified, and meanwhile, the precision is ensured.
Description
Technical Field
The invention relates to the technical field of medical equipment, in particular to a calibration system and a space positioning method of a C-arm X-ray machine.
Background
The C-arm X-ray machine is a common intraoperative image positioning device in orthopedic surgery, has the capability of real-time imaging, can be observed and navigated in real time in the surgical process, and is very important for the accuracy and safety of the surgery. The working principle of the device is that an X-ray bulb is used for emitting X-rays, and the X-rays form visible light images on tissues and organs after penetrating through a human body. The imaging principle of the C-arm X-ray machine is basically the same as that of a visible light camera, and the optical positioning operation can be realized by solving an imaging mathematical model. At present, a small-hole imaging model of a camera is commonly used as a mathematical model of C-shaped arm imaging, 12 external imaging parameters and 4 internal imaging parameters need to be solved, 16 parameters are totally needed, and usually more than 10 calibration images in different postures are needed to perform calibration calculation of the internal and external parameters of the C-shaped arm.
Because the X-ray emitting end and the receiving end of the C-shaped arm X-ray machine are respectively positioned at the two ends of the C-shaped arm, when the C-shaped arm is moved, tiny mechanical deformation is amplified to the two ends of the arm, so that huge change of the internal parameters of the C-shaped arm can be caused, and the changed real-time parameters can not be obtained. The existing calculation method is complicated in calibration process and cannot be calibrated in the patient environment.
Disclosure of Invention
In view of the above-mentioned drawbacks or shortcomings in the prior art, the present invention provides a calibration system and a spatial positioning method for a C-arm X-ray machine, which can solve the above-mentioned existing technical problems.
In one aspect of the present invention, there is provided a calibration system for a C-arm X-ray machine, comprising: the X-ray machine comprises a C-shaped arm X-ray machine, optical tracking equipment, a calibration plate, a three-coordinate probe and n targets which can be developed under X-rays, wherein n is more than or equal to 6; the n target points are arranged on the calibration plate, the calibration plate is fixed on the operating table through the supporting device, and the calibration plate is perpendicular to the optical axis of the C-arm X-ray machine and is positioned under the imaging view field of the C-arm X-ray machine; the three-coordinate probe is used for acquiring three-dimensional space coordinates of each target point relative to a basic coordinate system of the optical tracking equipment; the C-shaped arm X-ray machine is used for shooting X-ray images of targets on the calibration plate so as to acquire coordinates of each target on the X-ray images.
Further, four Y-shaped reflective marking points are arranged on the three-coordinate probe.
Further, the target points comprise small spherical target points, circular ring-shaped target points, plane circular target points or needle-shaped target points.
Further, the optical tracking device is a binocular camera.
Further, the length of the supporting device is adjustable.
In another aspect of the present invention, there is also provided a space positioning method of a calibration system based on the above-mentioned C-arm X-ray machine, including:
taking an optical center of the C-shaped arm X-ray machine as an origin of a C-shaped arm X-ray machine coordinate system, enabling a z-axis of the C-shaped arm X-ray machine coordinate system to coincide with an optical axis of the C-shaped arm X-ray machine, and enabling X-axis and y-axis of the C-shaped arm X-ray machine coordinate system to be parallel to an abscissa axis and an ordinate axis of an image coordinate system;
obtaining a mathematical model of C-arm X-ray machine imaging according to the conversion relation between the world coordinate system and the screen coordinate system:
（1）
（2）
wherein,is the abscissa and ordinate of the screen coordinate system, +.>Is three-dimensional coordinates of world coordinate system, +.>11 parameters to be solved;
acquiring three-dimensional space coordinates of each target point relative to a basic coordinate system of the optical tracking equipment through a calibration system of the C-arm X-ray machine, wherein the three-dimensional space coordinates are coordinates under a world coordinate system; acquiring the coordinates of each target point on an X-ray image, and taking the coordinates on the X-ray image as the coordinates under a screen coordinate system;
calculating parameters of the mathematical model according to the obtained three-dimensional space coordinates of the n targets and the coordinates of the targets under the screen coordinate system；
According to the coordinates of the to-be-positioned point in the world coordinate system, the calculated parametersAnd the mathematical model is used for obtaining the coordinates of the to-be-positioned point under a screen coordinate system.
Further, the step of calculating the mathematical model of the imaging of the C-arm X-ray machine according to the conversion relation between the world coordinate system and the screen coordinate system comprises the following steps:
homogeneous coordinates of a point in space in world coordinate systemHomogeneous coordinates to the screen coordinate systemThe conversion relation of (2) is recorded as follows:
（3）
wherein,is the focal length of the C-arm X-ray machine, +.>The coordinate of the optical center of the C-arm X-ray machine in an image coordinate system; />Length and width of one pixel in an image coordinate system; />The rotation parameter of the coordinate system of the C-arm X-ray machine relative to the world coordinate system; />Is a translation parameter of the coordinate system of the C-arm X-ray machine relative to the world coordinate system.
Further, the method further comprises the following steps:
according to the formula (3) and the matrix multiplication rule, the following is obtained:
（4）。
further, the method further comprises the following steps:
and (3) obtaining the formula (4) through matrix dot product operation:
（5）
will beAfter the elimination, the method can be used for obtaining:
（6）
will beAnd obtaining the mathematical model of the C-arm X-ray machine imaging after elimination.
Further, the parameters of the mathematical model are calculated according to the obtained three-dimensional space coordinates of the n targets and the coordinates of the targets under the screen coordinate systemComprises the steps of:
substituting the three-dimensional space coordinates of n targets and the coordinates under the screen coordinate system into a mathematical model of C-shaped arm X-ray machine imaging to obtain the following matrix expression:
；
wherein,，three-dimensional space coordinates for n targets, wherein +.>；/>For the coordinates of n targets in the screen coordinate system, wherein +.>；
Wherein,；
wherein,；
solving a parameter matrix by: 。
the invention provides a calibration system and a space positioning method of a C-arm X-ray machine, and provides an improved C-arm X-ray machine imaging mathematical model based on a small-hole imaging model, wherein an internal reference matrix and an external reference matrix in the model are fused together, so that the model is simplified into a conversion matrix, and the model calculation difficulty is greatly simplified. In addition, the calibration system uses a plurality of targets as 3D characteristics, and solves parameters of a transformation matrix in a mathematical model of the C-shaped arm X-ray machine, so that the calculation of the spatial mapping relation between 3D space data and 2D image data is realized. According to the invention, the mathematical model parameters of the C-arm X-ray machine under the current gesture can be calculated by shooting only one X-ray film with 3D characteristics, so that the model parameter calculation process is greatly simplified, and meanwhile, the precision is ensured.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments, made with reference to the following drawings, in which:
FIG. 1 is a schematic diagram of a calibration system provided in one embodiment of the present application;
FIG. 2 is a schematic diagram of a three-coordinate probe provided in one embodiment of the present application;
FIG. 3 is a schematic view of a calibration plate and pellet projection provided in one embodiment of the present application;
FIG. 4 is a flow chart of a spatial positioning method provided by one embodiment of the present application;
fig. 5 is a schematic diagram of a coordinate system conversion relationship according to an embodiment of the present application.
Reference numerals illustrate:
101-C-arm X-ray machine; 102-an optical tracking device; 103-calibrating a plate; 104-three-coordinate probe; 105-globules; 106-supporting means; 107-operating bed; 108-reflecting mark points; 109-measuring needle; 110-spherical grooves.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The terminology used in the embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this application and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be understood that although the terms first, second, third, etc. may be used in embodiments of the present invention to describe the acquisition modules, these acquisition modules should not be limited to these terms. These terms are only used to distinguish the acquisition modules from each other.
Depending on the context, the word "if" as used herein may be interpreted as "at … …" or "at … …" or "in response to a determination" or "in response to detection". Similarly, the phrase "if determined" or "if detected (stated condition or event)" may be interpreted as "when determined" or "in response to determination" or "when detected (stated condition or event)" or "in response to detection (stated condition or event), depending on the context.
It should be noted that, the terms "upper", "lower", "left", "right", and the like in the embodiments of the present invention are described in terms of the angles shown in the drawings, and should not be construed as limiting the embodiments of the present invention. In addition, in the context, it will also be understood that when an element is referred to as being formed "on" or "under" another element, it can be directly formed "on" or "under" the other element or be indirectly formed "on" or "under" the other element through intervening elements.
Referring to FIG. 1, one embodiment of the present invention provides a calibration system for a C-arm X-ray machine, comprising: a C-arm X-ray machine 101, an optical tracking device 102, a calibration plate 103, a three-coordinate probe 104 and n targets that can be developed under X-rays. The target point of the embodiment can be a small spherical target point, a circular target point, a plane circular target point or a needle-shaped target point, and the target points can be positioned in the same plane or in different planes. This embodiment will be described by taking n pellets 105 located on the same plane as an example. The number of the pellets 105 is required to meet the parameter calculation requirement of the mathematical model, and in the embodiment, the number of the pellets is n is more than or equal to 6.
Further, n balls 105 are disposed on the calibration plate 103, the calibration plate 103 is fixed on the operating table 107 through a vertical supporting device 106, and the length of the supporting device 106 is adjustable, so that the height of the calibration plate 103 can be adjusted. The calibration plate 103 is perpendicular to the optical axis of the C-arm X-ray machine 101 and is positioned in the imaging field of view of the C-arm X-ray machine 101.
Referring to fig. 2, the three-coordinate probe 104 includes four retro-reflective marker points 108 for tracking and a stylus 109, the bottom of the stylus 109 having a spherical recess 110 matching the sphere 105. The three-coordinate probe 104 calculates and obtains coordinate information of each of the pellets by detecting the distance between the pellets 105 and each of the retroreflective marker points 108. Specifically, the optical tracking device 102, which may be a binocular camera, tracks four reflective marker points on the three-coordinate probe 104 to determine coordinate position information of each reflective marker point 108 on the three-coordinate probe 104 in a world coordinate system, and further determines three-dimensional space coordinates of each ball 105 relative to a basic coordinate system (i.e., a world coordinate system) of the optical tracking device 102 according to a distance between each reflective marker point 108 and the ball 105.
Referring to fig. 3, the transmitting end of the c-arm X-ray machine 101 is used for capturing an X-ray image of the beads 105 on the calibration plate 103, and the receiving end is used for acquiring the projection coordinates of the center of each bead 105 on the X-ray image, and the coordinate positions are the coordinates in the image coordinate system.
Referring to fig. 4, another embodiment of the present invention further provides a space positioning method of a calibration system based on the above-mentioned C-arm X-ray machine, which includes the following steps:
and S101, taking an optical center of the C-shaped arm X-ray machine as an origin of a C-shaped arm X-ray machine coordinate system, enabling a z-axis of the C-shaped arm X-ray machine coordinate system to coincide with an optical axis of the C-shaped arm X-ray machine, and enabling X-axis and y-axis of the C-shaped arm X-ray machine coordinate system to be parallel to an abscissa axis and an ordinate axis of an image coordinate system.
In particular, in a camera model based on the principle of pinhole imaging, since the camera is placed anywhere in the environment, a reference coordinate system can be selected in the environment to describe the position of the camera and the position of any object in the environment, which is called the world coordinate system. A point in the world coordinate system is mapped to a corresponding point in the computer screen coordinate system through a series of coordinate transformations, see fig. 5 for the transformation relationship. In this embodiment, the basic coordinate system where the optical tracking device 102 is located is a world coordinate system, the basic coordinate system where the C-arm X-ray machine is located is a camera coordinate system, the basic coordinate system of the X-ray image is an image coordinate system, and the basic coordinate system of the computer display screen is a screen coordinate system. The relative relation between the coordinate systems is determined firstly, the optical center of the C-shaped arm X-ray machine is used as the origin of the coordinate system of the C-shaped arm X-ray machine, the z-axis of the coordinate system of the C-shaped arm X-ray machine is enabled to coincide with the optical axis of the C-shaped arm X-ray machine, and the X-axis and the y-axis of the coordinate system of the C-shaped arm X-ray machine are enabled to be parallel to the transverse and longitudinal coordinate axes of the image coordinate system.
Step S102, obtaining a mathematical model of C-arm X-ray machine imaging according to the conversion relation between the world coordinate system and the screen coordinate system:
（1）
（2）
wherein,is the abscissa and ordinate of the screen coordinate system, +.>Is three-dimensional coordinates of world coordinate system, +.>Is 11 parameters to be solved.
Specifically, the homogeneous coordinates of a certain point P in space in the world coordinate system and the screen coordinate system areAndthe transformation relationship is as follows:
（1）
wherein,for C-arm X-ray machinesFocal length, that is: a camera focal length; />The coordinates in the image coordinate system of the optical center of the C-arm X-ray machine, namely the camera optical center, are called internal parameters; />Is the length and width of a pixel in the image coordinate system.The coordinate system of the C-arm X-ray machine, namely a camera coordinate system, is a rotation parameter relative to a world coordinate system; />The translation parameter of the coordinate system of the C-arm X-ray machine, namely the camera coordinate system, relative to the world coordinate system is called external parameter.
Then, the formula (1) is modified into:
（2）
wherein,the mixed matrix A is formed, and each parameter in the mixed matrix A can be obtained to describe the mapping relation of a certain point in the world coordinate system and the screen coordinate system.
Thus, the mathematical model of C-arm X-ray imaging can be written in the form of:
（3）
in the mathematical model of the C-arm X-ray machine imaging, parametersThe model parameter is linearly related to the matrix A, so that the model parameter can be solved by only solving the matrix A.
Next, the following equation can be obtained by matrix point multiplication operation in the mathematical model:
（4）
next, the process willThe method can be obtained after the elimination calculation:
（5）
next, the process willEliminating primordial energy, and finishing to obtain two parts of ∈Analyne->Is a linear system of equations:
（6）
（7）
step S103, acquiring three-dimensional space coordinates of each small ball relative to a basic coordinate system of the optical tracking equipment through a calibration system of the C-arm X-ray machine, wherein the three-dimensional space coordinates are coordinates under a world coordinate system; and acquiring the coordinates of each target point on the X-ray image, and taking the coordinates on the X-ray image as the coordinates under a screen coordinate system.
Specifically, according to the above mathematical model (i.e., equation (6) and equation (7)), the parameters to be calculated are knownFrom->To->There are 11 total. Thus, a known parameter of 11 or more is required +.>The equation set can be solved from ∈ ->To->11 parameters to be solved are: equation (6) and equation (7) need to be extended each by 6 equations (2×6=12), which requires at least the world coordinates of 6 different reference points +.>And screen coordinates->。
In order to obtain the coordinate data of 6 reference points, the calibration system of the C-arm X-ray machine in the embodiment of the device is used for obtaining three-dimensional space coordinates of 6 targets (in this embodiment, 6 pellets located on the same plane are used as an example) relative to a basic coordinate system of the optical tracking deviceThe three-dimensional space coordinates are coordinates in a world coordinate system. The coordinates of the center of each sphere 105 on the X-ray image are then acquired and converted into coordinates in the screen coordinate system.
Step S104, calculating parameters of the mathematical model according to the three-dimensional space coordinates of the n balls and the coordinates of the sphere centers under the screen coordinate system。
Specifically, substituting the three-dimensional space coordinates of the sphere centers of the n pellets and the coordinates in the screen coordinate system into the formula (6) and the formula (7) to obtain 12 linear equation sets, wherein the 12 linear equation sets are expressed as a matrix:
（8）
wherein,three-dimensional space coordinates of the sphere centers of n pellets, wherein +.>；/>Is the coordinates of the sphere centers of n small spheres in the screen coordinate system, wherein +.>。
（9）
（10）
（11）
Thus can be solvedThe method comprises the following steps:
（12）
thereby obtainingThus, the solving of the imaging parameters of the mathematical model of the C-arm X-ray machine is completed.
Step S105, calculating according to the coordinates of the to-be-positioned point in the world coordinate systemParameters ofAnd the mathematical model is used for obtaining the coordinates of the to-be-positioned point under a screen coordinate system.
In calculating parameters of the mathematical modelAnd then, calculating the screen coordinates of any to-be-positioned point in the space, and directly obtaining the coordinate values of the to-be-positioned point corresponding to the screen coordinate system by only determining the space coordinates of the to-be-positioned point under the world coordinate system according to the optical tracking device and substituting the space coordinates into the mathematical model.
The C-arm X-ray machine imaging mathematical model of the embodiment fuses the internal parameters and the external parameter matrix in the model, simplifies the model into a conversion matrix, and greatly simplifies the model resolving difficulty; the calibration system uses a plurality of targets positioned in the same plane or different planes as 3D characteristics, and solves parameters of a transformation matrix in a mathematical model of the C-shaped arm X-ray machine, so that the calculation of the spatial mapping relation between 3D space data and 2D image data is realized. Therefore, the mathematical model parameters of the C-arm X-ray machine under the current gesture can be calculated by shooting only one X-ray film with 3D characteristics, the model parameter calculation process is greatly simplified, and meanwhile, the precision is ensured.
The foregoing description is only of the preferred embodiments of the invention. It will be appreciated by persons skilled in the art that the scope of the disclosure referred to in the present invention is not limited to the specific combinations of technical features described above, but also covers other technical features formed by any combination of the technical features described above or their equivalents without departing from the spirit of the disclosure. Such as the above-mentioned features and the technical features disclosed in the present invention (but not limited to) having similar functions are replaced with each other.
Claims (10)
1. A calibration system for a C-arm X-ray machine, comprising:
the X-ray machine comprises a C-shaped arm X-ray machine, optical tracking equipment, a calibration plate, a three-coordinate probe and n targets which can be developed under X-rays, wherein n is more than or equal to 6;
the n target points are arranged on the calibration plate, the calibration plate is fixed on the operating table through the supporting device, and the calibration plate is perpendicular to the optical axis of the C-shaped arm X-ray machine and is positioned under the imaging view field of the C-shaped arm X-ray machine;
the three-coordinate probe is used for acquiring three-dimensional space coordinates of each target point relative to a basic coordinate system of the optical tracking equipment;
the C-shaped arm X-ray machine is used for shooting X-ray images of targets on the calibration plate so as to acquire coordinates of each target on the X-ray images.
2. The calibration system of a C-arm X-ray machine according to claim 1, wherein four Y-shaped reflective marker points are provided on the three-coordinate probe.
3. The calibration system of claim 1, wherein the target comprises a small sphere target, a circular ring target, a planar circular target, or a needle target.
4. The calibration system of a C-arm X-ray machine according to claim 1, wherein the optical tracking device is a binocular camera.
5. Calibration system for a C-arm X-ray machine according to claim 1, characterized in that the length of the support means is adjustable.
6. A method of spatial positioning of a calibration system for a C-arm X-ray machine according to any one of claims 1-5, comprising:
taking an optical center of the C-shaped arm X-ray machine as an origin of a C-shaped arm X-ray machine coordinate system, enabling a z-axis of the C-shaped arm X-ray machine coordinate system to coincide with an optical axis of the C-shaped arm X-ray machine, and enabling X-axis and y-axis of the C-shaped arm X-ray machine coordinate system to be parallel to an abscissa axis and an ordinate axis of an image coordinate system;
obtaining a mathematical model of C-arm X-ray machine imaging according to the conversion relation between the world coordinate system and the screen coordinate system:
（1）;
（2）;
wherein,is the abscissa and ordinate of the screen coordinate system, +.>Is three-dimensional coordinates of world coordinate system, +.>11 parameters to be solved;
acquiring three-dimensional space coordinates of each target point relative to a basic coordinate system of the optical tracking equipment through a calibration system of the C-arm X-ray machine, wherein the three-dimensional space coordinates are coordinates under a world coordinate system; acquiring the coordinates of each target point on an X-ray image, and taking the coordinates on the X-ray image as the coordinates under a screen coordinate system;
calculating parameters of the mathematical model according to the obtained three-dimensional space coordinates of the n targets and the coordinates of the targets under the screen coordinate system；
According to the coordinates of the to-be-positioned point in the world coordinate system, the calculated parametersAnd the mathematical model is used for obtaining the coordinates of the to-be-positioned point under a screen coordinate system.
7. The method according to claim 6, wherein the step of calculating a mathematical model of the C-arm X-ray machine imaging based on the conversion relation between the world coordinate system and the screen coordinate system comprises:
homogeneous coordinates of a point in space in world coordinate systemAnd homogeneous coordinates of the screen coordinate system +.>The conversion relation of (2) is recorded as follows:
（3）;
wherein,is the focal length of the C-arm X-ray machine, +.>The coordinate of the optical center of the C-arm X-ray machine in an image coordinate system;length and width of one pixel in an image coordinate system; />The rotation parameter of the coordinate system of the C-arm X-ray machine relative to the world coordinate system; />Is a translation parameter of the coordinate system of the C-arm X-ray machine relative to the world coordinate system.
8. The spatial positioning method according to claim 7, further comprising:
according to the formula (3) and the matrix multiplication rule, the following is obtained:
（4）。
9. the spatial positioning method according to claim 8, further comprising:
and (3) obtaining the formula (4) through matrix dot product operation:
（5）;
will beAfter the elimination, the method can be used for obtaining:
（6）;
will beAnd obtaining the mathematical model of the C-arm X-ray machine imaging after elimination.
10. The method according to claim 6, wherein the parameters of the mathematical model are calculated based on the obtained three-dimensional coordinates of n targets and the coordinates of the targets in the screen coordinate systemComprises the steps of:
substituting the three-dimensional space coordinates of n targets and the coordinates under the screen coordinate system into a mathematical model of C-shaped arm X-ray machine imaging to obtain the following matrix expression:
;
wherein,，three-dimensional space coordinates for n targets, wherein +.>；/>For the coordinates of n targets in the screen coordinate system, wherein +.>；
Wherein,；
wherein,；
solving a parameter matrix by:。
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