CN114187175B - Emission chromatography weight matrix determination method for three-dimensional space free projection - Google Patents
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Abstract
本发明为一种用于三维空间自由投影的发射层析权重矩阵确定方法，其克服了现有技术中存在的模型不完善，效率和精度都比较低的问题，本发明方法简单，计算精度和效率高。本发明包括以下步骤：步骤一、建立考虑镜头成像效应和相机三维空间位置的三维空间自由投影发射层析模型；步骤二：投影积分离散化；步骤三：基于双线性插值原理，确定系统的权重矩阵。
The present invention is a method for determining an emission tomography weight matrix for free projection in three-dimensional space, which overcomes the problems of imperfect models, low efficiency and accuracy in the prior art. The method of the present invention is simple and has high calculation accuracy and efficiency. The present invention includes the following steps: Step 1, establishing a three-dimensional free projection emission tomography model considering the lens imaging effect and the three-dimensional spatial position of the camera; Step 2: discretization of the projection integral; Step 3: determining the weight matrix of the system based on the bilinear interpolation principle.
Description
Technical field:
The invention belongs to the technical field of optical calculation imaging and combustion field three-dimensional measurement, relates to a combustion field emission spectrum chromatography reconstruction method, and particularly relates to an emission chromatography weight matrix determination method for three-dimensional space free projection.
The background technology is as follows:
Imaging, measurement and diagnosis of combustion fields are the basis of key instrument and meter designs in modern aviation, aerospace, missile, weapon and energy industries. Among them, three-dimensional imaging and display of combustion processes is one of the essential means for studying and controlling combustion. Emission tomography (Emission Computerized Tomography, ECT) is a simple, efficient, non-contact combustion field three-dimensional imaging method. The method utilizes an area array CCD camera or an optical fiber array to collect two-dimensional projection images of the emission spectrum intensity of the combustion field in multiple directions, and then combines with a computed tomography theory (Computerized Tomography, CT) to reconstruct the combustion field in three dimensions. Because of simple measurement principle and device, the method becomes a research hot spot of combustion imaging detection technology in recent years, and has wide application prospect.
However, the existing emission tomography technology is based on two-dimensional Radon transformation, and for an emission tomography system for projection acquisition by using a CCD camera, the implementation process is limited in two aspects (1) the Radon transformation adopts a parallel projection model which is not established due to the imaging effect of a CCD camera lens, and (2) the existing parallel projection emission tomography technology has strict requirements on the camera position, generally cannot provide an optical window at an ideal position due to the limitation of an actual test environment, and position errors are unavoidable when a detector is assembled. These two constraints severely affect the accuracy of tomographic reconstruction, and therefore require two factors to be considered in modeling the emission tomography system (1) the imaging effect of the lens and (2) the three-dimensional spatial position of the camera.
Among the tomographic reconstruction algorithms, the algebraic iterative algorithm is the most commonly used reconstruction method in the tomographic technique. The method comprises the steps of performing discretization representation on a tomographic projection process, representing contribution of object functions of different discrete grids in a measured object to projection information by using a weight matrix, converting the projection process into a series of linear equation sets, and solving the linear equation sets by using algebraic iteration methods of different forms in a reconstruction process. The calculation accuracy of the weight matrix seriously influences the accuracy and quality of tomographic reconstruction. Different projection models determine different weight matrices, and therefore, the method has important significance for researching the weight matrix determination method considering the two factors. Although a small amount of research has been conducted on this problem using ray tracing, lens imaging theory, the computational efficiency and accuracy are low.
The invention comprises the following steps:
The invention aims to provide a method for determining an emission chromatography weight matrix for three-dimensional space free projection, which solves the problems of imperfect model and low efficiency and precision existing in the prior art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
The method for determining the emission tomography weight matrix for the free projection of the three-dimensional space is characterized by comprising the following steps of:
Step one, establishing a three-dimensional space free projection emission tomography model considering a lens imaging effect and a three-dimensional space position of a camera;
step two, discretizing projection integration;
and thirdly, determining a weight matrix of the system based on bilinear interpolation principle.
Step one comprises the following steps:
s1, the lens imaging effect is expressed as that coordinates (x, y, z) of an object point in a camera coordinate system and coordinates (x ', y') of an image point in a camera imaging plane coordinate system meet the relation
Wherein f is the focal length of the camera lens;
S2, representing the arbitrary three-dimensional space position of the camera as the world coordinate system (x w,yw,zw) and the camera coordinate system (x, y, z) satisfy the relation
Wherein R is a rotation matrix, and T is a translation vector;
s3, the finally obtained chromatographic projection model is
Where f (x, y, z) is the luminous intensity value of the object point in the camera coordinate system, and z min and z max are the upper and lower boundaries where each projection ray in the camera coordinate system intersects the reconstruction region.
The second step comprises the following steps:
S1: the three-dimensional measured object f (x w,yw,zw) is uniformly divided into M multiplied by N multiplied by P discrete grids with the grid size of delta g multiplied by delta g, let the value f i(xw,yw,zw) of each grid be a constant, where i=1, 2.
S2, determining an upper limit z max and a lower limit z min of projection integration according to camera coordinate values of 8 vertexes of the reconstruction region;
S3, uniformly dividing an integration interval into Q microelements, and assuming that an object function of each microelement interval is a constant, a projection model is that Wherein (x ', y') and (x m,ym,zm) satisfy the relationship
The position (x mw,ymw,zmw) of the integral infinitesimal in the world coordinate system is determined according to the conversion relation between the world coordinate system and the camera coordinate system.
The third step comprises the following steps:
s1, determining the serial number of the minimum adjacent discrete grid where each infinitesimal is located;
s2, determining the distance between the infinitesimal and the center of the minimum adjacent discrete grid;
S3, determining the object function value of the micro element by using the center point object functions of 8 adjacent discrete grids according to the bilinear interpolation principle to obtain the weight factor of each discrete grid on the micro element;
and S4, carrying out integral operation on all the infinitesimal to obtain a weight matrix of each discrete grid pair projection.
Compared with the prior art, the invention has the following advantages and effects:
1. The method obtains the chromatographic model considering the imaging effect of the lens and the three-dimensional space position of the camera, provides a theoretical basis for emission chromatographic reconstruction of free projection of the three-dimensional space, determines the weight matrix based on bilinear interpolation principle on the basis of the model, and has simple principle and high calculation precision and efficiency.
2. The invention can enlarge the projection acquisition range of the emission tomography system, improve the reconstruction precision, and has important significance for the practical application of the emission tomography technology.
Description of the drawings:
FIG. 1 is a schematic diagram of a multi-camera emission tomography system coordinate system definition;
FIG. 2 is a schematic diagram of a camera projection imaging model;
FIG. 3 is a projection imaging result of a cube at different rotation angles;
FIG. 4 is a hollow sphere and its reconstruction results;
FIG. 5 is a graph of the synthesis of the Shepp-Logan model and its reconstruction results.
The specific embodiment is as follows:
the present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The invention relates to a method for determining an emission tomography weight matrix for free projection in a three-dimensional space, which comprises the steps of firstly, establishing a free projection emission tomography model in the three-dimensional space on the basis of considering a lens imaging effect and a three-dimensional space position of a camera; and finally, determining a weight matrix of the chromatographic system by utilizing a bilinear interpolation principle.
The method specifically comprises the following steps:
Step one, establishing a three-dimensional free projection emission tomography model considering the imaging effect of a lens and the three-dimensional space position of a camera
S1, the lens imaging effect is expressed as that coordinates (x, y, z) of an object point in a camera coordinate system and coordinates (x ', y') of an image point in a camera imaging plane coordinate system meet the relation
Where f is the focal length of the camera lens.
S2, representing the arbitrary three-dimensional space position of the camera as the world coordinate system (x w,yw,zw) and the camera coordinate system (x, y, z) satisfy the relation
Where R is the rotation matrix and T is the translation vector.
S3, the finally obtained chromatographic projection model is
Where f (x, y, z) is the luminous intensity value of the object point in the camera coordinate system, and z min and z max are the upper and lower boundaries where each projection ray in the camera coordinate system intersects the reconstruction region.
Step two, discretizing projection integral:
S1: the three-dimensional measured object f (x w,yw,zw) is uniformly divided into M multiplied by N multiplied by P discrete grids with the grid size of delta g multiplied by delta g, let the value f i(xw,yw,zw) of each grid be a constant, where i=1, 2.
S2, determining an upper limit z max and a lower limit z min of projection integration according to camera coordinate values of 8 vertexes of the reconstruction region;
S3, uniformly dividing an integration interval into Q microelements, and assuming that an object function of each microelement interval is a constant, a projection model is that Wherein (x ', y') and (x m,ym,zm) satisfy the relationship
The position (x mw,ymw,zmw) of the integral infinitesimal in the world coordinate system is determined according to the conversion relation between the world coordinate system and the camera coordinate system.
Step three, determining a weight matrix of the system based on bilinear interpolation principle
S1, determining the serial number of the minimum adjacent discrete grid where each infinitesimal is located;
s2, determining the distance between the infinitesimal and the center of the minimum adjacent discrete grid;
S3, determining the object function value of the micro element by using the center point object functions of 8 adjacent discrete grids according to the bilinear interpolation principle to obtain the weight factor of each discrete grid on the micro element;
and S4, carrying out integral operation on all the infinitesimal to obtain a weight matrix of each discrete grid pair projection.
Examples:
the invention comprises the following steps:
1. The method for obtaining the three-dimensional space free projection emission tomography model specifically comprises the following steps:
Referring to FIG. 1, which is defined by a coordinate system of an emission tomography system with multiple cameras, the system has a fixed world coordinate system (x w,yw,zw), and the luminous intensity of the combustion field under test is denoted as f (x w,yw,zw). The camera at any position in the world coordinate system is represented by a camera coordinate system (x, y, z), wherein the (x, y) plane is parallel to the CCD target surface, the x-axis is the long side direction of the CCD target surface, the y-axis is the short side direction of the CCD target surface, and the origin of coordinates is the intersection point of the camera optical axis and the lens. Each camera imaging plane coordinate system (x ', y') is a CCD target plane, the x 'axis is the opposite direction of the x axis, the y' axis is the opposite direction of the y axis, and the origin of coordinates is the intersection point of the lens optical axis and the CCD target plane.
In three dimensions, from the world coordinate system (x w,yw,zw) to any camera coordinate system (x, y, z) can be determined by the Euler angles (nutation angle. Phi., precession angle. Theta., and rotation angle. Phi.) and three translation quantities (T x,Ty,Tz), the conversion relationships of which can be expressed as
Wherein the matrix is rotated
Translation vector
For simplicity, formula (1) is expressed as
In an actual emission tomography system, the parameter r 1,r2,…,r9 in the rotation matrix and the parameter T x,Ty,Tz in the translation vector corresponding to each camera can be accurately determined by a camera calibration method.
Since the imaging lens with proper depth of field can be selected according to the size of the combustion field area to be measured, the influence caused by the depth of field is not considered in the camera imaging model, and therefore the imaging model can be equivalently a pinhole camera model, as shown in fig. 2.
The line formed by any image point P' on the imaging plane and the origin O of the camera coordinate system is called a projection ray. The projected ray intersects the area being examined and all object points P m (m=1, 2..and n.) are imaged at the same image point P'. Assuming that the focal length of the camera lens is f, the positions of the object point and the image point satisfy the triangle similarity principle, namely:
the luminous intensity information acquired by the image point is
Where z min and z max are the upper and lower boundaries where each projection ray intersects the reconstruction region, and f (x, y, z) is the luminous intensity value of all object points on the projection ray.
2. Discretizing the projection integral specifically includes:
The three-dimensional measured object f (x w,yw,zw) is uniformly divided into M multiplied by N multiplied by P discrete grids with the grid size of delta g multiplied by delta g, let the value f i(xw,yw,zw) of each grid be a constant, where i=1, 2. If there are X cameras in the tomographic system, the number of pixels of each camera is Y, the tomographic system has XY projected light in total. If the intersection intercept of the jth projection ray with the ith grid is noted as ω ij, it is apparent that only a few of the i corresponding ω ij is non-zero. Thus, the pixel intensity I j corresponding to the jth projection ray may be expressed discretely as:
Where ω ij is referred to as the projection weight factor of the ith grid to the jth ray, and represents the contribution of the ith grid to the jth projection. All omega ij constitute the weight matrix of the chromatography system.
Reconstructing a world coordinate system of 8 vertexes of the region to be (x wc,ywc,zwc)p, wherein p=1, 2..8, substituting coordinate values of the 8 points into formula (1) to obtain positions of the 8 vertexes in the camera coordinate system (x c,yc,zc)p. Comparing values of 8 z c to obtain an integration interval [ z min,zmax ], discretizing a camera imaging projection model expressed by formula (4), uniformly dividing the integration interval [ z min,zmax ] into Q microcell intervals, namely, integrating the steps of Q, and the step length of Q
Assuming that the objective function of each bin is a constant, therefore
Wherein (x ', y') and (x m,ym,zm) satisfy the relationship
The position of the integral infinitesimal in the world coordinate system can be determined according to formula (1) as follows:
Thus can be obtained
3. The weight matrix of the chromatographic system is calculated by utilizing the bilinear interpolation principle, and specifically comprises the following steps:
According to bilinear interpolation principle, the object function value of any position in the discrete three-dimensional space can be determined by the object function value of the center point of the adjacent discrete grid. The specific process is as follows:
(1) Determining the minimum adjacent discrete grid sequence number of each infinitesimal
(2) The distance between the infinitesimal and the center of the smallest adjacent discrete grid is determined to be delta x m、Δym and delta z m respectively.
(3) Determining the object function value of the element by the object function of the center point of 8 adjacent discrete grids
And obtaining the weight factor of each discrete grid pair element according to the coefficient determined by the distance between the adjacent discrete grids.
(4) The projected pixel value for each ray may be written in the form of
And carrying out integral operation on all the infinitesimal elements according to the formula to obtain a weight matrix of each discrete grid pair projection.
Experimental example:
In order to intuitively reflect the accuracy of a three-dimensional space camera imaging model and a weight matrix calculation method based on bilinear difference values, firstly, the imaging projection of a cube in a three-dimensional space is calculated. The cube was divided into 50 x 50 discrete grids of 0.4mm in size, each with a value of 1. The number of pixels of the analog camera is 138×138, the pixel size is 3.75 μm, and the lens focal length is 12mm. When the translation vector is [0mm, 800mm ], projections at different rotation angles calculated according to the method proposed by the present invention are shown in fig. 3. The calculated projection result is completely matched with the theoretical visual projection result, and the correctness of the method is proved.
2 Three-dimensional simulation fields F 1 and F 2 were used to verify the validity and accuracy of the three-dimensional spatial free projection tomographic reconstruction algorithm. Wherein F 1 is a three-dimensional hollow sphere which can reflect the integrity of the reconstruction result, and F 2 is a synthetic Shepp-Logan model commonly used in chromatographic techniques. Both fields were divided into 50 x 50 square discrete grids of 0.4mm size. Assuming that there are 12 cameras in the tomosynthesis system to acquire projections in different directions, the number of pixels of the cameras is 138×138, the pixel size is 3.75 μm, and the focal length of the lens is 12mm. The translation vectors are [0mm, 800mm ], the precession angle theta and the rotation angle phi are 5 degrees, and the nutation angle phi is uniformly distributed in [ -90 degrees, 90 degrees ].
Firstly, the projection imaging of different cameras is calculated by using the method provided by the invention, and then the tomographic reconstruction is performed by using an ART algorithm. The reconstruction result of the hollow sphere F 1 is shown in fig. 4. From the structural point of view, the sphere structure in the F1 reconstruction result is very complete and is perfectly matched with the original model structure, which shows that the integrity of the reconstruction result is very high, and the root mean square error of the reconstruction result is 2.2083 X10 -4, which shows that the reconstruction precision is very high. The reconstruction result of the synthesized Shepp-Logan model is shown in fig. 5, and the root mean square error of the reconstruction result is 7.2078 x10 -5, so that the reconstruction precision is very high.
The 3 simulation results in the experimental example verify the correctness of the camera imaging projection mathematical model in the three-dimensional space and the accuracy of the weight matrix calculation method.
The foregoing description is only illustrative of the preferred embodiments of the present invention, and is not intended to limit the scope of the invention, and all changes that may be made in the equivalent structures described in the specification and drawings of the present invention are intended to be included in the scope of the invention.
Claims (3)
1. The method for determining the emission tomography weight matrix for the free projection of the three-dimensional space is characterized by comprising the following steps of:
Step one, establishing a three-dimensional space free projection emission tomography model considering a lens imaging effect and a three-dimensional space position of a camera;
step two, discretizing projection integration;
step three, determining a weight matrix of the system based on bilinear interpolation principle;
the third step comprises the following steps:
s1, determining the serial number of the minimum adjacent discrete grid where each infinitesimal is located;
s2, determining the distance between the infinitesimal and the center of the minimum adjacent discrete grid;
S3, determining the object function value of the micro element by using the center point object functions of 8 adjacent discrete grids according to the bilinear interpolation principle to obtain the weight factor of each discrete grid on the micro element;
and S4, carrying out integral operation on all the infinitesimal to obtain a weight matrix of each discrete grid pair projection.
2. The method for determining the emission tomography weight matrix for free projection of three-dimensional space according to claim 1, wherein the first step comprises the steps of:
s1, the lens imaging effect is expressed as that coordinates (x, y, z) of an object point in a camera coordinate system and coordinates (x ', y') of an image point in a camera imaging plane coordinate system meet the relation
Wherein f is the focal length of the camera lens;
S2, representing the arbitrary three-dimensional space position of the camera as the world coordinate system (x w,yw,zw) and the camera coordinate system (x, y, z) satisfy the relation
Wherein R is a rotation matrix, and T is a translation vector;
s3, the finally obtained chromatographic projection model is
Where f (x, y, z) is the luminous intensity value of the object point in the camera coordinate system, and z min and z max are the upper and lower boundaries where each projection ray in the camera coordinate system intersects the reconstruction region.
3. The method for determining the emission tomography weight matrix for free projection of three-dimensional space according to claim 1, wherein the second step comprises the steps of:
S1, uniformly dividing a three-dimensional measured object f (x w,yw,zw) into m×n×p discrete grids, wherein the grid size is ΔgχΔg, and the value f i(xw,yw,zw of each grid is assumed to be a constant, i=1, 2.
S2, determining an upper limit z max and a lower limit z min of projection integration according to camera coordinate values of 8 vertexes of the reconstruction region;
S3, uniformly dividing an integration interval into Q microelements, and assuming that an object function of each microelement interval is a constant, a projection model is that Wherein (x ', y') and (x m,ym,zm) satisfy the relationship
The position (x mw,ymw,zmw) of the integral infinitesimal in the world coordinate system is determined according to the conversion relation between the world coordinate system and the camera coordinate system.
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| CN106600687A (en) * | 2016-12-08 | 2017-04-26 | 南京理工大学 | Multi-direction flame emission chromatographic system |
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