A camera layout optimization method for computed tomography with limited projection angle

Abstract

The present invention provides a method for optimizing the layout of a computer tomography camera with limited projection angles, belonging to the technical field of chemiluminescence computer tomography imaging; the method comprises the following steps: S1. system modeling: establishing a mathematical relationship between a target flow field and its projection; S2. reconstructing the flow field using an inversion algorithm; performing tomographic reconstruction using a classical algebraic reconstruction technique, an ART algorithm; S3. optimizing the layout of a computer tomography camera with limited projection angles; constructing an objective function as an effective predictor of reconstruction error; solving the maximization problem using a simulated annealing (SA) algorithm for global optimization; and achieving an optimal solution using a simulated annealing algorithm. The present invention significantly increases the capture of effective projection information by optimizing the pitch and azimuth angles of the camera. The simulated annealing algorithm is used for camera layout optimization, enabling the system to flexibly adapt to dynamic environments. The present invention effectively reduces the pathological nature of the weight matrix, reduces computational complexity, and enhances the reliability of measurement results.

Description

Technical Field

[0001] The present invention provides a method for optimizing the layout of a computer tomography camera with a limited projection angle, and belongs to the technical field of chemiluminescence computer tomography. Background Art

[0002] Computed tomography of chemiluminescence (CTC) is an important technique for characterizing three-dimensional flow characteristics in combustion and fluid flow fields. CTC captures two-dimensional projections from multiple angles and uses mathematical inversion algorithms to reconstruct the three-dimensional flow field within a volume of interest (VoI). CTC is widely used in combustion diagnostics, gas detection, and high-temperature flow field analysis. This technique accurately provides information on the temperature field and chemical distribution within the combustion region, supporting a deeper understanding of the combustion process and the optimization of combustion equipment.

[0003] Although current chemiluminescence computed tomography (CTC) technology can provide high-temporal and spatial resolution three-dimensional flame structure measurements, in practice, especially in complex environments such as supersonic wind tunnels, limited optical access means that only a limited number of high-speed cameras can be deployed. Traditional camera layouts (such as uniform distribution along a circular plane) cannot fully capture useful information in the scene, resulting in suboptimal volume tomographic reconstruction quality. Summary of the Invention

[0004] The present invention aims to solve the problem of how to achieve high-quality volume tomography in complex flow and combustion diagnosis under limited projection angle conditions. By combining CTC technology with a fiber optic endoscope, a camera layout optimization method is proposed to maximize the angle of the weight matrix subspace, reduce correlation, improve imaging accuracy, and verify its stability under changing flame direction.

[0005] The specific technical solutions are:

[0006] A method for optimizing camera layout for computed tomography with limited projection angles comprises the following steps:

[0007] S1. System modeling: Establishing the mathematical relationship between the target flow field and its projection;

[0008] The region of interest (VOI) of the flow field is discretized into a rectangular area, and the world coordinate system X is established. w -Y w -Z w , the origin of the coordinate system is established at the upper left corner of VOI; the camera coordinate system X c -Y c -Z cBased on the optical center of the lens, the image plane defines the pixel coordinate system uov; the perspective projection transformation establishes the relationship between the geometric position in the physical space and the pixel position in the image, and the world coordinate system is established by the rigid body transformation. w (X w , Y w , Z w ) and the next point P in the camera coordinate system c (X c , Y c , Z c )

[0009]

[0010] in They are the rotation matrix and translation matrix from the world coordinate system to the camera coordinate system, r ij and t i Represents the matrix elements; the rotation matrix can also be determined by the pitch angle α, yaw angle β, and roll angle γ; this relationship is expressed as:

[0011]

[0012] A point P in the camera coordinate system c (X c , Y c , Z c ) is transformed to the pixel coordinate system uov:

[0013]

[0014] Where: (f x , f y ) is the focal length of the camera in the x and y directions, dx, dy represent the physical size of a single pixel, τ is the skew coefficient in the pixel coordinate system, indicating whether the two coordinate axes of the pixel coordinate system are strictly orthogonal, and (u0, v0) represents the coordinates of the principal point of the camera.

[0015] The pitch angle α, yaw angle β, roll angle γ and translation matrix T determine the position of the camera. In this process, the Zhang Zhengyou calibration method is used to calibrate the internal and external parameters of the camera to obtain the above parameters.

[0016] The part of interest in the flame area is divided into voxels in the x, y, and z directions, and the signal inside each voxel is considered to be uniform. Assuming that the flow field to be measured is a continuous function f(x, y, z), its projection on the imaging plane can be described as:

[0017] p(s, t) = ∫ V f(x,y,z)·w(x,y,z;s,t)dV (4)

[0018] Where p(s, t) is the signal intensity at the sth pixel of the projection image taken at the tth angle; w(x, y, z; s, t) represents the contribution of f(x, y, z) to the image point p(s, t); and V is the volume of the entire flow field to be measured. Discretizing the flow field to be measured into voxels of equal size, Equation 4 can be approximately expressed as:

[0019]

[0020] Where j and N represent the voxel index and the total number of voxels respectively, w(x j ,y j , z j ) represents the position of voxel j within the voxel; w(x j ,y j , z j ; s, t) represents f(x j ,y j , z j ) is the contribution weight of the s-th pixel on the t-th angle projection image; p s，t is the weighted sum of all voxel signals; the equation is expressed in matrix form as:

[0021]

[0022] Projection vector of the flow field to be measured is obtained through experimental measurement, W is calculated through imaging model, and projections from multiple angles are obtained. and the weight matrix W, which form a system of equations. The solution of this system of equations is the flow field to be measured. The distribution of .

[0023] S2. Inversion algorithm to reconstruct the flow field;

[0024] The classical algebraic reconstruction technique ART algorithm is used for tomographic reconstruction. The mathematical description of ART is as follows:

[0025]

[0026] Where k represents the number of iterations, w in represents the contribution rate of the n-th voxel to the i-th pixel, and λ is the relaxation factor, which usually ranges from 0 to 2.

[0027] In each iteration, ART modifies the current solution according to each equation; each equation represents a hyperplane, and the modification process is to make a vertical projection between the current solution and the line / plane corresponding to the equation; each row of the weight matrix W i A subspace is defined; the core idea of ​​ART iteration is to make the solution gradually approach the intersection of these subspaces through projection.

[0028] S3. Optimization of camera layout for computed tomography with limited projection angle;

[0029] S3.1 construct an objective function as an effective predictor of reconstruction error;

[0030] The weight corresponding to each CTC projection is in matrix form. The weight represents the effective constraint information obtained by the projection. Equation (6) is determined by the weight matrix. The angle between the two subspaces using the weight matrix columns is defined as:

[0031] θ ij =f(W i , W j ) (8)

[0032] where θ ij represents the subspace angle between any two weight matrices. Geometrically, this angle is the angle between two hyperplanes embedded in a higher dimensional space. The camera layout optimization problem is transformed into a maximization problem, whose cost function is defined as, for example, θ ij The objective function Fobj of the optimization problem is defined as:

[0033] Fobj=min(θ ij ) (9)

[0034] Here, min() returns the minimum value. The objective function Fobj is maximized by minimizing the angle between any matrix subspaces. The weight matrix W is calculated entirely from the camera calibration parameters and positions. W is determined by extrinsic parameters, including the rotation matrix and the translation matrix. The cameras are distributed on the same sphere and facing the VOI. The translation matrix T is constant, and the roll angle D = 0. α and β, which determine the camera position, are introduced as variables into the optimization objective function. The maximization problem is solved globally using the simulated annealing (SA) algorithm.

[0035] S3.2 Simulated annealing algorithm implementation:

[0036] Initial algorithm parameters, including the upper and lower bounds of the variable pitch angle α, yaw angle β, initial solutions α0, β0, initial temperature T0, and attenuation coefficient The variable boundary conditions ensure the effectiveness of optimizing the camera distribution under limited projection angles. Set the value range of α to (0, 2 / 3π) and the value range of β to (0, 1 / 4π) to simulate limited projection angles. During the optimization process, the angle θ between any two weight matrix subspaces is calculated from the initial position. ij, and obtain the initial value of the objective function Fobj_0. Generate a set of new solutions based on the initial position and calculate the new objective function value Fobj_new. If Fobj_new>Fobj_0, then accept the new solution, otherwise accept the new solution with probability exp(-ΔF / T), which is called the Metropolis criterion. Record the optimal solution and the corresponding objective function value Fobj_T in each cycle, generate a new solution in it, and calculate the new objective function value. Repeat the cycle before each temperature T is lowered to ensure the global search for the optimal solution. Achieve temperature reduction, where A constant belonging to (0, 1). When Fobj_T remains unchanged or is insignificant between several consecutive temperature states, that is, it is less than a positive integer, or when the maximum number of cycles is reached, the algorithm terminates.

[0037] The technical solution provided by the present invention has the following technical effects:

[0038] 1. Improved 3D reconstruction accuracy: This invention significantly increases the capture of effective projection information by optimizing the camera's pitch and azimuth angles. This optimization process effectively reduces reconstruction errors, making 3D flow field reconstructions from limited projection angles more accurate, especially in complex flow and combustion environments.

[0039] 2. Enhanced adaptability to dynamic scenes: Using a simulated annealing algorithm to optimize camera layout enables the system to flexibly adapt to dynamic environments. This means that even in high-speed combustion or highly variable flow fields, the system can maintain high reconstruction accuracy and stability.

[0040] 3. Reduced computational complexity: Compared to traditional layout methods, this method effectively reduces the pathological nature of the weight matrix and reduces computational complexity. This makes the CTC system more efficient in real-time imaging and rapid reconstruction, meeting the needs of fast-response experiments.

[0041] 4. Improved system stability: By optimizing the camera position, the introduction of redundant information during the reconstruction process is reduced, improving the stability of the imaging system in various experimental environments. The optimized layout makes the reconstruction results more consistent across different experimental conditions, enhancing the reliability of the measurement results. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 This is a linear imaging model diagram of this embodiment;

[0043] Figure 2 ART algorithm iteration diagram of this embodiment;

[0044] Figure 3 This is a Gaussian flow field diagram containing eddy currents in this embodiment;

[0045] Figure 4 This is a schematic diagram of the camera distribution in a quarter sphere of this embodiment;

[0046] Figure 5 Graph showing the model simulation results of this embodiment;

[0047] Figure 6 This is the optimized flow chart of this embodiment;

[0048] Figure 7 is a graph showing the objective function and reconstruction error of this embodiment;

[0049] Figure 8 This is a diagram of the deflected flame model of this embodiment;

[0050] Figure 9 This is a comparison diagram of the optimized distribution of 100 random models in this embodiment and the uniform distribution;

[0051] Figure 10 A realistic diagram of the optimized camera distribution for this embodiment. DETAILED DESCRIPTION

[0052] The specific technical solutions of the present invention are described with reference to the embodiments.

[0053] A method for optimizing camera layout for computed tomography with limited projection angles comprises the following steps:

[0054] S1. System modeling: Establishing the mathematical relationship between the target flow field and its projection;

[0055] The region of interest (VOI) of the flow field is discretized into a rectangular area, and the world coordinate system X is established. w -Y w -Z w , the origin of the coordinate system is established at the upper left corner of VOI; the camera coordinate system X c -Y c -Z c Based on the optical center of the lens, the image plane defines the pixel coordinate system uov, such as Figure 1 As shown. ; The perspective projection transformation establishes the relationship between the geometric position in the physical space and the pixel position in the image, and the rigid body transformation establishes the next point P in the world coordinate system w (X w , Y w , Z w ) and the next point P in the camera coordinate system c (X c , Y c , Z c )

[0056]

[0057] in They are the rotation matrix and translation matrix from the world coordinate system to the camera coordinate system, r ij and t i Represents the matrix elements; the rotation matrix can also be determined by the pitch angle α, yaw angle β, and roll angle γ; this relationship is expressed as:

[0058]

[0059] A point P in the camera coordinate system c (X c , Y c , Z c ) is transformed to the pixel coordinate system uov:

[0060]

[0061] Where: (f x , f y ) is the focal length of the camera in the x and y directions, dx, dy represent the physical size of a single pixel, τ is the skew coefficient in the pixel coordinate system, indicating whether the two coordinate axes of the pixel coordinate system are strictly orthogonal, and (u0, v0) represents the coordinates of the principal point of the camera.

[0062] The pitch angle α, yaw angle β, roll angle γ and translation matrix T determine the position of the camera. In this process, the Zhang Zhengyou calibration method is used to calibrate the internal and external parameters of the camera to obtain the above parameters.

[0063] The part of interest in the flame area is divided into voxels in the x, y, and z directions, and the signal inside each voxel is considered to be uniform. Assuming that the flow field to be measured is a continuous function f(x, y, z), its projection on the imaging plane can be described as:

[0064] p(s, t) = ∫ V f(x,y,z)·w(x,y,z;s,t)dV (4)

[0065] Where p(s, t) is the signal intensity at the sth pixel of the projection image taken at the tth angle; w(x, y, z; s, t) represents the contribution of f(x, y, z) to the image point p(s, t); and V is the volume of the entire flow field to be measured. Discretizing the flow field to be measured into voxels of equal size, Equation 4 can be approximately expressed as:

[0066]

[0067] Where j and N represent the voxel index and the total number of voxels respectively, w(x j ,y j , z j) represents the position of voxel j within the voxel; w(x j ,y j , z j ; s, t) represents f(x j ,y j , z j ) is the contribution weight of the s-th pixel on the t-th angle projection image; p s，t is the weighted sum of all voxel signals; the equation is expressed in matrix form as:

[0068]

[0069] Projection vector of the flow field to be measured is obtained through experimental measurement, W is calculated through imaging model, and projections from multiple angles are obtained. and the weight matrix W, which form a system of equations. The solution of this system of equations is the flow field to be measured. The distribution of .

[0070] S2. Inversion algorithm to reconstruct the flow field;

[0071] The classical algebraic reconstruction technique (ART) algorithm is used for tomographic reconstruction. Compared with other algorithms, it is relatively easy to implement and can obtain high-quality reconstruction results even in the presence of noise. The mathematical description of ART is as follows:

[0072]

[0073] Where k represents the number of iterations, w in It represents the contribution rate of the nth voxel to the i-th pixel, and λ is the relaxation factor, which usually ranges from 0 to 2. Figure 2 The ART algorithm is shown in the iterative diagram. In each iteration, ART modifies the current solution according to each equation. Each equation represents a hyperplane (or a line in two dimensions). The modification process is to make a perpendicular projection between the current solution and the line / plane corresponding to the equation. Each row of the weight matrix W i A subspace is defined. The core idea of ​​ART iteration is to project the solution closer to the intersection of these subspaces. The larger the angle between the subspaces, the more effective the projection and the faster the convergence. If the subspaces are nearly parallel (i.e., the angle is small), the algorithm converges more slowly because the projection correction is smaller.

[0074] S3. Optimization of camera layout for computed tomography with limited projection angle;

[0075] S3.1 construct an objective function as an effective predictor of reconstruction error;

[0076] The weight corresponding to each projection of CTC is in matrix form. The weight represents the effective constraint information obtained by the projection. Equation (6) is determined by the weight matrix. The greater the difference between the weight matrices, the more effective information the camera captures. In a geometric sense, the subspace defined by each weight matrix corresponds to a hyperplane. In the ART algorithm, the goal of the optimization problem is to maximize the correlation between the weight matrices calculated by any two cameras. Specifically, the larger the subspace angle between the weight matrices, the greater the distance between the two hyperplanes, thereby improving the effectiveness of the projection. In this case, the ART algorithm can converge to the intersection faster through an iterative correction process. The correlation is measured using the angle between the two subspaces of the weight matrix columns, defined as

[0077] θ ij =f(W i , W j ) (8)

[0078] where θ ij represents the subspace angle between any two weight matrices. Geometrically, this angle is the angle between two hyperplanes embedded in a higher dimensional space. The camera layout optimization problem is transformed into a maximization problem, and its cost function can be defined as, for example, θ ij The angle θ between the subspaces of the two matrices is ij There is a small value of , then the two corresponding cameras provide very similar spatial information, and one of the cameras is redundant. Therefore, the objective function Fobj of the optimization problem can be defined as:

[0079] Fobj=min(θ ij ) (9)

[0080] Where min() returns the minimum value. Take the minimum angle of the subspace between any matrices to maximize the objective function Fobj. The weight matrix W is completely calculated from the camera calibration parameters and position. Once the camera is selected, the internal parameters are determined. Therefore, W is determined by the external parameters including the rotation matrix and the translation matrix. The cameras are usually distributed on the sphere so that the distance from the camera to the center of the VOI is equal to the radius of the sphere, so that the translation matrix T is a constant. In addition, in general, in order to facilitate subsequent data processing and comparison, it is hoped that the flame projection obtained remains upright and the roll angle γ is set to 0. Finally, α and β, which determine the camera position, are introduced as variables into the optimization objective function. Subsequently, the maximization problem can be solved using the simulated annealing (SA) algorithm (global optimization).

[0081] S3.2 Simulated annealing algorithm implementation:

[0082] Figure 6The flowchart shown provides a detailed description of the simulated annealing algorithm for the finite projection angle problem. The initial algorithm parameters include the upper and lower bounds of the variables pitch angle α and yaw angle β, the initial solution α0, β0, the initial temperature T0, and the attenuation coefficient The variable boundary conditions ensure the effectiveness of optimizing the camera distribution under limited projection angles. Set the value range of α to (0, 2 / 3π) and the value range of β to (0, 1 / 4π) to simulate limited projection angles. This is because Figures 3 to 5 It shows that the reconstruction accuracy curve is symmetrically shaped like "W" as the camera pitch angle β increases. During the optimization process, the angle θ between any two weight matrix subspaces is calculated from the initial position. ij , and obtain the initial value of the objective function Fobj_0. Generate a set of new solutions based on the initial position and calculate the new objective function value Fobj_new. If Fobj_new>Fobj_0, then accept the new solution, otherwise accept the new solution with a certain probability exp(-ΔF / T), which is called the Metropolis criterion. In each cycle, record the optimal solution and the corresponding objective function value Fobj_T, generate a new solution from it, and calculate the new objective function value. Repeat a certain number of cycles before lowering the temperature T each time to ensure the global search for the optimal solution. Achieve temperature reduction, where A constant belonging to (0, 1), here we set When Fobj_T remains unchanged or is not significant between several consecutive temperature states, that is, it is less than a positive integer (10 -5 ), or when the maximum number of cycles is reached, the algorithm terminates.

[0083] This embodiment implements the above optimization process within a limited projection field of view range of 0-120°.

[0084] Step 1: System Initialization: At the beginning of the experiment, a high-speed camera was selected and combined with seven fiber optic imaging bundles, initially evenly distributed on a hemispherical surface. The camera's pitch (β) and azimuth (α) angles were initially set to 0°, the initial temperature T was 100°, and the attenuation coefficient t was 0.95.

[0085] Step 2: Set the projection range: Limit the camera's effective projection range to between 0° and 120° to accommodate the limitations of the optical channel in the actual environment.

[0086] Step 3: Weight Matrix Calculation: Perform a preliminary measurement of the projection signal from each camera and calculate the weight matrix corresponding to each projection. These weight matrices are used to describe the contribution of voxels to pixels and provide the necessary information for subsequent image reconstruction.

[0087] Step 4: Optimization: Apply a simulated annealing algorithm to optimize the camera's pitch and azimuth angles. During the optimization process, set boundary conditions for the pitch and azimuth angles to ensure the camera remains within the range of 0° to 120°. Record the objective function value and corresponding reconstruction error for each iteration, and decide whether to accept the new solution based on the Metropolis Criterion.

[0088] Step 5: Final Layout Deployment: After multiple iterations, the final camera position distribution is obtained, which effectively reduces reconstruction errors. The optimized camera positions are fixed and deployed in the CTC measurement system.

[0089] Step 6: Verify the results: Use the optimized camera layout to image the flame, acquiring projection data from multiple angles. Use the ART algorithm to reconstruct the image and analyze the relationship between reconstruction accuracy and the objective function. Experimental results show that the optimized layout significantly reduces reconstruction error, especially when the flame is rotated 90°, where reconstruction quality remains stable.

[0090] The flow field is reconstructed using projections from 7 cameras in different directions. Figure 7 In the figure, the evolution of the objective function (marked with a solid triangle in the blue curve) is plotted as a function of T reduction. For the sake of comparison, the objective function is inverted and then normalized. The solid red curve is the evolution of the reconstruction error under the corresponding objective function. Figure 3 Reconstruction of asymmetric flow field containing eddies. As T decreases, the algorithm becomes less and less likely to accept new solutions with smaller function values ​​and gradually converges to the global solution. Therefore, the inverse objective function value decreases with T. Figure 7 The relationship between the objective function and the reconstruction error is shown as the annealing temperature T decreases. Overall, the reconstruction error and the objective function value have a similar trend. This shows that the objective function Fobj can be used as an effective predictor of the reconstruction error.

[0091] To further verify our method, we use the set of solutions outputted at the end of the algorithm as the final camera position distribution. Looking only at the horizontal camera positions, we can see that they are evenly distributed, with angles of 0°, 20°, 40°, 60°, 80°, 100°, and 120°. The optimization result is consistent with our previous conclusion that the uniform distribution minimizes the reconstruction error. We then randomly generate one hundred models and test the reconstruction error of both the optimized distribution and the circular plane uniform distribution. The results are plotted on Figure 9 In fact, by changing Figure 8 The deflection size and direction of the flame are used to generate the first 50 random models, and the flame model is rotated 90° to generate another 50 random models. Figure 9The blue triangle and red diamond lines represent the results for the optimized and uniform distributions, respectively. For all models, the reconstruction error curve for the optimized camera distribution remains consistently below the uniform distribution error curve. More notably, when the flame is rotated 90°, the reconstruction error curve for the uniform distribution increases, while the reconstruction error for the optimized distribution remains essentially unchanged. This indicates that, within the limited projection angle space, this optimization method, by arranging cameras in two orthogonal directions, is insensitive to flame shape, resulting in both lower reconstruction error and greater stability.

[0092] Figure 10 Arrange the on-site physical map based on the optimization results of the example.

[0093] The experimental device of this embodiment includes:

[0094] Fiber optic bundle clamp: fixes the fiber optic image bundle and lens.

[0095] Fiber optic imaging bundle: transmits the projection signal of the flame area to the sensor of the high-speed camera to generate image data.

[0096] Lens: A lens is installed in front of each fiber optic imaging bundle to improve the clarity and resolution of the captured image.

[0097] High-speed camera: placed on the top of the device, dedicated to capturing the dynamic characteristics of high-speed flowing flames.

[0098] Bunsen burner: used to generate flame in combustion experiments as the flow field to be measured.

Claims

1. A method for optimizing camera layout for computed tomography with limited projection angle, characterized in that: The following steps are involved: S1. System modeling: Establishing the mathematical relationship between the target flow field and its projection; The pitch angle α, yaw angle β, roll angle γ and translation matrix T determine the position of the camera. In this process, the Zhang Zhengyou calibration method is used to calibrate the internal and external parameters of the camera to obtain the above parameters. The part of interest in the flame area is divided into voxels in the x, y, and z directions, and the signal inside each voxel is considered to be uniform. Let the flow field to be measured be a continuous function f(x, y, z), and its projection on the imaging plane is described as: p(s,t)=∫ V f(x,y,z)·w(x,y,z;s,t)dV (4) Where p(s, t) is the signal intensity at the sth pixel of the projection image taken at the tth angle; w(x, y, z; s, t) represents the contribution of f(x, y, z) to the image point p(s, t); and V is the volume of the entire flow field to be measured. If the flow field to be measured is discretized into voxels of the same size, Equation 4 can be expressed as: Where j and N represent the voxel index and the total number of voxels respectively, w(x j ,y j , z j ) represents the position of voxel j within the voxel; w(x j ,y j , z j ; s, t) represents f(x j ,y j , z j ) is the contribution weight of the s-th pixel on the t-th angle projection image; p s，t is the weighted sum of all voxel signals; the equation is expressed in matrix form as: Projection vector of the flow field to be measured is obtained through experimental measurement, W is calculated through imaging model, and projections from multiple angles are obtained. and the weight matrix W, which form a system of equations. The solution of this system of equations is the flow field to be measured. distribution of S2. Reconstruct the flow field using the inversion algorithm; perform tomographic reconstruction using the classical algebraic reconstruction technique ART algorithm; S3. Optimization of Computed Tomography Camera Layout with Limited Projection Angles; Constructing an Objective Function as an Effective Predictor of Reconstruction Error; The weight corresponding to each projection of CTC is in matrix form; the weight represents the effective constraint information obtained by the projection; the angle between the two subspaces of the weight matrix column is used to measure the correlation, which is defined as: θ ij =f(W i ,W j ) (8) where θ ij represents the subspace angle between any two weight matrices; geometrically, this angle is the angle between two hyperplanes embedded in a higher-dimensional space; the camera layout optimization problem is transformed into a maximization problem, whose cost function is defined as, for example, θ ij The average value or weighted sum of; the objective function Fobj of the optimization problem is defined as: Fobj=min(θ ij ) (9) Where min() returns the minimum value; the minimum angle between the subspaces of any matrix is ​​taken to maximize the objective function Fobj; the weight matrix W is completely calculated from the camera calibration parameters and position; W is determined by the external parameters including the rotation matrix and the translation matrix; the cameras are distributed on the same sphere and facing the VOI, the translation matrix T is a constant value, and the roll angle γ = 0; α and β, which determine the camera position, are introduced as variables into the optimization objective function; the maximization problem is solved globally using the simulated annealing SA algorithm; The maximization problem is solved by global optimization using the simulated annealing SA algorithm; the optimal solution is achieved using the simulated annealing algorithm.

2. The method for optimizing the layout of a computed tomography camera with a limited projection angle according to claim 1, wherein: The specific method of S1 is: The region of interest (VOI) of the flow field is discretized into a rectangular area, and the world coordinate system X is established. w -Y w -Z w , the origin of the coordinate system is established at the upper left corner of VOI; the camera coordinate system X c -Y c -Z c Based on the optical center of the lens, the image plane defines the pixel coordinate system uov; the perspective projection transformation establishes the relationship between the geometric position in the physical space and the pixel position in the image, and the world coordinate system is established by the rigid body transformation. w (X w , Y w , Z w ) and the next point P in the camera coordinate system c (X c , Y c , Z c ) in They are the rotation matrix and translation matrix from the world coordinate system to the camera coordinate system, r ij and t i Represents the matrix elements; the rotation matrix can also be determined by the pitch angle α, yaw angle β, and roll angle γ; this relationship is expressed as: A point P in the camera coordinate system c (X c , Y c , Z c ) is transformed to the pixel coordinate system uov: Where: (f x , f y ) is the focal length of the camera in the x and y directions, dx, dy represent the physical size of a single pixel, τ is the skew coefficient in the pixel coordinate system, indicating whether the two coordinate axes of the pixel coordinate system are strictly orthogonal, and (u0, v0) represents the coordinates of the principal point of the camera.

3. The method for optimizing the layout of a computed tomography camera with limited projection angle according to claim 2, wherein: The specific method of S2 is: The classical algebraic reconstruction technique ART algorithm is used for tomographic reconstruction. The mathematical description of ART is as follows: Where k represents the number of iterations, w in represents the contribution rate of the nth voxel to the i-th pixel, λ is the relaxation factor, ranging from 0 to 2; In each iteration, ART modifies the current solution according to each equation; each equation represents a hyperplane, and the modification process is to make a vertical projection between the current solution and the line / plane corresponding to the equation; each row of the weight matrix W i A subspace is defined; the core idea of ​​ART iteration is to make the solution gradually approach the intersection of these subspaces through projection.

4. The method for optimizing the layout of a computed tomography camera with limited projection angle according to claim 3, wherein: Implementation of simulated annealing algorithm in S3: Initial algorithm parameters, including the upper and lower bounds of the variable pitch angle α, yaw angle β, initial solutions α0, β0, initial temperature T0, and attenuation coefficient The variable boundary conditions ensure the effectiveness of optimizing the camera distribution under limited projection angles; set the value range of α to (0, 2 / 3π) and the value range of β to (0, 1 / 4π); during the optimization process, the angle θ between any two weight matrix subspaces is calculated from the initial position. ij , and obtain the initial value of the objective function Fobj_0; generate a set of new solutions based on the initial position, and calculate the new daily objective function value Fobj_new; if Fobj_new>Fobj_0, then accept the new solution, otherwise accept the new solution with probability exp(-ΔF / T), which is called the Metropolis criterion; record the optimal solution and the corresponding objective function value Fobj_T in each cycle, generate a new solution in it, and calculate the new objective function value; repeat the cycle number before each temperature reduction T to ensure the global search for the optimal solution; through Achieve temperature reduction, where A constant in (0,1). When Fobj_T remains unchanged or is insignificant between several consecutive temperature states, that is, it is less than a positive integer, or when the maximum number of cycles is reached, the algorithm terminates.

Images