A three-dimensional tomography camera arrangement optimization method

Abstract

The present invention belongs to an optimization method, and specifically relates to a three-dimensional tomography camera arrangement optimization method. It includes the following steps: Step 1: obtain projections; obtain projections in all possible directions; Step 2: preprocessing; Step 3: determine the distribution range of unknown voxels determined by each projection; Step 4: determine the effective number of corrections determined by each projection; Step 5: list all possible camera arrangements; Step 6: calculate the number of unknown voxels for different camera arrangements; Step 7: calculate the effective number of corrections for different camera arrangements; Step 8: calculate the average effective number of corrections for different camera arrangements; Step 9: determine the optimal arrangement. The present invention has the following beneficial effects relative to the prior art: the reconstruction result using the arrangement is highly accurate.

Description

Technical Field

[0001] The present invention relates to an optimization method, and in particular to a three-dimensional tomography camera arrangement optimization method. Background Art

[0002] Three-dimensional tomography technology reconstructs the three-dimensional spatial distribution of the measured target based on the two-dimensional projections of the measured target obtained simultaneously in different directions. It has high accuracy and spatial resolution, so it is widely used in flow and combustion problems. In the reconstruction process, the more two-dimensional projections are used for reconstruction, the higher the accuracy of the three-dimensional reconstruction result. However, due to the price and quantity of high-speed cameras, the number of cameras used in the actual reconstruction problem does not exceed 10. In addition, in actual measurements, combustion and flow occur inside a specific device. In order to avoid the device blocking the measured target, the camera can only be placed in a specific position, which limits the possible arrangement of the camera. According to previous studies, different camera arrangements will affect the reconstruction results. Therefore, in a confined space, when a limited number of cameras are used to perform tomographic reconstruction of a specific measured target, the camera arrangement needs to be optimized to improve the reconstruction efficiency and accuracy. Summary of the invention

[0003] The purpose of the present invention is to provide a three-dimensional tomography camera arrangement optimization method to address the defects of the prior art, so as to find the optimal arrangement of a limited number of cameras in a confined space and improve the reconstruction accuracy and efficiency.

[0004] The specific technical solution adopted by the present invention is as follows: a three-dimensional tomography camera arrangement optimization method, which includes the following steps:

[0005] Step 1: Get the projection;

[0006] Get projections in all possible directions;

[0007] Step 2: Preprocessing;

[0008] Step 3: Determine the distribution range of unknown voxels determined by each projection;

[0009] Step 4: Determine the effective number of corrections determined for each projection;

[0010] Step 5: List all possible camera arrangements;

[0011] Step 6: Calculate the number of unknown voxels for different camera arrangements;

[0012] Step 7: Calculate the effective correction times for different camera arrangements;

[0013] Step 8: Calculate the average effective correction times for different camera arrangements;

[0014] Step 9: Determine the optimal layout.

[0015] In the above-mentioned three-dimensional tomography camera arrangement optimization method, the step 1 includes placing a camera in sequence at all possible camera placement positions, and taking multiple projections of the measured target within a period of time.

[0016] In the above-mentioned three-dimensional tomography camera arrangement optimization method, the step 2 includes: for a stable target to be measured, no processing is performed; for a dynamically changing target to be measured, an average projection of the target to be measured within a period of time is calculated for subsequent calculations.

[0017] A three-dimensional tomography camera arrangement optimization method as described above, wherein the step 3 includes calculating the distribution range of effective voxels using the projection of the target to be measured or the average projection obtained in steps 1-2, firstly dividing the area on the projection into an imaging area, that is, the pixel value is not 0; and a non-imaging area, that is, the pixel value is 0, according to the distribution of pixel values ​​in the projection; starting from the pixels in the non-imaging area, the light path is traced in reverse, and all voxel values ​​in the measured area space through which the light path passes are 0, and the remaining voxels whose voxel values ​​cannot be determined are unknown voxels, which need to be solved iteratively.

[0018] In the above-mentioned three-dimensional tomography camera arrangement optimization method, the specific process of step 3 is as follows: first, the area where the target is located is discretized, and the smallest microelement after discretization is called a voxel. After the voxel passes through the imaging system, it will form a projection on the camera, and the smallest microelement in the projection is called a pixel.

[0019] The relationship between pixels and imaging systems is expressed by the projection equation:

[0020]

[0021] Where: P represents the pixel in the projection of the target, k represents the index value of the pixel, and K represents the number of all pixels; F represents the discretized voxel, q represents the index value of the voxel, and Q represents the number of all voxels; W represents the projection weight matrix, and W(k,q) represents the contribution value of the pth voxel to the kth pixel. The size of the contribution value is related to the imaging system and the position of the camera and the target. Since there are many 0 elements in W, Equation 1 cannot be solved directly. The commonly used solution method is the algebraic iteration method:

[0022]

[0023] Where: I represents the number of iterations; α represents the relaxation factor; ΔP(k) I Represents the difference between the reconstructed projection and the true projection after the Ith iteration,

[0024] The number of voxels is related to the spatial resolution of the target being measured. The higher the resolution, the more voxels need to be solved.

[0025] In the above-mentioned three-dimensional tomography camera arrangement optimization method, when the resolution remains unchanged in step 3, before iterative solution, the value of a part of voxels is determined by the value of the pixel in the projection, so as to reduce the amount of calculation in the iterative process.

[0026] In the above-mentioned three-dimensional tomography camera arrangement optimization method, the step 4 includes determining the projection matrix W in the direction according to the relative position relationship between the measured target and the camera, and it is concluded from the iterative relationship that an effective correction can be performed only when the elements in W are not 0.

[0027] In the above-mentioned three-dimensional tomography camera arrangement optimization method, step 5 includes arranging and combining the number of available cameras and the number of positions for placing the cameras, and listing all possible camera arrangements.

[0028] A three-dimensional tomography camera arrangement optimization method as described above, wherein the step 6 includes, in step 3, obtaining the unknown voxel distribution in different directions, and according to the different camera arrangements in step 5, taking the intersection of the unknown voxel distribution ranges in different directions to obtain the unknown voxel distribution range jointly determined by multiple cameras.

[0029] The above-mentioned three-dimensional tomography camera arrangement optimization method, wherein the step 7 includes, in step 4, obtaining the effective correction times in different directions, summing the effective correction times in different directions according to different camera arrangement modes in step 5, and obtaining a set of effective correction times determined by the camera arrangement,

[0030] The step 8 includes calculating the ratio of the total number of correction iterations obtained in step 7 to the number of unknown voxels obtained in step 6, and this ratio is called the average effective number of corrections.

[0031] The step 9 includes selecting the arrangement with the largest average number of effective corrections in step 8 as the optimal arrangement.

[0032] Compared with the prior art, the present invention has the following beneficial effects: the method quantifies the number of unknowns that need to be solved in the three-dimensional tomography problem and the number of effective corrections in the iterative process, and finally obtains the average effective correction number for each unknown, and applies it to the camera arrangement optimization problem in the tomography problem. When selecting a camera arrangement, the more average effective corrections a group of arrangements can provide, the higher the accuracy of the reconstruction result using the arrangement. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of three-dimensional tomography

[0034] Figure 2 Unknown voxel determination method DETAILED DESCRIPTION

[0035] The three-dimensional tomography problem first requires the establishment of a projection equation based on the projection relationship between the target and the target projection, and then the projection equation is solved to finally obtain the three-dimensional signal distribution of the target. Figure 1 As shown in the figure, the area where the target is located is first discretized. The smallest microelement after discretization is called a voxel. After the voxel passes through the imaging system, it will form a projection on the camera. The smallest microelement in the projection is called a pixel. Figure 1 The relationship between voxels, pixels and imaging systems can be expressed by the projection equation:

[0036]

[0037] In the formula: P represents the pixel in the projection of the measured target, k represents the index value of the pixel, and K represents the number of all pixels; F represents the discretized voxel, q represents the index value of the voxel, and Q represents the number of all voxels; W represents the projection weight matrix, and W(k,q) represents the contribution value of the pth voxel to the kth pixel. The size of the contribution value is related to the imaging system and the position of the camera and the measured target. Since there are many 0 elements in W, formula 1 cannot be solved directly. The commonly used solution method is the algebraic iteration method:

[0038]

[0039] Where: I represents the number of iterations; α represents the relaxation factor; ΔP(k) I Represents the difference between the reconstructed projection and the true projection after the Ith iteration.

[0040] In the iterative solution process of equation 1-2, the solution result will be affected by the number of voxels that need to be solved in the equation and the number of iterations. The number of voxels is related to the spatial resolution of the target being measured. The higher the resolution, the more voxels need to be solved. When the resolution remains unchanged, before the iterative solution, the value of some voxels can be determined by the value of the pixel in the projection to reduce the amount of calculation in the iterative process. The method for determining the voxel value is as follows: Figure 2 As shown. Figure 2In , there are three cameras around the target to be measured, and the projection of the target to be measured in three different directions can be obtained. According to whether the pixel value on the projection of the target to be measured is 0, the area on the projection can be divided into an imaging area and a non-imaging area. Starting from the pixels in the non-imaging area, the light path is traced backwards. The voxel values ​​in the area to be solved swept by the light path are all 0. The area where this part of the voxels is located is called the known number area. The voxel values ​​of the remaining part cannot be determined and need to be solved iteratively. The area where this part of the voxels that need to be iterated is called the unknown number area. After determining the distribution of unknown numbers that need to be iterated, it is necessary to use the iterative process in formula 2 to iteratively solve the unknown voxels. In the iterative solution process, only when W(k,q) is not 0, the projection error can be reversely transmitted to correct the voxel value. Such a correction is called an effective correction. Therefore, the number of non-zero elements in W is used to represent the number of effective corrections that the projection can provide. After quantifying the number of unknown voxels that need to be iteratively solved and the number of effective corrections in the iterative process, the ratio of the two is selected as the criterion for camera arrangement optimization. This ratio is called the average effective correction number. Its physical meaning is the average effective correction number for each unknown voxel. The more the average effective correction number, the more accurate the final reconstruction result. And in the iterative process, only the unknown voxels need to be corrected, so the speed of reconstruction calculation can be significantly improved.

[0041] The present invention will be further described and illustrated below in conjunction with the accompanying drawings and specific implementation methods.

[0042] Step 1: Get projections in all possible directions

[0043] Place a camera in turn at all possible camera placement locations and take multiple projections of the target over a period of time.

[0044] Step 2: Preprocess the projection

[0045] Preprocess the projection of the target captured in step 1. For a stable target (such as a laminar flame), the shape of the target will not change over time, so there is no need to preprocess the projection. For a dynamically changing target (such as a turbulent flame), the average projection of the target can be used to represent the fluctuation range of the target. Therefore, the average projection of the target over a period of time is calculated for subsequent calculations.

[0046] Step 3: Determine the distribution range of unknown voxels determined by each projection

[0047] The distribution range of valid voxels is calculated using the projection or average projection of the target obtained in step 1-2. First, according to the distribution of pixel values ​​in the projection, the area on the projection is divided into an imaging area (pixel value is not 0) and a non-imaging area (pixel value is 0). Starting from the pixels in the non-imaging area, the light path is traced in reverse. All voxel values ​​in the measured area space passed by the light path are 0. The remaining voxels whose voxel values ​​cannot be determined are unknown voxels and need to be solved iteratively.

[0048] Step 4: Determine the number of valid corrections for each projection

[0049] According to the relative position relationship between the measured target and the camera, the projection matrix W in this direction can be determined. From the iterative relationship, it can be concluded that an effective correction can only be performed when the elements in W are not 0, so the number of non-zero elements in the W matrix can represent the number of effective corrections.

[0050] Step 5: List all possible camera arrangements

[0051] Arrange and combine the number of available cameras and the number of positions where the cameras can be placed, and list all possible camera arrangements.

[0052] Step 6: Calculate the number of unknown voxels for different camera arrangements

[0053] In step 3, the unknown voxel distribution in different directions is obtained. According to the different camera arrangements in step 5, the intersection of the unknown voxel distribution ranges in different directions is taken to obtain the unknown voxel distribution range determined by multiple cameras.

[0054] Step 7: Calculate the effective number of corrections for different camera arrangements

[0055] In step 4, the effective correction times in different directions are obtained. According to different camera arrangements in step 5, the effective correction times in different directions are summed up to obtain a set of effective correction times determined by the camera arrangements.

[0056] Step 8: Calculate the average number of effective corrections for different camera arrangements

[0057] Calculate the ratio of the total number of correction iterations obtained in step 7 to the number of unknown voxels obtained in step 6. This ratio is called the average effective number of corrections. The physical meaning of this ratio represents the effective number of corrections for each unknown voxel. The larger the ratio, the more corrections are made to the unknown voxels during the iteration process, and the more accurate the reconstruction result is.

[0058] Step 9: Determine the optimal layout

[0059] The arrangement with the largest average number of effective corrections in step 8 is selected as the optimal arrangement.

Claims

1. A three-dimensional tomography camera arrangement optimization method, characterized in that: The steps include: Step 1: Get the projection; Get projections in all possible directions; Step 2: Preprocessing; Step 3: Determine the distribution range of unknown voxels determined by each projection; The step 3 includes calculating the distribution range of valid voxels using the projection of the target to be measured or the average projection obtained in steps 1-2, firstly dividing the area on the projection into an imaging area, i.e., the pixel value is not 0, and a non-imaging area, i.e., the pixel value is 0, according to the distribution of pixel values ​​in the projection; starting from the pixels in the non-imaging area, the light path is traced in reverse, and all voxel values ​​in the measured area space passed by the light path are 0, and the remaining voxels whose voxel values ​​cannot be determined are unknown voxels, which need to be solved iteratively; The specific process of step 3 is as follows: first, the area where the target is located is discretized, and the smallest microelement after discretization is called a voxel. After the voxel passes through the imaging system, it will form a projection on the camera. The smallest microelement in the projection is called a pixel. The relationship between pixels and imaging systems is expressed by the projection equation: Where: P represents the pixel in the projection of the target, k represents the index value of the pixel, F represents the discretized voxel, q represents the index value of the voxel, and Q represents the number of all voxels; W represents the projection weight matrix, W(k,q) represents the contribution value of the p-th voxel to the k-th pixel, and the size of the contribution value is related to the imaging system and the position of the camera and the target. Since there are many 0 elements in W, Equation 1 cannot be solved directly. The solution method is algebraic iteration method: Where: I represents the number of iterations; α represents the relaxation factor; ΔP(k) I represents the difference between the reconstructed projection and the true projection after the Ith iteration; K represents the number of all pixels; The number of voxels is related to the spatial resolution of the target being measured. The higher the resolution, the more voxels need to be solved. In step 3, when the resolution remains unchanged, before iterative solution, the values ​​of some voxels are determined by the values ​​of the pixels in the projection, so as to reduce the amount of calculation in the iterative process; Step 4: Determine the effective number of corrections determined for each projection; Step 5: List all possible camera arrangements; Step 6: Calculate the number of unknown voxels for different camera arrangements; Step 7: Calculate the effective correction times for different camera arrangements; Step 8: Calculate the average effective correction times for different camera arrangements; Step 9: Determine the optimal layout.

2. A three-dimensional tomography camera arrangement optimization method as claimed in claim 1, characterized in that: The step 1 includes placing a camera in turn at all possible camera placement positions, and taking a plurality of projections of the measured target within a period of time.

3. A three-dimensional tomography camera arrangement optimization method as claimed in claim 2, characterized in that: The step 2 includes: for a stable target to be measured, no processing is performed; for a dynamically changing target to be measured, an average projection of the target to be measured over a period of time is calculated for subsequent calculations.

4. A three-dimensional tomography camera arrangement optimization method as claimed in claim 3, characterized in that: The step 4 includes determining the projection matrix W in the direction according to the relative position relationship between the measured target and the camera, and it is concluded from the iterative relationship that an effective correction can be performed only when the elements in W are not 0.

5. A three-dimensional tomography camera arrangement optimization method as claimed in claim 4, characterized in that: The step 5 includes arranging and combining the number of available cameras and the number of positions for placing the cameras, and listing all possible camera arrangements.

6. A three-dimensional tomography camera arrangement optimization method as claimed in claim 5, characterized in that: The step 6 includes, in step 3, obtaining the unknown voxel distribution in different directions, taking the intersection of the unknown voxel distribution ranges in different directions according to the different camera arrangements in step 5, and obtaining the unknown voxel distribution range jointly determined by multiple cameras.

7. A three-dimensional tomography camera arrangement optimization method as claimed in claim 6, characterized in that: The step 7 includes, in step 4, obtaining the effective correction times in different directions, summing the effective correction times in different directions according to different camera arrangements in step 5 to obtain a set of effective correction times determined by the camera arrangement, The step 8 includes calculating the ratio of the total number of correction iterations obtained in step 7 to the number of unknown voxels obtained in step 6. This ratio is called the average effective number of corrections. The step 9 includes selecting the arrangement with the largest average number of effective corrections in step 8 as the optimal arrangement.

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