A multi-camera calibration method and system based on three-dimensional background-oriented schlieren

Abstract

The application discloses a multi-camera calibration method and system based on three-dimensional background-oriented schlieren, and belongs to the field of flow display and measurement. The method comprises the following steps: defining a world coordinate system; arranging a measurement system and a calibration device; performing single target calibration on each camera to obtain internal parameters of each camera; performing double target calibration on adjacent cameras to obtain relative external parameters of the adjacent cameras; converting the relative external parameters of the adjacent cameras to obtain the poses of the cameras in a reference camera coordinate system; calibrating the external parameters of the reference camera, i.e. calibrating the external parameters of the reference camera in the world coordinate system; calculating the positions and postures of all the cameras in the world coordinate system, and combining the internal parameters to establish the connection between a pixel coordinate system and the world coordinate system, thereby completing the multi-camera calibration. The application solves the problems of low calibration precision of multi-camera external parameters, excessive accumulation of single-direction correlation conversion errors and large overall error in the prior art when arranging large-angle cameras.

Description

Technical Field

[0001] This invention belongs to the field of mobile display and measurement, and specifically relates to a multi-camera calibration method and system based on three-dimensional background guided schlieren. Background Technology

[0002] Background-oriented schlieren (BOS) is increasingly widely used in flow field measurement due to its advantages such as simplicity, quantitative calculation, and no particle seeding. However, similar to traditional schlieren methods, BOS displays the integral effect of light rays passing through the flow field. To obtain three-dimensional quantitative information about the flow field, researchers proposed three-dimensional background-oriented schlieren. Multiple cameras and corresponding background patterns are arranged in a plane perpendicular to the flow direction, simultaneously capturing and recording the flow from different angles. A three-dimensional reconstruction algorithm is then used to obtain the three-dimensional flow field data. Multi-camera calibration is a crucial step, and the accuracy of the calibration results directly affects the accuracy of the three-dimensional reconstructed flow field.

[0003] In tomographic measurement systems like 3D background-guided schlieren, where the camera arrangement angle is large, it is often difficult to ensure that the calibration plate is simultaneously and completely imaged by all cameras. It is impossible to obtain the extrinsic parameters of all cameras in a unified world coordinate system through a single calibration; therefore, multi-camera calibration needs to be decomposed into multiple adjacent camera bi-target calibrations. Due to inherent limitations, 3D background-guided schlieren suffers from defocusing issues, where all cameras focus on the corresponding background pattern rather than the flow field region being measured. This results in relatively blurry calibration images taken at the flow field location, posing challenges to multi-camera calibration.

[0004] Currently, there are two main calibration methods. Method 1 involves first focusing all cameras on the flow field under test to calibrate its extrinsic parameters, and then refocusing the cameras on the background pattern to calibrate its internal parameters. The advantage of this method is that the calibration plate remains at the camera's focal point, effectively avoiding defocusing. However, the disadvantage is that the camera inevitably touches itself during refocusing, causing changes in extrinsic parameters. Method 2 involves keeping the cameras focused on the background pattern and placing the calibration plate on the background pattern to calibrate internal parameters and on the flow field under test to calibrate extrinsic parameters. This method eliminates the need for refocusing, but the calibration of all camera extrinsic parameters is performed on the relatively blurred flow field under test, resulting in lower detection accuracy for checkerboard corner points. Furthermore, both methods use unidirectional conversion in the conversion of extrinsic parameters between adjacent cameras, leading to accumulated errors that affect calibration accuracy after multiple conversions. With the increasing demands for accuracy in 3D reconstructed flow fields, the number of cameras involved in reconstruction is generally more than twelve. Therefore, it is necessary to develop new multi-camera calibration methods based on 3D background-guided schlieren to reduce calibration errors. Summary of the Invention

[0005] The technical problem to be solved:

[0006] To overcome the shortcomings of existing technologies, this invention provides a multi-camera calibration method based on 3D background guided schlieren, used to calculate the internal parameters and external parameters of multiple cameras in a 3D background guided schlieren measurement system in a unified world coordinate system. This invention solves the problems of low calibration accuracy of external parameters of multiple cameras when arranged at large angles, excessive accumulation of single-direction correlation transformation errors, and large overall errors in existing technologies.

[0007] The technical solution of this invention is: a multi-camera calibration method based on three-dimensional background guided schlieren, the specific steps of which are as follows:

[0008] Define the world coordinate system;

[0009] A measurement system and calibration device are set up; the measurement system consists of multiple cameras, and the calibration device consists of multiple calibration plates with calibration patterns.

[0010] Single-target positioning is performed on each camera to obtain the internal parameters of each camera;

[0011] Based on the internal parameters of each camera, dual-target positioning is performed on adjacent cameras to obtain the relative external parameters of adjacent cameras;

[0012] The pose of each camera in the reference camera coordinate system is obtained by transforming the relative external parameters of adjacent cameras.

[0013] Based on the camera's internal parameters, the external parameters of the reference camera are calibrated, that is, the external parameters of the reference camera in the world coordinate system are calibrated.

[0014] Based on the external parameters of the reference camera in the world coordinate system, the pose of the reference camera in the world coordinate system is calculated; then the poses of each camera in the reference camera coordinate system are transformed to the world coordinate system to obtain the position and orientation of all cameras in the world coordinate system. The relationship between the pixel coordinate system and the world coordinate system is established by combining the internal parameters to complete the multi-camera calibration.

[0015] A further technical solution of the present invention is: the world coordinate system is determined according to the required flow field region, the midpoint of the flow initiation section is taken as the origin, the flow direction is the x-axis, and the y-axis and z-axis directions are determined according to the right-hand rule.

[0016] A further technical solution of the present invention is: multiple cameras of the measurement system are located in the same plane and arranged circumferentially, and the plane is perpendicular to the direction of fluid flow.

[0017] A further technical solution of the present invention is: the calibration pattern of the calibration plate is a two-dimensional checkerboard, which is flatly attached to the calibration plate; the unit grid size of the checkerboard is determined according to the measurement distance, the larger the measurement distance, the larger the unit grid size, and the smaller the measurement distance, the smaller the unit grid size.

[0018] A further technical solution of the present invention is as follows: the method for single-target calibration of each camera is as follows: each calibration plate is placed on the background pattern plane of each camera's focus, and no less than 20 calibration images of randomly placed plates in different positions and postures are taken; the Zhang Zhengyou calibration method is adopted, with the calibration plate plane as the XY plane and the direction perpendicular to the calibration plate as the Z direction, to establish a calibration plate coordinate system. Then, the Z coordinate of the calibration pattern on the calibration plate is 0. Combining the physical dimensions of the calibration pattern cell, the coordinates (X, Y, Z) of its corner points are obtained. Q ,Y Q ,0); Detect the corner points of the calibration pattern on the calibration image, form a set of equations about the imaging model parameters, and optimize the solution to obtain the internal parameters of each camera.

[0019] A further technical solution of the present invention is as follows: the method for dual-target calibration of adjacent cameras is to place the calibration plate at the common field of view of the adjacent cameras closest to the background pattern, which is between the flow field to be measured and the background pattern, to obtain a calibration image that is clearer than that at the flow field to be measured; using the calibration plate that was captured together as the associated coordinate system, the internal parameters of each camera are used as known information to calculate the relative external parameters of the adjacent cameras.

[0020] A further technical solution of the present invention is: performing dual-target timing with adjacent cameras, the position determination of the calibration plate is related to the measurement system settings, that is, the smaller the distance between adjacent cameras, the closer the calibration plate is to the background plate, and the larger the distance between adjacent cameras, the closer the calibration plate is to the flow field region to be measured.

[0021] A further technical solution of the present invention is: the method for obtaining the pose of each camera in the reference camera coordinate system is to obtain the camera pose in the reference camera coordinate system by transforming the relative extrinsic parameters of adjacent cameras. L b =L a -O b T ab , of which O a L a and O b L b The poses of camera a and camera b are respectively, R ab and T ab These are the relative rotation matrix and relative displacement vector between camera a and camera b, respectively. The camera located in the middle is selected as the reference camera. In the reference camera coordinate system, the external parameters of the adjacent cameras are transformed to the right and left respectively to obtain the pose of each camera in the reference camera coordinate system.

[0022] A multi-camera calibration system based on 3D background guided schlieren includes a measurement system consisting of multiple cameras, a calibration device consisting of multiple calibration plates, and a host computer;

[0023] The multiple cameras are located in the same plane and arranged circumferentially, and this plane is perpendicular to the direction of fluid flow;

[0024] The calibration plate has calibration patterns, and the unit size of the calibration patterns is determined according to the measurement distance. The larger the measurement distance, the larger the unit size, and the smaller the measurement distance, the smaller the unit size.

[0025] The host computer is used for the acquisition and processing of measurement data.

[0026] A further technical solution of the present invention is: the host computer includes at least one processor and a memory communicatively connected to the at least one processor; wherein, the memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to execute the multi-camera calibration method based on three-dimensional background guided schlieren.

[0027] Beneficial effects

[0028] The beneficial effects of this invention are as follows: Applying the multi-camera calibration method based on 3D background-guided schlieren mapping, this invention effectively avoids defocusing and excessive error accumulation during external parameter conversion without adjusting the camera focal length, thus improving the accuracy of multi-camera calibration. By introducing a "reference camera," the calibration of the external parameters relative to the multi-cameras and the calculation of camera pose in the world coordinate system are separated. Specifically, during external parameter calibration, the calibration plate can be located not at the flow field to be measured, but at the common field of view of the adjacent camera closest to the background pattern. This location, between the flow field to be measured and the background pattern, depends on the tomographic measurement system settings and allows for a clearer calibration image compared to the flow field to be measured. Finally, only the "reference camera" is used to calculate the external parameters relative to the flow field to be measured, and the "reference camera" is used to convert the external parameters of all cameras to the world coordinate system. This reduces the external parameter calibration process, which involves relatively blurry calibration images, from all camera pairs to a single camera. With the "reference camera" selected in the middle position, multi-camera external parameter conversion is performed sequentially to the right and left, halving the error accumulation process. Attached Figure Description

[0029] Figure 1 This is a schematic flowchart of a multi-camera calibration method based on three-dimensional background guided schlieren, which is an optional embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram of an optional single-target positioning experiment setup for each camera according to an embodiment of the present invention;

[0031] Figure 3 This is a schematic diagram of an optional adjacent camera dual-target positioning experiment setup according to an embodiment of the present invention;

[0032] Figure 4 This is a schematic diagram of an optional experimental setup for calibrating the external parameters of a reference camera according to an embodiment of the present invention;

[0033] Figure 5 This is a schematic diagram of an optional calibration plate 1 according to an embodiment of the present invention;

[0034] Figure 6 This is a schematic diagram of an optional calibration plate 2 according to an embodiment of the present invention;

[0035] Figure 7 This is a schematic diagram of an optional multi-camera calibration result according to an embodiment of the present invention.

[0036] Explanation of reference numerals in the attached figures: 1. Reference camera; 2. Left camera of the reference camera; 3. Right camera of the reference camera; 4. Flow start section of the flow field to be measured; 5. Calibration plate 1 with a grid size of 15mm; 6. Calibration plate 2 with a grid size of 10mm; 7. Background plate with random dot pattern printed on it; 8. Camera 5 in the embodiment of the three-dimensional background-guided schlieren measurement system; 9. Camera 6 in the embodiment of the three-dimensional background-guided schlieren measurement system; 10. Camera 7 in the embodiment of the three-dimensional background-guided schlieren measurement system. Detailed Implementation

[0037] The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0038] In existing 3D background-guided schlieren camera calibration techniques, one approach is to keep the calibration plate at the camera's focal point, effectively avoiding defocusing. However, this inevitably leads to camera contact during refocusing, altering extrinsic parameters. Another approach involves calibrating all camera extrinsic parameters at the relatively blurred flow field, resulting in low accuracy for checkerboard corner detection. Furthermore, both methods employ unidirectional transformations in adjacent camera extrinsic parameter conversion, leading to accumulated errors and impacting calibration accuracy after multiple conversions. Therefore, this invention provides a multi-camera calibration method based on 3D background-guided schlieren, placing the calibration plate on the background pattern plane where each camera is focused to calibrate its internal parameters. The multi-camera calibration problem is decomposed into multiple adjacent camera dual-target calibrations. The calibration plate is placed at the common field of view of the adjacent cameras closest to the background pattern. Using the jointly captured calibration plate as the associated coordinate system, the relative extrinsic parameters of adjacent cameras are calculated. The middle camera is selected as the reference camera, and the extrinsic parameters of adjacent cameras are sequentially transformed to the right and left within the reference camera coordinate system to obtain the pose of each camera in the reference camera coordinate system. Place the calibration plate at the center of the flow field to be measured, and calibrate the extrinsic parameters of the reference camera in the calibration plate coordinate system. Based on the extrinsic parameters of the reference camera and the relative position of the calibration plate and the origin of the world coordinate system, calculate the pose of the reference camera in the world coordinate system. Using the reference camera, transform the poses of each camera to the world coordinate system to obtain the position and attitude of all cameras in the world coordinate system. Combine this with the intrinsic parameters to establish a relationship between the pixel coordinate system and the world coordinate system, completing the multi-camera calibration. The specific steps are as follows:

[0039] Step 1: Define the world coordinate system. Based on the flow field region to be measured, determine the origin and coordinate axis directions of the world coordinate system. Generally, the midpoint of the flow initiation section is taken as the origin, the flow direction is the x-axis, and the y-axis and z-axis directions are determined according to the right-hand rule.

[0040] Step two: Set up the measurement system and calibration device. Fix multiple cameras on the measurement system, each focusing on its corresponding background pattern. Use a two-dimensional checkerboard pattern with known grid dimensions for each square, and attach it flat to the calibration plate. To improve calibration accuracy, ensure the grid dimensions are accurate and the calibration plate is flat.

[0041] Specifically, the measurement system has multiple cameras located in the same plane and arranged circumferentially, and this plane is perpendicular to the direction of fluid flow.

[0042] Specifically, the calibration pattern of the calibration plate is a two-dimensional checkerboard, which is flatly attached to the calibration plate; the unit size of the checkerboard is determined according to the measurement distance, the larger the measurement distance, the larger the unit size, and the smaller the measurement distance, the smaller the unit size.

[0043] Step 3: Individual camera calibration. Place the calibration board on the background pattern plane that each camera is focusing on, and take no fewer than 20 calibration images from different positions and orientations. Using Zhang Zhengyou's calibration method, establish a calibration board coordinate system with the calibration board plane as the XY plane and the direction perpendicular to the calibration board as the Z direction. The Z coordinate of the checkerboard grid will then be 0. Combining this with the physical dimensions of each grid, the coordinates of its corner points (X, Y, Z) can be determined. Q ,Y Q (0). Detect the checkerboard corner points on the calibration image to form a system of equations about the imaging model parameters. Optimize and solve these equations to obtain the camera's intrinsic parameters.

[0044] Step 4: Adjacent Camera Dual-Target Calibration. Place the calibration plate at the common field of view of the adjacent cameras closest to the background pattern. This location lies between the flow field to be measured and the background pattern; the specific position depends on the tomographic measurement system settings. This allows for a clearer calibration image compared to the flow field to be measured. Using the jointly captured calibration plate as the associated coordinate system, and considering the known information of the internal parameters of each camera obtained in Step 3, calculate the relative external parameters of the adjacent cameras.

[0045] Specifically, when performing dual-target timing with adjacent cameras, the position of the calibration plate is determined by the measurement system settings. That is, the smaller the distance between adjacent cameras, the closer the calibration plate is to the background plate, and the larger the distance between adjacent cameras, the closer the calibration plate is to the flow field region to be measured.

[0046] Step 5, Extrinsic parameter transformation between adjacent cameras. The camera pose in the reference camera coordinate system is obtained through relative extrinsic parameter transformation between adjacent cameras. L b =L a -O b T ab , of which O a L a and O b L b The poses of camera a and camera b are respectively, R ab and T ab These are the relative rotation matrix and relative displacement vector between camera a and camera b, respectively. The middle camera is selected as the reference camera. In the reference camera coordinate system, the external parameters of the adjacent cameras obtained in step four are transformed sequentially to the right and left to obtain the pose of each camera in the reference camera coordinate system.

[0047] Step 6: Calibrate the external parameters of the reference camera. Place the calibration plate at the center of the flow field to be measured. The internal parameters of the reference camera obtained in Step 3 are known information. Calibrate the external parameters of the reference camera in the world coordinate system.

[0048] Step 7, World Coordinate System Pose Transformation. Based on the external parameters of the reference camera in the world coordinate system and the relative position of the calibration board to the origin of the world coordinate system, calculate the pose of the reference camera in the world coordinate system. Using the pose of the reference camera in the world coordinate system, transform the poses of each camera in the reference camera coordinate system to the world coordinate system, obtaining the position and orientation of all cameras in the world coordinate system. Combine this with the internal parameters to establish a connection between the pixel coordinate system and the world coordinate system, completing the multi-camera calibration.

[0049] Therefore, this invention effectively avoids defocusing without adjusting the camera focal length, reduces reprojection error, avoids excessive error accumulation during external parameter conversion, and improves the calibration accuracy of multi-camera systems.

[0050] The above technical solution will be further explained below with reference to the accompanying drawings:

[0051] See Figures 1-4 Based on Zhang Zhengyou's calibration method and the principle of binocular camera calibration, the multi-camera calibration problem is decomposed into multiple adjacent camera binocular calibrations. First, the calibration board is placed on the background pattern plane where each camera is focused to calibrate the internal parameters of each camera. Second, the calibration board is placed at the common field of view of the adjacent cameras closest to the background pattern, and the relative external parameters of the adjacent cameras are calculated using the calibration board as the associated coordinate system. Finally, the calibration board is placed at the center of the flow field to be measured to calibrate the external parameters of the reference camera in the calibration board coordinate system.

[0052] A specific embodiment of the present invention includes the following steps.

[0053] Step 1: Define the world coordinate system. Based on the flow field region to be measured, determine the origin and coordinate axis directions of the world coordinate system. Generally, the midpoint of the flow initiation section is taken as the origin, the flow direction is the x-axis, and the y-axis and z-axis directions are determined according to the right-hand rule.

[0054] Step two: Set up the measurement system and calibration device. The number of cameras is determined according to experimental needs. Theoretically, the more cameras, the better the reconstruction effect, but the corresponding cost and computational load will also increase. Usually, 8 to 24 industrial cameras are selected. The distance from the camera to the flow field to be measured is an important issue in background-guided schlieren imaging. Too close a distance will lead to low sensitivity, while too far a distance will reduce spatial resolution. It needs to be determined based on the specific range of the flow field to be measured, combined with experience and experiments. In this embodiment, 14 industrial cameras and 4 background boards printed with random dot patterns are used. The 14 industrial cameras are divided into 4 groups, forming an octagonal structure together with the 4 background boards. The distance from the camera to the flow field to be measured is 1000mm. The 14 cameras of the measurement system are fixed so that each camera is focused on the corresponding background board. Two checkerboard patterns are generated by the program, each consisting of 12×9 squares, with each square measuring 15mm and 10mm respectively. These are flatly attached to a 10mm thick acrylic plate as calibration plate 1 and calibration plate 2. Calibration plate 1 is placed on or near the background plate for calibration, and calibration plate 2 is placed at the location of the flow field to be measured for calibration.

[0055] Step 3: Individual camera calibration. Place calibration plate 1 on the background plate for each camera's focus, and take at least 20 calibration images from different positions and orientations; in this embodiment, 35 images are taken. Ideally, the calibration plate should appear completely in all four positions of the captured image (top, bottom, left, and right), rather than just in the center, and should be tilted at an appropriate angle, not entirely parallel to the background plate. Using Zhang Zhengyou's calibration method, with the calibration plate plane as the XY plane and the direction perpendicular to the calibration plate as the Z direction, establish a calibration plate coordinate system. The Z coordinate of the checkerboard grid is 0. Combining this with the physical size of each grid (15mm), the coordinates of its corner points (X, Y, Z, Z) can be determined. Q ,Y Q At this point, based on the pinhole camera imaging model, we can obtain:

[0056]

[0057] Among them, Z c Let f be the scale factor, (u,v) be the pixel coordinates, (u0,v0) be the coordinates of the origin of the image coordinate system in the pixel coordinate system, f be the focal length, and dx and dy be the size of each pixel in the X and Y directions, respectively. Let be a rotation matrix. Let K be the displacement vector, K be the camera's intrinsic parameter matrix (determined by the camera itself), and M be the extrinsic parameter matrix (related to the camera's spatial position and rotation). By detecting the checkerboard corner points on the calibration image, a system of equations concerning the imaging model parameters is formed. Optimizing and solving this system yields the camera's intrinsic parameters.

[0058] Step 4, Adjacent Camera Dual-Target Calibration. Place calibration board 1 at the common field of view of the adjacent cameras closest to the background pattern. Using the jointly captured calibration board as the associated coordinate system, and the internal parameters obtained in Step 3 as known information, calculate the relative external parameters of the adjacent cameras. Taking cameras a and b as an example:

[0059] Adjacent cameras a and b simultaneously capture H sets of calibration images of the same calibration plate at different positions and angles. A coordinate system (X, Y, Z) is established with the plane of the calibration plate as the XY plane and the direction perpendicular to the calibration plate as the Z direction. con ,Y con Z con From the camera imaging model, we can obtain:

[0060]

[0061]

[0062] Among them, (u a ,v a ) and (u b ,v b K represents the pixel coordinates of camera a and camera b, respectively. a and K b These are the internal parameter matrices of the two cameras, and Let be the rotation matrix and translation vector of the two cameras relative to the h-th (1≤h≤H) group of calibration board images, respectively. Let be the coordinates of the h-th calibration board image. The relative positional relationship between the two cameras can be solved using the associated calibration board coordinate system, let and For the h-th group of calibration target images, the rotation matrix and translation vector of camera b relative to camera a are:

[0063]

[0064] but:

[0065]

[0066] Right now:

[0067]

[0068] right and The median value is taken and optimized to obtain the rotation matrix and translation vector R of camera b relative to camera a. ab and T ab Similarly, for cameras bc, cd, ..., adjacent camera binocular positioning is performed to obtain the relative external parameters of adjacent cameras in turn.

[0069] Step 5, Transformation of Extrinsic Parameters of Adjacent Cameras. Transform the camera coordinate system back to the world coordinate system to determine the camera's position and orientation in the world coordinate system:

[0070]

[0071] in, Here is the pose rotation matrix. Let M be the pose displacement vector, which is combined to form the camera pose matrix P. Clearly, the camera pose matrix P and the extrinsic parameter matrix M are inverses of each other, i.e., P = M. -1 Therefore, we have:

[0072]

[0073] From equations (6) and (8), we can obtain:

[0074]

[0075] Among them, O a L a and O b L b Let b be the poses of camera a and camera b, respectively. Equation (9) obtains the camera poses through the transformation of the relative external parameters of adjacent cameras. Taking camera a as the reference camera, the poses of cameras b, c, ... to the right of camera a and camera b to the left of camera a are respectively... ′ c ′ ...The relative external parameters of adjacent cameras are transformed to obtain the poses of all cameras in the coordinate system of the reference camera a. In this embodiment, camera 6 is selected as the reference camera. Adjacent cameras are calibrated and transformed to the left and right sides respectively. The right side sequence is: 6-5, 5-4, 4-3, 3-2, 2-1, and the left side sequence is: 6-7, 7-8, 8-9, 9-10, 10-11, 11-12, 12-13, 13-14.

[0076] Step 6: Calibrate the external parameters of the reference camera. Place calibration plate 2 at the center of the flow field to be measured. The internal parameters of the reference camera obtained in step 3 are known information. Calibrate the external parameters R6 and T6 of the reference camera in the coordinate system of calibration plate 2.

[0077] Step 7, World Coordinate System Pose Transformation. Based on the external parameters R6 and T6 of the reference camera and the relative position of calibration board 2 to the origin of the world coordinate system, calculate the poses O6 and L6 of the reference camera 6 in the world coordinate system. Using the reference camera, transform the poses of each camera to the world coordinate system to obtain the position and orientation of all cameras in the world coordinate system. Combine this with the internal parameters to establish a connection between the pixel coordinate system and the world coordinate system, completing the multi-camera calibration.

[0078] Table 1 shows the multi-camera calibration results of the three-dimensional background-guided schlieren measurement system in this embodiment. The data volume of all 14 cameras is large, so only the parameter information of camera 5, camera 6 and camera 7 is listed.

[0079] Table 1. Multi-camera calibration results of the 3D background-guided schlieren measurement system

[0080]

[0081] Figure 7 The spatial distribution of cameras, plotted using multi-camera calibration of external parameters, is presented, with the center of the flow field under test at the origin of the world coordinate system. As shown in the figure, the 14 cameras are divided into four groups, each group roughly aligned along a straight line in the YZ plane, with the camera optical axes pointing towards the origin. The calibration distance (Z-component of the displacement vector) from camera 5 to the world coordinate origin plane is 1047.3 mm, which is essentially consistent with the design distance of 1000.0 mm. The average reprojection error is approximately 0.24 pixels, and the camera internal parameters also exhibit high calibration accuracy. This demonstrates that the proposed multi-camera calibration method can accurately solve for the spatial position and rotational attitude of multiple cameras with large included angles.

[0082] To verify that the calibration results obtained at the "common field of view of the adjacent cameras closest to the background pattern" in step four are more accurate than those at the "flow field under test," Table 2 shows a comparison of the average reprojection error of camera 6 when taking pictures of the same type of calibration board and the same number of calibration images at the two positions. It can be seen that the average reprojection error of camera 6 is significantly lower at the "common field of view of the adjacent cameras closest to the background pattern."

[0083] Table 2 shows the average reprojection error of camera 6 at different locations.

[0084]

[0085] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A multi-camera calibration method based on 3D background guided schlieren, characterized in that... The specific steps are as follows: Define the world coordinate system; A measurement system and calibration device are arranged; the measurement system consists of multiple cameras, and the calibration device consists of multiple calibration plates with calibration patterns; the multiple cameras of the measurement system are located in the same plane and arranged circumferentially, and this plane is perpendicular to the direction of fluid flow. Single-target positioning is performed on each camera to obtain the internal parameters of each camera; Based on the internal parameters of each camera, dual-target calibration is performed on adjacent cameras to obtain the relative external parameters of the adjacent cameras. The method for dual-target calibration of adjacent cameras is as follows: the calibration board is placed at the common field of view of the adjacent cameras closest to the background pattern, which is between the flow field to be measured and the background pattern, to obtain a clearer calibration image than the flow field to be measured. Using the jointly captured calibration board as the associated coordinate system, the internal parameters of each camera are used as known information to calculate the relative external parameters of the adjacent cameras. When performing dual-target calibration of adjacent cameras, the position of the calibration board is related to the measurement system settings, that is, the smaller the distance between adjacent cameras, the closer the calibration board is to the background board, and the larger the distance between adjacent cameras, the closer the calibration board is to the flow field region to be measured. The poses of each camera in the reference camera coordinate system are obtained by transforming the relative extrinsic parameters of adjacent cameras. The method for obtaining the poses of each camera in the reference camera coordinate system is to obtain the camera poses in the reference camera coordinate system through the transformation of the relative extrinsic parameters of adjacent cameras. , ,in, , and , Let A and B be the poses of camera A and camera B, respectively. and These are the relative rotation matrix and relative displacement vector between camera a and camera b, respectively; the camera located in the middle is selected as the reference camera, and the external parameters of the adjacent cameras are transformed to the right and left in the reference camera coordinate system to obtain the pose of each camera in the reference camera coordinate system; Based on the camera's internal parameters, the external parameters of the reference camera are calibrated, that is, the external parameters of the reference camera in the world coordinate system are calibrated. Based on the external parameters of the reference camera in the world coordinate system, the pose of the reference camera in the world coordinate system is calculated; then the poses of each camera in the reference camera coordinate system are transformed to the world coordinate system to obtain the position and orientation of all cameras in the world coordinate system. The relationship between the pixel coordinate system and the world coordinate system is established by combining the internal parameters to complete the multi-camera calibration.

2. The multi-camera calibration method based on three-dimensional background guided schlieren according to claim 1, characterized in that: The world coordinate system is determined based on the required flow field region. The origin is taken as the midpoint of the flow initiation section, the flow direction is the x-axis, and the y-axis and z-axis directions are determined according to the right-hand rule.

3. The multi-camera calibration method based on three-dimensional background guided schlieren according to claim 1, characterized in that: The calibration pattern of the calibration plate is a two-dimensional checkerboard, which is flatly attached to the calibration plate; the unit size of the checkerboard is determined according to the measurement distance. The larger the measurement distance, the larger the unit size, and the smaller the measurement distance, the smaller the unit size.

4. The multi-camera calibration method based on three-dimensional background guided schlieren according to claim 1, characterized in that: The method for single-target calibration of each camera is as follows: each calibration plate is placed on the background pattern plane that each camera is focusing on, and at least 20 calibration images are taken at randomly placed positions and in different postures; the Zhang Zhengyou calibration method is used, with the calibration plate plane as the XY plane and the direction perpendicular to the calibration plate as the Z direction, to establish a calibration plate coordinate system. Then, the Z coordinate of the calibration pattern on the calibration plate is 0. Combined with the physical dimensions of the calibration pattern cell, the coordinates of its corner points are obtained. The calibration pattern corner points on the calibration image are detected, forming a set of equations about the imaging model parameters. The internal parameters of each camera can be obtained by optimizing and solving these equations.

5. A multi-camera calibration system based on 3D background guided schlieren, characterized in that: It includes a measurement system consisting of multiple cameras, a calibration device consisting of multiple calibration plates, and a host computer; used to implement the multi-camera calibration method based on three-dimensional background guided schlieren as described in any one of claims 1-4; The multiple cameras are located in the same plane and arranged circumferentially, and this plane is perpendicular to the direction of fluid flow; The calibration plate has calibration patterns, and the unit size of the calibration patterns is determined according to the measurement distance. The larger the measurement distance, the larger the unit size, and the smaller the measurement distance, the smaller the unit size. The host computer is used for the acquisition and processing of measurement data.

6. The multi-camera calibration system based on three-dimensional background guided schlieren according to claim 5, characterized in that: The host computer includes at least one processor and a memory communicatively connected to the at least one processor; wherein the memory stores a computer program executable by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to execute the multi-camera calibration method based on 3D background guided schlieren.

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