A large field of view camera light ray calibration method and system based on polynomial fitting

Abstract

A large field of view camera light ray calibration method and system based on polynomial fitting, the method is that the camera and the calibration board rigid tooling are respectively provided with measurement targets, a fixed connection coordinate system is established, and an external high-precision device such as a laser tracker is used to directly measure the pose between the coordinate systems, and the decoupling of the pose error and the image algorithm is realized. A plurality of calibration board images are collected, a global polynomial curved surface fitting is respectively performed on the sparse feature corner points of each image, a continuous analytical mapping of pixels to three-dimensional space is established, and then a plurality of three-dimensional points corresponding to the same pixel are subjected to spatial straight line fitting, so that the accurate light ray equation of the pixel is obtained. The calibration result is stored based on the camera target seat coordinate system, and when actually measuring, only the conversion relationship between the coordinate system and the world coordinate system needs to be measured again, so that the calibration result can be directly migrated and used. The application is suitable for any complex imaging system, and has the advantages of high precision, strong universality, good robustness and outstanding engineering practicability.

Description

Technical Field

[0001] This invention belongs to the field of precision optical measurement and machine vision technology, specifically relating to a method and system for ray calibration of large field-of-view cameras based on polynomial fitting. This method is particularly suitable for vision measurement systems that require extremely high accuracy in camera ray direction, such as phase deflection measurement, structured light 3D imaging, and vision-guided precision assembly and inspection. It provides a universal, high-precision ray direction calibration solution for any imaging optical system (including systems with significant aberrations or using off-center projection models) that is independent of specific parameterized models. Background Technology

[0002] In precision measurement systems such as surface deflection measurement and structured light 3D reconstruction, the accuracy of camera ray calibration directly affects the overall measurement accuracy of the system. Traditional camera calibration models are mainly divided into two categories: parametric pinhole imaging models and non-parametric ray models. Among them, Zhang Zhengyou's calibration method based on the pinhole imaging model performs well under conventional perspective imaging conditions, but for scenarios with significant optical aberrations or using non-central projection imaging systems such as telecentric lenses and light field cameras, model errors often lead to a decrease in calibration accuracy. Calibration methods based on ray models do not rely on specific optical parametric models, treating the camera as a "black box" and achieving calibration by establishing a mapping relationship between pixels and rays in 3D space, thus exhibiting better adaptability to complex imaging systems.

[0003] However, existing ray calibration methods still face several technical challenges in their development towards higher precision and practicality: ① Calibration accuracy is constrained by image algorithms: Existing methods often rely on multiple calibration board images, estimating the relative pose between calibration boards through geometric constraints between feature points. This process tightly couples the final calibration accuracy with the quality of image feature extraction and the performance of optimization algorithms. Its accuracy is easily affected by image noise, feature point distribution, and numerical optimization stability, thus limiting its application in metrological high-precision applications. ② Insufficient locality and smoothness in spatial mapping construction: After obtaining the correspondence of sparse feature points, existing methods typically use local interpolation based on discrete point sets to estimate the spatial position of non-feature pixels. This type of method works well in regions with dense feature points, but it is prone to increased interpolation errors and unsmooth mapping results at the edges of the field of view or in regions with sparse features, which may lead to undesirable fluctuations in ray direction fitting. ③ Complex calibration process and lack of system integration: To obtain high-precision pose estimation, existing methods often require strict control over the placement of calibration boards, image acquisition conditions, and the consistency of feature extraction. In practice, factors that lead to a decline in image quality or unstable feature extraction can directly affect the repeatability and accuracy of calibration results, placing high demands on the operator's experience and the experimental environment. In addition, camera calibration results cannot be easily transferred to a new measurement system.

[0004] Therefore, a camera light calibration method that can ensure high accuracy while possessing better adaptability, stability, and ease of operation is still needed to support the further development and application of various precision vision measurement systems. Summary of the Invention

[0005] To address the problems of existing camera calibration techniques, such as strong dependence on image algorithms, uneven spatial mapping, complex calibration processes, and difficulty in transferring results, this invention provides a polynomial-based method and system for calibrating large field-of-view camera ray models. This method involves photographing a target with known 3D coordinates at different locations, using a polynomial to perform global surface fitting on the pixel-3D coordinate relationship within the camera's field of view at each location, and then performing spatial line fitting on multiple 3D points corresponding to each pixel. This yields the ray equation for each pixel, achieving high-precision, robust, and highly engineering-applicable camera ray model calibration.

[0006] The technical solution of the present invention is as follows:

[0007] A method for ray calibration of a large field-of-view camera based on polynomial fitting, characterized by the following steps:

[0008] S1. Establishment of external measurement benchmarks

[0009] Establish a calibration board pixel coordinate system {P}, with its origin located at the reference corner point of the calibration board feature pattern. The X-axis is aligned with the row direction of the feature pattern, the Y-axis is aligned with the column direction, and the Z-axis is perpendicular to the calibration board plane. For a calibration board with periodic features (such as a checkerboard pattern), the pixel coordinates (u) of any feature corner point are... P , v P , 0) is calculated based on its row and column indices (i, j) in the pattern and the known physical spacing d of the feature points, i.e., u P = j·d, v P = i·d.

[0010] Establish a calibration plate target coordinate system {S}, with its origin at one of the centers of at least three non-collinear target spheres on the rigid fixture of the calibration plate, the X-axis pointing from the origin to the center of the second target sphere, the Z-axis being the normal vector of the plane determined by the centers of the three target spheres, and the Y-axis being determined by the right-hand rule.

[0011] Establish a camera target coordinate system {C}, with its origin at one of the centers of at least three non-collinear target spheres on the rigid support of the camera, the X-axis pointing from the origin to the center of the second target sphere, the Z-axis being the normal vector of the plane determined by the centers of the three target spheres, and the Y-axis being determined by the right-hand rule.

[0012] Using high-precision external measuring equipment, the static transformation matrix T is solved by simultaneously measuring the physical feature points (such as the intersection of crosshairs, special markers, etc.) with known pixel coordinates on the calibration board and the target ball center coordinates in the calibration board target coordinate system {S}, and then using the least squares method to fit and solve. {P→S} The statement is as follows:

[0013]

[0014] Where R {P→S} It is a 3×3 rotation matrix, t {P→S} It is a 3×1 translation vector, 0 1×3 Represents a 1×3 zero vector;

[0015] S2. Multi-location data acquisition

[0016] Keeping the camera to be calibrated fixed, move the calibration plate to N different poses within the camera's field of view, among which... ;

[0017] For each pose , Perform the following operations:

[0018] S2.1 Using a high-precision external measuring device independent of the camera, the spatial positions of feature points of all current first and second measurement targets are directly measured, and the dynamic transformation matrix of the current calibration plate target coordinate system {S} relative to the camera target coordinate system {C} is calculated based on the measurement results. ;

[0019] S2.2 Acquire images of the calibration board and extract the pixel coordinates of each feature corner point. ;

[0020] S2.3 Calculate the three-dimensional coordinates of each feature corner point in the camera target coordinate system {C}. The formula is as follows:

[0021] S3. Global coordinate fitting based on polynomials

[0022] For each pose n, in pixel coordinates As the independent variable, in the corresponding three-dimensional coordinates in the {C} system As the dependent variable, independent polynomial surface fitting is performed on the X, Y, and Z coordinates respectively:

[0023]

[0024] Among them: Z k (u c , v c) is the k-th polynomial in pixel coordinates (u c , v c The value at ) , , The first The fitting coefficients of the X, Y, and Z components corresponding to each acquisition are obtained by the least squares method.

[0025] Using this fitting model, for any pixel coordinates Calculate the coordinates of the corresponding three-dimensional point in the {C} system during this acquisition:

[0026]

[0027] S4. Least squares fitting camera ray model

[0028] For any pixel coordinate (u) c , v c From the mapping function of Nth pose, obtain the N three-dimensional points corresponding to the pixel. ;

[0029] Theoretically, these N points should lie on the spatial ray corresponding to the pixel. A spatial straight line is fitted using the least squares method, such that this line extends to all points. The sum of squared vertical distances is minimized:

[0030]

[0031] To uniquely determine the ray parameters, this invention defines the ray origin O(u) as follows: c , v c ) is an overfitted line perpendicular to the direction vector D(u) c v c The foot of the perpendicular on the plane (e.g., the plane passing through the origin of the camera target coordinate system {C}).

[0032] By solving this optimization problem (e.g., using singular value decomposition), the pixel can be obtained. The corresponding optimal ray parameter O(u) c , v c ) and D(u c , v c );

[0033] In practice, to improve computational efficiency, sparse sampling (e.g., taking a point every M pixels) can be performed on the pixels of the camera image plane for line fitting to construct a sparse ray field. For unsampled pixels, their ray parameters can be obtained by interpolating the ray parameters of their neighboring calibrated pixels. Ultimately, a complete camera ray model is established, thus obtaining the ray field for each camera pixel. The corresponding spatial ray origin O(u) c , v c ) and direction vector D(u c , v c ).

[0034] Furthermore, it also includes S5. Coordinate system migration applications:

[0035] The calibrated ray model based on the {C} system is stored; in the actual measurement system, the transformation matrix T between the {C} system and the world coordinate system {W} is measured using the high-precision external measuring device. {C→W} This allows you to convert the ray model to the world coordinate system for use.

[0036] Furthermore, the high-precision external measuring equipment includes one or more of the following: laser tracker, lidar, total station, photogrammetric system, or coordinate measuring machine.

[0037] Furthermore, the polynomial mapping function uses Zernike polynomials or Legendre polynomials as basis functions, and achieves a continuous analytical expression for arbitrarily complex optical distortions through linear combination of basis functions.

[0038] Furthermore, the calibration plate is a medium or device capable of displaying a preset feature corner pattern.

[0039] Furthermore, the medium is ceramic, metal, or a flat panel coated with a printed pattern; the device is a programmable display device, such as a liquid crystal display, an OLED display, or a projector.

[0040] Furthermore, the feature corner points are checkerboard corner points, circular marker points, or marker points obtained through stripe decoding.

[0041] On the other hand, the present invention also provides a camera ray model calibration system for implementing the above method, characterized in that it includes:

[0042] The calibration plate unit has a preset feature corner point pattern on its surface, and at least three non-collinear first measurement targets are fixedly set on its rigid fixture.

[0043] The camera unit has at least three non-collinear second measurement targets fixedly mounted on its rigid fixture;

[0044] A high-precision external measurement unit, independent of the camera unit, is used to directly measure the spatial positions of feature points of the first and second measurement targets;

[0045] The data processing unit is connected to the camera unit and the high-precision external measurement unit respectively. It is used to receive image data and measurement data, perform coordinate transformation calculations, polynomial mapping function fitting and spatial line fitting, and generate and store the camera ray model.

[0046] Furthermore, the data processing unit communicates in real time with the high-precision external measurement unit to achieve synchronization of measurement data and image acquisition.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] 1) In the field of camera ray calibration, high-precision external measurement equipment (such as laser trackers) is directly introduced to measure the absolute spatial pose of the calibration board and the camera in real time and independently. This design fundamentally eliminates the constraint of image processing algorithms on calibration accuracy, making the benchmark for ray calibration directly traceable to the measurement accuracy (micrometer level) of external equipment, rather than the estimation accuracy (usually pixel level) of image algorithms.

[0049] 2) This invention employs a non-parametric ray model, treating the camera as a "black box," and does not rely on any prior assumptions such as pinhole imaging, telecentricity, or distortion models. By globally fitting the pixel-space mapping relationship using polynomial basis functions (such as Zernike polynomials), this method can accurately describe the ray behavior of arbitrarily complex imaging systems, including those with large distortions and non-central projections (such as light field cameras and astigmatic lenses). It is applicable to various imaging systems with aberrations, telecentric lenses, light field cameras, and other similar features.

[0050] 3) A polynomial is used for global analytical surface fitting. By utilizing the orthogonality and smoothness of the basis functions across the entire image plane, a continuous and differentiable analytical function is constructed from pixel coordinates to points in three-dimensional space. This not only effectively suppresses the influence of single-point measurement noise but also ensures the physical rationality (smooth change) of the light direction field across the entire field of view.

[0051] 4) By establishing and calibrating the camera target coordinate system {C}, all calibration results are rigidly bound to the physical fixture of the camera body. In actual measurement tasks (such as migrating from the laboratory to the production line), it is only necessary to remeasure the transformation relationship between the {C} system and the current world coordinate system {W} using external measuring equipment, and the calibrated high-precision ray model can be reused immediately without repeating the entire complex calibration process. Through the "one-time calibration, anywhere migration" model, the complexity, cycle, and cost of deploying high-precision vision measurement systems are reduced, paving the way for the industrial application of this invention. Attached Figure Description

[0052] Figure 1 This is a schematic diagram of the spatial relationship between the pre-established calibration board pixel coordinate system {P}, calibration board target coordinate system {S}, and camera target coordinate system {C} in an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram of the feature corner point patterns captured by the calibration board at multiple different positions and orientations within the camera's field of view during camera calibration in an embodiment of the present invention.

[0054] Figure 3 This is a schematic diagram of the structure of applying the calibrated camera to the phase deflection measurement system in an embodiment of the present invention;

[0055] Figure 4 The figures show a comparison of the deflection measurement surface shape results obtained using different calibration methods, where: (a) the surface shape result using the traditional calibration method based on the Zhang Zhengyou camera model (RMS=1.45λ), λ=632.8nm; (b) the interferometer measurement result (RMS=1.64λ); (c) the surface shape result after calibration using the method of this invention (RMS=1.61λ); (d) the residual between the traditional method and the interferometer surface shape measurement results (RMS=0.19λ); and (e) the residual between the method of this invention and the interferometer surface shape measurement results (RMS=0.04λ). Detailed Implementation

[0056] The present invention will now be described in detail with reference to the embodiments and accompanying drawings, but this should not be construed as limiting the scope of protection of the present invention.

[0057] A method for ray calibration of a large field-of-view camera based on polynomial fitting includes:

[0058] 1. System pre-configuration and coordinate system establishment

[0059] a) Establish a calibration board pixel coordinate system {P} based on the pixel coordinates of the feature corner points of the calibration board, and obtain the pixel coordinates of each feature corner point. :

[0060] Establish a calibration board pixel coordinate system {P} with the calibration board plane as the XY plane. The origin is the first pixel at the top-left corner of the calibration board's feature corner points. The X-axis is positive along the horizontal direction of the calibration board (from left to right), the Y-axis is positive along the vertical direction of the calibration board (from top to bottom), and the Z-axis is perpendicular to the calibration board plane and points outwards (consistent with a right-handed coordinate system). In the {P} system, the coordinates of any feature corner pixel p on the calibration board can be expressed as: ,in ， These are the column index and row index of that point on the calibration board, respectively.

[0061] b) Set at least three non-collinear measurement targets on the rigid fixture of the calibration plate. The three-dimensional spatial positions of these targets can be directly and accurately acquired by external high-precision measuring equipment (such as a laser tracker). Simultaneously measure the three-dimensional coordinates of feature points of these targets (such as the center of the target sphere, the vertex of the prism, the center of the marker point, etc.) using the high-precision measuring equipment. Select one of the feature points as the origin of the coordinate system. The vector pointing from the origin to the second feature point is selected as the X-axis direction. Calculate the unit normal vector of the plane defined by the origin, the second feature point, and the third feature point as the Z-axis direction. Finally, the right-hand rule is used. Determine the Y-axis direction. After orthogonalizing the three coordinate axes, the calibration plate target coordinate system {S} is obtained.

[0062] c) Set at least three non-collinear measurement targets on the rigid fixture of the camera. Using the same method as in step b, define the camera target coordinate system {C} based on the spatial positions of the feature points of these measurement targets, such as... Figure 1 As shown.

[0063] d) Using third-party measurement equipment (such as a coordinate measuring machine, CMM), accurately pre-calibrate the pose transformation relationship between the calibration board pixel coordinate system {P} and the calibration board target coordinate system {S}. This relationship is expressed using a 4×4 homogeneous transformation matrix T. {P→S} express.

[0064]

[0065] Where R {P→S} It is a 3×3 rotation matrix, t {P→S} It is a 3×1 translation vector, 0 1×3 This represents the zero vector of 1×3. Once calibrated, this transformation relationship remains valid as long as the physical structure of the calibration plate remains unchanged.

[0066] Therefore, for any pixel on the calibration board All can be done through T {P→S} Transform it to the {S} coordinate system:

[0067]

[0068] 2. Multi-location data acquisition

[0069] a) Fix the camera to be calibrated, move the calibration plate to N different positions within the camera's field of view, and change the orientation of the calibration plate, where... ;

[0070] b) For the first Location( ):

[0071] 1) Using high-precision 3D measuring equipment, directly measure the coordinates of all feature points of the measurement targets on the current calibration plate fixture and camera fixture. Based on these coordinates, calculate the pose transformation matrix of the current calibration plate target coordinate system {S} relative to the camera target coordinate system {C}. ;

[0072] 2) The camera captures a pattern on the calibration board with known feature corner points, and extracts the pixel coordinates of each feature corner point on the camera's image plane. ;

[0073] 3) For each feature corner point, its coordinates in the calibration board pixel coordinate system {P} are known to be... , combined and Calculate its three-dimensional coordinates in the camera target coordinate system {C}. :

[0074]

[0075] 3. Global coordinate fitting based on polynomials

[0076] For the nth (n=1,2,...,N) image acquired in step 2, obtain the camera pixel coordinates of all feature corner points. and the corresponding three-dimensional coordinates in the {C} system To reconstruct the mapping relationship of all pixels from sparse feature corner points, for each image... Perform polynomial surface fitting separately:

[0077]

[0078] Among them: Z k (u c , v c ) is the k-th polynomial in pixel coordinates (u c , v c The value at (). , , For the first The set of fitting coefficients corresponding to each sampling is obtained by solving the least squares method.

[0079] Using this fitting model, for any pixel coordinate (u) c , v c This allows us to calculate the corresponding three-dimensional point coordinates during this data acquisition.

[0080]

[0081] 4. Least squares fitting camera ray model

[0082] After step 3, for any pixel (u) on the camera sensor c , v c We obtained N three-dimensional points (in the camera target coordinate system {C}) corresponding to this pixel from N shots taken from N different positions: .

[0083] Theoretically, these N H C A point should lie on the spatial ray corresponding to that pixel. Therefore, we fit a spatial line using the least squares method, such that this line extends to all points. The sum of squared vertical distances is minimized.

[0084]

[0085] By solving this optimization problem, the pixel (u) can be obtained. c , v c The optimal ray parameter O(u) corresponds to ) c , v c ) and D(u c , v c ).

[0086] By iterating through each pixel of the camera and repeating the above line fitting process, a complete camera ray model can be established, thus obtaining the ray model for each camera pixel (u). c , v c The spatial ray origin O(u) corresponding to ) c , v c ) and direction vector D(u c ,v c ).

[0087] Once calibrated, the model remains unchanged indefinitely as long as the camera's optical state remains constant.

[0088] 5. Application of calibration results

[0089] The ray model calibrated using this method is based on the camera target coordinate system {C}. In actual measurement tasks (such as deflection measurement), it is only necessary to use a laser tracker to measure the pose relationship T between the camera target coordinate system {C} and the world coordinate system {W} of the entire measurement system once. {C→W} This allows for easy conversion of all camera light to the world coordinate system:

[0090]

[0091] R {C→W} It is T {C→W}The 3×3 rotation matrix in t {C→W} It is T {C→W} The 3×1 translation matrix in the model allows the ray model to be directly used in the 3D vision measurement of this system without any recalibration process.

[0092]

[0093] in, Represents a three-dimensional point on a ray in the world coordinate system; The world coordinates of the origin of the light ray; is the ray direction vector; t is a scalar parameter along the ray direction; the subscript W indicates the representation in the world coordinate system.

[0094] Example:

[0095] This embodiment uses the calibration of a high-resolution camera for a phase deflection measurement system as an example to illustrate the complete implementation process of the present invention in detail. A 24-inch high-resolution LCD screen (1920×1080 resolution) is used as a dynamic calibration board, and a laser tracker is used as a high-precision external measurement device.

[0096] Step 1. System pre-configuration and coordinate system establishment

[0097] a) Establish the calibration board pixel coordinate system {P}: Display a virtual checkerboard pattern with a known number of rows and columns (e.g., 40×30) in full-screen mode on the LCD screen. Using the plane of this virtual checkerboard pattern as the XY plane, establish the calibration board pixel coordinate system {P}: with the first interior corner point of the top left corner of the virtual checkerboard as the origin O. P The X-axis points to the right along the grid lines (horizontally), the Y-axis points downwards along the columns (vertically), and the Z-axis points outwards perpendicular to the screen plane. The coordinates (u) of each virtual feature corner point in the {P} system are... P , v P , 0) is precisely calculated from the known checkerboard size and screen pixel pitch d.

[0098] b) Establish the calibration plate target coordinate system {S}: Install three non-collinear laser tracker target ball bases on the rigid fixture of the display screen. During calibration, place a standard spherical mirror (SMR) on the base. Use the laser tracker to simultaneously measure the three-dimensional center coordinates of the three SMRs. Take one of the center balls as the origin O. S , to from O S The vector pointing to the second sphere center is the X-axis direction, the unit normal vector of the plane determined by the three sphere centers is the Z-axis direction, and the Y-axis is determined by the right-hand rule, thus establishing the calibration plate target coordinate system {S}.

[0099] c) Establish the camera target coordinate system {C}: On the rigid fixture of the camera to be calibrated, install three non-collinear target ball bases. Using the same method as in step b, establish the camera target coordinate system {C} based on the ball center coordinates measured by the laser tracker.

[0100] d) Calibration conversion relationship T {P→S} After the display screen and tooling are assembled, an offline precision calibration is performed using a high-precision external measuring device (in this embodiment, a high-precision coordinate measuring machine, CMM). The CMM probe performs two types of measurements simultaneously:

[0101] i. Measure physical feature points on the display surface: Measure at least three clearly identifiable points whose pixel coordinates (u...) P , v P Known physical features, such as specific marks at the four corners of the display screen or specially designed cross marks.

[0102] ii. Measure the center of the target ball: Measure the coordinates of the center of the target ball on the fixture (when placing the SMR);

[0103] Using these two sets of measurement data, a spatial fitting algorithm can be used to solve for the fixed pose transformation matrix T between the virtual {P} system on the display screen and the {S} system on the physical fixture. {P→S} Once this relationship is established, it remains valid as long as the physical state of the display screen does not change.

[0104] Step 2. Multi-location data acquisition

[0105] Step 2.1) Fix the camera to be calibrated, keeping its {C} system unchanged.

[0106] Step 2.2) Move the display screen with the fixture, changing its position and orientation approximately 12 different times within the camera's field of view (e.g., ...). Figure 2 (Illustration), denoted as the nth position (n=1,2,...,12).

[0107] Step 2.3) For the nth position:

[0108] 1) External high-precision pose acquisition: Place SMRs on all target sphere bases, and use a laser tracker to simultaneously measure the center coordinates of all SMRs on both the camera fixture and the display fixture. Based on these center coordinates, calculate the transformation matrix of the current display target coordinate system {S} relative to the camera target coordinate system {C}. .

[0109] 2) Image Acquisition and Pixel Extraction: The camera captures a clear checkerboard image displayed on the screen. Using a sub-pixel corner extraction algorithm, the pixel coordinates (u) of each virtual feature corner point on the camera's image plane are obtained. c, v c ).

[0110] 3) Calculate 3D coordinates: For each extracted corner point, combine its known {P} coordinates (u... P , v P , 0), Pre-calibrated fixed transformation T {P→S} and the current measurements According to the formula Calculate its three-dimensional coordinates in the camera target coordinate system {C}.

[0111] Step 3. Global coordinate fitting based on polynomials

[0112] The above 12 sets of data are processed separately. Taking the nth set as an example, the pixel coordinates (u) of all feature corner points obtained in this acquisition are processed. c , v c ) and its corresponding three-dimensional coordinates (x) in the {C} system C , y C , z C ) as the sample set. The first 10 Zernike polynomials are used to apply to x. C , y C , z C The three components are related to the pixel coordinates (u c , v c A global surface fitting is performed, and the fitting coefficient set for this acquisition is obtained by solving the least squares method. In this way, a continuous and smooth analytical mapping relationship from any camera pixel to a 3D point in the {C} system is established under this acquisition.

[0113] Step 4. Least squares fitting of the camera ray model

[0114] To improve computational efficiency while maintaining accuracy, this embodiment performs sparse sampling on the camera image plane. For example, a point is taken every 20 pixels in both the row and column directions to form a sparse pixel grid.

[0115] For each pixel (u) on the sparse grid c , v c From the fitting results of 12 acquisitions, 12 three-dimensional points in the {C} system can be calculated. .

[0116] The point set is fitted with spatial line least squares using Singular Value Decomposition (SVD) to obtain the direction vector D(u) of the spatial line corresponding to the pixel. c , v cTo uniquely determine the origin O of the ray, calculate the projection points of all points onto a plane passing through the origin of coordinate system {C} and perpendicular to the direction vector D, and take the centroid of these projection points as the origin O(u). c ,v c ).

[0117] After traversing all pixels on the sparse grid, a sparse, {C}-based camera ray model database is obtained. For unsampled pixels, their ray parameters can be obtained from the ray parameters of their four nearest-neighbor, calibrated sparse pixels using bilinear interpolation or more complex interpolation methods.

[0118] Step 5. Application and Verification of Calibration Results

[0119] Apply the calibrated camera to Figure 3 The phase deflection measurement system is shown. In actual measurement, only one measurement, T, is needed using a laser tracker to determine the transformation relationship T between the camera target coordinate system {C} and the world coordinate system {W}. {C→W} This allows all rays in a sparse ray model to be converted for use in a deflection measurement system.

[0120] To verify the accuracy, a plane mirror with a diameter of 200 mm was measured, and the results of the laser interferometer (Zygo GPIXP / D) were used as a reference. Figure 4 The results show: (a) Surface shape results using the traditional Zhang Zhengyou camera model calibration method (RMS=1.45λ), λ=632.8nm; (b) Interferometer measurement results (RMS=1.64λ); (c) Surface shape results calibrated using the method of this invention (RMS=1.61λ); (d) Residuals of the traditional method and interferometer surface shape measurement results (RMS=0.19λ); (e) Residuals of the method of this invention and interferometer surface shape measurement results (RMS=0.04λ).

[0121] Experiments show that the method of this invention decouples pose measurement error from image algorithm, optimizes spatial mapping using global polynomial fitting, and balances accuracy and efficiency through a reasonable sparse sampling strategy, improving measurement accuracy by approximately 5 times. This method effectively overcomes the accuracy bottleneck of traditional methods under complex optical systems and large field-of-view conditions, and has extremely high engineering practical value.

Claims

1. A method for ray calibration of a large field-of-view camera based on polynomial fitting, characterized in that, Includes the following steps: The benchmark establishment steps are as follows: Establish a calibration board pixel coordinate system {P} and a calibration board target coordinate system {S} fixed to the calibration board; establish a camera target coordinate system {C} fixed to the camera to be calibrated; and pre-calibrate the static transformation matrix T between the calibration board pixel coordinate system {P} and the calibration board target coordinate system {S}. {P→S} ; Data acquisition steps: Place the calibration board in multiple different poses within the camera's field of view. For each pose, use a high-precision external measurement device independent of the camera to directly measure the dynamic transformation matrix T of the calibration board target coordinate system {S} relative to the camera target coordinate system {C}. n {S→C} Simultaneously, images of the calibration board are acquired to obtain the pixel coordinates of the feature corner points. And according to the static transformation matrix T {P→S} and dynamic transformation matrix T n {S→C} Calculate the three-dimensional coordinates of each feature corner point in the camera target coordinate system {C}. Global mapping construction steps: For each pose n, using the pixel coordinates of the feature corner points Let be the independent variable, and let its three-dimensional coordinates in the {C} system be denoted as . As the dependent variable, independent polynomial surface fitting is performed on the three spatial coordinate components X, Y, and Z respectively to establish a global analytical mapping function P(u) from arbitrary pixel coordinates to three-dimensional points in the {C} system. c , v c ); Ray model generation steps: For any pixel coordinate Based on its global analytical mapping function P(u) in N different poses c , v c We obtain N three-dimensional points in the {C} system, and by fitting spatial straight lines to these N points, we obtain the ray parameters corresponding to the pixel, thereby generating a camera ray model.

2. The method for ray calibration of a large field-of-view camera based on polynomial fitting according to claim 1, characterized in that, In the benchmark establishment step, the static transformation matrix T {P→S} The pre-calibration is achieved by simultaneously measuring the physical feature points of at least three known pixel coordinates on the calibration board and the target feature points on the calibration board target coordinate system {S} using a high-precision external measuring device, and then solving the problem using point cloud fitting or absolute orientation algorithms.

3. The large field-of-view camera ray calibration method based on polynomial fitting according to claim 1, characterized in that, In the global mapping construction step, the polynomial surface fitting uses Zernike polynomials or Legendre polynomials as basis functions, and achieves a continuous analytical expression of any complex optical distortion through linear combination of basis functions.

4. The large field-of-view camera ray calibration method based on polynomial fitting according to claim 1, characterized in that, In the ray model generation step, the spatial line fitting further includes uniquely determining the ray origin O(u). c , u c The steps are as follows: Define the point on the fitted spatial straight line that satisfies the preset geometric constraints as the origin of the ray.

5. The large field-of-view camera ray calibration method based on polynomial fitting according to claim 4, characterized in that, The preset geometric constraint is: the intersection of the plane passing through the origin of the camera target coordinate system {C} and perpendicular to the direction of the spatial line with the line; or, the centroid of the projection points of the N three-dimensional points on the plane passing through the origin of the coordinate system {C} and perpendicular to the direction of the spatial line.

6. The large field-of-view camera ray calibration method based on polynomial fitting according to claim 1, characterized in that, In the ray model generation step, to improve computational efficiency, sparse sampling is performed on the pixels on the camera image plane, and spatial straight line fitting is performed only on the sampling points to generate a sparse ray field; for the ray parameters of non-sampling points, they are obtained by interpolating the ray parameters of their neighboring sampling points.

7. The method for ray calibration of a large field-of-view camera based on polynomial fitting according to claim 1, characterized in that, It also includes a coordinate system migration application step: storing the ray model obtained from calibration based on the camera target coordinate system {C}; and measuring the transformation matrix T between the {C} system and the world coordinate system {W} using the high-precision external measuring equipment in the actual measurement system. {C→W} This allows the ray model to be converted to the world coordinate system for use, thus decoupling and reusing the calibration results from the measurement scene.

8. The method for ray calibration of a large field-of-view camera based on polynomial fitting according to any one of claims 1-7, characterized in that, The high-precision external measuring equipment includes one or more of the following: laser tracker, lidar, total station, photogrammetry system, or coordinate measuring machine; the calibration plate is a physical medium or programmable display device capable of displaying a preset feature corner point pattern; the feature corner points are checkerboard corner points, circular marker points, or marker points obtained through stripe decoding.

9. A large field-of-view camera light calibration system, used to implement the method described in any one of claims 1-8, characterized in that, include: The calibration plate unit has a preset feature corner point pattern on its surface, and at least three non-collinear first measurement targets are fixedly set on its rigid fixture to establish the calibration plate target coordinate system {S}. The camera unit has at least three non-collinear second measurement targets fixedly mounted on its rigid fixture to establish the camera target coordinate system {C}. A high-precision external measuring device, independent of the camera unit, is used to directly measure the spatial positions of feature points on the first and second measurement targets in order to solve the static transformation matrix T. {P→S} and dynamic transformation matrix T n {S→C} ; The data processing unit is connected to the camera unit and the high-precision external measuring device, respectively, and is used to receive image data and measurement data, perform coordinate transformation calculations, polynomial mapping function fitting and spatial line fitting, and generate and store the camera ray model.

10. The large field-of-view camera light calibration system according to claim 9, characterized in that, The data processing unit communicates in real time with a high-precision external measuring device to synchronize measurement data with image acquisition, and is used to perform sparse sampling of camera image pixels and interpolation calculation of light parameters at non-sampling points.

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