Fringe projection contourgraph calibration method for suppressing complex distortion, storage medium and equipment

Abstract

The invention discloses a fringe projection contourgraph calibration method for suppressing complex distortion, a storage medium and equipment. According to the method, for complex distortion existing in a measurement environment of the fringe projection contourgraph, firstly, a mapping model from a pixel-level phase to a three-dimensional coordinate is established; the surface phase of the calibration plate is obtained by projecting a fringe pattern to the calibration plate which is placed arbitrarily. The two-dimensional coordinates of the plane of the calibration plate are obtained by fitting the B-spline curved surface; estimating the pose of the calibration plate by combining the perspective projection camera imaging principle so as to accurately reconstruct the three-dimensional coordinate of the calibration plate in a camera coordinate system; and calculating the calibration parameter of each pixel position according to the obtained phase and three-dimensional coordinates. According to the method, the influence of the complex distortion on the precision is fully considered from system modeling to calibration data acquisition, and the calibration precision of the fringe projection contourgraph containing the complex distortion in a measurement environment can be remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the field of optical measurement and relates to a fringe projection profilometer calibration method, storage medium and equipment for suppressing complex distortion. Background Art

[0002] A fringe projection profilometer is a precision optical measuring instrument consisting of a camera and a fringe projector. It projects a series of fringe patterns onto the surface of an object. The camera then captures the deformed fringe reflections, analyzes the surface phase, and combines this with the profilometer's calibration parameters to determine the object's three-dimensional profile. Due to its non-contact and high-precision capabilities, it is widely used in industrial automation, machine vision, and other fields.

[0003] However, in some industrial applications, the presence of special lenses in the measurement path (such as the curved protective shield used in robotic welding) can cause complex distortion in both the projected fringe pattern and the image captured by the camera, invalidating the original calibration parameters of the fringe projection profilometer and reducing its measurement accuracy. This complex distortion cannot be modeled as fixed parameters such as radial and tangential distortion parameters based on physical properties using traditional camera lens modeling methods. Therefore, a more accurate calibration method is needed to calibrate the lens that causes the distortion and the fringe projector as a whole to suppress the impact of complex distortion on measurement accuracy. Summary of the Invention

[0004] In response to the problems existing in the above-mentioned prior art, the present invention provides a fringe projection profilometer calibration method, storage medium, and device that suppresses complex distortion. A pixel-level phase-to-three-dimensional coordinate mapping model is established for each pixel of the fringe projection profilometer. A calibration plate is arbitrarily placed within the effective measurement range of the fringe projection profilometer, and a fringe pattern is projected onto the plate to obtain the phase of the plate surface. The two-dimensional coordinates of the calibration plate plane are then obtained by fitting a B-spline surface. The three-dimensional coordinates of the calibration plate plane are then obtained by estimating the calibration plate's position. The model parameters of the fringe projection profilometer are fitted pixel by pixel based on the phase and three-dimensional coordinates of the calibration plate surface to complete the calibration of all pixel positions.

[0005] The technical solution of the present invention:

[0006] A fringe projection profilometer calibration method for suppressing complex distortion includes the following steps:

[0007] S1-1: Establish the pixel-level phase to three-dimensional coordinate mapping model of the fringe projection profiler:

[0008]

[0009] Wherein, (u,v) represents the pixel coordinates; X(u,v), Y(u,v), and Z(u,v) represent the X-axis, Y-axis, and Z-axis coordinates of the object surface contour corresponding to the pixel coordinate (u,v), respectively; Φ(u,v) represents the surface phase of the object corresponding to the pixel coordinate (u,v); a0(u,v), a1(u,v), a2(u,v), and a3(u,v) represent the parameters to be calibrated in the X-axis direction corresponding to the pixel coordinate (u,v); b0(u,v), b1(u,v), b2(u,v), and b3(u,v) represent the parameters to be calibrated in the Y-axis direction corresponding to the pixel coordinate (u,v); c0(u,v), c1(u,v), c2(u,v), and c3(u,v) represent the parameters to be calibrated in the Z-axis direction corresponding to the pixel coordinate (u,v);

[0010] S1-2: Place the calibration plate at N different positions within the effective measurement range of the fringe projection profilometer, project a fringe pattern onto the calibration plate at each position, and analyze the phase Φ of the calibration plate surface through the collected fringe reflection image. k (u,v), k=1,2,…,N;

[0011] S1-3: Collect N calibration plate images at different positions in S1-2, detect the sub-pixel coordinates of the marker points in each calibration plate image, and assign them 2D coordinates on the calibration plate plane according to the order of the marker points; based on the sub-pixel coordinates of the marker points and their corresponding 2D coordinates, fit a B-spline surface that maps from pixel coordinates to 2D coordinates on the calibration plate plane:

[0012]

[0013] in, Indicates the mapping of pixel coordinates (u, v) to the two-dimensional coordinates on the calibration plate plane; n G and m G Respectively represent the number of control points of the control point grid of the B-spline surface in the U-axis and V-axis directions of the image; P i,j =(X P ,Y P ) represents the coordinates of the control point in row i and column j on the control point grid, X P and Y P They represent the coordinate components of the control point in the X-axis and Y-axis directions of the calibration plate plane; p is the order of the B-spline surface; N i,p (u) and N j,p (v) represents the control point P i,j The corresponding p-order basis function is calculated as follows:

[0014]

[0015] in, Represents the node vector of the control point grid in the U-axis direction of the image; Represents the node vector of the control point grid in the V-axis direction of the image;

[0016] S1-4: Calculate the two-dimensional coordinates of the calibration plate plane corresponding to all pixel coordinates according to formula (2):

[0017] [X k ′(u,v)Y k ′(u,v)]=S k (u,v) (4)

[0018] Among them, S k (u, v) represents the B-spline surface equation on the k-th calibration plate plane; X k ′(u,v) and Y k ′(u, v) represents the coordinate components of the pixel coordinate (u, v) mapped to the two-dimensional coordinate on the k-th calibration plate plane in the X-axis and Y-axis directions, respectively, k = 1, 2, ..., N;

[0019] S1-5: According to the calculation results of formula (4), the poses of the N calibration plate planes relative to the camera coordinate system are estimated as follows:

[0020]

[0021] Among them, the matrix Represents the pose matrix of the kth calibration plate plane relative to the camera coordinate system; matrix Represents the pose matrix M k The rotating part, Represents the pose matrix M k The translation part of

[0022] S1-6: Reconstruct the three-dimensional coordinates of the N calibration plate planes in the camera coordinate system according to the results of equations (4) and (5):

[0023]

[0024] Among them, X k (u,v),Y k (u,v) and Z k (u, v) represents the coordinate components of the k-th calibration plate plane reconstructed from the pixel coordinate (u, v) in the three dimensions of the camera coordinate system, X-axis, Y-axis, and Z-axis, k = 1, 2, ..., N;

[0025] S1-7: According to the phase Φ obtained in S1-2 k (u, v) and the coordinate X obtained in S1-6 k (u,v),Y k (u,v) and Z k(u, v), k = 1, 2, ..., N, calculate the parameters to be calibrated described in S1-1; complete the calibration of the fringe projection profilometer.

[0026] Furthermore, in step S1-2, the method for obtaining the surface phase of the calibration plate is:

[0027] S2-1: Use the phase deconvolution algorithm of the fringe projection profilometer to obtain the initial phase value Φ of the calibration plate surface. r (u,v);

[0028] S2-2: All pixel coordinates (u i ,v i ) and the corresponding initial phase value Φ of the calibration plate surface r (u i ,v i ) into equation (8), i = 1, 2, ..., M, M is the total number of camera pixels; fit the surface equation shown in equation (9):

[0029]

[0030] Φ(u,v)=g0u 3 +g1v 3 +g2u 2 v+g3uv 2 +g4uv+g5(9)

[0031] in,[] + represents the pseudo-inverse of the calculation matrix; g0, g1, …, g5 are the coefficients of the surface equation;

[0032] S2-3: Substitute the pixel coordinates (u, v) into equation (9) to calculate the phase value Φ used for calibration described in S1-2 k (u,v);

[0033] Furthermore, in step S1-3, the method of fitting the B-spline surface mapped from the pixel coordinates to the two-dimensional coordinates of the calibration plate plane is:

[0034] S3-1: Detect the sub-pixel coordinates of the marker points in the calibration plate image (u c ′,v c ′), and assign the two-dimensional coordinates (X c ′,Y c ′), c=1,2,…,n C , where n C is the number of detectable landmarks in the calibration plate image;

[0035] S3-2: Set the order p of the B-spline surface based on experience; set the number of control points n of the control point grid G and m G , so that (n G +1)×(m G +1)≤n C ; Construct n on the image G +1 row and m G +1 column regular grid, let (u′ Gi ,v′ Gj ) represents the sub-pixel coordinates of the grid intersection, i = 0, 1, ..., n G ,j=0,1,…,m G ;(u′ Gi ,v′ Gj ) is calculated as:

[0036]

[0037] Among them, n height and n width Respectively represent the pixel height and pixel width of the calibration plate image;

[0038] S3-3: According to the order p and the number of control points n G and m G The node vectors U and V are constructed using the following setting methods:

[0039]

[0040] S3-4: Search S3-1 to detect the distance (u′) in the sub-pixel coordinates of the marker point Gi ,v′ Gj ) the nearest point, and take its corresponding two-dimensional coordinates on the calibration plate plane as (u′ Gi ,v′ Gj ) corresponding control point P′ i,j Initial value, i=0,1,…,n G ,j=0,1,…,m G ; Calculate the sub-pixel coordinates of the marker points (u according to formula (3) c ′,v′ c ) corresponds to the basis function N i,p (u c ′) and N j,p (v′ c ), c=1,2,…,n C ; The N obtained above i,p (u′ c ), N j,p (v′ c ), P′ i,j and (u′ c,v′ c ) corresponds to the two-dimensional coordinates of the calibration plate plane [X′ c ,Y′ c ] is substituted into the minimization problem shown in formula (12);

[0041]

[0042] S3-5: Solve the control point coordinates P when equation (12) is minimized using the Levenberg-Marquardt optimization algorithm i,j ,i=0,1,…,n G ,j=0,1,…,m G ; Complete B-spline surface fitting;

[0043] Furthermore, in step S1-5, the method for estimating the poses of the N calibration plate planes relative to the camera coordinate system is:

[0044] S4-1: Randomly select n S Pixel coordinates (u s ,v s ), s=1,2,…,n S And n S >4, calculate the corresponding two-dimensional coordinates [X s,k ,Y s,k ],s=0,1,…,n S And k=1,2,…,N;

[0045] S4-2: Put n S Group 2D coordinates [X s,k ,Y s,k ] and the corresponding pixel coordinates (u s ,v s ) as the input of the homography estimation algorithm in the OpenCV algorithm library, and calculate the homography matrix from the N sets of calibration plate planes to the camera imaging plane

[0046] Η k =[h 1,k h 2,k h 3,k ](13)

[0047] Among them, h 1,k 、h 2,k 、h 3,k is the homography matrix Η k Three column vectors of , k = 1, 2, …, N;

[0048] S4-3: Assume that the intrinsic parameter matrix of the camera is Combined with the homography matrix column vector h obtained in S4-2 1,k and h 2,k ,establish

[0049] The matrix equations shown in equation (14) are:

[0050]

[0051] By solving equation (14), we can obtain the value of the internal parameter matrix K;

[0052] S4-4: The pose matrix M k The rotation part is represented by the matrix R k =[r 1,k r 2,k r 3,k ], where r 1,k 、r 2,k 、r 3,k Represents the matrix R k The three column vectors are calculated as:

[0053]

[0054] The pose matrix M k The translation part T k The calculation is:

[0055] T k =2K -1 h 3,k / (||K -1 h 1,k ||+||K -1 h 2,k ||) (16)

[0056] According to formula (15) and formula (16), R k and T k , and then synthesize the pose matrix M according to (5) k , complete the pose estimation of the calibration plate plane relative to the camera coordinate system in S1-5.

[0057] Furthermore, in step S1-7, when calculating the parameters a0(u,v), a1(u,v), a2(u,v), and a3(u,v) to be calibrated in the X-axis direction corresponding to the pixel coordinates (u,v), the calculation method is:

[0058]

[0059] in,[] +represents the pseudo-inverse of the calculation matrix; the method for calculating the parameters to be calibrated in the Y-axis and Z-axis directions is the same as equation (7); a set of corresponding calibration parameters is calculated for all pixels to complete the calibration of the fringe projection profilometer; the calculation methods of parameters b0(u,v), b1(u,v), b2(u,v), b3(u,v) and c0(u,v), c1(u,v), c2(u,v), c3(u,v) are the same.

[0060] A computer-readable storage medium stores at least one instruction, at least one program, a code set, or an instruction set, wherein the at least one instruction, at least one program, the code set, or the instruction set is loaded and executed by the processor to implement the above-mentioned fringe projection profilometer calibration method for suppressing complex distortion.

[0061] A server comprises a processor and a memory, wherein the memory stores at least one instruction, and the instruction is loaded and executed by the processor to implement the above-mentioned fringe projection profilometer calibration method for suppressing complex distortion.

[0062] Beneficial effects of the present invention: The present invention provides a fringe projection profilometer calibration method, which introduces complex distortion in the measurement environment into the model of the fringe projection profilometer for overall calibration; by establishing a pixel-level phase to three-dimensional coordinate mapping model, the influence of distortion is avoided in system modeling; by fitting the phase surface equation, a high-quality calibration plate surface phase is obtained; by fitting the B-spline surface that maps pixel coordinates to the calibration plate plane coordinates, the two-dimensional coordinates on the calibration plate plane under complex distortion are obtained, and the position of the calibration plate plane relative to the camera coordinate system is obtained in combination with the perspective projection camera imaging principle, thereby accurately reconstructing the three-dimensional coordinates of the calibration plate in the camera coordinate system; the calibration method of the present invention fully considers the influence of complex distortion on accuracy from system modeling to calibration data acquisition, and can significantly improve the calibration accuracy of the fringe projection profilometer containing complex distortion in the measurement environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is the calibration flow chart of the fringe projection profilometer.

[0064] Figure 2 It is a schematic diagram of the mapping of pixel-level phase to three-dimensional coordinates.

[0065] Figure 3 is the effect of the obtained calibration plate surface phase.

[0066] Figure 4 It is a schematic diagram of a B-spline surface.

[0067] Figure 5 It is the effect diagram of reconstructing the three-dimensional coordinates of the calibration plate surface.

[0068] Figure 6 This is the calibration experiment diagram of the fringe projection profilometer. DETAILED DESCRIPTION

[0069] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0070] Refer to the attached Figure 1 A fringe projection profilometer calibration method for suppressing complex distortion includes system modeling and three steps to obtain calibration data:

[0071] System modeling: The fringe projection profilometer consists of a camera and a projector. Its principle is to obtain a three-dimensional profile by combining the phase calculated from the fringe image with the geometric relationship between the camera and the projector. The system model represents the relationship between the phase and the three-dimensional profile, and the parameters to be calibrated in the model are determined by the geometric relationship between the camera and the projector. In the present invention, when only a single pixel is considered, the phase-to-three-dimensional coordinate mapping relationship of a single pixel is simulated by a third-order polynomial, avoiding physical modeling of the distortion within the measurement range of the fringe projection profilometer. That is, regardless of any form of lens distortion, the phase-to-three-dimensional coordinate mapping model shown in formula (1) is applicable.

[0072] In order to fit the third-order polynomial parameters in formula (1), the present invention places the calibration plate multiple times to accurately obtain the phase Φ(u,v) on the calibration plate at multiple positions and its three-dimensional coordinates X(u,v), Y(u,v) and Z(u,v) in the camera coordinate system; Appendix Figure 2 The phase of a single pixel and the corresponding three-dimensional coordinate distribution are displayed. It can be seen that the third-order polynomial can accurately reflect the distribution law of the sampling points, verifying the effectiveness of the system model in the present invention.

[0073] Step 1: Obtain the surface phase of the calibration plate

[0074] The phase solution algorithm carried by the fringe projection profilometer itself can calculate the initial phase value from the collected reflected fringe pattern. When measuring the contour of an object, the initial phase value can usually be substituted into formula (1) to calculate the three-dimensional coordinates, but the calculation accuracy of the initial phase value will be affected by the texture pattern on the surface of the calibration plate and produce errors. In the calibration, higher-precision data is required. Since the calibration plate itself is an ideal plane, the present invention fits the phase on the calibration plate plane along the image as the U axis and the V axis to the phase surface shown in formula (9), and uses the phase value on the phase surface as the effective value of the phase value that is not affected by the calibration plate pattern. Figure 3The fringe image of the calibration plate, the initial phase values obtained using the phase solution algorithm, and the effective phase values on the phase surface are displayed. It can be seen that the initial phase value image has significant phase errors near the marker points, while the effective phase value image significantly eliminates these errors, improving the data quality and accuracy of the acquired phase.

[0075] Step 2: Get the 2D coordinates of the calibration plate plane

[0076] In the field of the present invention, the traditional method for obtaining the mapping from the imaging plane to the calibration plate plane is to first dedistort the pixel coordinates and then calculate the two-dimensional coordinates corresponding to the undistorted pixels through the homography matrix. In the complex distortion scene involved in the present invention, the dedistortion method of the traditional method cannot accurately restore the undistorted pixels, so the calculated two-dimensional coordinates are not accurate. The present invention uses the B-spline surface of formula (2) to represent the mapping relationship between the pixel coordinates and the two-dimensional coordinates of the calibration plate plane. Figure 4 is a schematic diagram of this mapping relationship. B-spline surface has the properties of overall smoothness and local modifiable properties, such as Figure 4 As shown in Figure 2, the two-dimensional coordinates on the third-order B-spline surface are actually obtained by interpolating the coordinates of the 4×4 control points, and the interpolation ratio is determined by the basis function of formula (3). Therefore, the B-spline surface can simulate various complex distortions locally by modifying the coordinates of the control points.

[0077] The present invention determines a series of sub-pixel coordinates and their corresponding two-dimensional coordinates by detecting the marker points on the calibration plate, and constructs the minimization problem shown in formula (12) through the known coordinate mapping relationship. The optimization process can be regarded as adjusting the position of the control point so that the B-spline surface approaches the current known coordinate mapping relationship, and obtains the optimal control point position when formula (12) is minimum. In formula (12), the total number of control points (n G +1)×(m G +1) is the number of unknown numbers to be found, so when setting the number of grid rows and columns n G and m G When G +1)×(m G +1)<n C , to ensure that the optimization problem has a unique solution.

[0078] Step 3: Get the 3D coordinates of the calibration plate in the camera coordinate system

[0079] The two-dimensional coordinates in operation step 2 are determined based on the coordinate system of the marker points on the respective calibration plate planes. In order to unify them into the same coordinate system, it is necessary to estimate the pose of each calibration plate plane. In the present invention, the camera coordinate system is used as the coordinate system of the fringe projection profiler, and the pose of the calibration plate plane is equivalent to the external parameter matrix of the camera, which can be obtained in a similar manner to the traditional camera calibration method. The difference is that the traditional camera calibration method uses the sub-pixel coordinates and two-dimensional coordinates of the marker points to perform homography estimation to obtain the homography matrix of formula (13), while in the complex distortion scene of the present invention, the sub-pixel coordinate position of the marker point is affected by the complex distortion, which reduces the accuracy of the homography estimation.

[0080] The present invention obtains the B-spline surface representing the mapping between pixel coordinates and two-dimensional coordinates accurately by uniformly sampling n on the imaging plane. S pixels, calculate their 2D coordinates on the B-spline surface, and then use them to estimate the homography. Although only 4 sets of pixels and 2D coordinates are required to implement the homography estimation algorithm, the accuracy of the homography estimation can be improved through denser sampling. According to equations (15) and (16), the rotation and translation parts of the pose matrix can be calculated respectively, and then the 3D coordinates of each calibration plate plane in the camera coordinate system can be reconstructed through equation (6). Figure 5 The reconstruction results for each calibration plate plane are shown.

[0081] For a single pixel (u, v), N phases Φ can be obtained by operation 1 on the calibration plane at N positions. k (u, v), and the corresponding N sets of three-dimensional coordinates X k (u,v),Y k (u,v) and Z k (u, v), k = 1, 2, ..., N. Construct the matrix equation shown in formula (7) to calculate the calibration parameters corresponding to the pixel (u, v). This parameter is only valid for the pixel (u, v). In order to calibrate the entire fringe projection profiler, a specific set of calibration parameters needs to be calculated for each pixel position.

[0082] Example:

[0083] The calibration method of the present invention is used to calibrate Figure 6The fringe projection profilometer prototype shown in Figure 1 has a projector resolution of 1280×720, a camera resolution of 720×540, and a pinhole lens with a focal length of 10mm. The effective measurement range of the fringe projection profilometer is set to 400±80mm from the camera, with a near-end field of view of 160×120mm and a far-end field of view of 240×180mm. Calibration is performed using a 19×15 circular array calibration plate with a distance of 20mm between adjacent circle centers to ensure that the calibration plate covers the camera field of view within the effective range. The calibration plates are placed at 30 different locations. The order of the B-spline surface is set to p=3, and the number of control point grids is set to n. G =m G = 10; additional distortion is added by installing an anamorphic lens, and experiments are conducted with and without the anamorphic lens installed.

[0084] After calibration using the method described in the present invention, a step block with a height difference of 40 mm was measured at 20 locations. The error between the measured height difference and the true value of 40 mm was compared. In the experiment without the anamorphic lens, the maximum error was 0.1199 mm, and the average error was 0.0721 mm. In the experiment with the anamorphic lens, the maximum error was 0.2216 mm, and the average error was 0.1008 mm. The error was not significantly increased by the complex distortion introduced by the anamorphic lens, indicating that the calibration method of the fringe projection profilometer described in the present invention can suppress complex distortion.

Claims

1. A fringe projection profilometer calibration method for suppressing complex distortion, characterized in that: The following steps are involved: S1-1: Establish the pixel-level phase to three-dimensional coordinate mapping model of the fringe projection profiler: Wherein, (u,v) represents the pixel coordinates; X(u,v), Y(u,v), and Z(u,v) represent the X-axis, Y-axis, and Z-axis coordinates of the object surface contour corresponding to the pixel coordinate (u,v), respectively; Φ(u,v) represents the surface phase of the object corresponding to the pixel coordinate (u,v); a0(u,v), a1(u,v), a2(u,v), and a3(u,v) represent the parameters to be calibrated in the X-axis direction corresponding to the pixel coordinate (u,v); b0(u,v), b1(u,v), b2(u,v), and b3(u,v) represent the parameters to be calibrated in the Y-axis direction corresponding to the pixel coordinate (u,v); c0(u,v), c1(u,v), c2(u,v), and c3(u,v) represent the parameters to be calibrated in the Z-axis direction corresponding to the pixel coordinate (u,v); S1-2: Place the calibration plate at N different positions within the effective measurement range of the fringe projection profilometer, project a fringe pattern onto the calibration plate at each position, and analyze the phase Φ of the calibration plate surface through the collected fringe reflection image. k (u,v), k=1,2,…,N; S1-3: Collect N calibration plate images at different positions in S1-2, detect the sub-pixel coordinates of the marker points in each calibration plate image, and assign them 2D coordinates on the calibration plate plane according to the order of the marker points; based on the sub-pixel coordinates of the marker points and their corresponding 2D coordinates, fit a B-spline surface that maps from pixel coordinates to 2D coordinates on the calibration plate plane: in, Indicates the mapping of pixel coordinates (u, v) to the two-dimensional coordinates on the calibration plate plane; n G and m G Respectively represent the number of control points of the control point grid of the B-spline surface in the U-axis and V-axis directions of the image; P i,j =(X P ,Y P ) represents the coordinates of the control point in row i and column j on the control point grid, X P and Y P They represent the coordinate components of the control point in the X-axis and Y-axis directions of the calibration plate plane; p is the order of the B-spline surface; N i,p (u) and N j,p (v) represents the control point P i,j The corresponding p-order basis function is calculated as follows: in, Represents the node vector of the control point grid in the U-axis direction of the image; Represents the node vector of the control point grid in the V-axis direction of the image; S1-4: Calculate the two-dimensional coordinates of the calibration plate plane corresponding to all pixel coordinates according to formula (2): Among them, S k (u, v) represents the B-spline surface equation on the k-th calibration plate plane; X k ′(u,v) and Y k ′(u, v) represents the coordinate components of the pixel coordinate (u, v) mapped to the two-dimensional coordinate on the k-th calibration plate plane in the X-axis and Y-axis directions, respectively, k = 1, 2, ..., N; S1-5: According to the calculation results of formula (4), the poses of the N calibration plate planes relative to the camera coordinate system are estimated as follows: Among them, the matrix Represents the pose matrix of the kth calibration plate plane relative to the camera coordinate system; matrix Represents the pose matrix M k The rotating part, Represents the pose matrix M k The translation part of S1-6: Reconstruct the three-dimensional coordinates of the N calibration plate planes in the camera coordinate system according to the results of equations (4) and (5): Among them, X k (u,v),Y k (u,v) and Z k (u, v) represents the coordinate components of the k-th calibration plate plane reconstructed from the pixel coordinate (u, v) in the three dimensions of the camera coordinate system, X-axis, Y-axis, and Z-axis, k = 1, 2, ..., N; S1-7: According to the phase Φ obtained in S1-2 k (u, v) and the coordinate X obtained in S1-6 k (u,v),Y k (u,v) and Z k (u, v), k = 1, 2, ..., N, calculate the parameters to be calibrated described in S1-1; complete the calibration of the fringe projection profilometer.

2. The fringe projection profilometer calibration method for suppressing complex distortion according to claim 1, characterized in that: In step S1-2, the method for obtaining the surface phase of the calibration plate is: S2-1: Use the phase deconvolution algorithm of the fringe projection profilometer to obtain the initial phase value Φ of the calibration plate surface. r (u,v); S2-2: All pixel coordinates (u i ,v i ) and the corresponding initial phase value Φ of the calibration plate surface r (u i ,v i ) into equation (8), i = 1, 2, ..., M, M is the total number of camera pixels; fit the surface equation shown in equation (9): in,[] + represents the pseudo-inverse of the calculation matrix; g0, g1, …, g5 are the coefficients of the surface equation; S2-3: Substitute the pixel coordinates (u, v) into equation (9) to calculate the phase value Φ used for calibration described in S1-2 k (u,v).

3. The fringe projection profilometer calibration method for suppressing complex distortion according to claim 1, characterized in that: The method of fitting the B-spline surface mapped from pixel coordinates to the two-dimensional coordinates of the calibration plate plane in step S1-3 is: S3-1: Detect the sub-pixel coordinates (u′) of the marker points in the calibration plate image c ,v′ c ), and assign its two-dimensional coordinates (X′) on the calibration plate plane according to the result of the landmark point sorting c ,Y′ c ), c=1,2,…,n C , where n C is the number of detectable landmarks in the calibration plate image; S3-2: Set the order p of the B-spline surface based on experience; set the number of control points n of the control point grid G and m G , so that (n G +1)×(m G +1)≤n C ; Construct n on the image G +1 row and m G +1 column regular grid, let (u′ Gi ,v′ Gj ) represents the sub-pixel coordinates of the grid intersection, i = 0, 1, ..., n G ,j=0,1,…,m G ;(u′ Gi ,v′ Gj ) is calculated as: Among them, n height and n width Respectively represent the pixel height and pixel width of the calibration plate image; S3-3: According to the order p and the number of control points n G and m G The node vectors U and V are constructed using the following setting methods: S3-4: Search S3-1 to detect the distance (u′) in the sub-pixel coordinates of the marker point Gi ,v′ Gj ) the nearest point, and take its corresponding two-dimensional coordinates on the calibration plate plane as (u′ Gi ,v′ Gj ) corresponding control point P′ i,j Initial value, i=0,1,…,n G ,j=0,1,…,m G ; Calculate the sub-pixel coordinates of the marker point (u′) according to formula (3) c ,v′ c ) corresponds to the basis function N i,p (u′ c ) and N j,p (v′ c ), c=1,2,…,n C ; The N obtained above i,p (u′ c ), N j,p (v′ c ), P′ i,j and (u′ c ,v′ c ) corresponds to the two-dimensional coordinates of the calibration plate plane [X′ c ,Y′ c ] is substituted into the minimization problem shown in formula (12); S3-5: Solve the control point coordinates P when equation (12) is minimized using the Levenberg-Marquardt optimization algorithm i,j ,i=0,1,…,n G ,j=0,1,…,m G ; Complete B-spline surface fitting.

4. The fringe projection profilometer calibration method for suppressing complex distortion according to claim 1, characterized in that: In step S1-5, the method for estimating the poses of the N calibration plate planes relative to the camera coordinate system is as follows: S4-1: Randomly select n S Pixel coordinates (u s ,v s ), s=1,2,…,n S And n S >4, calculate the corresponding two-dimensional coordinates [X s,k ,Y s,k ],s=0,1,…,n S And k=1,2,…,N; S4-2: Put n S Group 2D coordinates [X s,k ,Y s,k ] and the corresponding pixel coordinates (u s ,v s ) as the input of the homography estimation algorithm in the OpenCV algorithm library, and calculate the homography matrix from the N sets of calibration plate planes to the camera imaging plane : Η k =[h 1,k h 2,k h 3,k ](13)Among them, h 1,k 、h 2,k 、h 3,k is the homography matrix Η k Three column vectors of , k = 1, 2, …, N; S4-3: Assume that the intrinsic parameter matrix of the camera is Combined with the homography matrix column vector h obtained in S4-2 1,k and h 2,k , establish the matrix equations shown in formula (14): By solving equation (14), we can obtain the value of the internal parameter matrix K; S4-4: The pose matrix M k The rotation part is represented by the matrix R k =[r 1,k r 2,k r 3,k ], where r 1,k 、r 2,k 、r 3,k Represents the matrix R k The three column vectors are calculated as: The pose matrix M k The translation part T k The calculation is: According to formula (15) and formula (16), R k and T k , and then synthesize the pose matrix M according to (5) k , complete the pose estimation of the calibration plate plane relative to the camera coordinate system in S1-5.

5. The fringe projection profilometer calibration method for suppressing complex distortion according to claim 1, characterized in that: In step S1-7, when calculating the parameters a0(u,v), a1(u,v), a2(u,v), and a3(u,v) to be calibrated in the X-axis direction corresponding to the pixel coordinates (u,v), the calculation method is: in,[] + represents the pseudo-inverse of the calculation matrix; the method for calculating the parameters to be calibrated in the Y-axis and Z-axis directions is the same as equation (7); a set of corresponding calibration parameters is calculated for all pixels to complete the calibration of the fringe projection profilometer; the calculation methods of parameters b0(u,v), b1(u,v), b2(u,v), b3(u,v) and c0(u,v), c1(u,v), c2(u,v), c3(u,v) are the same.

6. A computer-readable storage medium, characterized in that The storage medium stores at least one instruction, at least one program, a code set or an instruction set, and the at least one instruction, the at least one program, the code set or the instruction set are loaded and executed by the processor to implement the fringe projection profiler calibration method for suppressing complex distortion as described in any one of claims 1-5.

7. A server, characterized in that: The server includes a processor and a memory, wherein the memory stores at least one instruction, and the instruction is loaded and executed by the processor to implement the fringe projection profilometer calibration method for suppressing complex distortion according to any one of claims 1-5.

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