CN118015095A - A camera calibration algorithm - Google Patents

Abstract

The present invention discloses a camera calibration algorithm, which relates to the field of non-contact measurement technology, including: using an improved Harris corner detection algorithm to extract corner points from a pantograph image, using the extracted corner points and an imaging model, using Zhang's calibration method to estimate camera intrinsic parameters and distortion parameters; using the camera intrinsic parameters and distortion parameters to perform distortion correction on the pantograph image; using the improved Harris corner detection algorithm to extract feature points in the pantograph image after distortion correction, and constructing matching feature point pairs; using the matching feature point pairs, estimating the geometric transformation relationship between pantograph images according to the imaging model; and correcting the pantograph image according to the geometric transformation relationship between pantograph images. The present invention is easy to operate, does not smooth the image corner points, improves the accuracy of the Harris corner detection result, and selecting a suitable neighborhood size can also improve the accuracy.

Description

A camera calibration algorithm

Technical Field

The present invention relates to the field of non-contact measurement technology, and in particular to a camera calibration algorithm.

Background technique

The pantograph is one of the most important current-collecting devices of the train, and its main function is to enable the train to obtain electrical energy. Due to its functional characteristics, the carbon slide plate and the contact line adopt the form of sliding friction contact, so the carbon slide plate is in a state of continuous wear during use. In order to ensure the safety of train operation, the carbon slide plate that exceeds the wear limit should be replaced in time; at the same time, during the operation of the train, due to the structural characteristics of the pantograph, the pantograph will deviate left and right. Excessive centerline deviation makes it difficult to ensure the normal operation of the pantograph. Therefore, it is of great significance to detect the centerline deviation of the pantograph and discover possible safety problems in time.

In order to detect the pantograph centerline deviation, a camera is needed to obtain the pantograph related images.

In computer vision, the process of projecting a three-dimensional object onto a plane figure is called an imaging model. A large amount of research data shows that the camera imaging model can be replaced by a pinhole model. To describe the imaging model, the coordinate system is divided into a world coordinate system, a camera coordinate system, and an image coordinate system. The camera coordinate system is obtained by rotating and translating the world coordinate system. However, due to factors such as lens technology and installation, the camera is not an ideal pinhole imaging model during the imaging process, and an offset will occur during the imaging process, which is perspective distortion. Distortion correction is also called camera calibration. Common camera calibration methods are divided into camera self-calibration method, active vision calibration method, and calibration method based on calibration objects. The three calibration methods should be reasonably selected according to the detection scene and detection requirements.

Some existing camera calibration algorithms use the Harris corner detection algorithm when extracting feature points. The principle is to detect corners by sliding window pixel changes. For an image f(x, y), take an arbitrary size window W, translate Δx and Δy at the point (x, y), and consider the change of local characteristics. The grayscale transformation formula of the pixel points in the window before and after sliding is described as follows:

In the formula, Δx and Δy represent the offset of window W before and after sliding, (x, y) is the pixel coordinate corresponding to W, w(x, y) represents the weighting function, the simplest weight coefficient is 1, and sometimes the w(x, y) function is set to a binary normal distribution with the center of the window as the origin. The transformation formula is expanded according to Taylor, and the image is approximated to the first order after translation Δx and Δy:

f(x+Δx,v+Δy)≈f(u,v)+ _fx (u,v)Δx+ _fy (u,v)Δy

Substitute it into the grayscale transformation formula of the pixel points in the window before and after sliding and simplify it to get:

Where _fx , _fy are the gradient values of the pixel point (x, y) in the window in the x and y directions respectively, and M is the Harris matrix. Since whether a pixel point is a corner point is reflected by the image gradient transformation, the two eigenvalues _λ1 and _λ2 of the M matrix can be analyzed to determine whether it is a corner point. Usually, an R value is calculated for each window to measure the corner response. The R value is used to determine whether there is a corner point in the window. The calculation formula is as follows:

R = det(M) - k(trace(M)) ²

Where k is a sensitive parameter, usually 0.04＜k＜0.06, detM＝λ ₁ λ ₂ , traceM＝λ ₁ +λ ₂ . Therefore, the evaluation criteria of the Harris corner detection algorithm are:

1) When R approaches 0, there are no corner points in the window;

2) When R>0, there are corner points in the window, and the larger R is, the more obvious the corner point features are;

3) When R < 0, the window contains an edge.

However, the current Harris corner detection uses Gaussian filtering to smooth the image. If the Gaussian window is too small, the filtering effect cannot be achieved and pseudo corners may be generated. If the Gaussian window is too large, the image smoothing may cause the corner position to shift. At the same time, the accuracy of the Harris algorithm is pixel-level, that is, the detected corner position is the pixel position, which may cause large errors when the image quality is not high.

According to the imaging principle, when the distance between the camera and the object is different, the farther the object is, the fewer pixels it occupies on the image, and the larger the pixel size. When there is a certain angle between the object and the camera and the distances between the two ends of the object and the camera are different, the final image will show a phenomenon of "larger near and smaller far", that is, perspective deformation, which can generally be corrected by affine transformation. However, the pantograph image does not have the affine transformation feature. Therefore, in order to measure accurately, the present invention proposes a pixel size calibration method.

Summary of the invention

The present invention provides a camera calibration algorithm, which can solve the above problems.

In order to solve the above problems, the technical solution adopted by the present invention is as follows:

The present invention provides a camera calibration algorithm, comprising:

Harris corner detection algorithm is used to extract corners from pantograph images, bilateral filtering is used to filter noise, and Zhang calibration method is used to estimate camera intrinsic parameters and distortion parameters using the extracted corners and imaging model.

Use camera intrinsic parameters and distortion parameters to correct the pantograph image distortion;

Harris corner detection algorithm is used to extract feature points in the pantograph image after distortion correction, and matching feature point pairs are constructed.

Using the matched feature point pairs, the geometric transformation relationship between the pantograph images is estimated according to the imaging model;

According to the geometric transformation relationship between pantograph images, the pantograph images are corrected, and the pixel size calibration method is used to correct the perspective deformation to make the measurement results more accurate.

Among them, the Harris corner detection algorithm uses bilateral filtering. Compared with Gaussian filtering, it does not smooth the image corners while filtering noise, thereby improving the accuracy of Harris corner detection results; sub-pixel corner extraction, let q point be the pixel-level corner coordinates required, there are two types of p points in its neighborhood, one is the p ₀ point with a gradient value G ₀ of 0, and the second is the p ₁ point on the edge, the gradient of which is not 0, but is perpendicular to the q and p ₁ vectors. Therefore, for any point p _i in the neighborhood of point q, let its gradient value be G _i , and then introduce weights ω _i according to the different distances between different p _i points and point q, and then get a unique q point, that is:

Specifically, the imaging model is described by classifying the coordinate system, and the relationship model among the world coordinate system, the camera coordinate system, the image coordinate system and the pixel coordinate system is taken as the imaging model, which is:

In the formula, _fx = f/ _dx , _fy = f/ _dy , _uo is the distance between the origins of the two plane coordinate systems in the x-axis direction, _vo is the distance between the origins of the pixel coordinate system and the origins of the image coordinate system in the y-axis direction, the actual physical distances of the pixels in the u-axis and v-axis directions are _dx and _dy respectively, _fx , _fy , _uo , and _vo are collectively referred to as camera intrinsic parameters, and R and T are camera extrinsic parameters.

Specifically, distortion is divided into radial distortion and tangential distortion;

The radial distortion is described using the first two terms _k1 and _k2 of the Taylor series expansion around the principal point. The radial distortion correction formula is as follows:

Where (x, y) is the position of the distortion point on the image, (x′, y′) is the position after distortion correction, r is the distance from the pixel to the center of the image, that is, r ² = x ² + y ² , k ₁ and k ₂ are radial distortion parameters;

The tangential distortion correction formula is as follows:

Where p ₁ and p ₂ are tangential distortion coefficients.

Specifically, the world coordinate system ( _Xw , _Yw , _Zw ) is placed on the calibration plate so that _Zw = 0 in the world coordinate system. Then the relationship between the four coordinate systems can be simplified as follows:

Where s = 1/Z _c , M is the camera intrinsic parameter matrix; let the homography matrix of the matrix sM[R ₁ R ₂ T] be H, which is defined as follows:

When the number of corner points of the calibration plate image is greater than or equal to 4, the pixel coordinates (u, v) of the corner points on the calibration plate image are obtained by corner point detection. At the same time, the physical size of the calibration plate is known, and the matrix H corresponding to the calibration plate image can be obtained. Then the internal and external parameters of the camera are calculated from H. The first two columns R ₁ and R ₂ of the rotation moment R have a unit orthogonal relationship, that is:

From the relationship between H and R ₁ and R ₂ , we can get:

Substituting into the matrix H, we get:

Let N = Z _c ² M ^- TM ^-1 be a symmetric matrix. Then, by solving the matrix N, we can solve the camera intrinsic parameter matrix M. Substituting the inverse matrix of the camera intrinsic parameter matrix M into N = Z _c ² M ^- TM ^-1 , we have:

Since H is known, each calibration plate image can provide a constraint relationship. From the formula after substituting into the matrix H, we can know that N is a symmetric matrix. Solving N requires three calibration plate images. According to the corresponding relationship between N and the camera intrinsic parameters, Z _C is solved.

Compared with the prior art, the present invention has the following beneficial effects:

The present invention experiments on camera calibration and uses reprojection error for evaluation. In addition, the improved Harris corner detection algorithm has higher accuracy, thereby improving the detection accuracy of the detection system and making the analysis data reliable and accurate.

1) Zhang’s calibration method based on calibration objects uses a calibration plate composed of two-dimensional grids for camera calibration, which is highly accurate and easy to operate;

2) Bilateral filtering, i.e. nonlinear filtering, is used. The algorithm includes two parts: spatial matrix and range matrix. The spatial matrix can be used for fuzzy denoising similar to Gaussian filtering. The range matrix is obtained based on grayscale similarity and is used to protect the edge. In this way, the image corners will not be smoothed while filtering the noise, thereby improving the accuracy of Harris corner detection results.

3) Through the extraction of sub-pixel corner points, it can be concluded that the obtained pixel-level corner point coordinates are not only related to the initial point coordinates, but also to the neighborhood size of the selected pixel-level corner point coordinates. Therefore, choosing a suitable neighborhood size has the effect of improving accuracy;

4) In the implementation manner, the camera calibration algorithm described in the solution of the present invention is experimented and evaluated using the reprojection error. The reprojection error is the Euclidean distance between the theoretical pixel point a and the measured pixel point a′ after distortion correction ||aa′|| _2. The smaller the reprojection error, the better the camera calibration result. According to the experimental results, the accumulation of the number of checkerboard photos in the reprojection error of the two algorithms does not significantly improve the accuracy of the camera calibration results, because the accuracy of corner point detection is not only related to the algorithm, but also to the quality of the image. However, when the number of checkerboard photos is the same, the reprojection error of the improved Harris corner point detection algorithm is smaller, and the difference in accuracy between the two is very obvious, that is, the improved corner point detection algorithm has higher accuracy, thereby improving the detection accuracy of the detection system;

5) In the implementation method, in order to avoid perspective deformation during the imaging process, a pixel size calibration method is used for correction to make the measurement of the carbon slide plate image more accurate.

In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the embodiments of the present invention are specifically cited below and described in detail with reference to the attached drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

Figure 1 is a schematic diagram of the relationship between imaging coordinate systems. The imaging model is divided into the world coordinate system ( _Xw , _Yw , _Zw ), the camera coordinate system ( _Xc , _Yc , _Zc ), the image coordinate system (x, y), and the pixel coordinate system (u, v).

Figure 2 shows the reprojection errors of the two algorithms.

Figure 3 shows the reprojection error of controlling the neighborhood size.

Figure 4 is a graph showing the longitudinal pixel size variation trend of the left and right carbon slide images.

Detailed ways

In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

This embodiment provides an improved camera calibration algorithm, and the operation steps are as follows:

Step 1: Improve the Harris corner detection algorithm.

In order to effectively avoid the Gaussian filter from smoothing the pantograph image corners while filtering noise, thereby improving the accuracy of the Harris corner detection result, the improvements of the Harris corner detection algorithm used in the present invention are as follows:

(1) Bilateral filtering is a nonlinear filtering. Compared with Gaussian filtering, it does not smooth the image corners while filtering noise, thereby improving the accuracy of Harris corner detection results.

Bilateral filtering is a nonlinear filter. The algorithm consists of two parts: the spatial matrix and the range matrix. The spatial matrix can be used for fuzzy denoising similar to Gaussian filtering, and the range matrix is obtained based on grayscale similarity to protect edges. The definition is as follows:

In the formula, The spatial domain of bilateral filtering is defined as follows:

The pixel domain is defined as follows:

Where S is the selected matrix box; q is the input pixel point; m and n are the horizontal and vertical coordinates of the input pixel point respectively; I (m, n) is the input pixel value; p is the center pixel point of the box; i and j are the horizontal and vertical coordinates of the center pixel point of the box respectively; I (i, j) is the center pixel value of the box; is the output pixel value size; σ _s and σ _r are custom values.

(2) Sub-pixel corner point extraction, let q be the pixel-level corner point coordinates to be sought. There are two types of p points in its neighborhood. One is _p0 with a gradient value _G0 of 0, and the other is _p1 at the edge. The gradient of this point is not 0, but it is perpendicular to the q and _p1 vectors. Therefore, for any point p _i in the neighborhood of point q, let its gradient value be G _i , and introduce different weight values ω _i according to the different distances between different p _i points and point q, then the unique position of point q is obtained. The formula is defined as follows:

In the formula, the obtained q point is not only related to the initial q point coordinates, but also to the selected q point neighborhood size. Choosing a suitable neighborhood size can improve the accuracy.

Step 2: Use the improved Harris corner detection algorithm to extract corner points from the pantograph image. Using the extracted corner points and the imaging model, the Zhang calibration method is used to estimate the camera intrinsic parameters and distortion parameters.

In the present invention, the imaging model is divided into a world coordinate system ( _Xw , _Yw , _Zw ), a camera coordinate system ( _Xc , _Yc , _Zc ), an image coordinate system (x, y), and a pixel coordinate system (u, v). The relationship diagram of the four coordinate systems is shown in FIG1.

The world coordinate system is used to describe the actual coordinates of the object. The camera coordinate system is the bridge connecting the image physical coordinate system and the world coordinate system. The image coordinate system represents the position of the pixel in the image, and the pixel coordinate system is the scaling and translation of the image coordinate system.

Suppose the matrix expression of rotating the world coordinate system around the Z _w axis by an angle of θ is:

Assume that the rotation matrix around three directions is R = R _X R _Y R _Z. The translation matrix expression is:

The matrix form of converting the world coordinate system to the camera coordinate system is:

The mathematical expressions of the four coordinate systems: world coordinate system, camera coordinate system, image coordinate system, and pixel coordinate system are:

The image coordinate system and the pixel coordinate system are plane coordinate systems with different units. Assuming that the actual physical distances of pixels in the u-axis and v-axis directions are d _x and _dy respectively, we have:

The relationship between the image coordinate system and the pixel coordinate system is:

Therefore, the relationship model between the four coordinate systems, namely the world coordinate system, the camera coordinate system, the image coordinate system, and the pixel coordinate system, is the imaging model:

In the present invention, Zhang's calibration method is used to estimate camera intrinsic parameters and distortion parameters.

Place the world coordinate system ( _Xw , _Yw , _Zw ) on the calibration board, that is, _Zw = 0, then the formula is:

Where, s = 1/Z _c , and M is the camera intrinsic parameter matrix.

Let the homography matrix of the matrix sM[R ₁ R ₂ R ₃ ] be H, which is defined as follows:

When the number of corner points of the calibration plate image is greater than or equal to 4, the corner point coordinates (u, v) on the calibration plate image are obtained by corner point detection. At the same time, the physical size of the calibration plate is known, and the matrix H corresponding to the calibration plate image can be obtained. Then the internal and external parameters of the camera are calculated from H. The first two columns R ₁ and R ₂ of the rotation moment R have a unit orthogonal relationship, that is:

From the relationship between H and R ₁ and R ₂ , we can get:

Connecting the above formula, we can get:

Let N = Z _c ² M ^{-TM -1} be a symmetric matrix. Then, by solving the matrix N, we can solve the camera intrinsic parameter matrix M. Substituting the inverse matrix of the M matrix into N = Z _c ² M ^{-TM -1} , we have:

Since H is known, each calibration plate image can provide a constraint relationship, and N is a symmetric matrix. Three calibration plate images are required to solve N. Z _C is obtained based on the corresponding relationship between N and the camera intrinsic parameters.

Step 3: Use the camera intrinsic parameters and distortion parameters to correct the distortion of the pantograph image.

In the present invention, distortion is divided into radial distortion and tangential distortion.

The radial distortion is described using the first two terms _k1 and _k2 of the Taylor series expansion around the principal point. The radial distortion correction formula is as follows:

Where (x, y) is the position of the distortion point on the image, (x′, y′) is the position after distortion correction, r is the distance from the pixel to the center of the image, that is, r ² =x ² +y ² , k ₁ and k ₂ are radial distortion parameters.

Tangential distortion is caused by the fact that the camera sensor plane is not parallel to the lens during installation and manufacturing. The tangential distortion correction formula is as follows:

Where p ₁ and p ₂ are tangential distortion coefficients.

Step 4: Use the improved Harris corner detection algorithm to extract feature points in the distortion-corrected pantograph image and construct matching feature point pairs.

Step 5: Use the matched feature point pairs to estimate the geometric transformation relationship between pantograph images according to the imaging model.

Step 6: According to the geometric transformation relationship between pantograph images, the pantograph image is corrected, and the pixel size calibration method is used to correct the perspective deformation to make the measurement result more accurate.

According to the imaging principle, when the distance between the camera and the object is different, the farther the object is, the fewer pixels it occupies on the image, and the larger the pixel size; when there is a certain angle between the object and the camera and the distances between the two ends of the object and the camera are different, the final image will show a phenomenon of "large near and small far", that is, perspective deformation. For this phenomenon, the near end and the far end have different scaling ratios. If the image size can be enlarged to the actual length in the horizontal direction and different scaling ratios are used in the vertical direction, the two ends can be enlarged to the actual physical size. If the near end and the far end are divided into multiple segments, then each segment has a near end and a far end at both ends. When the scale factor of each segment's near end and far end is known, the actual size can be accurately solved. Divide the multiple segments into pixel sizes, then one of every two adjacent pixels is the near end and the other is the far end. When the pixel sizes at both ends are known, the image size can be converted to the actual physical size.

The calibration of the horizontal pixel size can be obtained from two sets of pantograph images. Assume that the horizontal pixel sizes of the left and right carbon slides are lx and rx respectively, and the numbers of complete horizontal pixels of the left and right carbon slides are L and R respectively, then:

Where, δ represents the distance between the two contact lines, which is 40 mm, and the total length of the carbon slide plate is 1050 mm.

In practice, in order to ensure the effective measurement length of the carbon slide, the carbon slide cannot completely fill the entire field of view. It will cause a large error, which is mainly caused by the left and right deviation of the pantograph, the height of the pantograph, and other factors. The present invention counts the vertical pixel size of the actual captured image, and plots the 18 horizontal pixel positions of the left and right carbon slide images as the horizontal coordinate and the pixel size as the vertical coordinate. The result is shown in Figure 4. The pixel size trend line in the figure is not a horizontal straight line. The left carbon slide curve shows an increasing trend, and the right carbon slide curve shows a decreasing trend, which is consistent with the actual relative position of the camera and the pantograph.

The improved camera calibration algorithm described in the present invention is evaluated below.

This experiment conducts experiments on camera calibration and uses reprojection error for evaluation, that is, the Euclidean distance between the theoretical pixel point a and the measured pixel point a′ after distortion correction ||aa′|| ₂ . The smaller the reprojection error, the better the camera calibration result, that is, the more the distortion correction conforms to the actual situation.

The experimental results are shown in Figure 2. The results show that the accumulation of the number of chessboard photos does not significantly improve the accuracy of the camera calibration results, because the accuracy of corner detection is not only related to the algorithm, but also to the quality of the image. However, when the number of chessboard photos is the same, the reprojection error of the improved Harris corner detection algorithm is smaller, and the difference in accuracy between the two is very obvious, that is, the improved corner detection algorithm has higher accuracy, which can improve the detection accuracy of the detection system.

The present invention uses the neighborhood size as the only variable and conducts experiments with 30 photos, and the results are shown in Figure 3. As the neighborhood size increases, the reprojection error decreases first and then increases. This is because the corner point obtained is closer to the theoretical corner point position as the neighborhood increases, and the excessive size of the neighborhood will lead to an increase in the number of points far away from the theoretical corner point in the neighborhood. It can be concluded that the corner point obtained will be far away from the theoretical corner point position, and the reprojection error will become larger, that is, the accuracy will decrease. Therefore, a suitable neighborhood size should be selected when performing camera calibration calculations.

According to statistics, the thickness of the carbon plate in the pantograph image accounts for about 80 pixels. If the pixel size deviation is 0.01 units, the error of the actual thickness value will reach 0.8mm, which obviously does not meet the detection accuracy requirements.

The present invention calculates the longitudinal pixel size for each horizontal pixel position obtained by statistics, rather than using only the same value. Although the operation is complicated, it has the effect of improving the accuracy of carbon slide wear detection, and the result is shown in FIG4 .

The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (4)

1. A camera calibration algorithm, comprising: Harris corner detection algorithm is used to extract corners from pantograph images, bilateral filtering is used to filter noise, and Zhang calibration method is used to estimate camera intrinsic parameters and distortion parameters using the extracted corners and imaging model. Use camera intrinsic parameters and distortion parameters to correct the pantograph image distortion; Harris corner detection algorithm is used to extract feature points in the pantograph image after distortion correction, and matching feature point pairs are constructed. Using the matched feature point pairs, the geometric transformation relationship between the pantograph images is estimated according to the imaging model; According to the geometric transformation relationship between pantograph images, the pantograph images are corrected, and the pixel size calibration method is used to correct the perspective deformation to make the measurement results more accurate. Among them, the Harris corner detection algorithm uses bilateral filtering; sub-pixel corner extraction, let q point be the pixel-level corner coordinates required, there are two types of p points in its neighborhood, one is the _p0 point with a gradient value _G0 of 0, and the second is the _p1 point on the edge, the gradient of this point is not 0, but it is perpendicular to the q and _p1 vectors. Therefore, for any point p _i in the neighborhood of point q, let its gradient value be G _i , and then introduce weight ω _i according to the different distances between different p _i points and point q, then the unique q point is obtained, that is: 2. The camera calibration algorithm according to claim 1 is characterized in that the imaging model is described by classifying the coordinate system, and the relationship model among the world coordinate system, the camera coordinate system, the image coordinate system and the pixel coordinate system is used as the imaging model, which is: In the formula, _fx = f/ _dx , _fy = f/ _dy , _uo is the distance between the origins of the two plane coordinate systems in the x-axis direction, _vo is the distance between the origins of the pixel coordinate system and the origins of the image coordinate system in the y-axis direction, the actual physical distances of the pixels in the u-axis and v-axis directions are _dx and _dy respectively, _fx , _fy , _uo , and _vo are collectively referred to as camera intrinsic parameters, and R and T are camera extrinsic parameters. 3. The camera calibration algorithm according to claim 2, wherein the distortion is divided into radial distortion and tangential distortion; The radial distortion is described using the first two terms _k1 and _k2 of the Taylor series expansion around the principal point. The radial distortion correction formula is as follows: Where (x, y) is the position of the distortion point on the image, (x′, y′) is the position after distortion correction, r is the distance from the pixel to the center of the image, that is, r ² = x ² + y ² , k ₁ and k ₂ are radial distortion parameters; The tangential distortion correction formula is as follows: Where p ₁ and p ₂ are tangential distortion coefficients. 4. The camera calibration algorithm according to claim 3, characterized in that the world coordinate system ( _Xw , _Yw , _Zw ) is placed on the calibration plate so that _Zw = 0 in the world coordinate system, then the relationship between the world coordinate system, the camera coordinate system, the image coordinate system and the pixel coordinate system is simplified to: Where s = 1/Z _c , M is the camera intrinsic parameter matrix; let the homography matrix of the matrix sM[R ₁ R ₂ T] be H, which is defined as follows: When the number of corner points of the calibration plate image is greater than or equal to 4, the pixel coordinates (u, v) of the corner points on the calibration plate image are obtained by corner point detection. At the same time, the physical size of the calibration plate is known, that is, the matrix H corresponding to the calibration plate image is obtained, and then the internal and external parameters of the camera are calculated from H. The first two columns R ₁ and R ₂ of the rotation moment R have a unit orthogonal relationship, that is: From the relationship between H and R ₁ and R ₂ , we can get: Substituting into the matrix H, we get: Let N = Z _c ² M ^- TM ^-1 be a symmetric matrix. Then, by solving the matrix N, we can solve the camera intrinsic parameter matrix M. Substituting the inverse matrix of the camera intrinsic parameter matrix M into N = Z _c ² M ^- TM ^-1 , we have: Since H is known, each calibration plate image can provide a constraint relationship. From the formula after substituting into the matrix H, we can know that N is a symmetric matrix. Solving N requires three calibration plate images. According to the corresponding relationship between N and the camera intrinsic parameters, Z _C is solved.