A self-calibration method for internal parameters of fisheye lens

Abstract

The present invention proposes a method for self-calibration of internal parameters of a fisheye lens, the method comprising: establishing a fisheye imaging model and obtaining the internal parameters of the fisheye lens to be calibrated; establishing a calibration equation according to the ideal projection ellipse constraint of a spatial straight line on a horizontal plane; using the ellipse contour boundary of the effective area of ​​the fisheye image and the projection ellipse arc segment information of the spatial straight line on the fisheye image to give the initial value of the internal parameters of the fisheye lens to be calibrated and iteratively solving the calibration equation to obtain the least squares estimate of the calibration parameters. The present invention establishes a calibration equation based on the ideal projection ellipse constraint of the spatial straight line on the horizontal plane to estimate the internal parameters of the fisheye lens, the calibration calculation does not involve the external parameters of the camera, not only avoiding the over-parameterization problem, but also the calibration parameters more accurately characterize the spherical perspective projection model, and the calibration calculation form and process are unified, with high precision, and can be flexibly applied to single-view and multi-view conditions.

Description

Technical Field

[0001] The invention relates to the fields of computer vision and digital photogrammetry, and in particular to a method for self-calibration of internal parameters of a fisheye lens. Background Art

[0002] Fisheye lenses have the advantages of wide viewing angle (close to or even more than 180°), rich information, and small size. They are ideal optical sensors for the development of lightweight and small all-round visual systems, and have extremely broad application prospects in many fields such as security monitoring, robot navigation, and panoramic parking. However, due to the short focal length, large field of view, and constraints of optical principles, fisheye images are severely distorted. Before use, they need to be converted into a planar perspective projection image that conforms to the visual habits of the human eye. The prerequisite is to obtain a set of high-precision parameters associated with the optical imaging model of the fisheye lens. Fisheye lenses are usually composed of more than 10 groups, or even dozens of groups of optical lenses. The calculation of the optical path is very difficult. Traditional fisheye lens calibration algorithms mostly use spherical projection models to characterize their optical imaging process, and obtain calibration images of artificial calibration reference objects to solve model parameters. For example, they directly use 3D control point information and DLT model iteration to solve spatial parameters, or use 2D targets as calibration reference objects to first obtain the initial parameter values ​​based on the coordinate mapping relationship of the target points in the world coordinate system, spherical coordinate system and fisheye image coordinate system, and then use the spatial linear position characteristics and their projection characteristics for nonlinear optimization, etc. However, the construction of high-precision, large-scale 3D calibration fields is relatively complex. , high cost and need constant maintenance. Although the two-dimensional target is flexible and low-cost, it is necessary to move the target position to obtain the calibration images of different areas of the fisheye image and require special patterns (such as non-uniformly spaced dot matrix and chessboard); on the other hand, the traditional fisheye lens calibration algorithm based on artificial calibration reference often introduces a large number of external parameters, and there is an over-parameterization problem. Inaccurate initial values ​​of external parameters can easily cause the optimization to fall into local optimality. Other parameter calibration methods for the purpose of fisheye image correction, such as longitude and latitude correction and polynomial correction, have a simple calibration parameter calculation process and low complexity, but the accuracy is not high and it is impossible to obtain parameters such as the equivalent focal length of the fisheye lens, which is not conducive to the acquisition of measurement information. The widespread adoption of low-cost, ultra-wide-angle fisheye lenses in many fields has prompted the search for fisheye lens calibration methods with high accuracy, simple operation, and low dependence on implementation conditions to solve the fisheye image measurement needs in multiple application environments. From this perspective, the fisheye lens self-calibration method that only relies on the scene's own feature information to achieve parameter solution will have a broader market application prospect. Summary of the invention

[0003] In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a method for self-calibration of internal parameters of a fisheye lens.

[0004] To achieve the above object and other related objects, the present invention provides a method for self-calibration of internal parameters of a fisheye lens, the method comprising:

[0005] Establish a fisheye imaging model and obtain the internal parameters of the fisheye lens to be calibrated;

[0006] The calibration equation is established according to the ideal projection ellipse constraint of the space straight line on the horizontal plane;

[0007] The initial values ​​of the internal parameters of the fisheye lens to be calibrated are given by using the elliptical contour boundary of the effective area of ​​the fisheye image and the projection elliptical arc segment information of the spatial straight line on the fisheye image, and the calibration equation is iteratively solved to obtain the least squares estimate of the calibration parameters.

[0008] Optionally, obtaining internal parameters of the fisheye lens to be calibrated specifically includes:

[0009] Space coordinate transformation, any space point P in the world coordinate system W , after rotation and translation of the spatial coordinate transformation, it is converted into point P in the camera coordinate system C ;

[0010] Unit sphere mapping, point P C Along ray O C P C Direction mapping to point P on the unit sphere S ;

[0011] Spherical projection, point P S Orthographic projection is performed onto a fixed plane perpendicular to the main optical axis of the fisheye lens to obtain the ideal projection point P. m (x m ,y m ),

[0012] Pixel coordinate transformation, using the camera internal parameters to transform the ideal projection point coordinates to the fisheye image pixel coordinates;

[0013] The coordinate transformation relationship from the ideal projection point to the fisheye image pixel is:

[0014] (uu 0 )*(1+k 1 r 2 +k 2 r 4 )=Af*x m ,(vv 0 )*(1+k 1 r 2 +k 2 r 4 )=f*y m

[0015] r 2=(uu 0 ) 2 +(vv 0 ) 2

[0016] Where: (u, v) is the actual pixel coordinate of the fisheye image, (u 0 ,v 0 ) is the camera principal point coordinate, f is the camera equivalent focal length, A is the aspect ratio, k 1 ,k 2 is the radial distortion coefficient, parameter (u 0 ,v 0 ,f,A,k 1 ,k 2 ) are the internal parameters of the fisheye lens to be calibrated.

[0017] Optionally, the ideal projection ellipse constraint based on the spatial straight line on the horizontal plane includes:

[0018] ① Different spatial straight lines project ellipses on the horizontal plane under spherical perspective projection. The center of the ellipse is the center of the projection sphere, and the major semi-axis a is always equal to the radius R of the projection sphere. g , the length of the minor semi-axis b is related to the direction of the normal line of the space plane passing through the center of the sphere and the space straight line;

[0019] ② For the same straight line in space, the change in the radius of the projection sphere only causes the long and short semi-axes of the projection ellipse to scale in equal proportion.

[0020] Optionally, the calibration equation is:

[0021]

[0022] in, b is the minor semi-axis of the ellipse, and γ is the rotation angle between the major axis of the ellipse and the coordinate X-axis.

[0023] Optionally, the calibration equations are solved iteratively as follows:

[0024]

[0025] in, represents the least squares adjustment result of the error equation,

[0026] The error equation V is:

[0027]

[0028]

[0029]

[0030]

[0031]

[0032] in, is the initial value of the given parameter; is the coefficient of the equation, which is the partial derivative of the nonlinear function E under the given initial value of the parameter; (du 0 ,dv 0 ,dk 1 ,dk 2 ,dA,df,db,dγ) are the unknowns in the equation and are the parameter increments of the nonlinear function E.

[0033] As described above, the method for self-calibration of internal parameters of a fisheye lens of the present invention has the following beneficial effects:

[0034] The present invention establishes a calibration equation to estimate the internal parameters of the fisheye lens based on the ideal projection ellipse constraint of a spatial straight line on a horizontal plane. The calibration calculation does not involve external parameters of the camera, which not only avoids the over-parameterization problem, but also its calibration parameters more accurately characterize the spherical perspective projection model. The calibration calculation form and process are unified and the accuracy is high, and it can be flexibly applied to single-view and multi-view conditions. It is applicable to any spatial straight line in the scene and is independent of the direction, position, and length of the straight line. It does not rely on a specific calibration reference object pattern and its measurement information. Self-calibration can be achieved for artificial scenes with a large number of parallel straight lines. The application method is flexible and has good application prospects and value. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to further illustrate the contents described in the present invention, the specific embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings. It should be understood that these drawings are only used as typical examples and should not be regarded as limiting the scope of the present invention.

[0036] Figure 1 is a structural diagram of a method for self-calibration of internal parameters of a fisheye lens according to an embodiment of the present invention;

[0037] Figure 2 Schematic diagram of the fisheye imaging stage of an embodiment of the present invention; wherein (a) is a spatial transformation process, and (b) is an orthogonal projection process;

[0038] Figure 3 is a schematic diagram of a space straight line unit sphere projection of an embodiment of the present invention;

[0039] Figure 4 is the effective pixel area of ​​the fisheye image under the unit sphere projection of the embodiment of the present invention; wherein (a) indicates that the ellipse outline boundary is within the field of view, and (b) indicates that part of the ellipse outline boundary is outside the field of view;

[0040] Figure 5Schematic diagram of elliptical contour (arc) detection of fisheye image and its edge map according to an embodiment of the present invention; wherein: (a), (c), (e) are online fisheye images used for testing, (b), (d), (f) are elliptical contours (arcs) detected on the edge map of the fisheye image;

[0041] Figure 6 1 is a diagram of an iterative calculation process of a single-view calibration of a fisheye lens according to an embodiment of the present invention; wherein: (a), (b), (c), and (d) are respectively iterative estimation results of fisheye lens parameters (f, A, k1, k2) corresponding to an online fisheye image, and (e) is an iterative estimation accuracy result;

[0042] Figure 7 1 is a graph of online fisheye image calibration parameter correction test results of an embodiment of the present invention; wherein (a) is the visual effect of fisheye image plane correction (cubic box) under the calibration parameters of the method of the present invention, and (b) is the visual effect of local area plane correction of fisheye image of DXO, a well-known French image software. DETAILED DESCRIPTION

[0043] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0044] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present invention, and thus the drawings only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0045] like Figure 1 As shown, this embodiment provides a new method for self-calibration of internal parameters of a fisheye lens. The method is based on the principle of spherical perspective projection. First, a fisheye imaging model is established and the internal parameters of the fisheye lens to be calibrated are given. Then, a calibration equation is established according to the ideal projection ellipse constraint of a spatial straight line on a horizontal plane. Finally, the ellipse contour (arc) information on the fisheye image is used to give the initial value of the internal parameter of the fisheye lens to be calibrated, and the calibration equation is iteratively solved to obtain the least squares estimate of the calibration parameter.

[0046] like Figure 2 As shown in (a), in one embodiment, the fisheye imaging model adopts the principle of spherical perspective projection, and the entire imaging process is transformed from a spatial point to a fisheye image pixel coordinate through four stages:

[0047] 1. Space coordinate transformation, that is, any space point P in the world coordinate system W =[X W ,Y W ,Z W ] T , after rotation and translation of the spatial coordinate transformation, it is converted into point P in the camera coordinate system C =[X C ,Y C ,Z C ] T , the two satisfy the following relationship:

[0048] P C =R·P W +T (1)

[0049] Where: T is the translation vector and R is the rotation matrix.

[0050] 2. Unit sphere mapping, that is, point P C Along ray O C P C (O C Represents the origin of the coordinate system) direction is mapped to the unit sphere Point P on S :

[0051]

[0052] Where: θ is the incident angle, α is the incident light at X C Y C Projection of the plane and X C The angle between the axes is:

[0053]

[0054] 3. Spherical projection, point P S Projected onto the fisheye image plane. Figure 2 As shown in (b), the present invention adopts an orthogonal projection model to transform point P S Orthographic projection is performed onto a fixed plane (image plane) perpendicular to the Z axis (the main optical axis of the fisheye lens) to obtain the ideal projection point P. m (x m ,y m ), the coordinate transformation relationship between the two is as follows:

[0055] x m =X s ,y m =Y s (4)

[0056] 4. Pixel coordinate transformation, that is, using the camera internal parameters to transform the ideal projection point coordinates to the fisheye image pixel coordinates. The camera internal parameters are usually expressed as a matrix Considering the optical distortion of the fisheye lens and the fact that it is mainly affected by the radial distortion error, the coordinate transformation relationship from the ideal projection point to the fisheye image pixel is:

[0057] (uu 0 )*(1+k 1 r 2 +k 2 r 4 )=Af*x m ,(vv 0 )*(1+k 1 r 2 +k 2 r 4 )=f*y m (5)

[0058] r 2 =(uu 0 ) 2 +(vv 0 ) 2

[0059] Where: (u, v) is the actual pixel coordinate of the fisheye image, (u 0 ,v 0 ) is the camera principal point coordinate, f is the camera equivalent focal length, A is the aspect ratio, k 1 ,k 2 is the radial distortion coefficient. In the above fisheye imaging process, the parameter (u 0 ,v 0 ,f,A,k 1 ,k 2 ) is related to the optical design and processing of the fisheye lens itself, and is called an internal parameter. The present invention estimates the internal parameter with high precision.

[0060] like Figure 3 As shown, in this embodiment, the calibration equation is established according to the ideal projection ellipse constraint of the spatial straight line on the horizontal plane. The principle is that the spatial straight line L under the spherical perspective projection is mapped to a great circle g passing through the projection center (the center of the sphere). The great circle can be given by the spherical equation and the plane equation passing through the center of the sphere:

[0061]

[0062] Where: R g is the radius of the projection sphere, (x, y, z) is a point on the sphere, and (P, Q, S) is the coefficient of a certain spatial plane equation passing through the origin O(0, 0, 0) at the center of the sphere. The spatial plane equation in equation (6) is rewritten as: Substituting into the spherical equation and eliminating z we get:

[0063]

[0064] Formula (7) can be regarded as the projection of the spherical great circle on the horizontal plane. The projection is an ellipse. If the center of the ellipse is defined as (x0, y0), the major and minor semi-axes are (a, b), the rotation angle between the major axis of the ellipse and the coordinate X axis is γ, and let:

[0065]

[0066] Divide both sides of equation (7) by L 1 , that is (here C=0, D=0):

[0067]

[0068] Formula (8) is the conic section equation that represents the ellipse. The geometric parameters of the ellipse can be derived from the conic section equation coefficients:

[0069]

[0070]

[0071] x 0 =y 0 =0

[0072] The above formula shows that: ① Different spatial straight lines project ellipses on the horizontal plane under spherical perspective projection, the center of the ellipse is the center of the projection sphere, and the major semi-axis a is always equal to the projection sphere radius R g , the length of the minor semi-axis b is related to the direction of the normal of the space plane passing through the center of the sphere and the space line; ② For the same space line, the change in the size of the projection spherical radius only makes the major and minor semi-axes of the projection ellipse scaled in proportion. The present invention refers to ①② as the ideal horizontal projection ellipse constraint of the space line under spherical perspective projection. Due to the influence of radial distortion and the aspect ratio of the camera not being equal to 1, the horizontal projection ellipse of the space line on the fisheye image does not meet the above ideal constraint, which is manifested as the major semi-axis a is not equal. Therefore, the constraint can be used to establish the calibration equation to solve the internal parameters of the fisheye lens (u 0 ,v 0 ,f,A,k 1 ,k 2 ).

[0073] Let P(x,y) be any point on the plane ellipse e, and the geometric parameters of the ellipse are (x 0 ,y 0 ,a,b,γ), where: (x 0 ,y 0) represents the center position of the ellipse, (a, b) are the major and minor semi-axes of the ellipse respectively, γ is the rotation angle between the major axis of the ellipse and the coordinate X axis, if (F1, F2) represents the two foci of the ellipse, then according to the geometric characteristics of the ellipse: |PF1|+|PF2|=2a, we have:

[0074]

[0075] Where: F1 = (x 0 -c*cosγ,y 0 -c*sinγ), F2=(x 0 +c*cosγ,y 0 +c*sinγ), c 2 =a 2 -b 2 When the projection sphere radius R g =1, a=1 in formula (9), then (xx 0 ,yy 0 ) is equivalent to P in formula (4) m (x m ,y m ),have:

[0076]

[0077] Multiplying both sides of equation (10) by the equivalent focal length f of the camera, we get: (here c is the calculation result after the major and minor semi-axes of the projected ellipse are enlarged by the scale factor f)

[0078]

[0079] According to formula (5), formula (11) can be rewritten as:

[0080]

[0081] in:

[0082] Therefore, equation (12) is about the unknown number (u 0 ,v 0 ,f,A,k 1 ,k 2 ) and the nonlinear function E(u 0 ,v 0 ,f,A,k 1 ,k 2 ,b,γ), formula (12) is the calibration equation for solving the internal parameters of the fisheye lens in the present invention. However, this equation is nonlinear. By expanding it by Taylor series and taking the first-order term, the error equation V can be obtained:

[0083]

[0084]

[0085]

[0086]

[0087]

[0088] In formula (13): is the initial value of the given parameter; is the coefficient of the equation, which is the partial derivative of the nonlinear function E under the given initial value of the parameter; (du 0 ,dv 0 ,dk 1 ,dk 2 ,dA,df,db,dγ) are the unknowns in the equation and are the parameter increments of the nonlinear function E. Let e i =(x 0 ,y 0 ,a,b,γ)(i=0,1,...,N-1) represents the projection ellipse (arc) of different spatial lines i on the fisheye image, is the projection ellipse e i If N≥2 and M≥5, the error equation V is established according to equation (13) with any image point on the projection ellipse as the observation value, and the total number of unknowns to be estimated is 6+2N, that is,

[0089]

[0090]

[0091]

[0092] According to the indirect adjustment principle, the least squares adjustment calculation is performed on the above error equation to obtain the optimal solution:

[0093]

[0094] Since equation (12) is nonlinear, the parameters can be solved iteratively under the condition of given initial values ​​of the parameters, as follows:

[0095]

[0096] In one embodiment, (k 1 ,k 2 ) is directly set to 0, and the initial values ​​of the remaining parameters are calculated as follows:

[0097] Let (x i ,y i)(i=1,2,...,S) represents the projection ellipse (arc) e of the spatial straight line on the fisheye image j Contour points, and fit the ellipse (arc) using the following conic section equation:

[0098] x 2 +Axy+By 2 +Cx+Dy+E=0 (13)

[0099] If S is not less than 5, the least squares solution of the equation coefficients A, B, C, D, and E can be obtained by minimizing the following objective function Min(F), and then e can be derived j The geometric parameter values ​​are:

[0100]

[0101]

[0102]

[0103] According to formula (13)-(14), we can calculate e j After the geometric parameters are calculated, (b, γ) is directly used as the initial value, and the average value of the major semi-axis parameter a of the ellipse projected by all spatial straight lines on the fisheye image is used as the initial value of f.

[0104] Assuming that the fisheye lens field of view meets 180°, according to the given fisheye imaging model, the effective pixels of the fisheye image under the unit sphere projection will be a circular area, see Figure 4 (a), the radius of this region is determined by the maximum incident angle θ, see Figure 2 (b), that is, the points on the boundary of the fisheye image contour should theoretically satisfy:

[0105]

[0106] Substituting into formula (5) we can get:

[0107]

[0108] From formula (15), we can see that the aspect ratio parameter A is not equal to 1, which makes the fisheye image contour change from a circle to an ellipse. Similarly, let (x i ,y i )(i=1,2,...,S) represents the detected elliptical contour points in the effective area of ​​the fisheye image. The geometric parameters of the elliptical contour E can be calculated according to equations (13)-(14). The initial value of the aspect ratio parameter A=a / b can be given by the ratio of the long and short axis geometric parameters of E, and the initial value of the principal point coordinates (u 0 ,v 0 )=(x 0 ,y 0). When the fisheye lens field of view is less than 180°, it can be considered that part of the ellipse outline boundary is outside the field of view, see Figure 4 (b), but the center position and major and minor axis parameter values ​​of the ellipse can still be obtained by fitting the points on the boundary of the remaining ellipse contour.

[0109] This embodiment also provides a performance test experiment of the method of this embodiment. Taking the fisheye image with rich straight line features published on the Internet as the object, the internal parameters of the fisheye lens when the image is acquired are obtained through single-view calibration calculation, see Figure 5 (a), 5(c) and 5(e). This embodiment obtains the elliptical contour (arc) on a single fisheye image through Canny edge detection and random Hough ellipse extraction operations. Figure 5 (b), 5(d) and 5(f), the initial values ​​of the internal parameters of the fisheye lens are given by the extracted elliptical contour (arc) and iteratively optimized using the calibration equation, see Figure 6 ,Table 1 lists the final calibration parameters and their estimation error RMSE. Figure 7 The calibration parameters of this embodiment and the calibration of the well-known commercial software DXO are given. Figure 5 The plane perspective correction result of the fisheye image in the figure. Since the software DXO cannot perform cubic box expansion, the DXO plane perspective correction here selects the central area of ​​the fisheye image with relatively small deformation (corresponding to the middle part of the cubic box expansion in this article) and obtains the best correction effect through manual adjustment. Figure 7 It can be seen that the correction effect of the proposed method is better than that of the commercial software DXO. Even for image C with relatively poor parameter calibration accuracy, the straight lines within the field of view covered by the extracted ellipse (arc) also have good perspective characteristics, which is in line with the visual habits of the human eye.

[0110] Table 1. The values ​​of the calibration parameters of the image with single view for the method in this paper

[0111]

[0112] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A method for self-calibration of internal parameters of a fisheye lens, characterized in that: The method includes: Establish a fisheye imaging model and obtain the internal parameters of the fisheye lens to be calibrated; A calibration equation is established according to the ideal projection ellipse constraint of the space straight line on the horizontal plane, and the calibration equation is expanded according to the Taylor series and the first-order term is taken to obtain the error equation; The initial values ​​of the internal parameters of the fisheye lens to be calibrated are given by using the elliptical contour boundary of the effective area of ​​the fisheye image and the elliptical arc segment information of the projection of the spatial straight line on the fisheye image, and the calibration equation is iteratively solved to obtain the least squares estimate of the calibration parameters; The constraints of the ideal projection ellipse on the horizontal plane according to the spatial straight line include: ① Different spatial straight lines project ellipses on the horizontal plane under spherical perspective projection. The center of the ellipse is the center of the projection sphere, and the major semi-axis a is always equal to the radius R of the projection sphere. g , the length of the minor semi-axis b is related to the direction of the normal line of the space plane passing through the center of the sphere and the space straight line; ② For the same spatial straight line, the change in the radius of the projection sphere only causes the long and short semi-axes of the projection ellipse to scale in equal proportion; The obtaining of the internal parameters of the fisheye lens to be calibrated specifically includes: Space coordinate transformation, any space point P in the world coordinate system W , after rotation and translation of the spatial coordinate transformation, it is converted into point P in the camera coordinate system C ; Unit sphere mapping, point P C Along ray O C P C Direction mapping to point P on the unit sphere S ; Spherical projection, point P S Orthographic projection is performed onto a fixed plane perpendicular to the main optical axis of the fisheye lens to obtain the ideal projection point P. m (x m ,y m ), Pixel coordinate transformation, using the camera internal parameters to transform the ideal projection point coordinates to the fisheye image pixel coordinates; The coordinate transformation relationship from the ideal projection point to the fisheye image pixel is: (u0)*(1+k1r 2 +k2r 4 )=Af*x m ,(v-v0)*(1+k1r 2 +k2r 4 )=f*y m r 2 =(u-u0) 2 +(v-v0) 2 Where: (u, v) is the actual pixel coordinate of the fisheye image, (u0, v0) is the coordinate of the camera principal point, f is the equivalent focal length of the camera, A is the aspect ratio, k1, k2 are the radial distortion coefficients, and the parameters (u0, v0, f, A, k1, k2) are the internal parameters of the fisheye lens to be calibrated; The calibration equation is: in, b is the minor semi-axis of the ellipse, and γ is the rotation angle between the major axis of the ellipse and the coordinate X-axis.

2. The method for self-calibration of internal parameters of a fisheye lens according to claim 1, characterized in that: The calibration equations are solved iteratively as follows: in, represents the least squares adjustment result of the error equation, The error equation V is: in, is the initial value of the given parameter; are the coefficients of the equation, which are the partial derivatives of the nonlinear function E under the given initial values ​​of the parameters; (du0, dv0, dk1, dk2, dA, df, db i ,dγ i ) is the unknown number in the equation and is the parameter increment of the nonlinear function E.

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