Physical parameter model of camera-mirror variable line-of-sight system and its calibration method

Abstract

This invention provides a physical parameter model and calibration method for a camera-galvanometer variable line-of-sight system. It models the complete geometric process of a spatial point being imaged in the camera after deflection by a galvanometer, and parameterizes the deflection and imaging processes. The variable line-of-sight system parameters include 2D scanning galvanometer parameters, camera parameters, relative mounting pose parameters of the camera and 2D scanning galvanometer, and pose parameters of the variable line-of-sight system in the world coordinate system. It describes the specific mathematical relationship between the spatial point and the imaging point under any deflection line of sight. The calibration method completes the modeling and calibration of the camera-galvanometer variable line-of-sight imaging system. This invention enables the imaging process of the variable line-of-sight imaging system under any line of sight to be solved through the model parameters, making the variable line-of-sight imaging system usable in quantitative visual applications. Furthermore, the model has clear physical meaning, concise and clear parameters, a simple calibration process, and high reliability and stability of the calibration results.

Description

Technical Field

[0001] This invention relates to the field of machine vision technology, specifically to a physical parameter model and calibration method for a camera-galvanometer variable line-of-sight imaging system. Background Technology

[0002] A two-dimensional scanning galvanometer is a vector scanning device that uses two special oscillating motors to rapidly deflect two optical lenses around their respective axes. By changing the deflection angles of the two axes, the outgoing light can be deflected in two dimensions. With the continuous development of two-dimensional scanning galvanometer manufacturing technology, the positioning accuracy, repeatability, and scanning speed of the galvanometer have been greatly improved, leading to its widespread application in many fields. For example, changing the outgoing direction of the incident laser beam by rapidly deflecting the two optical lenses around their axes is widely used in laser marking, laser processing, laser labeling, and laser medical aesthetics. In recent years, two-dimensional scanning galvanometers have also been used in conjunction with visual imaging systems to change the line-of-sight of the imaging system and expand the camera's field of view. For example, Liu Chenyi (Liu Chenyi. Research on Visual Tracking Technology for Small Targets with Large Field of View [Master's Thesis]. Huazhong University of Science and Technology, 2019) studied the tracking technology of a system combining a galvanometer and a camera in a large field of view; Zhou Kai (Zhou Kai. Research on Long-Distance Large Field of View Iris Recognition Technology Based on Galvanometer Scanning [Master's Thesis]. Xi'an University of Electronic Science and Technology, 2019) applied the galvanometer-camera system to high-resolution imaging of a local small area. In these studies, the two-dimensional scanning galvanometer was simply used to change the imaging area of ​​the camera each time it took a picture, without establishing a quantitative relationship between the three-dimensional scene and the points on the camera's imaging plane under different galvanometer deflection angles. However, in various applications related to three-dimensional vision, establishing a three-dimensional imaging model of the imaging system is an essential prerequisite and foundation. However, for camera-galvanometer combined variable-line imaging systems, the light deflection process of a two-dimensional scanning galvanometer involves many uncertainties, such as the difficulty in determining the incident light position and direction, the precise deflection angle, and the difficulty in accurately measuring the distance between the two axes of the galvanometer. These factors make it difficult to accurately model the reflection process. Furthermore, unlike laser-galvanometer systems where only one laser beam is incident on the central axis of the first optical lens, in a camera-galvanometer imaging system, each pixel on the two-dimensional image plane corresponds to a principal ray. This principal ray is reflected by two galvanometers, converges through a set of lenses to the camera's optical center, and is imaged at the corresponding pixel position on the image plane. Therefore, the imaging position of the three-dimensional scene on the imaging plane is not only related to the three-dimensional scene and the camera's imaging parameters, including nonlinear distortion, but also has a complex relationship with the two deflection angles of the galvanometer. These factors combined make it very difficult to establish an accurate working model for the camera-galvanometer variable-line imaging system. Currently, Han Zidong et al. (Three-dimensional imaging model and calibration method of variable line-of-sight system combining camera and galvanometer, Chinese patent, CN202110469560.1) have proposed a three-dimensional imaging model and calibration method for such variable line-of-sight imaging systems. The proposed camera-galvanometer variable line-of-sight imaging system model is a neural network black box model. The model calibration is achieved by relying on a data-driven method. Therefore, a large amount of data needs to be collected for calibration, which is difficult and the model is not intuitive. The parameters in the model lack clear physical meaning.Zhang Liyan et al. (An Equivalent Multi-View Vision Model and Calibration Method for a Variable Line-of-Sight Imaging System, Chinese Patent Application No.: 202211692983.0) proposed an equivalent multi-view vision system model and calibration method for a variable line-of-sight imaging system. This method discretizes the line-of-sight direction of the variable line-of-sight system and calibrates each sampled line of sight separately. While this calibration method is simple, it cannot model the complete imaging area of ​​the variable line-of-sight system. Therefore, establishing a high-precision imaging model that can completely and intuitively represent the imaging process, with parameters having practical physical meaning, and providing a simple, reliable, and highly executable calibration method is of great significance. Summary of the Invention

[0003] This invention provides a physical parameter model and calibration method for a camera-galvanometer variable line-of-sight imaging system;

[0004] The physical parameter model of the camera-galvanometer variable line-of-sight imaging system provided by the present invention parametrically models the complete geometric process of a spatial point being imaged in the camera after being deflected by the galvanometer, based on the geometric optical path of the imaging process of the variable line-of-sight imaging system. The parameters of the parametric model include the intrinsic parameters of the two-dimensional scanning galvanometer describing the deflection of the two-dimensional scanning galvanometer, the imaging parameters of the camera and lens itself, the relative installation pose parameters between the camera and the two-dimensional scanning galvanometer, and the pose parameters of the two-dimensional scanning galvanometer in the world coordinate system.

[0005] The physical parameter model of the camera-galvanometer variable line-of-sight imaging system transforms spatial points to the two-dimensional scanning galvanometer coordinate system through the pose parameters of the two-dimensional scanning galvanometer in the world coordinate system. The three-dimensional points in the two-dimensional scanning galvanometer coordinate system are obtained as virtual mirror points after two total internal reflections by the two-dimensional scanning galvanometer through the two-dimensional scanning galvanometer parameters. The virtual mirror points are then transformed to the camera coordinate system through the relative installation pose parameters between the camera and the two-dimensional scanning galvanometer. Finally, the pixel coordinates of the imaging point are obtained through the imaging parameters of the camera and lens itself.

[0006] The parameterization process of the two-dimensional scanning galvanometer is as follows: by parameterizing the relationship between the deflection angles (α,β) of the two axes in the galvanometer and the input control quantity (a,b) of the two-dimensional scanning galvanometer, a functional relationship of (α,β)=g(a,b) is established. The galvanometer deflection transformation matrix H corresponding to the deflection control quantity (a,b) is calculated by using the deflection angle (α,β) corresponding to a given galvanometer deflection control quantity (a,b) and the distance e between the rotation axes of the two reflecting mirrors in the galvanometer.

[0007] The functional relationship (α,β)=g(a,b) is parameterized by the deflection angle (α,β) of the galvanometer through the polynomial form of the two-dimensional scanning galvanometer input control quantity (a,b);

[0008] The imaging parameters of the camera and lens itself establish a functional relationship (u,v) = f(x,y,z) between the pixel coordinates (u,v) of the captured image and the corresponding three-dimensional spatial points (x,y,z) in the camera coordinate system.

[0009] The relative mounting pose parameters between the camera and the 2D scanning galvanometer are used to establish separate Cartesian coordinate systems for the camera and the scanning galvanometer, respectively, through a rigid body transformation matrix. It describes the transformation relationship between two coordinate systems, representing the transformation of a 3D point from the galvanometer coordinate system to the camera coordinate system, and realizes the parameterization of the assembly pose;

[0010] The pose parameters of the two-dimensional scanning galvanometer in the world coordinate system are obtained through a rigid body transformation matrix. Establish the transformation relationship between the two-dimensional scanning galvanometer coordinate system and the world coordinate system to represent the transformation of three-dimensional points from the world coordinate system to the two-dimensional scanning galvanometer coordinate system;

[0011] This invention also provides a method for calibrating the physical parameter model of a camera-galvanometer variable line-of-sight imaging system, comprising the following steps:

[0012] 1) Complete the calibration of the galvanometer's internal parameters and the camera and lens's own parameters;

[0013] 2) The mounting pose parameters of the camera and galvanometer and the pose parameters of the 2D scanning galvanometer coordinate system in the world coordinate system are calibrated;

[0014] 3) Perform nonlinear optimization on all parameters of the variable line-of-sight imaging system;

[0015] The calibration method is as follows:

[0016] 1) The imaging parameters of the camera and lens in the physical parameter model of the camera-galvanometer variable line-of-sight imaging system are calibrated in advance to obtain the imaging parameter matrix K and distortion coefficient vector kd of the camera and lens; the distance e between the two rotation axes of the two-dimensional scanning galvanometer in the physical parameter model of the camera-galvanometer variable line-of-sight imaging system is taken as its nominal value as the initial value; in the polynomial function relationship (α,β)=g(a,b) between the deflection angle of the two-dimensional scanning galvanometer and the galvanometer control quantity in the physical parameter model of the camera-galvanometer variable line-of-sight imaging system, the constant term in the polynomial is taken as the nominal initial angle k of the two lenses. a0 k b0 As the initial value, the coefficients of the first-order terms in the polynomial are taken as the approximate deflection angle k corresponding to the unit deflection control quantity. a1 k b1 The initial value is 0, and the initial values ​​of the other higher-order coefficients of the polynomial are set to 0;

[0017] 2) By providing M sets of galvanometer deflection control values ​​(a, b) mm = 1, 2, ..., M, Adjust the line of sight of the variable line-of-sight system to photograph a spatial point (X, Y, Z) with known coordinates in the world coordinate system. i Let i = 1, 2, ..., I, and extract spatial points (X, Y, Z). i In the galvanometer deflection control values ​​(a, b) m Image pixel coordinates under the corresponding line of sight In each viewpoint, there should be at least four spatial points with known coordinates. The transformation matrix T from the world coordinate system to the camera imaging coordinate system for each viewpoint is obtained using the Projective n Points (PnP) algorithm under a single viewpoint. m ;

[0018] 3) Based on (a, b) described in step 2). m The corresponding galvanometer deflection matrix can be calculated. Therefore, M linear equations can be established:

[0019]

[0020] In formula (1) Since the variables are unknown and all are invertible, formula (2) can be rewritten as:

[0021]

[0022] Equation (2) of the form AX = ZB has 24 unknowns. The equations constructed from the two deflected views can provide 12 equality constraints. Therefore, when there are at least 3 view deflections, i.e., M ≥ 3, the system of equations has a solution. At this point, we have obtained the initial values ​​of all parameters in the variable line-of-sight imaging system.

[0023] 5) Substitute all the initial values ​​of the obtained variable line imaging system parameters into the physical parameter model of the variable line imaging system, calculate the reprojected pixel coordinates of each known three-dimensional point in the world coordinate system, optimize all parameters in the physical parameter model of the variable line imaging system by minimizing the error between the reprojected pixel coordinates and the acquired pixel coordinates, and complete the system calibration.

[0024] The beneficial effects of this invention are as follows:

[0025] 1. The physical parameter model of the galvanometer-camera variable line-of-sight imaging system proposed in this invention has a clear physical meaning and the model parameters are concise and clear; the parameter calibration process of the model is simple to operate and the calibration results are highly reliable and stable.

[0026] 2. The three-dimensional imaging model and calibration method of the variable line imaging system proposed in this invention provide a complete geometric optical model of the variable line imaging system. Based on this, the variable line imaging system can be more conveniently applied to quantitative three-dimensional vision applications, meeting the needs of applications such as large-scene three-dimensional precision measurement, and has broad application prospects. Attached Figure Description

[0027] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the variable line-of-sight imaging system of the present invention.

[0029] Figure 2 This is a schematic diagram of an embodiment of the system model calibration method of the present invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] This invention provides a complete imaging model of a variable line-of-sight system that combines a camera and a galvanometer;

[0032] The variable line-of-sight imaging system includes a two-dimensional scanning galvanometer, an area array camera, an optical lens, a galvanometer controller, and a computer host.

[0033] The computer host is connected to the two-dimensional scanning galvanometer through the galvanometer controller, and the two digital signals (a, b) emitted by the computer host are used as the galvanometer rotation angle control quantities.

[0034] The two-dimensional galvanometer contains two total internal reflection mirrors. Under the control of the galvanometer rotation angle control, the two total internal reflection mirrors deflect rapidly around the axis to change the line of sight and the corresponding imaging area of ​​the image sensor composed of the area array camera and the optical lens.

[0035] The deflection angles (α, β) of the two lenses of the galvanometer can be considered as exhibiting an approximately linear change with the control quantity (a, b), while also possessing certain nonlinear characteristics. Therefore, the functional relationship between the deflection angles (α, β) and the control quantity (a, b) is parameterized using a polynomial approximation method. In this embodiment, the constant term k of the polynomial...a0 k b0 Let k be the initial angle between the two lenses, and k be the coefficient of the first-order term. a1 k b1 The parameter is the linear proportionality between the galvanometer control quantity and the deflection angle. The other higher-order coefficients are the nonlinear distortion compensation parameters of the galvanometer. In this embodiment, the polynomial function relationship (α,β)=g(a,b) is specifically taken as follows:

[0036]

[0037] Since the rotation axes of the two mirrors in the galvanometer are perpendicular to each other, the distance between the two axes is represented by the parameter e. Taking the rotation axis of mirror-2 as the X-axis, the common perpendicular of the rotation axes of mirror-1 and mirror-2 as the Y-axis, and the intersection of the common perpendicular with the rotation axis of mirror-2 as the origin of the coordinate system, a galvanometer coordinate system (G-CF) is established. Figure 1 As shown, the coordinate transformation matrix H of a point in the galvanometer coordinate system after reflection by mirror-2 and mirror-1 can be obtained:

[0038]

[0039] The camera and lens constitute a camera imaging system. A coordinate system (C-CF) is established with the camera's imaging plane as the XY plane and the center of the imaging plane as the origin. Figure 1 As shown, the imaging parameters of the camera and lens themselves consist of an imaging matrix K and a set of lens distortion parameters k. d This means that, based on the imaging parameters of the camera and lens, a coordinate transformation relationship from a 3D point in the camera coordinate system to the pixel coordinate system can be obtained:

[0040]

[0041]

[0042] In equation (5), [x,y,z,1] T Let [u, v, 1] be the homogeneous coordinates of a 3D point in the camera coordinate system. T Given the homogeneous coordinates of the corresponding ideal pixel in the image, the pixel coordinates of the image under this model can be obtained by applying equation (6) using the distortion coefficients of the camera imaging system. d ,v d ] T λ is the scaling factor.

[0043] The variable-line-of-view imaging system consists of a camera imaging system fixed to one end of a two-dimensional scanning galvanometer. By changing the field of view of the camera imaging system through the scanning galvanometer, the variable-line-of-view function is achieved. Therefore, the relative mounting pose between the camera system and the two-dimensional scanning galvanometer, i.e., the relative mounting pose parameters between the camera and the galvanometer, is determined by a three-dimensional rigid body transformation matrix from a point in the galvanometer coordinate system to the camera coordinate system. To indicate;

[0044] The pose parameters of the variable-line imaging system in the world coordinate system (W-CF) are obtained through the three-dimensional rigid body transformation matrix from a point in the W-CF to the G-CF. To indicate;

[0045] In summary, the ideal imaging model of a variable line-of-sight imaging system can be written as:

[0046]

[0047] In the formula, [X,Y,Z,1] T Let [u, v, 1] be the homogeneous coordinates of a 3D point in the world coordinate system. T Given the homogeneous coordinates of the corresponding ideal pixel in the image, equation (6) can be used to further obtain the distorted imaging pixel coordinates under the physical parameter model of the complete camera-galvanometer variable line-of-sight imaging system. d ,v d ] T λ is the scaling factor.

[0048] In this embodiment, the specific calibration method is as follows:

[0049] 1) The camera imaging system was calibrated using Zhang Zhengyou's calibration method to obtain the camera imaging parameter matrix K and distortion parameter k. d1 k d2 k d3 k d4 ;

[0050] 2) Refer to the galvanometer manufacturer's manual to obtain the distance e between the two rotation axes of the 2D scanning galvanometer and the initial angle k between the two lenses. a0 k b0 And the deflection angle k corresponding to the unit control quantity a1 k b1 A cubic polynomial is used to approximate the relationship between the control quantity of the galvanometer and the deflection angle of the lens. The initial value of the constant term in the cubic polynomial is taken as k. a0 k b0 The nominal value, the initial value of the coefficient of the first-order term in the cubic polynomial is taken as k. a1 k b1 The initial values ​​of the remaining higher-order deflection angle parameters are set to 0;

[0051] 3) By providing 25 sets of galvanometer deflection control values ​​(a, b) m m = 1, 2, ..., 25, Adjust the field of view of the variable line-of-sight imaging system to capture spatially encoded points (X, Y, Z) with known coordinates in the world coordinate system. i For i = 1, 2, ..., 100, the coordinates of the image pixels in each field of view are: Using the Projectiven Points (PnP) algorithm for a single viewpoint, the transformation matrix T from the world coordinate system to the imaging coordinate system for each viewpoint is obtained. m ;

[0052] 4) Based on (a, b) in step 3). m The corresponding galvanometer deflection matrix H can be calculated. m m = 1, 2, ..., 25, from which 25 linear equations as in equation (1) can be established to construct a system of equations;

[0053]

[0054] 5) Use the Kronecker product to solve the system of equations (8) to obtain the parameter matrix. At this point, the initial values ​​of all parameters in the variable line-of-sight imaging system have been obtained.

[0055] 6) Perform nonlinear optimization on all parameters in the obtained physical parameter models of the variable line-of-sight imaging system, and optimize the spatial points (X,Y,Z). i i = 1, 2, ..., 100 are reprojected onto the variable line imaging system using the physical parameter model shown in formula (7) to obtain the ideal reprojected pixel coordinates. The distorted pixel coordinates are then calculated by substituting the distortion parameters into formula (6). The error between the distorted reprojected pixel coordinates and the acquired real pixel coordinates is then calculated.

[0056]

[0057] Where ζ(·) is the distortion function shown in equation (6).

[0058] In this embodiment, the Gauss-Newton method is used to optimize all parameters in equation (9) to minimize the reprojection error, thereby obtaining the final variable line-of-sight imaging system parameters and completing the system calibration.

[0059] The various embodiments in this specification are described in a progressive manner. Similar or identical parts between embodiments can be referred to interchangeably. Each embodiment focuses on its differences from other embodiments. In particular, for the device embodiments, the above descriptions are merely preferred embodiments of the present invention. Since they are fundamentally similar to the method embodiments, the descriptions are relatively simple, and relevant parts can be referred to the descriptions of the method embodiments. The above descriptions are merely specific embodiments of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention, without departing from the principle of the present invention, should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A physical parameter model of a camera-galvanometer variable line-of-sight imaging system, characterized in that: A parametric model is constructed to model the complete optical process of a spatial point being deflected by a 2D scanning galvanometer and then imaged in a camera. All parameters in the constructed model have clear physical meanings, including 2D scanning galvanometer parameters describing the control of light deflection and reflection, imaging parameters of the camera and lens, relative mounting pose parameters between the camera and the 2D scanning galvanometer, and pose parameters of the 2D scanning galvanometer in the world coordinate system. The constructed parametric model transforms the spatial point to the 2D scanning galvanometer coordinate system using the pose parameters of the 2D scanning galvanometer in the world coordinate system. The 3D point in the 2D scanning galvanometer coordinate system is then transformed into a virtual mirror point after two total internal reflections by the 2D scanning galvanometer parameters. The virtual mirror point is then transformed to the camera coordinate system using the relative mounting pose parameters between the camera and the 2D scanning galvanometer. Finally, the pixel coordinates of the image point are obtained using the imaging parameters of the camera and lens. Specifically, the parametric process of the 2D scanning galvanometer involves adjusting the deflection angles of the two axes within the galvanometer. Input control quantity with two-dimensional scanning galvanometer Parameterize the relationships between them and establish The functional relationship is based on the distance e between the rotation axes of the two reflecting mirrors in the galvanometer and the given galvanometer deflection control amount. Corresponding deflection angle The galvanometer deflection control quantity was calculated. The corresponding galvanometer deflection transformation matrix H.

2. The physical parameter model of the camera-galvanometer variable line-of-sight imaging system according to claim 1, characterized in that: The functional relationship The input control quantity of the two-dimensional scanning galvanometer The polynomial approximation method for the deflection angle of the galvanometer Perform parameterization.

3. The physical parameter model of the camera-galvanometer variable line-of-sight imaging system according to claim 1, characterized in that: The aforementioned galvanometer deflection transformation matrix H is used to describe the transformation process of points in the two-dimensional scanning galvanometer coordinate system being reflected sequentially by mirror-2 and mirror-1 in the two-dimensional scanning galvanometer to obtain virtual mirror points.

4. The physical parameter model of the camera-galvanometer variable line-of-sight imaging system according to claim 1, characterized in that: The relative mounting pose parameters between the camera and the 2D scanning galvanometer are used to establish separate Cartesian coordinate systems for the camera and the scanning galvanometer, respectively, through a rigid body transformation matrix. It describes the transformation relationship between two coordinate systems, representing the transformation of a 3D point from the 2D scanning galvanometer coordinate system to the camera coordinate system, and realizes the parameterization of the assembly pose between the camera and the 2D scanning galvanometer.

5. The physical parameter model of the camera-galvanometer variable line-of-sight imaging system according to claim 1, characterized in that: The pose parameters of the two-dimensional scanning galvanometer in the world coordinate system are obtained through a rigid body transformation matrix. Establish the transformation relationship between the two-dimensional scanning galvanometer coordinate system and the world coordinate system to represent the transformation of a three-dimensional point from the world coordinate system to the two-dimensional scanning galvanometer coordinate system.

6. A method for calibrating the physical parameter model of the camera-galvanometer variable line-of-sight imaging system as described in claim 1, characterized in that... Includes the following operations: 1) Complete the calibration of the two-dimensional scanning galvanometer parameters, camera and lens parameters; 2) The mounting pose parameters of the camera and galvanometer, and the pose parameters of the 2D scanning galvanometer coordinate system in the world coordinate system are calibrated; 3) Perform nonlinear optimization on all parameters in the physical parameter model of the variable line imaging system.

7. The calibration method for the physical parameter model of the camera-galvanometer variable line-of-sight imaging system according to claim 6, characterized in that: Step 2) describes the method for calibrating the camera and galvanometer mounting pose parameters and the pose parameters of the 2D scanning galvanometer coordinate system in the world coordinate system, and then sequentially inputs the control parameters into the variable line-of-sight imaging system. Calculate the deflection control value for each given galvanometer. The coordinate transformation matrix from the world coordinate system to the camera imaging coordinate system under the corresponding imaging line of view. ,according to ； A system of linear equations consisting of M equations corresponding to M viewpoints is obtained. The rigid body transformation matrix is ​​obtained by solving the system of linear equations. and rigid body transformation matrix .

8. The calibration method for the physical parameter model of the camera-galvanometer variable line-of-sight imaging system according to claim 7, characterized in that: Variable line-of-sight imaging system in galvanometer deflection control The coordinate transformation matrix from the world coordinate system to the camera imaging coordinate system under the corresponding imaging view. Based on the calibrated camera and lens parameters, at least four known coordinates of three-dimensional points in the world coordinate system, and the galvanometer deflection control values ​​of each known three-dimensional point... The pixel coordinates of the image under the corresponding camera imaging line of view are obtained.

9. The calibration method for the physical parameter model of the camera-galvanometer variable line-of-sight imaging system according to claim 6, characterized in that: The nonlinear optimization process described in step 3) involves reprojecting spatial points onto the image plane of the variable line-of-sight imaging system through the physical parameter model of the variable line-of-sight imaging system to obtain the reprojected pixel coordinates. By minimizing the error between the reprojected pixel coordinates and the acquired pixel coordinates, all parameters in the physical parameter model of the variable line-of-sight imaging system are optimized to obtain the final variable line-of-sight imaging system parameters.

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