CN108805935B - Linear array camera distortion correction method based on orthogonal pixel equivalence ratio - Google Patents
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Abstract
一种基于正交像素当量比的线阵相机畸变校正方法，通过分析线阵相机成像模型，推演出理想镜头下正交方向像素当量比值恒定的理论，从而最终得到线阵相机的畸变参数。具体步骤是首先求取棋盘格图片上的角点，其次任取相邻两行的角点，推导出它们的无畸变坐标表达式，然后求取小方格对角线中点的x轴与y轴方向像素当量值，再然后根据理想镜头下正交方向像素当量比值恒定的理论得出待优化目标函数，最后利用非线性优化方法即可得到畸变参数。本发明方法能够同时得到图片的纵向拉伸比例，无需进行二次校正，因此计算量更小，同时稳定性好，实施条件易达到。
A distortion correction method for line scan cameras based on the orthogonal pixel equivalence ratio. By analyzing the imaging model of the line scan camera, the theory that the pixel equivalence ratio in the orthogonal direction is constant under the ideal lens is deduced, and finally the distortion parameters of the line scan camera are obtained. The specific steps are to first obtain the corner points on the checkerboard picture, and then take the corner points of two adjacent rows, deduce their undistorted coordinate expressions, and then obtain the x-axis and the midpoint of the diagonal of the small square. The pixel equivalent value in the y-axis direction is obtained, and then the objective function to be optimized is obtained according to the theory that the pixel equivalent ratio in the orthogonal direction is constant under the ideal lens, and finally the distortion parameter can be obtained by using the nonlinear optimization method. The method of the invention can obtain the longitudinal stretching ratio of the picture at the same time, and does not need to perform secondary correction, so the calculation amount is smaller, the stability is good, and the implementation conditions are easy to achieve.
Description
Technical Field
The invention belongs to the technical field of image processing, relates to a distortion correction technology of a camera, and particularly relates to a linear array camera distortion correction method based on an orthogonal pixel equivalence ratio.
Background
The linear array camera has simple structure, low cost and high resolution, and is increasingly applied to a non-contact real-time measuring system, a surface defect detecting system and a high-speed moving target attitude measuring system. In the applications of high-precision size measurement, linear array binocular vision and the like, the system performance can be seriously influenced by the existence of lens distortion. Therefore, the distortion of the camera lens must be calibrated and compensated in the line camera vision system with higher requirements.
At present, the research on the lens distortion theory of the linear array camera is mature, the classical calibration method of Zhangyingyou or the single distortion calibration method have good precision performance, but the distortion model theory of the linear array camera is not perfect. At present, linear array camera lens distortion calibration methods include a method based on an intersection ratio invariant theory, a polynomial fitting method, a precise angle measurement method and the like. The cross ratio invariant theory is based on the property of invariant cross ratio in perspective projection, and the result of the theory used in the distortion calibration of the area-array camera is not very stable and is easy to fall into local optimum. The polynomial fitting method does not consider the actual imaging model of the camera, and only uses the polynomial to model the distortion characteristics in the scene, so that the adaptability of the method in different scenes is not good and the calculation amount is large. The precise angle measurement method depends on an additional high-precision calibration tool, and the operation is inconvenient.
In addition, the linear array camera is typically applied to continuously scan an object moving at a constant speed line by line, a stretching ratio in the longitudinal direction is often caused due to the mismatch between the scanning frequency and the target traveling speed, and the longitudinal stretching correction cannot be performed based on the distortion removal method with a constant cross ratio.
Disclosure of Invention
The invention aims to solve the problems that: a new method for correcting distortion of a linear array camera is provided, and the longitudinal stretching ratio of pictures can be obtained simultaneously.
The technical scheme of the invention is as follows: a distortion correction method of a linear array camera based on orthogonal pixel equivalence ratio lists pixel equivalence formulas of two directions of a linear array camera scanning direction and a vertical scanning direction according to imaging characteristics of the linear array camera, deduces a conclusion that the pixel equivalence ratio of the orthogonal direction under an ideal lens is constant, designs a distortion parameter solving function accordingly, and performs distortion correction of the linear array camera, and comprises the following steps:
the method comprises the following steps: designing a plane multi-square-grid checkerboard, recording the length and width of each unit square grid, and enabling the checkerboard to pass below the linear array camera at a constant speed so as to acquire images;
step two: preprocessing the collected checkerboard image, and extracting angular points of all the squares of the checkerboard;
step three: optionally taking angular points of two adjacent lines, obtaining a distortion model of the linear array camera from the distortion model of the area array camera, and deducing a distortion-free coordinate expression of the angular points according to the distortion model of the linear array camera;
step four: calculating pixel equivalent values in the directions of the x axis and the y axis of the middle point of the oblique diagonal line of the small square grid;
step five: and designing an objective function according to the conclusion that the pixel equivalent ratio in the orthogonal direction under the ideal lens is constant, optimizing the objective function by using a nonlinear optimization method, solving to obtain distortion parameters, and using the obtained distortion parameters for distortion correction during actual acquisition of the linear array camera.
And further, in the fifth step, the longitudinal stretching ratio of the image is obtained by solving the optimization objective function and is used for longitudinal stretching correction of the linear array camera.
Preferably, in the second step, the extracted corner points are in a sub-pixel level, and the more accurate the coordinates of the corner points are, the more favorable the calculation of the distortion parameters is.
The third step is specifically as follows:
the distortion model of the area-array camera is as follows:
wherein x isuAnd yuRepresenting undistorted coordinates, xdAnd ydRepresenting distortion coordinates, δxAnd deltayIs lens distortionThe components in the x and y directions are changed,
in the above formula
(cx,cy) Pixel coordinate of center of distortion, k1As radial distortion coefficient, p1,p2Is the centrifugal distortion coefficient, s1,s2Is the thin prism distortion coefficient;
the standard model of the linear array camera lens distortion is
Wherein, b ═ k1；
In the image collected by the linear array camera, the undistorted coordinates of the obtained angular point are as follows:
wherein b is the radial distortion coefficient, cxIs the distortion center of the line camera.
In the fourth step, the pixel equivalent of the middle point of the oblique diagonal line of the square lattice is obtained as follows: calculating two angular points A (x) of diagonal line1,y1)，B(x2,y2) Pixel equivalent of the midpoint of (1):
wherein, | A0B0|xRepresenting checkerboardThe value of the space distance between the characteristic angular points A and B in the direction of the scanning line, | A0B0|yRepresenting the value of the checkerboard feature corner point a and B spatial distance in the direction perpendicular to the scan line.
The fifth step is specifically as follows: the pixel equivalent ratio of the orthogonal direction under an ideal lens is constant, namely the pixel equivalent D of the x direction in an undistorted imagex(xu) Pixel equivalent D with y directiony(xu) Is equal at any position, has Dx(xu)/Dy(xu) C is a constant, representing the image longitudinal stretch ratio, and sets the objective function:
in the formula, L is the number of the transverse collinear feature points; at this time, the solution of the lens distortion coefficient b is converted into the process of the minimum equation (5).
On the basis of fully analyzing the imaging characteristics of the linear array camera, the invention deduces the theory that the pixel equivalent ratio of the linear array camera in the orthogonal direction is constant after the linear array camera is imaged by an ideal lens, provides a novel method for correcting the distorted image of the linear array camera, can simultaneously obtain the longitudinal stretch coefficient, and has good distortion correction effect through experiments. Compared with a precise angle measurement method, the method does not need to rely on an extra high-precision calibration tool, is more convenient to operate, and has better adaptability in different application scenes. Compared with the cross ratio invariant method, the method has the advantages that the stability is better, the longitudinal stretching correction is carried out while the distortion coefficient is obtained, the secondary correction is not needed, and the calculated amount is smaller. In addition, the distortion calibration method of the linear array camera is also provided in the prior art, namely, a calibration method of lens distortion of the linear array camera (sovereign, xiao hua, xiao yan, guo rui, the university of western-security traffic bulletin, 2013, month 1, volume 47, phase 1), and compared with the calibration method provided by restoring the equidistant collinear characteristic of a calibration object in the text of the calibration method of lens distortion of the linear array camera, the calibration precision of the method is higher, the method can reach 0.2 pixel, the method in the text of the calibration method of lens distortion of the linear array camera is 0.5 pixel, and the scheme of the invention can obtain a longitudinal stretching coefficient while correcting distortion without secondary correction, which cannot be completed by the prior art.
Drawings
FIG. 1 is a flowchart of a distortion correction method of a line camera based on an orthogonal pixel equivalence ratio according to the present invention.
Fig. 2 is an experimental image 1 of a checkerboard calibration plate according to an embodiment of the present invention.
Fig. 3 is an experimental image 2 of a checkerboard calibration plate according to an embodiment of the present invention.
Fig. 4 is a checkerboard calibration plate experimental image 3 according to an embodiment of the present invention.
Fig. 5 is a graph of the average distance from a feature point to a line fitted to the feature point after distortion correction using the method of the present invention.
Fig. 6 is a comparison graph of the length-width ratio of the unit cell after the longitudinal stretching correction of the line camera is carried out by adopting the method of the invention.
Detailed Description
In order to make those skilled in the art better understand the technical solution of the present invention, the technical solution in the embodiment of the present invention will be clearly and completely described below with reference to the drawings in the embodiment of the present invention, and it is obvious that the described embodiment is only a part of the embodiment of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, it is a flow chart of the distortion correction method of the line camera based on the equivalence ratio of orthogonal pixels, and the distortion parameter is obtained by using the pixel equivalence ratio in the orthogonal direction under the distortion-free condition, which will be described below.
And (3) enabling a chessboard pattern calibration board with equidistant collinear feature points to pass through the linear array camera at a constant speed to obtain an image and image coordinates (x, y). Calculating the x direction at the corresponding position, namely the scanning line of the line-scan camera, through the checkerboard imagePixel equivalent of direction DxAnd y-direction, i.e. the pixel equivalent D perpendicular to the line-scan direction of the line-scan cameray。
The inventor researches and discovers that the following 3 conclusions can be obtained according to the imaging characteristics of the linear array camera:
(1) in the column direction, namely the direction perpendicular to the scanning line, the influence of lens distortion is negligible, the y-direction (perpendicular to the scanning line direction of the line camera) pixel equivalent is only related to the distance from an object point to the camera in the optical axis direction, namely the object distance, and since the line camera only scans one line at a time, the object distance is only related to x, the y-direction pixel equivalent is a function of an independent variable x, let Dy(x) F (x), where f (x) characterizes the effect of object distance on pixel equivalence.
(2) The x-direction pixel equivalent on different columns is not only related to the object distance, but also affected by the lens distortion, and the distortion quantity is only related to the coordinate x according to the lens distortion model, so that D can be controlledx(x) Cg (x) f (x), where g (x) characterizes the effect of distortion on pixel equivalents, and the constant C is a fixed ratio of pixel equivalents in the x and y directions, also the longitudinal stretch ratio, due to the incomplete matching of the camera scan frequency to the object movement rate.
(3) D at the same column positionxAnd DyAre constant values since the coordinate x is now determined.
In practical applications, the camera is not completely aligned with the target plane, i.e. the target plane is not perpendicular to the optical axis, and there is lens distortion in general, so that in a certain column, the ratio D of the x-direction pixel equivalent to the y-direction pixel equivalentx(xi)/Dy(xi)＝CG(xi) Affected only by distortion, in other words, D of a column in the imagex/DyThe distortion of the lens is characterized. Thus, in the case of an ideal lens, there is no distortion, and G (x) does not existi) The pixel equivalence ratio in the orthogonal direction is Dx(xu)/Dy(xu) The value is constant, which is the theoretical basis for the inventive method of distortion removal.
The method comprises the following specific steps:
the method comprises the following steps: designing and manufacturing a plane multi-grid checkerboard, recording the length and width of each unit grid, and enabling the unit grids to pass below a linear array camera at a constant speed on a guide rail so as to acquire images, wherein three representative images are respectively shown in figures 2-4;
step two: preprocessing a picture, and extracting checkerboard angular points, wherein the extracted angular points are in a sub-pixel level, and more accurate angular point coordinates can obtain more accurate distortion parameters;
step three: and (3) optionally taking the corner points of two adjacent lines, and deriving an undistorted coordinate expression of the corner points, wherein the corner point of the middle line is preferably taken, and the relation between the ideal undistorted coordinate and the actual coordinate is as follows:
xu＝xd+b(xd-cx)3
yu＝yd
wherein (x)u，yu) Is an ideal coordinate, (x)d，yd) Are the actual coordinates.
Step four: the pixel equivalent of the midpoint of the cross diagonal of the square can be found by: two angular points A (x)1,y1),B(x2,y2) Can be approximated as the pixel equivalent of
Wherein, | A0B0|xRepresenting the value of the space distance between the corner points A and B of the checkerboard in the scanning line direction, | A0B0|yRepresenting the value of the checkerboard feature corner point a and B spatial distance in the direction perpendicular to the scan line.
Step five: obtaining an objective function to be optimized according to the theory that the equivalent ratio of pixels in the orthogonal direction under an ideal lens is constant, and solving distortion parameters and a longitudinal stretch ratio by using a nonlinear optimization method, wherein the method specifically comprises the following steps:
in the absence of distortion, Dx(xu)/Dy(xu) C is a constant. Therefore can be provided withDetermining an objective function
Wherein L is the number of the transverse collinear characteristic points. Therefore, the solution of the lens distortion coefficient is converted into the process of the minimum above formula, namely
F(b*,cx *,C*)＝min F(b,cx,C)
b*，cx *I.e. the distortion coefficient of the lens, and C can be used to perform the vertical scale-expansion correction of the image, and the distortion coefficient and the vertical scale-expansion ratio can be obtained by performing the nonlinear optimization by using the Levenberg-Marquardt method (Levenberg-Marquardt algorithm).
The distortion size of the lens of the linear array camera only changes in a nonlinear way along with the image coordinate x, the nonlinear relation enables the inclined straight line on the image to be a curve, then after distortion correction is completed, straight line fitting is carried out on collinear points on the checkerboard, and the smaller the average distance between the characteristic points and the straight line fitted by the characteristic points is, the better the distortion correction effect is. Because the deformation degrees of the straight lines with different slopes influenced by distortion are different, the point set on the main diagonal line of the calibration plate is selected consistently in the experiment for experimental verification. The change in the average distance value from the sample point to the straight line fitted thereto before and after the distortion correction is shown in fig. 5. After distortion correction, the average distance from the characteristic point to the straight line is stabilized within 0.2 pixel, and the distortion correction effect is good.
The coefficient C obtained by the method can be used for longitudinal stretching correction of the linear array camera, the acquired original image and the length-width ratio of the unit small square grid which is subjected to longitudinal stretching correction are compared, as shown in FIG. 6, the length-width ratio of the unit small square grid in the completely uncorrected picture is least close to the length-width ratio 1.005025 (6.00 mm in length and 5.97mm in width) of the real object, and the average value is 0.971649; the aspect ratio for which only the lateral distortion correction was made was closer to the actual value 1.005025, with an average value of 0.989952, relative to being completely uncorrected; the aspect ratio for simultaneous transverse distortion correction and longitudinal stretch correction is closest to the actual value 1.005025, with an average value of 1.004943.
The invention fully analyzes the imaging characteristics of the linear array camera, and performs distortion correction by utilizing the characteristic that the pixel equivalent ratio in the orthogonal direction is constant after the linear array camera is imaged by an ideal lens, thereby having good effect. Compared with the prior art, the method does not need to rely on an additional high-precision calibration tool, has better adaptability in different application scenes, simple operation and good stability, can obtain the distortion coefficient and the longitudinal stretching coefficient at the same time, does not need secondary correction, and has small calculation amount.
Although the present invention has been described in detail with reference to the embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted without departing from the spirit and scope of the invention as defined in the appended claims.
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| CN110310340B (en) * | 2019-07-05 | 2022-10-11 | 河南科技大学 | Single linear array distortion calibration method based on collinear characteristic |
| CN110927965B (en) * | 2019-12-20 | 2021-08-17 | 易思维（杭州）科技有限公司 | Design method of compensation lens for compensating error caused by light deflection |
| CN110986779B (en) * | 2019-12-25 | 2025-05-30 | 上海交通大学 | Visual measurement system for inner and outer walls of small holes and calibration device and calibration method thereof |
| CN111047586B (en) * | 2019-12-26 | 2023-07-14 | 中国矿业大学 | A Pixel Equivalent Measurement Method Based on Machine Vision |
| CN111242858B (en) * | 2020-01-07 | 2023-10-27 | 曲建涛 | Distortion correction method and system for camera lens |
| CN111968182B (en) * | 2020-07-14 | 2024-04-16 | 南京航空航天大学 | A calibration method for nonlinear model parameters of binocular camera |
| CN112529792B (en) * | 2020-11-20 | 2022-03-29 | 暨南大学 | Distortion correction method for distortion-free model camera |
| CN112950493B (en) * | 2021-02-01 | 2022-11-01 | 中车青岛四方车辆研究所有限公司 | Method and device for correcting image distortion of linear array camera of rail train |
| CN112985265B (en) * | 2021-04-20 | 2021-07-30 | 苏州维嘉科技股份有限公司 | Linear array camera, precision compensation method thereof and storage medium |
| CN113516721B (en) * | 2021-09-13 | 2021-11-12 | 中科慧远视觉技术(北京)有限公司 | Multi-camera-based measurement method and device and storage medium |
| CN113808049B (en) * | 2021-09-23 | 2023-06-02 | 成都货安计量技术中心有限公司 | Train line image distortion correction method and electronic equipment |
| CN115641326B (en) * | 2022-11-09 | 2025-05-27 | 中国计量大学 | Sub-pixel size detection method and system for ceramic antenna PIN needle image |
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