CN111968182B - Calibration method for nonlinear model parameters of binocular camera - Google Patents
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Abstract
The invention provides a calibration method for parameters of a nonlinear model of a binocular camera, which uses a black-and-white checkerboard as a calibration target, estimates radial distortion parameters and tangential distortion parameters of a lens by using the invariance of the cross ratio of collinear inner angular points on a checkerboard calibration plate, estimates the internal and external parameters of the camera according to a linear imaging model of the camera after correcting the distortion of a shot image, and performs overall nonlinear optimization as an initial value to obtain the accurate calibration parameters of the binocular camera. Compared with the traditional method, the method has the advantages of higher operation speed and fewer steps, can obtain a reliable high-precision calibration result, and provides a new idea for binocular camera calibration.
Description
Technical Field
The invention belongs to the field of machine vision, and relates to a calibration method for nonlinear model parameters of a binocular camera.
Background
The optical three-dimensional measurement has the advantages of non-contact, high speed, high measurement efficiency and the like, is widely applied to industrial automatic detection in recent years, and plays an increasingly important role in the fields of geometric measurement and mechanical manufacturing.
Camera calibration is one of the key technologies in the field of vision measurement, is an indispensable step for recovering a three-dimensional image from a two-dimensional image, and is widely applied to the fields of three-dimensional measurement, three-dimensional object reconstruction, object identification, industrial detection, virtual reality and the like. The essence of camera calibration is: based on the mathematical model and the geometric relationship, metrology information is extracted between the 3D object located in the world coordinate system and its projection located in the image plane or the image coordinate system. The binocular camera calibration in the binocular vision measurement system is the basis of subsequent calculation, and the calibration precision directly influences the precision of the measurement result.
Along with the increasing wide application of vision measurement, a great number of students at home and abroad perform a great deal of theoretical research and experimental verification in the field of camera calibration, and a plurality of methods are provided for different application fields. In general, binocular camera models may be divided into linear models and nonlinear models. The linear model does not consider the distortion of the camera lens, and the precision is low, so the nonlinear model is the current mainstream camera calibration model. Nonlinear camera calibration methods can be divided into two categories: 1. the self-calibration method based on epipolar constraint does not need to predict the three-dimensional coordinates of the target, but lacks stability; 2. the traditional camera calibration method needs to place a target with known three-dimensional information in the field of view of a camera, and then deduces the relation between a space coordinate system and an image coordinate system according to a camera parameter model.
The traditional calibration method has higher calibration precision for a single camera, but has the defects of nonlinear calibration for a binocular camera. The current mainstream dual-camera calibration method needs to calibrate a single camera, then solves the rotation translation relation between the two cameras in a matrix transformation mode, and uses the rotation translation relation as an initial value to perform nonlinear optimization to obtain the final internal and external parameters of the dual-camera. The nonlinear optimization process has the advantages that the nonlinear optimization steps are excessive, the time consumption is long, and for a camera with large lens distortion, the coupling of the nonlinear parameter and the linear parameter can be caused by the simultaneous calibration optimization of the linear parameter and the lens distortion coefficient of the camera, so that the calibration result is inaccurate.
Disclosure of Invention
Aiming at the defects of the traditional binocular camera calibration method, the invention provides a rapid calculation method for the nonlinear model parameter calibration of the binocular camera. And (3) taking a black-and-white checkerboard as a calibration target, estimating radial distortion parameters and tangential distortion parameters of the lens by utilizing the invariance of the cross ratio of the collinear inner angular points on the checkerboard calibration plate, estimating the inner and outer parameters of the camera according to the linear imaging model of the camera after correcting the distortion of the shot image, and then carrying out integral nonlinear optimization as an initial value to obtain the accurate calibration parameters of the binocular camera. Compared with the traditional method, the method has the advantages of higher operation speed and fewer steps, can obtain a reliable high-precision calibration result, and provides a new idea for binocular camera calibration.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a calibration method of nonlinear model parameters of a binocular camera comprises the following steps:
step 1: shooting for a plurality of times from a plurality of view angles and directions towards the same calibration plate by using a binocular camera to obtain a plurality of pairs of left and right images, keeping the focal length of the binocular camera unchanged and the relative positions of the left and right cameras unchanged when the images are acquired, and enabling all inner corner points to be clearly visible in a picture;
step 2: detecting sub-pixel coordinates of inner angle points in all images and corresponding to world coordinates thereof one by one;
step 3: constructing a distortion model of the binocular camera lens, and solving distortion parameters of the distortion model;
step 4: estimating an internal reference matrix of the binocular camera;
step 5: correcting the left and right images by using the distortion model determined in the step 3, and establishing a linear camera model according to the corrected left and right images;
step 6: solving internal and external parameters of the camera according to the linear camera model;
step 7: and obtaining a final accurate binocular camera calibration parameter value by using the obtained camera internal and external parameters as initial values of global nonlinear optimization and using an optimization algorithm.
Further, in step 3, solving the distortion parameters of the distortion model includes the following steps:
the distortion model is as follows:
where (x ', y') is the ideal undistorted image coordinate value and (x, y) is the corresponding distorted image coordinate value, k 1 ,k 2 For radial distortion parameter, p 1 ,p 2 For tangential distortion parameters, r is the distance of the point from the imaging center, r 2 ＝x 2 +y 2 ；
Taking four points P of the image contour along collinearly adjacent lines i I=1, 2,3,4, let the distortion coordinates of the four points on the image be P 1 (x 1 ,y 1 ),P 2 (x 2 ,y 2 ),P 3 (x 3 ,y 3 ),P 4 (x 4 ,y 4 ) The method comprises the steps of carrying out a first treatment on the surface of the From the cross-ratio invariance it is possible to:
wherein CR is P 1 ,P 2 ,P 3 ,P 4 Four-point cross ratio, SR is simple ratio, a is the side length of small square in the checkerboard;
each edge of the image contour takes continuous 4-point coordinate data to participate in operation, P i I=1, 2,..16, substituting the distortion model into the (2) set of upright distortion parameters solving equations:
p in the formula i Representing 4 consecutive points on each side, CR representing the cross ratio thereof; solving the formula (3) to obtain a distortion parameter k 1 ,k 2 ,p 1 ,p 2 The distortion parameters of the left and right cameras can be estimated by performing the operation on the left and right cameras.
Further, in step 2, the sub-pixel coordinates of the inner corner points in all the images are detected by using the corner detection algorithm in OpenCV.
Further, the algorithm in the step 7 is a Levenberg-Marquardt optimization algorithm.
The beneficial effects are that:
1. and the distortion parameters are estimated by using a shot single image, so that an accurate initial value of the distortion parameters is provided for subsequent nonlinear optimization.
2. The camera linear imaging model is utilized to solve the internal parameters and the external parameters of the camera, so that the operation amount of nonlinear optimization is greatly reduced, and the time cost is superior to that of the traditional binocular camera calibration algorithm.
3. Under the condition that the accurate initial value of part of parameters is solved in advance, the nonlinear optimization is prevented from being trapped into local optimum, and the calibration precision is slightly higher than that of the traditional binocular camera calibration method.
Drawings
FIG. 1 is a flow chart of the general steps of the present invention;
FIG. 2 is a schematic diagram of cross-ratio invariance;
FIG. 3 is a schematic view of a lens distortion model;
FIG. 4 is a schematic view of an image plane taking intersection points;
fig. 5 is a schematic view of a camera linear perspective projection model.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear and clear, the present invention will be described in further detail below with reference to the accompanying drawings.
The invention provides a rapid calculation method for parameter calibration of a nonlinear model of a binocular camera, and the general flow chart is shown in figure 1. A schematic diagram of the principle of cross-ratio invariance is shown in fig. 2. A schematic diagram of a camera distortion model used in the invention is shown in FIG. 3. The selection of the points in time for calculating the distortion parameters using cross-ratio invariance is shown in fig. 4. A schematic diagram of the camera linear perspective projection model is shown in fig. 5. The binocular camera calibration method for preferentially calculating the internal and external parameters of the camera is implemented as follows:
step 1: collecting calibration plate image
The invention requires that the binocular camera is used for shooting for a plurality of times from a plurality of view angles and directions towards the same black-white checkerboard calibration plate, 15-20 pairs of left and right images are obtained, the focal length of the camera is kept unchanged, the relative positions of the left and right cameras are fixed when the images are acquired, and all inner corner points are clearly visible in a picture. And the first acquisition is required to enable the camera to be perpendicular to the calibration plate as much as possible, all inner corner points can be clearly seen, and the chessboard is distributed over two thirds of the whole picture as much as possible.
Step 2: sub-pixel corner detection
The invention detects the sub-pixel coordinates of the inner angle points in all images by using the angular point detection algorithm in OpenCV, and corresponds to the world coordinates one by one.
Step 3: distortion parameter estimation
The invention solves the distortion parameters of the camera by utilizing the left and right image pairs shot by the calibration plate for the first time.
(1) Invariance of cross ratio
In the spatial geometric transformation, some geometric characteristics have characteristics that do not change before and after transformation, and such characteristics or feature amounts are called invariant characteristics or invariant. As shown in fig. 2, three points A, B, C on the straight line L are A, B as a base point, a point C is a minute point (the point C is an inner minute point or an outer minute point), and the ratio of two directional line segments determined by the minute point to the base point is referred to as a shorthand ratio, which is expressed as:
SR(A,B；C)＝AC/BC (1)
the ratio of the simple ratios of two of the four points on a straight line is called the cross ratio. The cross ratio of four points A, B, C, D (also called the cross ratio of collinear points) on the straight line L as in FIG. 2 is
In the formula (2), points a, B are basic point pairs, and points C, D are separation point pairs.
The following relationship can be demonstrated:
CR(A,B；C,D)＝CR(A′,B′；C′,D′) (3)
the cross ratio of the perspective projection is unchanged.
(2) Distortion model of lens:
due to the objective existence of lens distortion, in actual camera calibration, a proper lens distortion model must be selected and corrected. The essence of lens distortion correction is to estimate the distortion coefficient of the lens from the lens distortion model.
Fig. 3 shows a lens distortion model used in the present invention, which avoids the unstable numerical solution caused by introducing excessive distortion parameters, and only considers the influence of second-order radial distortion and tangential distortion.
The distortion of the radial distortion in the imaging center (optical center) is 0, and the distortion becomes more serious along with the movement to the edge, and the radial distortion model can be set as follows:
in (x) dr ,y dr ) Is thatIdeal undistorted image coordinate values, (x, y) are the corresponding distorted image coordinate values, k 1 Is a first order radial distortion parameter, k 2 Is a second-order radial distortion parameter, r is the distance of the point from the imaging center, r 2 ＝x 2 +y 2 。
Tangential distortion is caused by imperfections in the manufacture of the lens such that the lens itself is not parallel to the image plane. The tangential distortion model can be set as:
in (x) dt ,y dt ) Is ideal undistorted image coordinate value, (x, y) is corresponding distorted image coordinate value, p 1 Is a first order tangential distortion parameter, p 2 Is a second order tangential distortion parameter.
A camera distortion model including radial distortion and tangential distortion can be provided as:
where (x ', y') is the ideal undistorted image coordinate value and (x, y) is the corresponding distorted image coordinate value, k 1 ,k 2 For radial distortion parameter, p 1 ,p 2 Is a tangential distortion parameter.
(3) Distortion parameter solving
The distortion model used in the present invention contains k 1 ,k 2 ,p 1 ,p 2 Four distortion parameters. The distortion is more pronounced at the edges away from the optical center as seen by the distortion model, and the rectangular outline (marked with red dotted circles in fig. 4) consisting of the inner corners of the outermost layers of the checkerboard is thus distorted.
Four points P with collinearly adjacent upper edges of red outline are taken i I=1, 2,3,4, let the distortion coordinates of the four points on the image be P 1 (x 1 ,y 1 ),P 2 (x 2 ,y 2 ),P 3 (x 3 ,y 3 ),P 4 (x 4 ,y 4 ). From the cross-ratio invariance it is possible to:
wherein CR is P 1 ,P 2 ,P 3 ,P 4 Four-point cross ratio, SR is simple ratio, and a is the side length of small square in the checkerboard.
On the red outline of fig. 4, each side takes coordinate data of 4 consecutive points to participate in the operation (P i I=1, 2,..16), substituting the distortion model into (7) can establish a distortion parameter solving equation set: .
P in the formula i Representing consecutive 4 points on each side, CR represents the cross ratio thereof. Solving the formula (8) to obtain a distortion parameter k 1 ,k 2 ,p 1 ,p 2 The distortion parameters of the left and right cameras can be estimated by performing the operation on the left and right cameras.
Step 4: camera internal parameter estimation
Let the reference matrix of the left and right cameras be A 1 And A 2 Assuming that the resolution of the camera is m×n, the focal length of the camera lens is f, and the pixel size is d x ×d y The camera reference matrix can be estimated as:
step 5: distortion correction for left and right images
And (3) correcting the distortion of the left and right image pairs by using the distortion coefficient obtained in the step (3).
Step 6: linear camera imaging model solution
The linear camera imaging model is idealized according to the pinhole imaging principle, and involves four coordinate systems, respectively representing imagingWorld coordinate system O of three-dimensional coordinates of target space w X w Y w Z w Camera coordinate system O c X c Y c Z c Image coordinate system O corresponding to two-dimensional coordinates of image 1 xy and a planar coordinate system O in pixels 0 uv, whose correspondence is shown in fig. 5.
Main Point O in FIG. 5 1 Is the intersection point of the central optical axis of the camera lens and the imaging plane pi, and the coordinate in the pixel coordinate system is (u) 0 ,v 0 ) Any point P in the space within the field of view w The homogeneous world coordinate of [ X ] w Y w Z w 1] T Projected onto imaging plane pi, corresponding point P 1 Plane coordinates of [ x y 1 ]] T The corresponding pixel coordinates are [ u v 1] T The imaging geometrical relationship of the image point and the object point is written into a perspective projection matrix under homogeneous coordinates according to the direct linear transformation principle, and the form is as follows:
f in x ,f y Represents the equivalent focal length in the x and y directions, u 0 ,v 0 The pixel coordinates representing the principal point, matrix A being the intrinsic matrix of the camera, [ R t ]]And (3) calibrating an external parameter matrix for the camera, wherein s is an unknown scale factor. The corresponding relation between the space points and the image points can be described by the above formula, and the internal and external parameters of the camera can be solved according to the corresponding relation between the angular points and the space points in the checkerboard.
Step 7: global nonlinear optimization
The solved internal and external parameters and distortion coefficients of the camera are only rough calibration results which are mutually separated, in order to achieve the optimal calibration result, according to the principle of minimum reprojection error, namely, according to the calibration result, space point two-dimensional projection calculation is carried out, the calculation result is compared with an actual measurement value, and the principle of minimum difference value is carried out, so that a nonlinear global optimization objective function is established:
in the middle ofRepresenting plane pi j N on j Inner corner points->Is->Pixel coordinates on the ith camera image plane. In->Representation->The pixel coordinates of the re-projection are used for obtaining the internal and external parameter values of the final binocular camera by using a Levenberg-Marquardt optimization algorithm.
It should be noted that the above-mentioned embodiments are merely preferred embodiments of the present invention, and are not intended to limit the scope of the present invention, and the equivalents or alternatives made on the basis of the above description are all included in the scope of the present invention.
Claims (4)
1. The calibration method of the nonlinear model parameters of the binocular camera is characterized by comprising the following steps of:
step 1: shooting for a plurality of times from a plurality of view angles and directions towards the same calibration plate by using a binocular camera to obtain a plurality of pairs of left and right images, keeping the focal length of the binocular camera unchanged and the relative positions of the left and right cameras unchanged when the images are acquired, and enabling all inner corner points to be clearly visible in a picture;
step 2: detecting sub-pixel coordinates of inner angle points in all images and corresponding to world coordinates thereof one by one;
step 3: constructing a distortion model of the binocular camera lens, and solving distortion parameters of the distortion model;
step 4: estimating an internal reference matrix of the binocular camera;
step 5: correcting the left and right images by using the distortion model determined in the step 3, and establishing a linear camera model according to the corrected left and right images;
step 6: solving internal and external parameters of the camera according to the linear camera model;
step 7: establishing a nonlinear global optimization objective function, utilizing the obtained internal and external parameters of the camera as initial values of global nonlinear optimization, and utilizing an optimization algorithm to obtain final accurate calibration parameter values of the binocular camera;
in step 3, solving distortion parameters of the distortion model includes the steps of:
the distortion model is as follows:
where (x ', y') is the ideal undistorted image coordinate value and (x, y) is the corresponding distorted image coordinate value, k 1 ,k 2 For radial distortion parameter, p 1 ,p 2 For tangential distortion parameters, r is the distance of the point from the imaging center, r 2 ＝x 2 +y 2 ；
Taking four points P of the image contour along collinearly adjacent lines i I=1, 2,3,4, let the distortion coordinates of the four points on the image be P 1 (x 1 ,y 1 ),P 2 (x 2 ,y 2 ),P 3 (x 3 ,y 3 ),P 4 (x 4 ,y 4 ) The method comprises the steps of carrying out a first treatment on the surface of the From the cross-ratio invariance it is possible to:
wherein CR is P 1 ,P 2 ,P 3 ,P 4 Four-point cross ratio, SR is simple ratio, a is the side length of small square in the checkerboard;
each edge is taken on the image contourCoordinate data of 4 continuous points participate in operation, P i I=1, 2,..16, substituting the distortion model into the (2) set of upright distortion parameters solving equations:
p in the formula i Representing 4 consecutive points on each side, CR representing the cross ratio thereof; solving the formula (3) to obtain a distortion parameter k 1 ,k 2 ,p 1 ,p 2 The distortion parameters of the left and right cameras can be estimated by performing the operation on the left and right cameras.
2. The method for calibrating parameters of a nonlinear model of a binocular camera according to claim 1, wherein in step 2, the sub-pixel coordinates of the inner corners in all the images are detected by using a corner detection algorithm in OpenCV.
3. The method for calibrating parameters of a nonlinear model of a binocular camera according to claim 1, wherein the nonlinear global optimization objective function in step 7 is:
in the middle ofRepresenting plane pi j N on j Inner corner points->Is->Pixel coordinates on the ith camera image plane,/->Representation->And (5) pixel coordinates of the re-projection.
4. The method for calibrating nonlinear model parameters of a binocular camera according to claim 1, wherein the algorithm in the step 7 is a Levenberg-Marquardt optimization algorithm.
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| CN107507246A (en) * | 2017-08-21 | 2017-12-22 | 南京理工大学 | A kind of camera marking method based on improvement distortion model |
| CN108805935A (en) * | 2018-05-02 | 2018-11-13 | 南京大学 | It is a kind of based on orthogonal pixel equivalent than line-scan digital camera distortion correction method |
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