CN104167001B - Large-visual-field camera calibration method based on orthogonal compensation - Google Patents

Abstract

The invention discloses a large-visual-field camera calibration method based on orthogonal compensation, belongs to the field of computer visual inspection and image processing and relates to a method for calibrating internal parameters and external parameters of a camera in a large forged piece dimension measurement system. Generally, in an active visual calibration process, two translation guide rails of an electric-control platform are not complete orthogonally, and calibration is conducted simply by blindly selecting a high-precision electric-control platform and regarding that the translation guide rails of the selected electric-control platform are orthogonal approximately. According to the large-visual-field camera calibration method based on orthogonal compensation, the internal parameters and the external parameters of a camera are obtained by obtaining the principal point, the scale factor, the translation vector and the rotation matrix. According to the large-visual-field camera calibration method based on orthogonal compensation, the guide rail orthogonal degree is considered during calibration, namely orthogonal compensation is introduced, and thus the errors, caused by the guide rail orthogonal degree, of a calibration result are reduced.

Description

Large-view-field camera calibration method based on orthogonal compensation

Technical Field

The invention belongs to the field of computer vision detection and image processing, relates to a method for calibrating internal and external parameters of a camera in a large forging dimension measurement system, and particularly relates to a method for calibrating a large-field-of-view camera based on orthogonal compensation.

Background

One of the basic tasks of the large forging dimension visual measurement is to recover three-dimensional geometric information according to the two-dimensional image information of the large forging in the forging process and obtain real-time dimension parameters. To perform the task of finding the corresponding surface points of the spatial object using the image points, a geometric model of the camera imaging is determined, the parameters of which are referred to as camera parameters. The camera intrinsic parameters are parameters of the camera itself related to geometric and optical characteristics, and the extrinsic parameters are the three-dimensional position and orientation of the camera relative to a world coordinate system.

The main factors influencing the calibration accuracy of the camera include: and (5) accurate and robust extraction of the calibration characteristic points. The process of determining the internal and external parameters of the camera is called camera calibration, and the precision of the calibration method directly influences the precision of computer vision measurement. Therefore, the research of quickly, simply and accurately calibrating the camera is undoubtedly of great significance.

At present, according to different camera calibration modes, the method can be divided into a traditional calibration method, a camera self-calibration method and a camera calibration method based on active vision; based on the advantages of high stability and robustness of the active vision calibration method, two translation guide rails of the electric control platform are not completely orthogonal in the active vision calibration process, and the calibration is only carried out by blindly selecting the electric control platform with high precision to be approximately considered as the orthogonality. Aiming at the problem, the factor of the orthogonality of the guide rail is considered to be added in the calibration process, namely, the orthogonality compensation is introduced, so that the error of the orthogonality of the guide rail on the calibration result is reduced.

Disclosure of Invention

The invention relates to a large-view-field camera calibration method based on orthogonal compensation, which comprises the steps of firstly obtaining a principal point coordinate by utilizing a varifocal principal point solving technology, then obtaining 12 images by utilizing four groups of orthogonal motions, and solving a scale factor by utilizing the 12 images under the condition of considering the orthogonality of a four-dimensional electric control platform, wherein internal parameters are calibrated; and finally, calculating external parameters by combining the calculated internal parameters.

The technical scheme adopted by the invention is as follows:

a large visual field camera calibration method based on orthogonal compensation, usually two translation guide rails of an electric control platform are not completely orthogonal in the active visual calibration process, and the calibration only selects the electric control platform with high precision to be approximately orthogonal, so that the camera calibration method based on orthogonal compensation is provided to obtain the internal and external parameters of the camera by respectively solving a principal point and a scale factor, a translation vector and a rotation matrix; the method comprises the following specific steps:

step 1: principal point of zoom method

The method comprises the steps of shooting a two-dimensional target by a camera under different focal lengths, moving an optical center along an optical axis when the focal length is changed, and expanding and contracting the two-dimensional target in a camera view field in an equal proportion to obtain target images under different view fields, wherein images with one point in different images are kept unchanged and are called expansion and contraction centers, and the expansion and contraction centers in the images of different view fields are main points, so that intersection points of all characteristic points of the target under the least square meaning of connecting lines under different focal lengths are the main points.

Step 2: target image acquisition method by using active vision calibration method of four-dimensional electric control platform

The four-dimensional electric control platform is controlled to drive the camera to do orthogonal motion in four groups of planes, each group of orthogonal motion comprises two translations, the camera stays at three positions in each orthogonal motion to further obtain three images, the camera has a pitching angle or a panning angle which is not less than 5 degrees between each group of orthogonal motion on the premise of ensuring that the target is in a view field, and a total of 12 target images are obtained through two pure translation motions of the four groups.

And step 3: determining a scale factor

The parallel straight line intersects with the plane at the same infinite point, namely a vanishing point, the 12 images after distortion correction are grouped for the vanishing point estimation, the connecting line of the corresponding points in each group of 3 images obtains 2 vanishing points, and 4 groups of 8 vanishing points; the obtained 8 blanking point coordinates, principal point coordinates and inter-rail angles are substituted into the following formula:

wherein theta is the angle between the two translation guide rails of the electric control platform, v_i1、v_i2Pixel coordinates (homogeneous form) of pairs of blanking points obtained for two translational movements under the ith set of orthogonal movements, w-K^-TK^-1Is an image of an absolute quadratic curve, which is specified in the form:

obtaining a binary equation set containing four nonlinear equations through the two equations and the eight blanking point coordinates, and iteratively solving the scale factor f by using a nonlinear least square method_xAnd f_y。

And 4, step 4: calibrating external parameters

A linear equation can be obtained from a homogeneous set of coordinates of corresponding image points, as follows:

uu′f₁₁+vu′f₁₂+u′f₁₃+uv′f₂₁+vv′f₂₂+v′f₂₃+uf₃₁+vf₃₂+f₃₃＝0 (3)

wherein f is_ijThe element in the ith row and the jth column of the basic matrix;

[uu′,vu′,u′,uv′,vv′,v′,u,v,1]f＝0 (4)

wherein f ═ f₁₁,f₁₂,f₁₃,f₂₁,f₂₂,f₂₃,f₃₁,f₃₂,f₃₃]^TIs a 9-dimensional column vector;

if given n sets of corresponding points m_i,m_i' } the following homogeneous linear equation set

At least 8 groups of corresponding image points are given, the homogeneous linear equation set can be linearly solved under the condition of an unknown non-zero scale factor difference, constraint | | | f | | | | 1 is applied, and when the corresponding image points are accurately matched, a basic matrix can be obtained by only using 8 groups of corresponding points; and then the essential matrix under the condition of a non-zero scale factor difference can be obtainedWhereins is a phase difference scale factor; by using E^*＝Udiag((σ₁+σ₂)/2,(σ₁+σ₂)/2,0)V^TAsWherein the eigenvalue σ is₁≥σ₂≥σ₃。

From the essence matrix E^*External parameters between cameras can be estimatedHas the following 4 possible combinations:

[UWV^T|u₃]；[UWV^T|-u₃]；[UW^TV^T|u₃]；[UW^TV^T|-u₃]. (6)

wherein,u₃is the 3 rd column vector of U,

by using Chirality constraint, the yaw angle is taken as a positive acute angle and a translational vectorComponent of (A) in the X directionJudging the correct parameter combination if the value is negative; and (3) reconstructing two characteristic points with accurately known distance information by using the obtained internal parameters of the cameras and the external parameters between the cameras with a difference of a scale factor, wherein the ratio of the reconstructed distance to the actual distance is the scale factor s.

Drawings

Fig. 1 is a schematic diagram of a principal point of zoom.

FIG. 2 is a schematic structural diagram of the apparatus of the present invention.

Fig. 3 is a schematic diagram of epipolar geometry in binocular stereo vision.

In the figure: 1, a platform; 2, electrically controlling the platform by the left camera; 3, electrically controlling the platform by the right camera; 4, a left camera; 5 a right camera; 6 two-dimensional chessboard format calibration plate.

Detailed Description

The following describes the embodiments of the present invention in further detail with reference to the drawings and technical solutions.

Camera calibration typically employs a classical pinhole imaging model, whose expression is as follows:

wherein (X)_w,Y_w,Z_w,1)^TIs the homogeneous coordinate of a space point in a world coordinate system, (u, v,1)^TFor corresponding image pixel coordinate system o₀Homogeneous coordinates in uv, α_xF/dx is o₀Scale factor on the u-axis in the uv coordinate system, α_yF/dy is o₀The scale factor on the v axis in the uv coordinate system, f is the focal length of the camera lens, dx and dy are the horizontal and vertical physical dimensions of the pixel respectively, (u₀,v₀) As principal point coordinates, p_cFor the scale factor, K is the camera internal parameter matrix, [ R | t]Is the external parameter matrix of the camera, wherein R is the rotation matrix and t is the translation vector.

The camera internal parameters include principal point coordinates (u)₀,v₀) Scale factor α_x、α_yCoefficient of radial distortion k₁、k₂And tangential distortion coefficient p₁、p₂. The camera external parameters are the orientation of the camera coordinate system relative to the world coordinate system, and comprise a rotation matrix R and a translation vector t.

Step 1: calculating a principal point by a zoom method;

the two-dimensional targets are shot by a camera under different focal lengths, as shown in fig. 1, when the focal length is changed, an optical center moves along an optical axis, the two-dimensional targets are expanded and contracted in equal proportion in the field of view of the camera to obtain target images under different field of view, images with one point in different images are kept unchanged and are called expansion and contraction centers, and the expansion and contraction centers in the images of different field of view are main points, so that intersection points of all characteristic points of the targets under the least square meaning of connecting lines under different focal lengths are the main points.

Step 2: acquiring a target image by using an active vision calibration method of a four-dimensional electric control platform;

as shown in fig. 2, experimental equipment is set up, two cameras are fixed on two four-dimensional electronic control platforms, the four-dimensional electronic control platforms are controlled to drive the cameras to do orthogonal motion in four groups of planes, each group of orthogonal motion comprises two translations, the cameras stay at three positions in each orthogonal motion to obtain three images, the cameras in each group of orthogonal motion have a pitch angle or a pan angle not less than 5 degrees on the premise that a target is ensured to be in a view field, and a total of 12 target images are obtained through two pure translation motions of the four groups.

And step 3: calculating a scale factor;

the parallel straight line intersects with the plane at the same infinite point, namely a vanishing point, the 12 images after distortion correction are grouped for the vanishing point estimation, the connecting line of the corresponding points in each group of 3 images obtains 2 vanishing points, and 4 groups of 8 vanishing points; the obtained 8 blanking point coordinates, principal point coordinates and inter-rail angles are substituted into the following formula:

wherein theta is the angle between the two translation guide rails of the electric control platform, v_i1、v_i2Pixel coordinates (homogeneous form) of pairs of blanking points obtained for two translational movements under the ith set of orthogonal movements, w-K^-TK^-1Is an image of an absolute quadratic curve, which is specified in the form:

obtaining a binary equation set containing four nonlinear equations through the two equations and the eight blanking point coordinates, and iteratively solving the scale factor f by using a nonlinear least square method_xAnd f_y。

And 4, step 4: calibrating external parameters;

fig. 3 is a schematic diagram of epipolar geometry in binocular stereo vision.

A linear equation can be obtained for each group of homogeneous coordinates of the corresponding image points, as follows:

uu′f₁₁+vu′f₁₂+u′f₁₃+uv′f₂₁+vv′f₂₂+v′f₂₃+uf₃₁+vf₃₂+f₃₃＝0 (3)

wherein f is_ijThe element in the ith row and the jth column of the basic matrix;

[uu′,vu′,u′,uv′,vv′,v′,u,v,1]f＝0 (4)

wherein f ═ f₁₁,f₁₂,f₁₃,f₂₁,f₂₂,f₂₃,f₃₁,f₃₂,f₃₃]^TIs a 9-dimensional column vector;

if given n sets of corresponding points m_i,m_i' } the following homogeneous linear equation set

At least 8 groups of corresponding image points are given, the homogeneous linear equation set can be linearly solved under the condition of an unknown non-zero scale factor difference, constraint | | | f | | | | 1 is applied, and when the corresponding image points are accurately matched, a basic matrix can be obtained by only using 8 groups of corresponding points; and then the essential matrix under the condition of a non-zero scale factor difference can be obtainedWhereins is a phase difference scale factor; by using E^*＝Udiag((σ₁+σ₂)/2,(σ₁+σ₂)/2,0)V^TAsWherein the eigenvalue σ is₁≥σ₂≥σ₃；

From the essence matrix E^*External parameters between cameras can be estimatedHas the following 4 possible combinations:

[UWV^T|u₃]；[UWV^T|-u₃]；[UW^TV^T|u₃]；[UW^TV^T|-u₃]. (6)

wherein,u₃is the 3 rd column vector of U,

by using Chirality constraint, the yaw angle is taken as a positive acute angle and a translational vectorComponent of (A) in the X directionJudging the correct parameter combination if the value is negative; and (3) reconstructing two characteristic points with accurately known distance information by using the obtained internal parameters of the cameras and the external parameters between the cameras with a difference of a scale factor, wherein the ratio of the reconstructed distance to the actual distance is the scale factor s.

Claims (1)

1. A calibration method based on orthogonal compensation is characterized by comprising the following steps:

step 1: principal point of zoom method

Shooting the two-dimensional target by using a camera under different focal lengths, wherein when the focal length is changed, the optical center moves along the optical axis, the two-dimensional target is expanded and contracted in equal proportion in the field of view of the camera to obtain target images under different field of view, the images of one point in different images are kept unchanged and are called as expansion and contraction centers, and the expansion and contraction centers in the images of different field of view are main points, so that the intersection point of each characteristic point of the target under the least square meaning of connecting lines under different focal lengths is the main point;

step 2: target image acquisition method by using active vision calibration method of four-dimensional electric control platform

Controlling a four-dimensional electric control platform to drive a camera to do orthogonal motion in four groups of planes, wherein each group of orthogonal motion comprises two translations, the camera stays at three positions in each orthogonal motion to further obtain three images, and under the premise of ensuring that a target is in a view field, the camera has a pitching angle or a panning angle which is not less than 5 degrees between each group of orthogonal motion, and a total of 12 target images are obtained through two pure translation motions of the four groups;

and step 3: determining a scale factor

The parallel straight line intersects with the plane at the same infinite point, namely a vanishing point, the 12 images after distortion correction are grouped for the vanishing point estimation, the connecting line of the corresponding points in each group of 3 images obtains 2 vanishing points, and 4 groups of 8 vanishing points; the obtained 8 blanking point coordinates, principal point coordinates and inter-rail angles are substituted into the following formula:

$\cos \mathrm{\θ}=\frac{v_{i1}^T{\mathrm{wv}}_{i2}}{\sqrt{v_{i1}^T{\mathrm{wv}}_{i1}}\sqrt{v_{i2}^T{\mathrm{wv}}_{i2}}},i=1,2,3,4---\left(1\right)$

wherein theta is the angle between the two translation guide rails of the electric control platform, v_i1、v_i2Pixel coordinates of pairs of blanking points obtained for two translational movements under the ith set of orthogonal movements, w ═ K^-TK^-1Is an image of an absolute quadratic curve, which is specified in the form:

$w=\left[\begin{array}{ccc}1/f_x^2& 0& -u_0/f_x^2\\ 0& 1/f_y^2& -v_0/f_y^2\\ -u_0/f_x^2& -v_0/f_y^2& u_0^2/f_x^2+v_0^2/f_y^2+1\end{array}\right]---\left(2\right)$

through the twoObtaining a binary equation set containing four nonlinear equations by the equation and the coordinates of eight blanking points, and iteratively solving a scale factor f by using a nonlinear least square method_xAnd f_yWherein u is₀，v₀Is the coordinate of the principal point of the camera;

and 4, step 4: calibrating external parameters;

a linear equation can be obtained from a homogeneous set of coordinates of corresponding image points, as follows:

uu′f₁₁+vu′f₁₂+u′f₁₃+uv′f₂₁+vv′f₂₂+v′f₂₃+uf₃₁+vf₃₂+f₃₃＝0 (3)

wherein f is_ijThe element in the ith row and the jth column of the basic matrix;

[uu′,vu′,u′,uv′,vv′,v′,u,v,1]f＝0 (4)

wherein f ═ f₁₁,f₁₂,f₁₃,f₂₁,f₂₂,f₂₃,f₃₁,f₃₂,f₃₃]^TIs a 9-dimensional column vector;

if given n sets of corresponding points m_i,m′_iThe following homogeneous linear equation set

$Af=\left[\begin{array}{ccccccccc}{u}_1{u}_1^{\′}& v_1{u}_1^{\′}& u_1^{\′}& u_1{v}_1^{\′}& v_1{v}_1^{\′}& v_1^{\′}& u_1& v_1& 1\\ .& .& .& .& .& .& .& .& .\\ .& .& .& .& .& .& .& .& .\\ .& .& .& .& .& .& .& .& .\\ u_n{u}_n^{\′}& v_n{u}_n^{\′}& u_n^{\′}& u_n{v}_n^{\′}& v_n{v}_n^{\′}& v_n^{\′}& u_n& v_n& 1\end{array}\right]f=0---\left(5\right)$

At least 8 groups of corresponding image points are given, the homogeneous linear equation set can be linearly solved under the condition of an unknown non-zero scale factor difference, constraint | | | f | | | | 1 is applied, and when the corresponding image points are accurately matched, a basic matrix is solved by using only 8 groups of corresponding points; further obtaining the essential matrix under the condition of a non-zero scale factor differenceWhereins is a phase difference scale factor; by using E^*＝Udiag((σ₁+σ₂)/2,(σ₁+σ₂)/2,0)V^TAsWherein the eigenvalue σ is₁≥σ₂≥σ₃；

From the essence matrix E^*Estimating extrinsic parameters between camerasHas the following 4 possible combinations:

[UWV^T|u₃]；[UWV^T|-u₃]；[UW^TV^T|u₃]；[UW^TV^T|-u₃]. (6)

wherein,u₃is the 3 rd column vector of U,

by using Chirality constraint, the yaw angle is taken as a positive acute angle and a translational vectorComponent of (A) in the X directionJudging the correct parameter combination if the value is negative; and (3) reconstructing two characteristic points with accurately known distance information by using the obtained internal parameters of the cameras and the external parameters between the cameras with a difference of a scale factor, wherein the ratio of the reconstructed distance to the actual distance is the scale factor s.