CN104167001A - 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-field shooting machine scaling method based on quadrature compensation

Technical field

The invention belongs to Computer Vision Detection and image processing field, relate to the scaling method of the inside and outside parameter of video camera in large forgings Size Measuring System, specifically refer to a kind of large-field shooting machine scaling method based on quadrature compensation.

Background technology

One of basic task of heavy forging size vision measurement is to recover three-dimensional geometric information according to the two-dimensional image information of heavy forging in forging process, asks for real-time dimensional parameters.Realize task of utilizing picture point to ask for corresponding space object surface point, need to determine video camera imaging geometric model, the parameter of this geometric model is called camera parameters.Camera intrinsic parameter is the parameter relevant with optical characteristics with how much of video camera self, and outer parameter is three-dimensional position and the direction of video camera with respect to a certain world coordinate system.

The principal element that affects camera calibration precision comprises: accurate, the robust of feature point for calibration extract.The process of determining the inside and outside parameter of video camera is called camera calibration, and the precision of scaling method directly has influence on the precision of computer vision measurement.Therefore, video camera being carried out to research quick, simple and direct, accurate demarcation is significant undoubtedly.

According to the difference of camera calibration mode, can be divided into traditional standardization, camera self-calibration method and the camera marking method based on active vision at present; Based on active vision scaling method stability and the high advantage of robustness, and conventionally in active vision calibration process automatically controlled platform two translation guide rails not completely orthogonal, and demarcate, automatically controlled platform that just blindly choice accuracy is high is approximate thinks that it is orthogonal.For this problem, consider in calibration process, to add guide rail intercept factor, introduce quadrature compensation, the error of calibration result being brought to reduce guide rail intercept.

Summary of the invention

Large-field shooting machine scaling method based on quadrature compensation of the present invention, first utilize varifocal to ask principal point technology to obtain principal point coordinate, then utilize four groups of orthogonal motions to obtain 12 images, in the case of considering the intercept of four-dimensional automatically controlled platform, utilize 12 images to ask for scale factor, so far, inner parameter has been demarcated complete; Finally, ask for external parameter in conjunction with the inner parameter of asking for.

The technical scheme that the present invention takes is:

A kind of large-field shooting machine scaling method based on quadrature compensation, conventionally in active vision calibration process, automatically controlled platform two translation guide rails are not completely orthogonal, think that it is orthogonal and the demarcation automatically controlled platform that just blindly choice accuracy is high is approximate, therefore propose a kind of camera marking method based on quadrature compensation and obtain the inside and outside parameter of video camera by asking for respectively principal point and scale factor, translation vector and rotation matrix; Concrete steps are as follows:

Step 1: varifocal method is asked principal point

Under different focal, take two-dimentional target with video camera, in the time that focal length changes, photocentre moves along optical axis, in camera field of view, two-dimentional target is will equal proportion scalable, obtain target image under different visual fields, in different images, have the image of any to remain unchanged, be called scalable center, in the image of different visual fields, scalable center is principal point, and therefore by each unique point of target, the intersection point under the least square meaning of the line under different focal is principal point.

Step 2: utilize the active vision scaling method of four-dimensional automatically controlled platform to obtain target image

Controlling four-dimensional automatically controlled platform drives video camera to do four groups of orthogonal motions in plane, every group of orthogonal motion contains twice translation, video camera stops three positions in each orthogonal motion, and then obtain three images, and guaranteeing under the prerequisite of target in visual field, between every group of orthogonal motion, video camera all has the luffing angle or the pan angle that are not less than 5 degree, obtains totally 12 target images by twice pure flat shifting movement of four groups.

Step 3: ask for scale factor

Parallel lines and plane at infinity intersect at same infinity point, i.e. 12 image packets after distortion correction are carried out vanishing point estimation by hidden disappearing a little, and in every group of 3 images, corresponding point line obtains 2 vanishing points, 4 groups of totally 8 vanishing points; Angle between 8 the vanishing point coordinates, principal point coordinate and the guide rail that obtain is brought in following formula:

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

Wherein, θ is the angle between two translation guide rails of automatically controlled platform, v _i1, v _i2be the right pixel coordinate (homogeneous form) of vanishing point that twice translation motion under the orthogonal motion of i group obtained, w=K ^-Tk ^-1be the image of absolute conic, its concrete form is as follows:

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

Can obtain by above-mentioned two formulas and eight vanishing point coordinates the equation with two unknowns group that comprises four nonlinear equations, go out scale factor f with nonlinear least square method iterative _xand f _y.

Step 4: demarcate outer parameter

The homogeneous coordinates of one group of corresponding picture point can obtain a linear equation, as follows:

uu′f ₁₁+vu′f ₁₂+u′f ₁₃+uv′f ₂₁+vv′f ₂₂+v′f ₂₃+uf ₃₁+vf ₃₂+f ₃₃＝0 (3)

Wherein, f _ijfor the element that i is capable, j lists of fundamental matrix;

[uu′,vu′,u′,uv′,vv′,v′,u,v,1]f＝0 (4)

Wherein, f=[f ₁₁, f ₁₂, f ₁₃, f ₂₁, f ₂₂, f ₂₃, f ₃₁, f ₃₂, f ₃₃] ^tbe 9 dimensional vectors;

If provide the corresponding { m of n group point _i, m ' _i, there is following system of homogeneous linear equations

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

The corresponding picture points of given at least 8 groups can solve above-mentioned system of homogeneous linear equations differing a unknown non-zero proportions factor lower linear, in this ‖ f ‖=1 that imposes restriction, in the time of corresponding picture point exact matching, can only utilize 8 groups of corresponding point to ask for fundamental matrix; And then can obtain and differ an essential matrix under the non-zero proportions factor wherein s is the scale factor differing; Utilize E ^*=Udiag ((σ ₁+ σ ₂)/2, (σ ₁+ σ ₂)/2,0) V ^tas approximate, wherein eigenwert σ ₁>=σ ₂>=σ ₃.

From essential matrix E ^*can estimate the external parameter between video camera there are following 4 kinds of possible array configurations:

[UWV ^T|u ₃]；[UWV ^T|-u ₃]；[UW ^TV ^T|u ₃]；[UW ^TV ^T|-u ₃]. (6)

Wherein, $W=\left[\begin{array}{ccc}0& -1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$ U ₃for the 3rd column vector of U,

By Chirality retrain, crab angle is an acute angle and on the occasion of and the X of translation vector _cto component for negative value is carried out correct judgment parameter combinations; Utilize the intrinsic parameters of the camera obtaining and differ external parameter between the video camera under a scale factor and rebuild accurately two known unique points of range information, rebuild distance and be scale factor s with the ratio of actual range.

Brief description of the drawings

Fig. 1 is that varifocal is asked principal point schematic diagram.

Fig. 2 is apparatus structure schematic diagram of the present invention.

Fig. 3 is to utmost point geometrical principle figure in binocular stereo vision.

In figure: 1 platform; The automatically controlled platform of 2 left video camera; The automatically controlled platform of 3 right video camera; 4 left video cameras;

5 right video cameras; 6 two-dimentional gridiron pattern scaling boards.

Embodiment

Further describe the specific embodiment of the present invention below in conjunction with accompanying drawing and technical scheme.

Camera calibration adopts classical pinhole imaging system model conventionally, and the expression formula of this model is as follows:

Wherein, (X _w, Y _w, Z _w, 1) ^tfor the homogeneous coordinates of spatial point in world coordinate system, (u, v, 1) ^tfor corresponding image picture point pixel coordinate is o ₀homogeneous coordinates in uv, α _x=f/dx is o ₀scale factor in uv coordinate system on u axle, α _y=f/dy is o ₀scale factor in uv coordinate system on v axle, f is camera lens focal length, dx and dy are respectively the horizontal stroke of pixel, vertical physical size, (u ₀, v ₀) be principal point coordinate, ρ _cfor scale-up factor, K is intrinsic parameters of the camera matrix, the external parameter matrix that [R|t] is video camera, and wherein, R is rotation matrix, t is translation vector.

Intrinsic parameters of the camera comprises principal point coordinate (u ₀, v ₀), scale factor α _x, α _y, coefficient of radial distortion k ₁, k ₂with tangential distortion coefficient p ₁, p ₂.Video camera external parameter is the orientation of camera coordinate system with respect to world coordinate system, comprises rotation matrix R and translation vector t.

Step 1: varifocal method is asked principal point;

Under different focal, take two-dimentional target with video camera, as shown in Figure 1, in the time that focal length changes, photocentre moves along optical axis, and in camera field of view, two-dimentional target is will equal proportion scalable, obtains target image under different visual fields, in different images, there is the image of any to remain unchanged, be called scalable center, in the image of different visual fields, scalable center is principal point, and therefore by each unique point of target, the intersection point under the least square meaning of the line under different focal is principal point.

Step 2: utilize the active vision scaling method of four-dimensional automatically controlled platform to obtain target image;

As Fig. 2 builds experimental facilities, two video cameras are fixed on two automatically controlled platforms of the four-dimension, controlling four-dimensional automatically controlled platform drives video camera to do four groups of orthogonal motions in plane, every group of orthogonal motion contains twice translation, video camera stops three positions in each orthogonal motion, and then obtain three images, and guaranteeing under the prerequisite of target in visual field, between every group of orthogonal motion, video camera all has the luffing angle or the pan angle that are not less than 5 degree, obtains totally 12 target images by twice pure flat shifting movement of four groups.

Step 3: ask for scale factor;

Parallel lines and plane at infinity intersect at same infinity point, i.e. 12 image packets after distortion correction are carried out vanishing point estimation by hidden disappearing a little, and in every group of 3 images, corresponding point line obtains 2 vanishing points, 4 groups of totally 8 vanishing points; Angle between 8 the vanishing point coordinates, principal point coordinate and the guide rail that obtain is brought in following formula:

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

Wherein, θ is the angle between two translation guide rails of automatically controlled platform, v _i1, v _i2be the right pixel coordinate (homogeneous form) of vanishing point that twice translation motion under the orthogonal motion of i group obtained, w=K ^-Tk ^-1be the image of absolute conic, its concrete form is as follows:

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

Can obtain by above-mentioned two formulas and eight vanishing point coordinates the equation with two unknowns group that comprises four nonlinear equations, go out scale factor f with nonlinear least square method iterative _xand f _y.

Step 4: demarcate outer parameter;

Fig. 3 is to utmost point geometrical principle figure in binocular stereo vision.

Each homogeneous coordinates of organizing corresponding picture point can obtain a linear equation, as follows:

uu′f ₁₁+vu′f ₁₂+u′f ₁₃+uv′f ₂₁+vv′f ₂₂+v′f ₂₃+uf ₃₁+vf ₃₂+f ₃₃＝0 (3)

Wherein, f _ijfor the element that i is capable, j lists of fundamental matrix;

[uu′,vu′,u′,uv′,vv′,v′,u,v,1]f＝0 (4)

Wherein, f=[f ₁₁, f ₁₂, f ₁₃, f ₂₁, f ₂₂, f ₂₃, f ₃₁, f ₃₂, f ₃₃] ^tbe 9 dimensional vectors;

If provide the corresponding { m of n group point _i, m ' _i, there is following system of homogeneous linear equations

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

The corresponding picture points of given at least 8 groups can solve above-mentioned system of homogeneous linear equations differing a unknown non-zero proportions factor lower linear, in this ‖ f ‖=1 that imposes restriction, in the time of corresponding picture point exact matching, can only utilize 8 groups of corresponding point to ask for fundamental matrix; And then can obtain and differ an essential matrix under the non-zero proportions factor wherein s is the scale factor differing; Utilize E ^*=Udiag ((σ ₁+ σ ₂)/2, (σ ₁+ σ ₂)/2,0) V ^tas approximate, wherein eigenwert σ ₁>=σ ₂>=σ ₃;

From essential matrix E ^*can estimate the external parameter between video camera there are following 4 kinds of possible array configurations:

[UWV ^T|u ₃]；[UWV ^T|-u ₃]；[UW ^TV ^T|u ₃]；[UW ^TV ^T|-u ₃]. (6)

Wherein, $W=\left[\begin{array}{ccc}0& -1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$ U ₃for the 3rd column vector of U,

By Chirality retrain, crab angle is an acute angle and on the occasion of and the X of translation vector _cto component for negative value is carried out correct judgment parameter combinations; Utilize the intrinsic parameters of the camera obtaining and differ external parameter between the video camera under a scale factor and rebuild accurately two known unique points of range information, rebuild distance and be scale factor s with the ratio of actual range.

Claims (1)

1. the calibration process based on quadrature compensation, is characterized in that following steps:

Step 1: varifocal method is asked principal point

Under different focal, take two-dimentional target with video camera, in the time that focal length changes, photocentre moves along optical axis, in camera field of view, two-dimentional target is will equal proportion scalable, obtain target image under different visual fields, in different images, have the image of any to remain unchanged, be called scalable center, in the image of different visual fields, scalable center is principal point, and therefore by each unique point of target, the intersection point under the least square meaning of the line under different focal is principal point;

Step 2: utilize the active vision scaling method of four-dimensional automatically controlled platform to obtain target image

Controlling four-dimensional automatically controlled platform drives video camera to do four groups of orthogonal motions in plane, every group of orthogonal motion contains twice translation, video camera stops three positions in each orthogonal motion, and then obtain three images, and guaranteeing under the prerequisite of target in visual field, between every group of orthogonal motion, video camera all has the luffing angle or the pan angle that are not less than 5 degree, obtains totally 12 target images by twice pure flat shifting movement of four groups;

Step 3: ask for scale factor

Parallel lines and plane at infinity intersect at same infinity point, i.e. 12 image packets after distortion correction are carried out vanishing point estimation by hidden disappearing a little, and in every group of 3 images, corresponding point line obtains 2 vanishing points, 4 groups of totally 8 vanishing points; Angle between 8 the vanishing point coordinates, principal point coordinate and the guide rail that obtain is brought in following formula:

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

Wherein, θ is the angle between two translation guide rails of automatically controlled platform, v _i1, v _i2be the right pixel coordinate of vanishing point that twice translation motion under the orthogonal motion of i group obtained, w=K ^-Tk ^-1be the image of absolute conic, its concrete form is as follows:

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

Obtain by above-mentioned two formulas and eight vanishing point coordinates the equation with two unknowns group that comprises four nonlinear equations, go out scale factor f with nonlinear least square method iterative _xand f _y;

Step 4: demarcate outer parameter;

The homogeneous coordinates of one group of corresponding picture point can obtain a linear equation, as follows:

uu′f ₁₁+vu′f ₁₂+u′f ₁₃+uv′f ₂₁+vv′f ₂₂+v′f ₂₃+uf ₃₁+vf ₃₂+f ₃₃＝0 (3)

Wherein, f _ijfor the element that i is capable, j lists of fundamental matrix;

[uu′,vu′,u′,uv′,vv′,v′,u,v,1]f＝0 (4)

Wherein, f=[f ₁₁, f ₁₂, f ₁₃, f ₂₁, f ₂₂, f ₂₃, f ₃₁, f ₃₂, f ₃₃] ^tbe 9 dimensional vectors;

If provide the corresponding { m of n group point _i, m ' _i, there is following system of homogeneous linear equations

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

The corresponding picture points of given at least 8 groups can solve above-mentioned system of homogeneous linear equations differing a unknown non-zero proportions factor lower linear, in this ‖ f ‖=1 that imposes restriction, in the time of corresponding picture point exact matching, only utilize 8 groups of corresponding point to ask for fundamental matrix; And then obtain and differ an essential matrix under the non-zero proportions factor wherein s is the scale factor differing; Utilize E ^*=Udiag ((σ ₁+ σ ₂)/2, (σ ₁+ σ ₂)/2,0) V ^tas approximate, wherein eigenwert σ ₁>=σ ₂>=σ ₃;

From essential matrix E ^*estimate the external parameter between video camera there are following 4 kinds of possible array configurations:

[UWV ^T|u ₃]；[UWV ^T|-u ₃]；[UW ^TV ^T|u ₃]；[UW ^TV ^T|-u ₃]. (6)

Wherein, $W=\left[\begin{array}{ccc}0& -1& 0\\ 1& 0& 0\\ 0& 0& 1\end{array}\right],$ U ₃for the 3rd column vector of U,

By Chirality retrain, crab angle is an acute angle and on the occasion of and the X of translation vector _cto component for negative value is carried out correct judgment parameter combinations; Utilize the intrinsic parameters of the camera obtaining and differ external parameter between the video camera under a scale factor and rebuild accurately two known unique points of range information, rebuild distance and be scale factor s with the ratio of actual range.