CN101216296A - Binocular vision rotating axis calibration method - Google Patents

Abstract

The invention belongs to detection techniques with visual principle, particularly relates to a method for calibrating rotating shaft by binocular vision with convenient operation and simple calibration process. The technical proposal of the invention includes that the method for calibrating rotating shaft by binocular vision comprises the following steps of: (1) obtaining edge of a spherical target; (2) calculating the coordinates of the spatial spherical center; and (3) calibrating and calculating parameters of the rotating shaft. The invention measures the spatial characteristic points mainly by using two cameras to simulate the structure of human eyes.

Description

Binocular vision rotating axis calibration method

Technical field

The invention belongs to the technology of utilizing visual theory to detect, particularly binocular vision rotating axis calibration method.

Technical background

The binocular measuring technique is an important component part of Computer Vision Detection technology, utilizes the structure of two video camera simulation human eyes that the space characteristics point is measured.In order to enlarge the measurement range of binocular measuring system, need in measuring system, add a universal stage, so just can finish measurement to 360 ° of testees.In order to guarantee the accuracy of measured object with measurement after the turntable rotation, need demarcate turntable, find out the rotation of universal stage.

The method main standard plane or the known standard ball of high precision radius of demarcating for the computer vision measurement shaft realizes now.Obtain the surface three dimension data of standard flat or standard ball by the at first a plurality of position of rotation of being demarcated of vision measurement equipment, according to the surface equation of three-dimensional point data fitting out-of-plane or ball, seek out the position of the rotation of universal stage at last according to the geometric properties of plane or standard ball then.These methods need standard flat or the known standard ball of high precision radius, and calibration cost is than higher; Need obtain the surface three dimension data of plane or standard ball in a plurality of positions, the demarcation efficiency ratio is lower.At the characteristics of binocular vision measuring system, it measures the full surface three-dimensional data process complexity of testee, need design the turntable scaling method that a cover is applicable to the binocular measuring system.

Summary of the invention

For overcoming the deficiencies in the prior art, the objective of the invention is to: provide a kind of easy to operate, fairly simple binocular vision rotating axis calibration method and the device for carrying out said of demarcating of process, the technical solution used in the present invention is: binocular vision rotating axis calibration method comprises the following steps:

1) spherical target edge obtains: hunt out the edge of target roughly by the searching of gray-scale value saltus step pixel, according to the curved transition between the adjacent image point point on the edge edge is screened then, obtain spherical accurately target marginal point;

2) the space sphere centre coordinate is asked for:

If spherical target edge l _cLast image coordinate is (u _i, v _i), its corresponding central coordinate of circle (u then _o, v _o) should satisfy:

(u _i-u _o) ²+(v _i-v _o) ²＝r ² i＝1，2，…，n (1)

Use least square method solving equation group (1) can obtain l _cCorresponding central coordinate of circle O, according to video camera pinhole imaging system model, video camera is (u as the coordinate of central coordinate of circle O under camera coordinate system on the plane _o, v _o,-f), f is the focal length of camera lens, obtains by camera calibration, connects the photocentre O of O and camera lens _c(0,0,0) obtains space line l ₀:

$\frac{x-t_x}{r_1{u}_o+r_2{v}_o-r_{3}f}=\frac{y-t_y}{r_4{u}_o+r_5{v}_o-r_{6}f}=\frac{z-t_z}{r_7{u}_o+r_8{v}_o-r_{9}f}---\left(2\right)$

Wherein:

$R=\left(\begin{array}{ccc}{r}_1& r_2& r_3\\ r_4& r_5& r_6\\ r_7& r_8& r_9\end{array}\right),T=\left(\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right)$

Be respectively camera coordinates and be tied to the rotation matrix and the translation matrix of measuring system world coordinate system, r ₁, r ₂R ₉Be the rotational component of rotation matrix, represent the angular relationship of each coordinate axis between the camera coordinate system and the measuring system world system, t _x, t _y, t _zTranslational component between being respectively coordinate two and being is two mutual alignments between the coordinate system true origin.They are by obtaining the demarcation of binocular measuring system.

The camera coordinate system of two video cameras about being provided with respectively, they and measuring system world coordinate system O _w-X _wY _wZ _wBetween mutual alignment relation demarcate by the binocular vision measuring system and obtain, respectively spherical target edge on the left and right cameras image planes is screened their spatially corresponding two great circle l that demarcate on the spherical target ₁And l ₂, can obtain l respectively by system of equations 1 _C1And l _C2Central coordinate of circle (u under camera coordinate system separately _O1, v _O1,-f ₁) and (u _O2, v _O2,-f ₂), the center of circle space line l that obtains according to formula (2) then ₀₁And l ₀₂Intersection point be the sphere centre coordinate of spherical displacer target on current location;

3) the rotating shaft parameter calibration calculates:

On several positions, ask for the sphere centre coordinate of spherical displacer target respectively, obtain one group of some O around the rotation of rotating shaft central axis _n(x _n, y _n, z _n) n=1,2 ..., N, with these sphere centre coordinate substitution space plane equations, the structure system of linear equations:

Ax _n+By _n+Cz _n+D＝0 n＝1，2，…，N (3)

Wherein A, B, C, D are the plane equation parameter.Utilize least square method to find the solution this system of equations, can obtain the plane equation P at centre of sphere rotational trajectory place _B, the normal vector on this plane can be thought the direction vector of universal stage rotating shaft:

$u=\left[\begin{array}{ccc}{u}_1& u_2& u_3\end{array}\right]=\left[\frac{A}{\sqrt{A^2+B^2+C^2}}\frac{B}{\sqrt{A^2+B^2+C^2}}\frac{C}{\sqrt{A^2+B^2+C^2}}\right]---\left(4\right)$

P in trajectory plane _BIn utilize search method to ask for and the point of sphere centre coordinate apart from minimum, promptly in constraint condition: ask for objective function under the Ax+By+Cz+D=0:

$f(x_n,y_n,z_n)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\sqrt{{(x_A-x_i)}^2+{(y_A-y_i)}^2+{(z_A-z_i)}^2}---\left(5\right)$

Minimum value, the some O _A(x _A, y _A, z _A) can think the intersection point of rotating shaft and centre of sphere trajectory plane, therefore this point also is a bit in the rotating shaft, utilize the direction vector of rotating shaft and any in the rotating shaft just the orientation of universal stage rotating shaft can be showed in the space, promptly finished the demarcation of universal stage rotating shaft.

The edge that described searching by gray-scale value saltus step pixel hunts out target roughly is meant, at first begins to carry out the edge along the edge that hunts out to both sides respectively from the peak that hunts out the edge and picks out.

The present invention possesses following technique effect:

The present invention has mainly designed the computing method that the spherical target that utilizes a unknown radius in the binocular vision measuring system is rotated the platform rotating axis calibration.Utilization is at the spherical target image of the demarcation of the diverse location photographs of some groups of universal stage rotations, and by Flame Image Process, the space centre of sphere calculates and the rotating shaft calculation of parameter can be obtained the position of rotating shaft in the binocular measuring system.More need be on each calibration position not complete surface profile of demarcating target of measuring of this method and existing rotating axis calibration method, therefore easy to operate, the process of demarcating is fairly simple, and has avoided the rare problem of binocular vision measuring system Measuring Object surface profile data well.And the spherical target that uses in the calibration process do not had the accuracy requirement of radius, saved calibration cost.

Description of drawings

Fig. 1 rotating axis calibration ball target.

Fig. 2 ball target edge extracting result.

Fig. 3 ball target edge The selection result.

Fig. 4 space sphere centre coordinate is asked for.

Fig. 5 rotating shaft parameter calibration.

Fig. 6 rotating axis calibration image.

Embodiment

The present invention is described further below in conjunction with accompanying drawing.

Be to demarcate the required spherical target of rotating shaft as shown in Figure 1, target uses the column of white to prop the spherical target of a black, and guarantees conveniently that for the target profile extracts background color is a white.

1) spherical target edge obtains

Picture mark on a map because background gray levels is higher for Spherical Target, and spherical target gray-scale value is lower, therefore can hunt out the edge of target roughly by the searching of gray-scale value saltus step pixel, as shown in Figure 2.But the true edge that this edge is not a target that influences owing to base need screen the edge that hunts out.At first beginning to carry out the edge along the edge that hunts out to both sides respectively from the peak that hunts out the edge picks out, because this point is not subjected to the influence of base, can think to be exactly point on the spherical target edge, pick out search edge between the curved transition trip point of both sides according to the curved transition of consecutive point in the edge then, obtain believable ball target edge pixel, as shown in Figure 3.

2) the space sphere centre coordinate is asked for

If spherical target edge l _cThe image coordinate of point is (u _i, v _i), its corresponding central coordinate of circle (u then _o, v _o) should satisfy:

(u _i-u _o) ²+(v _i-v _o) ²＝R ² i＝1，2，…，n (1)

Use least square method solving equation group 1 can obtain l _cCorresponding central coordinate of circle O _oAccording to video camera pinhole imaging system model, video camera is (u as the coordinate of central coordinate of circle O under camera coordinate system on the plane _o, v _o,-f), f is the focal length of camera lens, obtains by camera calibration.The photocentre O that connects O and camera lens _c(0,0,0) obtains space line l ₀:

$\frac{x-t_x}{r_1{u}_o+r_2{v}_o-r_{3}f}=\frac{y-t_y}{r_4{u}_o+r_5{v}_o-r_{6}f}=\frac{z-t_z}{r_7{u}_o+r_8{v}_o-r_{9}f}---\left(2\right)$

Wherein:

$R=\left(\begin{array}{ccc}{r}_1& r_2& r_3\\ r_4& r_5& r_6\\ r_7& r_8& r_9\end{array}\right),T=\left(\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right)$

Be respectively camera coordinates and be tied to the rotation matrix and the translation matrix of measuring system world coordinate system, r ₁, r ₂R ₉Be the rotational component of rotation matrix, represent the angular relationship of each coordinate axis between the camera coordinate system and the measuring system world system, t _x, t _y, t _zTranslational component between being respectively coordinate two and being is two mutual alignments between the coordinate system true origin.They are by obtaining the demarcation of binocular measuring system.By the demarcation of binocular measuring system is obtained.The centre of sphere by spherical displacer necessarily according to this straight line of video camera projection theory of object pinhole imaging system.

The method synoptic diagram of asking for the space sphere centre coordinate by spherical target edge as shown in Figure 4.O _C1-X _C1Y _C1Z _C1And O _C2-X _C2Y _C2Z _C2The camera coordinate system of two video cameras about being respectively, they and measuring system world coordinate system O _w-X _wY _wZ _wBetween mutual alignment relation demarcate by the binocular vision measuring system and obtain.l _C1And l _C2Be respectively spherical target edge The selection result on the left and right cameras image planes, two great circle l on the spherical target of they spatially corresponding demarcation ₁And l ₂Can obtain l respectively by system of equations 1 _C1And l _C2Central coordinate of circle (u under camera coordinate system separately _O1, v _O1,-f ₁) and (u _O2, v _O2,-f ₂), center of circle space line l then ₀₁And l ₀₂Intersection point be the sphere centre coordinate of spherical displacer target on current location.

3) the rotating shaft parameter calibration calculates

On several positions of universal stage rotation, ask for the sphere centre coordinate of spherical displacer target respectively, obtain one group of some O around the rotation of rotating shaft central axis _n(x _n, y _n, z _n) n=1,2 ..., N, as shown in Figure 5.With these sphere centre coordinate substitution space plane equations, the structure system of linear equations:

Ax _n+By _n+Cz _n+D＝0 n＝1，2，…，N (3)

Wherein A, B, C, D are the plane equation parameter.Utilize least square method to find the solution this system of equations, can obtain the plane equation P at centre of sphere rotational trajectory place _B, the normal vector on this plane can be thought the direction vector of universal stage rotating shaft:

$u={\left[\begin{array}{ccc}{r}_1& r_2& r_3\end{array}\right]}^{\mathrm{\Γ}}=\left[\frac{A}{\sqrt{A^2+B^2+C^2}}\frac{B}{\sqrt{A^2+B^2+C^2}}\frac{C}{\sqrt{A^2+B^2+C^2}}\right]---\left(4\right)$

P in trajectory plane _BIn utilize search method to ask for and the point of sphere centre coordinate apart from minimum, promptly in constraint condition: ask for objective function under the Ax+By+Cz+D=0:

$f(x_n,y_n,z_n)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\sqrt{{(x_A-x_i)}^2+{(y_A-y_i)}^2+{(z_A-z_i)}^2}---\left(5\right)$

Minimum value, the some O _A(x _A, y _A, z _A) can think the intersection point of rotating shaft and centre of sphere trajectory plane, therefore this point also is a bit in the rotating shaft.

Utilize the direction vector of rotating shaft and any in the rotating shaft just the orientation of universal stage rotating shaft can be showed in the space, promptly finished the demarcation of universal stage rotating shaft.

In calibration process, at first on the different position of rotation of universal stage, utilize left and right cameras to take the image of spherical displacer target respectively, as shown in Figure 6.In every width of cloth image according to ball target and background between the variation of gray scale extract the contour edge of ball target, and utilize curved transition between the contour edge neighbor pixel to finish the screening of contour edge, obtain believable ball target edge contour pixel and simulate the position at place, the profile center of circle.According to the space geometry relation of binocular vision measuring system, find the solution the intersection point of left and right cameras profile center of circle projection imaging straight line, can obtain the volume coordinate of this position spherical displacer target centre of sphere, the result is as shown in table 1.

Table 1 centre of sphere volume coordinate

	0°	60°	120°	180°	240°	300°
							X w	-51.604	-48.399	-47.271	-49.391	-52.623	-53.723
Y w	-11.006	-11.007	-11.017	-11.011	-11.007	-10.996
							Z w	3.814	3.218	0.132	-2.373	-1.788	1.316

These 6 sphere centre coordinates are used planar fit method, utilize least square to find the solution the plane equation group, obtain the plane equation at centre of sphere track place, then the normal vector u=[-0.002251-0.999997 0.001034 on this plane] ^ΓBe the direction vector of universal stage rotating shaft.By finding the solution the objective function of 5 formulas, the point that obtains in the rotating shaft is O _A(50.502749 ,-11.007636,0.713734).

The present invention can substitute common rotating axis calibration method, is applied to based on the binocular stereo vision measuring principle, need be rotated in the measuring system of platform rotating axis calibration to go.

Claims (2)

1. a binocular vision rotating axis calibration method is characterized in that, comprises the following steps:

1) spherical target edge obtains: hunt out the edge of target roughly by the searching of gray-scale value saltus step pixel, according to the curved transition between the adjacent image point point on the edge edge is screened then, obtain spherical accurately target marginal point;

2) the space sphere centre coordinate is asked for:

If spherical target edge l _cLast image coordinate is (u _i, v _i), its corresponding central coordinate of circle (u then _o, v _o) should satisfy:

(u _i-u _o) ²+(v _i-v _o) ²＝r ² i＝1，2，…，n (1)

Use least square method solving equation group (1) can obtain l _cCorresponding central coordinate of circle O, according to video camera pinhole imaging system model, video camera is (u as the coordinate of central coordinate of circle O under camera coordinate system on the plane _o, v _o,-f), f is the focal length of camera lens, obtains by camera calibration, connects the photocentre O of O and camera lens _c(0,0,0) obtains space line l ₀:

$\frac{x-t_x}{r_1{u}_o+r_2{v}_o-r_{3}f}=\frac{y-t_y}{r_4{u}_o+r_5{v}_o-r_{6}f}=\frac{z-t_z}{r_7{u}_o+r_8{v}_o-r_{9}f}---\left(2\right)$

Wherein:

$R=\left(\begin{array}{ccc}{r}_1& r_2& r_3\\ r_4& r_5& r_6\\ r_7& r_8& r_9\end{array}\right),T=\left(\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right)$

Be respectively camera coordinates and be tied to the rotation matrix and the translation matrix of measuring system world coordinate system, r ₁, r ₂R ₉Be the rotational component of rotation matrix, represent the angular relationship of each coordinate axis between the camera coordinate system and the measuring system world system, t _x, t _y, t _zTranslational component between being respectively coordinate two and being is two mutual alignments between the coordinate system true origin, and they are by obtaining the demarcation of binocular measuring system;

The camera coordinate system of two video cameras about being provided with respectively, they and measuring system world coordinate system O _w-X _wY _wZ _wBetween mutual alignment relation demarcate by the binocular vision measuring system and obtain, respectively spherical target edge on the left and right cameras image planes is screened their spatially corresponding two great circle l that demarcate on the spherical target ₁And l ₂, can obtain l respectively by system of equations 1 _C1And l _C2Central coordinate of circle (u under camera coordinate system separately _O1, v _O1,-f ₁) and (u _O2, v _O2,-f ₂), the center of circle space line l that obtains according to formula (2) then ₀₁And l ₀₂Intersection point be the sphere centre coordinate of spherical displacer target on current location;

3) the rotating shaft parameter calibration calculates:

On several positions, ask for the sphere centre coordinate of spherical displacer target respectively, obtain one group of some O around the rotation of rotating shaft central axis _n(x _n, y _n, z _n) n=1,2 ..., N, with these sphere centre coordinate substitution space plane equations, the structure system of linear equations:

Ax _n+By _n+Cz _n+D＝0 n＝1，2，…，N (3)

Wherein A, B, C, D are the plane equation parameter, utilize least square method to find the solution this system of equations, can obtain the plane equation P at centre of sphere rotational trajectory place _B, the normal vector on this plane can be thought the direction vector of universal stage rotating shaft:

$u=\left[\begin{array}{ccc}{u}_1& u_2& u_3\end{array}\right]=\left[\frac{A}{\sqrt{A^2+B^2+C^2}}\frac{B}{\sqrt{A^2+B^2+C^2}}\frac{C}{\sqrt{A^2+B^2+C^2}}\right]---\left(4\right)$

P in trajectory plane _BIn utilize search method to ask for and the point of sphere centre coordinate apart from minimum, promptly in constraint condition:

Ask for objective function under the Ax+By+Cz+D=0:

$f(x_n,y_n,z_n)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}\sqrt{{(x_A-x_i)}^2+{(y_A-y_i)}^2+{(z_A-z_i)}^2}---\left(5\right)$

Minimum value, the some O _A(x _A, y _A, z _A) can think the intersection point of rotating shaft and centre of sphere trajectory plane, therefore this point also is a bit in the rotating shaft, utilize the direction vector of rotating shaft and any in the rotating shaft just the orientation of universal stage rotating shaft can be showed in the space, promptly finished the demarcation of universal stage rotating shaft.

2. a kind of binocular vision rotating axis calibration method according to claim 1, it is characterized in that, the edge that described searching by gray-scale value saltus step pixel hunts out target roughly is meant, at first begins to carry out the edge along the edge that hunts out to both sides respectively from the peak that hunts out the edge and picks out.

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