CN104374338A - Single-axis rotation angle vision measurement method based on fixed camera and single target - Google Patents

Abstract

The invention provides a single-axis rotation angle vision measurement method based on a fixed camera and a single target. The method includes the four steps of firstly, calibrating internal parameters and external parameters of the camera; secondly, obtaining the initial values of the external parameters related to pivoting movement; thirdly, conducting nonlinear optimization on the internal parameter pin and the external parameter pout; fourthly, measuring the rotation angle through the calibrated internal parameters and the calibrated external parameters. The method is a method for measuring the rotation angle of the pivoting movement through the monocular camera, and solves the problem that the target is hard to install in an existing angle vision measurement method; meanwhile, the method is suitable for the conditions with blockage as well and is quite high in practicability.

Description

A kind of vision measuring method of the single-shaft-rotation angle based on fixed camera and single target

Technical field

The present invention relates to a kind of vision measuring method of the single-shaft-rotation angle based on fixed camera and single target, belong to technical field of visual measurement.

Background technology

Angle displacement measurement is widely used in the field such as industry, Aero-Space.Due in rugged environment, the parameter such as electric, mechanical of angular displacement sensor can change, and therefore needs regularly to carry out demarcations rectification to it.Vision measurement technology is simple because having structure, Non contact real time measurement, in-site installation and the advantage such as debugging is convenient and enjoy favor.Existing vision angle-measuring method is divided into the method for binocular vision and monocular vision.Binocular vision method, because its public view field is little, installs complicated and is very restricted.The method of existing monocular vision is provided with certain requirement mostly to target, and installation difficulty is large.Therefore, present patent application proposes a kind of vision measuring method of the single-shaft-rotation angle based on fixed camera and single target, and the installation of the method to target has no requirement.In addition, the present invention sets up equally to there being the situation of blocking, more practical.

Summary of the invention

The present invention proposes a kind of vision measuring method of the single-shaft-rotation angle based on fixed camera and single target, it is a kind of method utilizing the rotation angle of monocular camera to pivoting movement to measure.It solve target in existing vision angle-measuring method and the problem of difficulty is installed.Meanwhile, the present invention is applicable equally to there being the situation of blocking, and practicality is fine.

The method, by two-dimensional target, demarcates to camera internal reference and relative to the outer parameter of axle, and then measures rotation angle, and the method is installed target and had no requirement, and target can be fixed to optional position.

The camera model that the present invention adopts is non-linear perspective projection model, and model is described below:

1. linear camera model

As shown in figure (1), P image space in the picture in any point, space can use pin-hole imaging model approximate representation, namely puts P projected position p in the picture, is photocentre O and the some line of P and the intersection point of the plane of delineation.Thus P point coordinate (X under world coordinate system _w, Y _w, Z _w) ^twith the pixel coordinate (u, v) of subpoint p ^tbetween relation as follows:

$s\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{cccc}{\mathrm{\α}}_x& 0& u_0& 0\\ 0& {\mathrm{\α}}_y& v_0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}{R}_{\mathrm{cw}}& T_{\mathrm{cw}}\\ 0& 1\end{array}\right]\left[\begin{array}{c}{X}_w\\ Y_w\\ Z_w\\ 1\end{array}\right]---\left(1.1\right)$

Wherein α _x=f/dX is the scale factor on u axle, α _y=f/dY is the scale factor on v axle.α _x, α _y, u ₀, v ₀only relevant with intrinsic parameters of the camera, be called the intrinsic parameter of video camera.R _cw, T _cwbe respectively rotation matrix and the translation vector of camera coordinates system and world coordinate system, be called the external parameter of video camera.

1. non-linear camera model

In fact, camera lens is not desirable perspective imaging, but with distortion to a certain degree.What the present invention adopted is nonlinear distortion model, by world coordinates (X _w, Y _w, Z _w) ^task for pixel coordinate (u, v) ^tprocess as follows:

$\left[\begin{array}{c}{X}_c\\ Y_c\\ Z_c\end{array}\right]=R_{\mathrm{cw}}\left[\begin{array}{c}{X}_w\\ Y_w\\ Z_w\end{array}\right]+T_{\mathrm{cw}},---\left(1.2\right)$

x＝X _c/Z _c,y＝Y _c/Z _c,r ²＝x ²+y ², (1.3)

$x_d=\left[\begin{array}{c}(1+k_1{r}^2+k_2{r}^4+k_5{r}^6)x+{2k}_3\mathrm{xy}+k_4(r^2+{2x}^2)\\ (1+k_1{r}^2+k_2{r}^4+k_5{r}^6)y+{2k}_4\mathrm{xy}+k_3(r_2+{2y}^2)\end{array}\right],---\left(1.4\right)$

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}{\mathrm{\α}}_x& 0& u_0\\ 0& {\mathrm{\α}}_y& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_d\\ 1\end{array}\right],---\left(1.5\right)$

Wherein, k ₁, k ₂, k ₃, k ₄, k ₅for distortion factor.α _x, α _y, u ₀, v ₀, k ₁, k ₂, k ₃, k ₄, k ₅form the intrinsic parameter of video camera, R _cw, T _cwfor the outer parameter of video camera.

For convenience of description, we remember u, and v is p _in=(α _x, α _y, u ₀, v ₀, k ₁, k ₂, k ₃, k ₄, k ₅) ^t, R _cw, T _cw, X _w, Y _w, Z _wfunction, namely

u＝f _u(p _in,R _cw,T _cw,X _w,Y _w,Z _w),v＝f _v(p _in,R _cw,T _cw,X _w,Y _w,Z _w) (1.6)

The world coordinate system that the present invention sets up is as figure (2). and getting rotating shaft is Z _waxle, and make the target initial point when reference position be positioned at X _won axle.Suppose that rotation matrix between reference position target co-ordinates system and world coordinate system and translation vector are and set the rotation matrix of camera coordinates system and world coordinate system as R _cw, translation vector is T _cw.

Method proposed by the invention comprises two steps: inside and outside parameter information is demarcated and arbitrarily angledly to be solved.Inside and outside parameter information is demarcated, and is on the basis that general camera is demarcated, utilizes the special geometric relation between pivoting movement coordinate system, ask for the process of required external parameter information. t,R _cw, T _cwand the angle between each position and reference position is that inside and outside ginseng information demarcates the outer parameter that will estimate.Arbitrarily angledly to solve, being the inside and outside parameter information according to having tried to achieve, asking for rotation angle.In arbitrarily angled solution procedure, we have proposed a kind of point matching algorithm, thus make angle-measuring method can ask for the solution of occlusion issue.

In sum, the vision measuring method at a kind of single-shaft-rotation angle based on fixed camera and single target of the present invention, the method concrete steps are as follows:

Step one: camera inside and outside parameter is demarcated.

In specific implementation process, we utilize two-dimentional gridiron pattern (as Fig. 5) as target.The sequence of pictures that we adopt, picture when comprising a reference position and m open picture when rotary part rotates to different angles.Suppose that this m angle is θ ₁, θ ₂..., θ _m.Next, the X-comers that MATLAB 2014 can be utilized to carry extracts function detectChecker--boardPoints and carries out angle point grid, and carries out internal reference demarcation in conjunction with MATLAB calibration tool, tries to achieve intrinsic parameter p _inwith the external parameter of m+1 pose.This calibration tool case, can download on http://www.vision.caltech.edu/bouguetj/calib_doc/.These external parameters can be expressed as

$[R_{{\mathrm{cb}}_i},T_{{\mathrm{cb}}_i}],i=\mathrm{0,1,2},...,m.$

represent in rotation angle to be θ _itime, the rotation matrix between camera and target and translation vector, when representing reference position during i=0, the rotation matrix between camera and target and translation vector.

Step 2: the outer initial parameter values that pivoting movement is relevant is asked for

1, we are according to the outer parameter of trying to achieve in step one, and asking in rotation angle by (1.7) is θ _itime, target is relative to the rotation matrix of target during benchmark and translation vector $[R_{b_i{b}_0},T_{b_i{b}_0}],i=\mathrm{1,2},...,m.$

$R_{b_i{b}_0}=R_{{\mathrm{cb}}_i}^T{R}_{{\mathrm{cb}}_0},T_{b_i{b}_0}=R_{{\mathrm{cb}}_i}^T(T_{{\mathrm{cb}}_0}-T_{{\mathrm{cb}}_i}).---\left(1.7\right)$

2, ask for t and θ _iinitial value:

Definition r ₁, r ₂, r ₃be respectively the 1st, 2,3 row, and vector [t] _×be expressed as follows matrix

${\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right]}_{\×}=\left[\begin{array}{ccc}0& {-t}_z& t_y\\ t_z& 0& {-t}_x\\ {-t}_y& t_x& 0\end{array}\right].---\left(1.8\right)$

Then, we can be in the hope of

$r_2=\frac{{(S_{\mathrm{3,2}},S_{\mathrm{1,3}},S_{\mathrm{2,1}})}^T}{\left|\right|(S_{\mathrm{3,2}},S_{\mathrm{1,3}},S_{\mathrm{2,1}})\left|\right|},\mathrm{\μ}=t\sin \mathrm{\θ}=\frac{1}{2\left|\right|(S_{\mathrm{3,2}},S_{\mathrm{1,3}},S_{\mathrm{2,1}})\left|\right|},---\left(1.9\right)$

Wherein, s _i,jthe element that representing matrix S i-th row j arranges.Then, r ₁can be tried to achieve by following formula

$(\frac{1}{\mathrm{\μ}}{\left[T_{b_i{b}_0}\right]}_{\×}{R}_{b_i{b}_0}+{\left[r_2\right]}_{\×})x=0,\left|\right|x\left|\right|=1.---\left(1.10\right)$

Above formula can by right do SVD decomposition to try to achieve, if $\frac{1}{\mathrm{\μ}}{\left[T_{b_i{b}_0}\right]}_{\×}{R}_{b_i{b}_0}+{\left[r_2\right]}_{\×}={\mathrm{USV}}^T,$ Then x is the 3rd row of V.Then, we can obtain

$R_{b_{0}w}=\left[\begin{array}{ccc}{r}_1& r_2& r_1\×r_2\end{array}\right].---\left(1.11\right)$

θ _i＝2arctan((A ^TA) ^-1(A ^TB))， (1.12)

Wherein $A=\mathrm{vec}(r_2{r}_3^T+r_3{r}_2^T),$ $B=\mathrm{vec}(\frac{1}{\mathrm{\μ}}{\left[T_{b_i{b}_0}\right]}_{\×}{R}_{b_i{b}_0}+{\left[r_2\right]}_{\×}).$ Here vec () representing matrix stretching.So,

$R_{{\mathrm{wb}}_0}=R_{b_{0}w}^T---\left(1.13\right)$

$t=\frac{\mathrm{\μ}}{\sin {\mathrm{\θ}}_i}.---\left(1.14\right)$

3, basis is tried to achieve t and θ _iinitial value solves, and according to (1.16), asks R _cw, T _cwvalue

$R_{\mathrm{cw}}=R_{{\mathrm{cb}}_0}{R}_{{\mathrm{wb}}_0}^T,T_{\mathrm{cw}}={(t,\mathrm{0,0})}^T-R_{\mathrm{cw}}{T}_{{\mathrm{wb}}_0}.---\left(1.15\right)$

Step 3: internally parameter p _inwith outer parameter p _outcarry out nonlinear optimization.Here p _in∈ ⁹, p _out∈ ¹⁰be expressed as follows

$p_{\mathrm{in}}={({\mathrm{\α}}_x,{\mathrm{\α}}_y,u_{0,}{v}_0,k_1,k_2,k_3,k_4,k_5)}^T,p_{\mathrm{out}}={(v_{{\mathrm{wb}}_0}^T,t,v_{\mathrm{cw}}^T,T_{\mathrm{cw}}^T)}^T,$

Wherein, be respectively r _cwcorresponding Rodrigues vector.Transformational relation between the rotation matrix R that Rodrigues vector v is corresponding with it is as follows

$\sin \left(\right|\left|v\right|\left|\right){\left[v\right]}_{\×}=\frac{R-R^T}{2},$

$R=\cos \left(\right|\left|v\right|\left|\right)I_3+\frac{(1-\cos \left(\right|\left|v\right|\left|\right))}{{\left|\right|v\left|\right|}^2}{\mathrm{vv}}^T+\sin \left(\right|\left|v\right|\left|\right){\left[v\right]}_{\×},$

Wherein, I ₃represent the unit matrix on 3 rank.

We make following mark to the coordinate of each picture point, on target 1, are θ in rotation angle _itime, the angular coordinate corresponding to a jth target unique point is designated as $(u_j^i,v_j^i),i=\mathrm{0,1},...,m,j=\mathrm{1,2},...,n,$ Point on target is designated as

X _b＝{(x _j，y _j，0) ^T，j＝1，2，...，n}.

Owing to there is error in image zooming-out process, therefore, we choose image re-projection error and as optimization aim.By target point and p _out, obtain re-projection point process as follows:

1, rotation angle is θ _itime, target point be converted into the point under world coordinate system

$\left[\begin{array}{c}{x}_{i,j}^w\\ y_{i,j}^w\\ z_{i,j}^w\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\θ}}_i& -{\sin \mathrm{\θ}}_i& 0\\ {\sin \mathrm{\θ}}_i& {\cos \mathrm{\θ}}_i& 0\\ 0& 0& 1\end{array}\right](R_{{\mathrm{wb}}_0}\left[\begin{array}{c}{x}_j\\ y_j\\ 0\end{array}\right]+\left[\begin{array}{c}t\\ 0\\ 0\end{array}\right]).---\left(1.16\right)$

2, corresponding re-projection point is asked for

Re-projection error is defined as

$E_r=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}\underset{j=1}{\overset{n}{\mathrm{\Σ}}}[{(u_i^j-g_u(p_{\mathrm{in}},p_{\mathrm{out}},x_j,y_j,{\mathrm{\θ}}_i))}^2+{(v_i^j-g_v(p_{\mathrm{in}},p_{\mathrm{out}},x_j,y_j,{\mathrm{\θ}}_i))}^2]---\left(1.19\right)$

Optimization problem can be described as

$(p_{\mathrm{in}}^{*},p_{\mathrm{out}}^{*},{\mathrm{\θ}}_1^{*},{\mathrm{\θ}}_2^{*},...,{\mathrm{\θ}}_m^{*})=\arg \underset{p_{\mathrm{in}},p_{\mathrm{out}},,{\mathrm{\θ}}_1,...,{\mathrm{\θ}}_m}{\min }{E}_r.---\left(1.20\right)$

This optimization problem can utilize sparse Levenberg-Marquardt algorithm to solve optimization problem, and the Optimization Toolbox of sparse LM algorithm can be downloaded on http://users.ics.forth.gr/ ~ lourakis/sparseLM/.Utilize above-mentioned optimization, we can obtain t,R _cw, T _cwinformation, the anglec of rotation being used for step 4 is asked for by these information.

Step 4: utilize the inside and outside parameter of demarcating, measures the anglec of rotation.

First, we, according to the information of having demarcated, mate angle point.Suppose that at the angular coordinate of photo of θ place shooting be X ^c={ (u _i, v _i) ^t, i=1,2 ..., N _c, now may exist in picture and block, therefore coupling can not complete automatically, can according to following algorithm:

1, the point set that may mate is found.

To each angle point and target point pair calculate a score S _i,j, computing method are as follows:

(1) (x is asked for _j, y _j, 0) ^tcorresponding world coordinates

$\left[\begin{array}{c}{x}_j^w\\ y_j^w\\ z_j^w\end{array}\right]=R_{{\mathrm{wb}}_0}\left[\begin{array}{c}{x}_j\\ y_j\\ 0\end{array}\right]+\left[\begin{array}{c}t\\ 0\\ 0\end{array}\right].$

(2) picture point (u is asked for _i, v _i) ^t? preimage in plane acquiring method is as follows

$X_w^j=\mathrm{\ρ}(x_i^n,y_i^n,1)r_1+t$

$Y_w^j=\mathrm{\ρ}(x_i^n,y_i^n,1)r_2,$

$Z_w^j=z_w^j,$

Wherein, $\mathrm{\ρ}=\frac{z_w^j}{(x_i^n,y_i^n,1)r_3},$ $[r_1,r_2,r_3]=R_{{\mathrm{wb}}_0}\·{(x_i^n,y_i^n)}^T$ For (u _i, v _i) ^tcorresponding normalization coordinate, can be tried to achieve by iteration.

(3) we define S _i,jas shown in the formula

$S_{i,j}=\sqrt{{\left(X_w^j\right)}^2+{\left(Y_w^j\right)}^2}-\sqrt{{\left(x_w^j\right)}^2+{\left(y_w^j\right)}^2}.---\left(1.21\right)$

(4) selected threshold τ _m=0.1d, d is the length of gridiron pattern grid here, then defines the set of the point that may mate

$\mathrm{\&Omega;}=\{{(u_i,v_i)}^T\&LeftRightArrow;{(x_j,y_j,0)}^T,j=\mathrm{1,2},...,n,i=\mathrm{1,2},...,N_c|S_{i,j}<{\mathrm{\&tau;}}_m\}.---\left(1.22\right)$

2, utilize histogram, calculate angle.

For the element in Ω, calculate θ by following formula _i,j

$\left[\begin{array}{c}{x}_j^w\\ y_j^w\\ z_j^w\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\&theta;}}_{i,j}& -{\sin \mathrm{\&theta;}}_{i,j}& 0\\ {\sin \mathrm{\&theta;}}_{i,j}& {\cos \mathrm{\&theta;}}_{i,j}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{X}_j^w\\ Y_j^w\\ Z_j^w\end{array}\right].---\left(1.23\right)$

Then draw the histogram of distribution, have 360 Nogata blocks in this histogram, the element in a kth Nogata block is the element number in ((k-181) °, (k-179) °) ∩ Ω.We to the estimated value of θ are

3, utilize the angle of trying to achieve, select correct coupling right.

Target point M (j) corresponding to i corresponds in correct angular region, the point that score is minimum, namely

$M\left(i\right)=\underset{j}{\min }{S}_{i,j},$ Meet θ _i,j∈ [θ-1 °, θ+1 °].

If there is not θ _i,j∈ [θ-1 °, θ+1 °], then make M (i)=0.

4, nonlinear optimization

Optimization problem is described as

${\mathrm{\&theta;}}^{*}=\arg \underset{\mathrm{\&theta;}}{\min }\underset{i=1}{\overset{N_c}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}\left(i\right){\left((u_i-g_u(p_{\mathrm{in}}^{*},p_{\mathrm{out}}^{*},x_{M\left(i\right)},y_{M\left(i\right)},\mathrm{\&theta;})\right)}^2+\left({v_i-g_v(p_{\mathrm{in}}^{*},p_{\mathrm{out}}^{*},x_{M\left(i\right)},y_{M\left(i\right)},\mathrm{\&theta;}))}^2\right)---\left(1.24\right)$

Wherein, $\mathrm{\&delta;}\left(i\right)=\left\{\begin{array}{c}1,M\left(i\right)>0\\ 0,M\left(i\right)=0\end{array}\right..$

The lsqnonlin function that this optimization problem can be carried by MATLAB solves.

Advantage and effect:

The present invention is a kind of vision measuring method of the single-shaft-rotation angle based on fixed camera and single target, it is a kind of method utilizing monocular camera and two-dimentional gridiron pattern to measure single-shaft-rotation angle, its advantage is, solve Current vision angle measurement problem to being provided with many requirements, inconvenient problem.The present invention adopts two-dimensional target as demarcation characteristic body, by optimized algorithm, and can single-shaft-rotation angle.It is simple that the method has installation process, the advantages such as stated accuracy is high, with low cost, and the method can solve occlusion issue after demarcation simultaneously.

Accompanying drawing explanation

Fig. 1: pin-hole imaging model schematic

Fig. 2: experimental facilities scheme of installation

Fig. 3 a: measuring error average is with noise variation diagram

Fig. 3 b: measuring error variance is with noise variation diagram

Fig. 4 a: the angle point number figure detected during angle change

Fig. 4 b: during angle change, angular error figure

Fig. 5: truly test the two-dimentional gridiron pattern target picture used

Fig. 6: FB(flow block) of the present invention

In figure, symbol description is as follows:

Symbol description in Fig. 1: O represents video camera photocentre, O ₁represent image coordinate system initial point.X, Y represent the coordinate axis of image coordinate system, and x, y, z represent the coordinate axis of camera coordinate system.P (X _w, Y _w, Z _w) representing the coordinate of three-dimensional point under camera coordinate system, p represents the projection of a P on image.

Symbol description in Fig. 2: O _w-X _wy _wz _wfor world coordinate system, Z _waxle is turning axle, and the initial point of target when reference position is positioned at X _won axle; The target co-ordinates of target when reference position is this coordinate system is around Z _wrotate θ _iafter, target co-ordinates system becomes camera coordinates is O _c-X _cy _cz _c.

Embodiment

See Fig. 1-Fig. 6, the invention provides a kind of vision measuring method of the single-shaft-rotation angle based on fixed camera and single target, and carried out emulation experiment and true experimental verification.

Emulation experiment

Emulation experiment is on the computing machine of dominant frequency 3.07GHz, internal memory 4.00GB, and the MATLAB2014a under Windows XP environment carries out.Emulating camera model used is second order distortion model, and each parameter is as follows:

α _x＝782.5109,α _y＝782.9155,u ₀＝357.3909,v ₀＝264.5240

k ₁＝-0.4232,k ₂＝0.2664,k ₃＝-0.000555,k ₄＝-0.0031,k ₅＝0

Target is the gridiron pattern of 6 × 8, and single checker's length is 39.5mm × 39.5mm.Emulation experiment mainly demonstrates stability and the high precision of calibration algorithm.Simulation process is as follows:

Simulated environment is arranged: according to the intrinsic parameter of setting, and pose, obtains picture point coordinate.The angle chosen when wherein rotating is (unit degree of being)

θ _i＝2.25×i

Step one: utilize MATLAB calibration tool case, obtains the initial value of intrinsic parameter, result following (demarcating internal reference picture noise is 2 pixels):

α _x＝774.34147,α _y＝773.91064,u ₀＝349.58372,v ₀＝269.85450

k ₁＝-0.43943,k ₂＝0.33274,k ₃＝-0.00222,k ₄＝-0.00206,k ₅＝0

Step 2: the result of demarcating according to general camera, joins initial value outside calculating.

Step 3: according to inside and outside parameter initial value, carries out bundle adjustment.

Step 4: choose angle, measures.

In order to the robustness of verification algorithm, in step 4, we choose 100 angles, measure, and using the maximal value of angular error as measuring error.In picture point, add average is μ=0, the white Gaussian noise of standard deviation sigma=0 4 pixels, and get average and the variance mapping of 100 Experimental measurement error, result is as shown in Fig. 3 (a), (b).Result shows, even if add the white Gaussian noise that standard deviation is 4 pixels, still can obtain the result that angular error average is less than 0.5 degree, and this proves that our angle-measuring method is to robust during picture noise.In order to verify that our method is effective to blocking situation, situation when we rotate in (-180 °, 180 °) target, emulates.Fig. 4 (a), (b) list simulation result, and (a) represents the number of the angle point detected, (b) represents the angular error measured.Experimental result shows, our method effectively can solve occlusion issue.

True experiment

In order to verify feasibility of the present invention further, We conducted true experimental verification.The target that we adopt is the gridiron pattern (as shown in Figure 5) printed, and specification is 6 × 9, and the length of each grid is 29.5mm; The camera adopted is Basler camera, and resolution is 658 × 492 pixels, and focal length is about 800 pixels.Angle checking adopts photoelectric follow-up, and this system perspective measuring accuracy is 0.01 degree.Result is as table 1, and error shows under this experiment condition, and the maximal value of angular error is less than 0.15 degree.

Table 1. is experiment anglec of rotation estimated result truly

	1	2	3	4	5	6	7	8	9	10
											Turntable value	-54.00	-36.00	-27.00	-10.80	-1.8	5.40	16.20	28.80	36.00	54.00
True value	-53.985	-35.978	-26.966	-10.749	-0.036	5.477	0.070	28.894	36.135	54.147
											Error	-0.015	-0.022	-0.034	-0.051	-1.764	0.077	16.270	0.094	0.135	0.147

Claims (1)

1., based on the vision measuring method at the single-shaft-rotation angle of fixed camera and single target, it is characterized in that: the method concrete steps are as follows:

Step one: camera inside and outside parameter is demarcated;

In specific implementation process, utilize two-dimentional gridiron pattern as target; The sequence of pictures adopted, picture when comprising a reference position and m open picture when rotary part rotates to different angles; Suppose that this m angle is θ ₁, θ ₂..., θ _m, next, the X-comers utilizing MATLAB 2014 to carry extracts function detectCheckerboardPoints and carries out angle point grid, and carries out internal reference demarcation in conjunction with MATLAB calibration tool, tries to achieve intrinsic parameter p _inwith the external parameter of m+1 pose; This calibration tool case, http://www.vision.caltech.edu/bouguetj/calib_doc/ downloads; These external parameters are expressed as

$[R_{{\mathrm{cb}}_i},T_{{\mathrm{cb}}_i}],i=\mathrm{0,1,2},...,m.$

represent in rotation angle to be θ _itime, the rotation matrix between camera and target and translation vector, when representing reference position during i=0, the rotation matrix between camera and target and translation vector;

Step 2: the outer initial parameter values that pivoting movement is relevant is asked for

(1), according to the outer parameter of trying to achieve in step one, asking in rotation angle by (1.7) is θ _itime, target is relative to the rotation matrix of target during benchmark and translation vector $[R_{b_i{b}_0},T_{b_i{b}_0}],i=\mathrm{1,2},...,m.$

$R_{b_i{b}_0}=R_{{\mathrm{cb}}_i}^T{R}_{{\mathrm{cb}}_0},T_{b_i{b}_0}=R_{{\mathrm{cb}}_i}^T(T_{{\mathrm{cb}}_0}-T_{{\mathrm{cb}}_i}).---\left(0.1\right)$

(2), ask for t and θ _iinitial value:

Definition r ₁, r ₂, r ₃be respectively the 1st, 2,3 row, and vector [t] _×be expressed as follows matrix

${\left[\begin{array}{c}{t}_x\\ t_y\\ t_z\end{array}\right]}_{\&times;}=\left[\begin{array}{ccc}0& {-t}_z& t_y\\ t_z& 0& {-t}_x\\ {-t}_y& t_x& 0\end{array}\right].---\left(0.2\right)$

Then, try to achieve

$r_2=\frac{{(S_{\mathrm{3,2}},S_{\mathrm{1,3}},S_{\mathrm{2,1}})}^T}{\left|\right|(S_{\mathrm{3,2}},S_{\mathrm{1,3}},S_{\mathrm{2,1}})\left|\right|},\mathrm{\&mu;}=t\sin \mathrm{\&theta;}=\frac{1}{2\left|\right|(S_{\mathrm{3,2}},S_{\mathrm{1,3}},S_{\mathrm{2,1}})\left|\right|},---\left(0.3\right)$

Wherein, s _i,jthe element that representing matrix S i-th row j arranges, then, r ₁tried to achieve by following formula

$(\frac{1}{\mathrm{\&mu;}}{\left[T_{b_i{b}_0}\right]}_{\&times;}{R}_{b_i{b}_0}+{\left[r_2\right]}_{\&times;})x=0,\left|\right|x\left|\right|=1.---\left(0.4\right)$

Above formula is by right do SVD decomposition to try to achieve, if $\frac{1}{\mathrm{\&mu;}}{\left[T_{b_i{b}_0}\right]}_{\&times;}{R}_{b_i{b}_0}+{\left[r_2\right]}_{\&times;}={\mathrm{USV}}^T,$ Then x is the 3rd row of V, then, obtains

$R_{b_{0}w}=\left[\begin{array}{ccc}{r}_1& r_2& r_1\&times;r_2\end{array}\right].---\left(0.5\right)$

θ _i＝2arctan((A ^TA) ^-1(A ^TB)), (0.6)

Wherein $A=\mathrm{vec}(r_2{r}_3^T+r_3{r}_2^T),$ $B=\mathrm{vec}(\frac{1}{\mathrm{\&mu;}}{\left[T_{b_i{b}_0}\right]}_{\&times;}{R}_{b_i{b}_0}+{\left[r_2\right]}_{\&times;}).$ Here vec () representing matrix stretching, so,

$R_{{\mathrm{wb}}_0}=R_{b_{0}w}^T---\left(0.7\right)$

$t=\frac{\mathrm{\&mu;}}{\sin {\mathrm{\&theta;}}_i}.---\left(0.8\right)$

(3), basis is tried to achieve t and θ _iinitial value solves, and according to (1.16), asks R _cw, T _cwvalue

$R_{\mathrm{cw}}=R_{{\mathrm{cb}}_0}{R}_{{\mathrm{wb}}_0}^T,T_{\mathrm{cw}}={(t,\mathrm{0,0})}^T-R_{\mathrm{cw}}{T}_{{\mathrm{wb}}_0}.---\left(0.9\right)$

Step 3: internally parameter p _inwith outer parameter p _outcarry out nonlinear optimization; Here p _in∈ ⁹, p _out∈ ¹⁰be expressed as follows

$p_{\mathrm{in}}={({\mathrm{\&alpha;}}_x,{\mathrm{\&alpha;}}_y,u_{0,}{v}_0,k_1,k_2,k_3,k_4,k_5)}^T,p_{\mathrm{out}}={(v_{{\mathrm{wb}}_0}^T,t,v_{\mathrm{cw}}^T,T_{\mathrm{cw}}^T)}^T,$

Wherein, be respectively r _cwcorresponding Rodrigues vector; Transformational relation between the rotation matrix R that Rodrigues vector v is corresponding with it is as follows

$\sin \left(\right|\left|v\right|\left|\right){\left[v\right]}_{\&times;}=\frac{R-R^T}{2},$

$R=\cos \left(\right|\left|v\right|\left|\right)I_3+\frac{(1-\cos \left(\right|\left|v\right|\left|\right))}{{\left|\right|v\left|\right|}^2}{\mathrm{vv}}^T+\sin \left(\right|\left|v\right|\left|\right){\left[v\right]}_{\&times;},$

Wherein, I ₃represent the unit matrix on 3 rank;

Making following mark to the coordinate of each picture point, on target 1, is θ in rotation angle _itime, the angular coordinate corresponding to a jth target unique point is designated as $(u_j^i,v_j^i),i=\mathrm{0,1},...,m,j=\mathrm{1,2},...,n,$ Point on target is designated as

X _b＝{(x _j,y _j,0) ^T,j＝1,2,...,n}.

Owing to there is error in image zooming-out process, therefore, choose image re-projection error and as optimization aim, by target point and p _out, obtain re-projection point process as follows:

<1>, rotation angle are θ _itime, target point (x _j, y _j, 0) ^tbe converted into the point under world coordinate system

$\left[\begin{array}{c}{x}_{i,j}^w\\ y_{i,j}^w\\ z_{i,j}^w\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\&theta;}}_i& -{\sin \mathrm{\&theta;}}_i& 0\\ {\sin \mathrm{\&theta;}}_i& {\cos \mathrm{\&theta;}}_i& 0\\ 0& 0& 1\end{array}\right](R_{{\mathrm{wb}}_0}\left[\begin{array}{c}{x}_j\\ y_j\\ 0\end{array}\right]+\left[\begin{array}{c}t\\ 0\\ 0\end{array}\right]).---\left(0.10\right)$

<2>, ask for corresponding re-projection point

Re-projection error is defined as

$E_r=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}[{(u_i^j-g_u(p_{\mathrm{in}},p_{\mathrm{out}},x_j,y_j,{\mathrm{\&theta;}}_i))}^2+{(v_i^j-g_v(p_{\mathrm{in}},p_{\mathrm{out}},x_j,y_j,{\mathrm{\&theta;}}_i))}^2]---\left(0.13\right)$

Optimization problem is described as

$(p_{\mathrm{in}}^{*},p_{\mathrm{out}}^{*},{\mathrm{\&theta;}}_1^{*},{\mathrm{\&theta;}}_2^{*},...,{\mathrm{\&theta;}}_m^{*})=\arg \underset{p_{\mathrm{in}},p_{\mathrm{out}},,{\mathrm{\&theta;}}_1,...,{\mathrm{\&theta;}}_m}{\min }{E}_r.---\left(0.14\right)$

This optimization problem utilizes sparse Levenberg-Marquardt algorithm to solve optimization problem, and the Optimization Toolbox of sparse LM algorithm is downloaded on http://users.ics.forth.gr/ ~ lourakis/sparseLM/; Utilize above-mentioned optimization, obtain t,R _cw, T _cwinformation, the anglec of rotation being used for step 4 is asked for by these information;

Step 4: utilize the inside and outside parameter of demarcating, measures the anglec of rotation;

First, according to the information of having demarcated, angle point is mated; Suppose that at the angular coordinate of photo of θ place shooting be X ^c={ (u _i, v _i) ^t, i=1,2 ..., N _c, now may exist in picture and block, therefore coupling can not complete, automatically according to following algorithm:

(i) the point set that may mate, is found;

To each angle point and target point pair calculate a score S _i,j, computing method are as follows:

(1) (x is asked for _j, y _j, 0) ^tcorresponding world coordinates

$\left[\begin{array}{c}{x}_j^w\\ y_j^w\\ z_j^w\end{array}\right]=R_{{\mathrm{wb}}_0}\left[\begin{array}{c}{x}_j\\ y_j\\ 0\end{array}\right]+\left[\begin{array}{c}t\\ 0\\ 0\end{array}\right].$

(2) picture point (u is asked for _i, v _i) ^t? preimage in plane acquiring method is as follows

$X_w^j=\mathrm{\&rho;}(x_i^n,y_i^n,1)r_1+t$

$Y_w^j=\mathrm{\&rho;}(x_i^n,y_i^n,1)r_2,$

$Z_w^j=z_w^j,$

Wherein, $\mathrm{\&rho;}=\frac{z_w^j}{(x_i^n,y_i^n,1)r_3},$ $[r_1,r_2,r_3]=R_{{\mathrm{wb}}_0}\&CenterDot;{(x_i^n,y_i^n)}^T$ For (u _i, v _i) ^tcorresponding normalization coordinate, is tried to achieve by iteration;

(3) S is defined _i,jas shown in the formula

$S_{i,j}=\sqrt{{\left(X_w^j\right)}^2+{\left(Y_w^j\right)}^2}-\sqrt{{\left(x_w^j\right)}^2+{\left(y_w^j\right)}^2}.---\left(0.15\right)$

(4) selected threshold τ _m=0.1d, d is the length of gridiron pattern grid here, then defines the set of the point that may mate

$\mathrm{\&Omega;}=\{{(u_i,v_i)}^T\&LeftRightArrow;{(x_j,y_j,0)}^T,j=\mathrm{1,2},...,n,i=\mathrm{1,2},...,N_c|S_{i,j}<{\mathrm{\&tau;}}_m\}.---\left(0.16\right)$

(ii), utilize histogram, calculate angle;

For the element in Ω, calculate θ by following formula _i,j

$\left[\begin{array}{c}{x}_j^w\\ y_j^w\\ z_j^w\end{array}\right]=\left[\begin{array}{ccc}\cos {\mathrm{\&theta;}}_{i,j}& -{\sin \mathrm{\&theta;}}_{i,j}& 0\\ {\sin \mathrm{\&theta;}}_{i,j}& {\cos \mathrm{\&theta;}}_{i,j}& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{X}_j^w\\ Y_j^w\\ Z_j^w\end{array}\right].---\left(0.17\right)$

Then draw the histogram of distribution, have 360 Nogata blocks in this histogram, the element in a kth Nogata block is the element number in ((k-181) °, (k-179) °) ∩ Ω; To the estimated value of θ be

(iii), utilize the angle of trying to achieve, select correct coupling right;

Target point M (j) corresponding to i corresponds in correct angular region, the point that score is minimum, namely

$M\left(i\right)=\underset{j}{\min }{S}_{i,j},$ Meet θ _i,j∈ [θ-1 °, θ+1 °].

If there is not θ _i,j∈ [θ-1 °, θ+1 °], then make M (i)=0.;

(iv), nonlinear optimization

Optimization problem is described as

${\mathrm{\&theta;}}^{*}=\arg \underset{\mathrm{\&theta;}}{\min }\underset{i=1}{\overset{N_c}{\mathrm{\&Sigma;}}}\mathrm{\&delta;}\left(i\right){\left((u_i-g_u(p_{\mathrm{in}}^{*},p_{\mathrm{out}}^{*},x_{M\left(i\right)},y_{M\left(i\right)},\mathrm{\&theta;})\right)}^2+\left({v_i-g_v(p_{\mathrm{in}}^{*},p_{\mathrm{out}}^{*},x_{M\left(i\right)},y_{M\left(i\right)},\mathrm{\&theta;}))}^2\right)---\left(0.18\right)$

Wherein, $\mathrm{\&delta;}\left(i\right)=\left\{\begin{array}{c}1,M\left(i\right)>0\\ 0,M\left(i\right)=0\end{array}\right.$

The lsqnonlin function that this optimization problem is carried by MATLAB solves.