CN103208122A - Multi-camera calibration method based on one-dimensional calibration rod design - Google Patents

Abstract

The invention provides a multi-camera calibration tool under calibration of multiple camera groups and mutual alignment requirements of attached markers on the tool. A one-dimensional calibration object calibration method is the most convenient and fastest method among the camera-group calibration methods. Designing of a one-dimensional calibration object is the primary problem of the one-dimensional calibration method. A one-dimensional calibration object design standard is provided by combining projective transformation property and space range restraining. Theoretical analysis shows that whether the one-dimensional calibration object meets a restraining relation can be judged by using a mutual distance as a condition, and image points of the one-dimensional calibration object can be matched. Experiments show that the one-dimensional calibration object meeting the design standard is simple to operate and convenient to match, and parameters inside and outside the camera groups after the camera groups are calibrated meet use requirements.

Description

Demarcate the polyphaser scaling method of bar design based on one dimension

1. technical field

The demarcation of multicamera system, be research focus and the difficult point of computer vision field always, be in the key core status in about application systems such as recreation, safety in that attitude acquisition system, tracker, supervisory system etc. are many, be that each universities and colleges of university, research institute, the researchist of mechanism pay close attention to both at home and abroad, the present invention relates to a kind of calibration tool and algorithm design of many cameras, when mainly being fit to many cameras around placement, the inside and outside ginseng of camera is demarcated.

2. background technology

In the demarcation of camera, for the polyphaser number, currently used traditional scaling method is not only loaded down with trivial details but also precision is low.Tradition polyphaser standardization is mainly in two steps: 1) confidential reference items of single camera are demarcated.2) the outer parametric solution of camera set.The traditional camera intrinsic parameter is demarcated the normal plane chessboard standardization that adopts, there are a lot of defectives in the method at the polyphaser timing signal, as can only demarcating the inner parameter of a camera at every turn, and also need some angle point image coordinate of manual input after each the demarcation, carry out the outer ginseng of camera set then and demarcate.Therefore, use the inside and outside ginseng of traditional camera scaling method to have the slow inefficient shortcoming of speed, camera set is demarcated very inconvenient.The present invention proposes a kind of one dimension and demarcate the method for designing of thing, one dimension is demarcated these defectives of the plane reference method that overcome of object space case, only need in demarcating the space, brandish the one dimension of a period of time and demarcate thing, just can obtain the inside and outside parameter of all cameras simultaneously, the method simple and fast, the parameter calibration result is comparatively accurate.

The fundamental purpose that thing is demarcated in design is the convenient coupling of determining between picture point, i.e. corresponding relation between the image coordinate of same object in the different cameral image in the space.According to the dimension of demarcating thing, demarcate thing at present and be divided three classes: 1) three-dimensional cube is demarcated thing.2) two dimensional surface is demarcated thing.3) one dimension is demarcated thing.Demarcate the feature that often has obvious discrimination on the thing, be to utilize color as distinguishing characteristic as one of method, demarcate thing with the label of different colours as feature, then with the object of same color on each width of cloth image as a class, finish the coupling of image coordinate.

Traditional one dimension is demarcated the matching process that the thing design is based on color, this method is vulnerable to the coupling of the interference generation picture point mistake of external environment, for example the illumination meeting has a strong impact on the color of object, the coupling that leads to errors, influence the solving result of fundamental matrix, cause and demarcate the failure of polyphaser inside and outside parameter.The present invention has designed a new one dimension and has demarcated the thing design criteria, is satisfying under this criterion, keeps the constant character of length distance according to label actual range and projector distance, can avoid using color to realize the coupling of picture point as matching characteristic.

3. summary of the invention

The present invention has designed a kind of polyphaser calibration tool and has reached adhering to the mutual alignment requirement of label on the instrument, the problem that solves is that the distance that pixel distance between image subscript earnest and one dimension are demarcated between thing is consistent substantially, therefore provide a kind of one dimension to demarcate the thing design criteria, and use this criterion to make one dimension and demarcate bar, label is simply to identify on camera image, can finish the coordinate coupling between different video image tagged thing then based on Infrared or ordinary ray identification.

3.1 one dimension is demarcated the model of bar under camera

Finishing the coupling of many image tagged thing, is as foundation by the pixel distance relation.In the general pattern between label corresponding pixel distance be not consistent with real marking thing phase mutual edge distance, but under concrete environment, give some restrictive condition, can utilize pixel distance to finish coupling.At first determine the corresponding relation of one dimension demarcation bar central marker thing, the pixel distance according to two ends label and central marker thing mates again.

See that " Figure of description " one dimension shown in Figure 1 demarcates mapping relations between the point on bar L and the plane of delineation P, the space one dimension is demarcated on the bar L three labels, is made as A respectively, B, C wherein | AB|=d ₁, | BC|=d ₂And d ₁＜d ₂, the O that sets up an office is the photocentre of camera, and a, b, c are that one dimension is demarcated each label of bar at the subpoint of picture plane P, and θ represents that one dimension demarcates the angle of bar and camera optical axis, A as can be known, B, C and a, b, c, O is coplanar.Be initial point with the O point, the camera optical axis is the Z axle, and the axle of parallel picture plane P is Y-axis, sets up the ZOY coordinate system.The focal length of camera is made as f, establish one dimension demarcate the coordinate of bar central marker point be (h, z), a then, b, the coordinate that c is 3 are respectively a (f, y ₁), b (f, y ₂), c (f, y ₃), the angle that bidding is decided bar L and Z axle is θ, some B according to the character of similar triangles, tries to achieve y apart from the Z wheelbase from h ₁, y ₂, y ₃As follows respectively:

$\left\{\begin{array}{c}{y}_1=\frac{f(h-d_2\sin \mathrm{\θ})}{z-d_2\cos \mathrm{\θ}}\\ y_2=\frac{\mathrm{fh}}{z}\\ y_3=\frac{f(h+d_2\sin \mathrm{\θ})}{z+d_2\cos \mathrm{\θ}}\end{array}\right.---\left(1\right)$

Distance table between each label mid point is shown:

$g_1=|y_3-y_2|,g_2=|y_1-y_2|---\left(2\right)$

One dimension marking rod actual distance difference and correspondence image pixel distance difference keep jack per line then:

$\mathrm{\ρ}=(g_2-g_1)(d_2-d_1)>0---\left(3\right)$

After formula (1) (2) (3) associating, obtain the condition of equivalence of formula (4), i.e. the one dimension that the present invention sets is demarcated the design criteria of thing: the distance of proximal points and remote point must satisfy following inequality condition in the one dimension demarcation bar:

$\frac{1}{d_1}-\frac{1}{d_2}>\frac{2}{z_{\min }}---\left(4\right)$

Wherein: establish d ₂＞d ₁, z _MinThe expression one dimension is demarcated in the pole brand point on Z-direction the position nearest from the center of circle.

Therefore, making is satisfied the one dimension of inequality (4) and is demarcated bar, can guarantee the far and near distance relationship consistency in corresponding space on the far and near relation of image coordinate pixel distance of two ends label image coordinate that the spatial dimension motion obtains and central marker and one dimension demarcation bar.ρ in the formula (3) is elementary function, and according to the zero of a function theorem, the inference of carrying out inequality (3) in 3.2 trifles proves.

3.2 the permanent positive proof of inequality

According to the inference of zero point theorem, as just proving the inequality perseverance or permanent bearing, only need the proof function not exist separate zero point, and exist a value to make that inequality is plus or minus.When one dimension was demarcated thing perpendicular to the camera optical axis, it was obvious that inequality is set up.So necessarily exist a value that inequality (3) is set up.Only need proof function ρ not exist separate zero point now.In order to narrate conveniently, function can be discussed earlier to have the condition of separating zero point.Illustrating that function is impossible satisfy the condition of separating existence zero point to get final product.

3.2.1 the infinitely great zero of a function in space

Suppose θ ∈ [0 180 °], can remove formula (2) absolute value sign; When θ ∈ (1,800 360 °], according to symmetry, formula (3) is still set up.Because planar point is can not change in projective transformation upper/lower positions ordinal relation, so y is arranged ₁＜y ₂＜y ₃Utilize reduction to absurdity, adopt the definition at zero point, make expression formula (3) be:

$\mathrm{\ρ}=(g_2-g_1)(d_2-d_1)=(y_3+y_1-2y_2)(d_2-d_1)=0---\left(5\right)$

(1) substitution (5) abbreviation can be got:

$z^2\sin \mathrm{\θ}(d_2-d_1)-\mathrm{hz}\cos \mathrm{\θ}(d_2-d_1)-d_1{d}_{2}z\sin 2\mathrm{\θ}+2{\mathrm{hd}}_1{d}_2{\cos }^2\mathrm{\θ}=0---\left(6\right)$

Constructing variable l:

$l=\frac{d_2-d_1}{d_2{d}_1}=\frac{1}{d_1}-\frac{1}{d_2}---\left(7\right)$

Obviously parameter l is about d ₁, d ₂Function, this parameter is only relevant with the character of one dimension demarcation bar self.With (6) formula the right and left simultaneously divided by d ₂d ₁And (7) substitution got:

$z^2\sin \mathrm{\θl}-\mathrm{hz}\cos \mathrm{\θl}-z\sin 2\mathrm{\θ}+2h{\cos }^2\mathrm{\θ}=0---\left(8\right)$

Turn equation (8) into about l function

$l=\frac{z\sin 2\mathrm{\θ}-2h{\cos }^2\mathrm{\θ}}{z^2\sin \mathrm{\θ}-\mathrm{hz}\cos \mathrm{\θ}}=\frac{2\cos \mathrm{\θ}(z\sin \mathrm{\θ}-h\cos \mathrm{\θ})}{z(z\sin \mathrm{\θ}-h\cos \mathrm{\θ})}---\left(9\right)$

One dimension is demarcated thing and is not allowed to overlap at three subpoints as the plane, and this is because can not satisfy 3 necessary visible conditions of uncalibrated image, and should give when this situation therefore occurring needs to reject, so:

$\begin{array}{c}\underset{\‾}{z\sin \mathrm{\θ}-h\cos \mathrm{\θ}\≠0---\left(10\right)}\\ l=\frac{2\cos \mathrm{\θ}}{z}---\left(11\right)\end{array}$

Keep the constraint of length unchangeability if one dimension is demarcated bar under projective transformation, there is not zero point in function ρ so.Because one dimension is demarcated bar and created and namely be fixed constantly, the value of l also keeps necessarily, and when spatial dimension was unrestricted, there was zero point forever in function, namely can find suitable z and θ value in the space, makes the function zero-point existence.This is unallowed, therefore needs to increase constraint formula (11) is false.

3.2.2 space finite function zero existence

Because it is limited that one dimension is demarcated the thing space, and label also has certain photosensitive region on camera image, so under true environment, the z value always has constraint, namely has the constraint condition shown in the formula (12).

$z_{\min }<z<z_{\max }---\left(12\right)$

Have-1≤cos θ≤1 according to hypothesis θ ∈ [0 180 °], so

$\frac{2\cos \mathrm{\&theta;}}{z}\&le;\frac{2}{z_{\min }}---\left(13\right)$

In conjunction with (7), (11) only need satisfy formula (14), and then there is not zero point in function ρ.

$\frac{1}{d_1}-\frac{1}{d_2}>\frac{2}{z_{\min }}---\left(14\right)$

So guarantee three labels of one dimension marking rod and corresponding image coordinate satisfy under projective transformation apart from consistance, just must satisfy formula (14).Therefore determine the design criteria of one dimension demarcation bar: satisfied (14) formula of distance of proximal points and remote point in one dimension demarcation bar can guarantee to demarcate image coordinate distance relation and the space length relationship consistency that thing and centre demarcation thing are demarcated in the bar two ends.

One dimension is demarcated the design of bar and is wanted the coverage of combining camera and obtain the range of movement that one dimension is demarcated thing, in the design criteria that the foundation one dimension is demarcated bar, determines to demarcate the position of bar subscript earnest.In actual applications, only within 1 to 10 meter on distance camera lens, could shooting clear and complete image.Therefore, demarcate image that bar takes in this scope just effectively, overrun be can not image present complete and clearly as, then obtained by formula (14):

$\begin{array}{c}\frac{1}{d_1}-\frac{1}{d_2}>2---\left(15\right)\\ d_2<\frac{1}{2},d_1<\frac{d_2}{1-2d_2}---\left(16\right)\end{array}$

The coverage of combining camera, when demarcating the bar total length and be 0.25 meter, in the space of location one dimension demarcate bar can present complete clearly as.According to formula (16), establish d ₁=0.087 meter, d ₂=0.163 meter is satisfied one dimension demarcation bar design criteria, and therefore, the mutual pixel distance of shiner can be used as basis for estimation and finishes the coordinate coupling.

4. description of drawings

Mapping relations between the point on Fig. 1 one dimension demarcation bar L and the plane of delineation P

Fig. 2 arrangements of cameras mode

One dimension demarcation thing corresponding diagram picture point when Fig. 3 satisfies consistent the constraint apart from situation

Fig. 4 do not satisfy the consistent one dimension demarcation thing corresponding diagram picture point that retrains apart from situation

5. specific implementation method

5.1, the finding the solution of fundamental matrix

Give the corresponding point of two width of cloth pictures, can calculate corresponding point rotation and the translation relation of photograph.This relation can be passed through a matrix description.This matrix is designated as fundamental matrix.Fundamental matrix is 3 * 3 matrixes, and its degree of freedom is 7, wherein relative rotation and the translation of 5 corresponding relative two cameras of degree of freedom.Other 2 focal lengths that degree of freedom is camera.Calculating fundamental matrix has had a lot of methods, as: 7 methods, 8 methods, these methods of RANSAC and Lemds can both effectively solve fundamental matrix.Image characteristic of correspondence point satisfies the polar curve equation of constraint:

$m_2^{T}F{m}_1=0---\left(17\right)$

F=(f wherein _Ij) fundamental matrix m ₁=[u ＇ ₀V ＇ ₀1] ^Tm ₂=[u ₀v ₀1] ^TDifference correspondence image characteristic point coordinates.Note:

$f={\left(\begin{array}{ccccccccc}{f}_{11}& f_{12}& f_{13}& f_{21}& f_{22}& f_{23}& f_{31}& f_{32}& f_{33}\end{array}\right)}^T$

This matrix can be rewritten into:

$\mathrm{Af}=\left[\begin{array}{ccccccccc}{u}_1^{\&prime;}{u}_1& u_1^{\&prime;}{v}_1& u_1^{\&prime;}& v_1^{\&prime;}{u}_1& v_1^{\&prime;}{v}_1& v_1^{\&prime;}& u_1& v_1& 1\\ & & & & .& & & & \\ & & & & .& & & & \\ & & & & .& & & & \\ u_N^{\&prime;}{u}_N& u_N^{\&prime;}{v}_N& u_N^{\&prime;}& v_N^{\&prime;}{u}_N& v_N^{\&prime;}{v}_N& v_N^{\&prime;}& u_N& v_N& 1\end{array}\right]f=0---\left(19\right)$

Utilize SVD to decompose and can solve fundamental matrix, the order of fundamental matrix is 2.

5.2, confidential reference items extract

The extraction of camera focus depends on the absolute conic theory, according to the Krupper equation camera equation of constraint is arranged:

$F{\mathrm{\&omega;}}^{*}{F}^T=s{\left[e_r\right]}_{\&times;}{\mathrm{\&omega;}}^{\&prime;*}{{\left[e_r\right]}_{\&times;}}^T---\left(20\right)$

E wherein _rLimit for left and right sides image.

This prescription journey only provides 2 constraints, and interior parameter is 10 variablees, supposes that at first the main heart of camera is positioned at center picture, and camera pixel is square (can the passing ratio factor being converted to foursquare situation if not square).We can calculate focal length according to constraint condition.If the confidential reference items matrix of camera is:

${\tilde{K}}_0=\left[\begin{array}{ccc}{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="HDA00003068707500022.png"\; state="\{\{state\}\}">f</figure-callout>}}_0& 0& {\mathrm{<figure-callout\; id="0"\; label="u"\; filenames="HDA00003068707500022.png"\; state="\{\{state\}\}">u</figure-callout>}}_0\\ 0& f_0& {\mathrm{<figure-callout\; id="0"\; label="v"\; filenames="HDA00003068707500022.png"\; state="\{\{state\}\}">v</figure-callout>}}_0\\ 0& 0& 1\end{array}\right]{\tilde{K}}_1=\left[\begin{array}{ccc}{f}_1& 0& u_1\\ 0& f_1& v_1\\ 0& 0& 1\end{array}\right]---\left(21\right)$

Two visual point image absolute conics then:

${\mathrm{\&omega;}}^{*}=f^2\stackrel{\&OverBar;}{I}+{\mathrm{pp}}^T{\mathrm{\&omega;}}^{\&prime;*}=f^{\&prime;2}\stackrel{\&OverBar;}{I}+p^{\&prime;}{p}^{\&prime;T}---\left(22\right)$

With formula (22) substitution formula (20), namely the Kruppa equation then has:

$f^{2}F\stackrel{\&OverBar;}{I}{F}^T+{\mathrm{Fpp}}^T{F}^T={\mathrm{sf}}^{\&prime;2}{\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}{\left[e_r\right]}_{\&times;}^T+s{\left[e_r\right]}_{\&times;}{p}^{\&prime;}{p}^{\&prime;T}{\left[e_r\right]}_{\&times;}^T---\left(23\right)$

Principal point p ＇ (u is taken advantage of on the right side simultaneously ₁v ₁1) ^TCan get:

$f^{2}F\stackrel{\&OverBar;}{I}{F}^T{p}^{\&prime;}+{\mathrm{Fpp}}^T{F}^T{p}^{\&prime;}={\mathrm{sf}}^{\&prime;2}{\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}{\left[e_r\right]}_x^T{p}^{\&prime;}---\left(24\right)$

Multiply by at the same time

Know:

$f^2{p}^{\&prime;T}{\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}F\stackrel{\&OverBar;}{I}{F}^T{p}^{\&prime;}+p^{\&prime;T}{\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}{\mathrm{Fpp}}^T{F}^T{p}^{\&prime;}={\mathrm{sf}}^{\&prime;2}{p}^{\&prime;T}\left({\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}{\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}{\left[e_r\right]}_{\&times;}^T\right)p^{\&prime;}=0---\left(25\right)$

Therefore have:

$f^2=-\frac{p^{\&prime;T}{\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}{\mathrm{Fpp}}^T{F}^T{p}^{\&prime;}}{p^{\&prime;T}{\left[e_r\right]}_{\&times;}\stackrel{\&OverBar;}{I}F\stackrel{\&OverBar;}{I}{F}^T{p}^{\&prime;}}---\left(26\right)$

In like manner can get:

$f^{\&prime;2}=\frac{p^T{\left[e_l\right]}_{\&times;}\stackrel{\&OverBar;}{I}{F}^T{p}^{\&prime;}{p}^{\&prime;T}\mathrm{Fp}}{p^T{\left[e_l\right]}_{\&times;}\stackrel{\&OverBar;}{I}{F}^T\stackrel{\&OverBar;}{I}\mathrm{Fp}}---\left(27\right)$

5.3, outer parameter estimation

Outer CALCULATION OF PARAMETERS is a classical P/NP problem, and is verified as long as exist 6 groups of corresponding point just can uniquely solve outer parameter in theory.According to the camera calibration theory, essential matrix is the rotation of two cameras of contact and the matrix of translation as can be known, namely

, only essential matrix need be decomposed and to obtain outer parameter.Svd as E is E=USV ^T, establish:

$w=\left[\begin{array}{ccc}0& 1& 0\\ -1& 0& 0\\ 0& 0& 1\end{array}\right]---\left(28\right)$

Then

Four kinds of feasible solutions are arranged:

$(R,\tilde{t})=\left\{\begin{array}{c}({\mathrm{UWV}}^T,U{\left(\mathrm{0,0,1}\right)}^T)\\ ({\mathrm{UWV}}^T,-U{\left(\mathrm{0,0,1}\right)}^T)\\ ({\mathrm{UW}}^T{V}^T,U{\left(\mathrm{0,0,1}\right)}^T)\\ ({\mathrm{UW}}^T{V}^T,-U{\left(\mathrm{0,0,1}\right)}^T)\end{array}\right.---\left(29\right)$

Can get rid of according to camera constraint itself and go 3 solutions.

1, the Z value of the monumented point three-dimensional coordinate of reconstruct must be greater than 0, though Z can be less than 0, camera can only shine the object of relative camera lens front.

2, according to relative camera relative position, be to there being camera can conclude that then the x component of translational movement must be greater than 0. from left camera as camera

5.4, have a camera model ginseng global optimization adjustment of distortion factor

Think unit because system is visible light, so the single parameter of finding the solution out is not system optimal, make system optimal so need carry out global optimization.After linear solution goes out the inside and outside parameter of each camera, often adopt non-linear method to be optimized.It is exactly as optimizing variable, to minimize back projection's error as optimization purpose technology with all camera parameters and all spatial point that binding is adjusted.

$\underset{\{p_i,A_j,B_j,C_j\}}{\min }\underset{i=0}{\overset{m}{\mathrm{\&Sigma;}}}\underset{j=0}{\overset{n}{\mathrm{\&Sigma;}}}({\left|\right|a_{\mathrm{ij}}-P_i{A}_j\left|\right|}^2+{\left|\right|b_{\mathrm{ij}}-P_i{B}_j\left|\right|}^2+{\left|\right|c_{\mathrm{ij}}-P_i{C}_j\left|\right|}^2)---\left(30\right)$

Nonlinear optimization is the normal method that adopts levenberg-Marquardt on mathematics, when initial value is distant from optimal value, just becomes method of steepest descent, just approximate newton Gauss process of iteration when initial value is closer from optimal value.It should be noted that one dimension demarcate in three be not independence, so unknown number that can the abbreviation space.Utilize the spherical co-ordinate expression formula:

When picture noise point was obeyed the Gaussian distribution of same sex zero-mean separately and independent distribution, the system after the optimization was exactly the Euclidean reconstruct under the maximum likelihood meaning.

Introduce distortion model and carry out global optimization.If A _jVolume coordinate is [x, y, z], at first needs normalized coordinates system:

$x_n=(\frac{x}{z},\frac{y}{z})---\left(32\right)$

Substitution distortion model formula:

$x_d=\left[\begin{array}{c}{x}_d\left(1\right)\\ x_d\left(2\right)\end{array}\right]=(1+\mathrm{kc}\left(1\right)r^2+\mathrm{kc}\left(2\right)r^4+\mathrm{kc}\left(5\right)r^6)x_n+\mathrm{dx}---\left(33\right)$

R=x^2+y^2 wherein, expression formula dx represents the tangential distortion vector:

$\mathrm{dx}=\left[\begin{array}{c}2\mathrm{kc}\left(3\right)\mathrm{xy}+\mathrm{kc}\left(4\right)(r^2+2x^2)\\ \mathrm{kc}\left(3\right)(r^2+2y^2)+2\mathrm{kc}\left(4\right)\mathrm{xy}\end{array}\right]---\left(34\right)$

The kc vector is the distortion vector, therefore, five whole distortion variablees of component statement, these five parameters are according to the error effect ordering to camera, and two the component influences in the front of wherein radial distortion are the most obvious.

This expression formula model representation is:

$\left\{\begin{array}{c}{x}_p=\mathrm{fc}\left(1\right)(x_d\left(1\right)+\mathrm{alpha}\_c*x_d\left(2\right))+\mathrm{cc}\left(1\right)\\ y_p=\mathrm{fc}\left(2\right)x_d\left(2\right)+\mathrm{cc}\left(2\right)\end{array}\right.---\left(35\right)$

Calculation expression can abbreviation be in the optimization model:

${\left|\right|a_{\mathrm{ij}}-P_i{A}_j\left|\right|}^2={\left|\right|a_{\mathrm{ijx}}-x_p\left|\right|}^2+{\left|\right|a_{\mathrm{ijy}}-y_p\left|\right|}^2---\left(36\right)$

In like manner obtain:

$\begin{array}{c}{\left|\right|b_{\mathrm{ij}}-P_i{A}_j\left|\right|}^2={\left|\right|b_{\mathrm{ijx}}-x_p\left|\right|}^2+{\left|\right|b_{\mathrm{ijy}}-y_p\left|\right|}^2---\left(37\right)\\ {\left|\right|c_{\mathrm{ij}}-P_i{A}_j\left|\right|}^2={\left|\right|c_{\mathrm{ijx}}-x_p\left|\right|}^2+{\left|\right|c_{\mathrm{ijy}}-y_p\left|\right|}^2---\left(38\right)\end{array}$

Bring in the target function type (30) and be optimized the Euclidean reconstruct of the Maximum Likelihood Model of the band distortion factor of asking.

5.5 one dimension is demarcated the experimental analysis of bar

Suppose that it is to carry out that heterogeneous unit is demarcated in the spatial dimension of 5m * 5m, put 6 cameras, and all cameras are around putting that arrangements of cameras is seen the arrangements of cameras mode that " Figure of description " is shown in Figure 2.The design that one dimension is demarcated thing was divided into for two steps.1) definite environment of demarcating.2) determine that one dimension demarcates the mutual alignment of three labels of thing.

The design that one dimension is demarcated bar should guarantee that three images of demarcating thing can extract centre coordinate easily, guarantees again to satisfy the length consistency constraint in the scope of motion.According to 3 trifle analyses, it is 0.25 meter that experiment adopts one dimension to demarcate the thing total length, and the central marker object distance is 0.087 meter from near-end mark length, is 0.163 meter apart from distal marker.Demarcate the thing design criteria according to one dimension, can calculate and demarcate thing from the minimum distance of camera:

$\begin{array}{c}l=\frac{1}{d_1}-\frac{1}{d_2}\&ap;5.3593---\left(39\right)\\ z_{\min }>\frac{2}{5.3593}=0.3704\&GreaterEqual;\frac{2\cos \mathrm{\&theta;}}{l}---\left(40\right)\end{array}$

One dimension is demarcated thing and is brandished scope in the space generally at 1-10 rice.This is regional limited because camera is taken, and when one dimension was demarcated pole clearance and exceeded this scope from camera lens, demarcating bar can't be at three complete picture of label clearly of picture plane formation.Formula (40) shows: one dimension demarcate pole clearance from the camera lens minimum distance greater than more than 0.38 meter, optional position and angular movement, the distance relation of the pixel distance of three image coordinate of the one dimension demarcation bar demarcation thing that the infrared camera group is taken and the distance relation that one dimension is demarcated the true length of bar are consistent.Therefore, can carry out the gauge point coupling from the pixel distance of intermediate point according to picture point.Demarcate thing when one dimension and be positioned at z=3 rice, during h=0 rice, it is constant that table 1 is listed one dimension marking rod central marker object location, increases with angle, and the image coordinate of thing is demarcated at two ends and the pixel distance of middle shiner image coordinate changes.

One dimension demarcation bar far point and near point that table 1 satisfies consistent constraint criterion get relative position in picture point

See that " Figure of description " is shown in Figure 3, the one dimension demarcation thing corresponding diagram picture point when satisfying consistent the constraint apart from situation, as seen with the angle variation, remote point apart from the pixel distance of intermediate point all the time greater than the pixel distance of proximal points apart from intermediate point.This shows in motion at any angle, and one dimension is demarcated bar and kept the consistent of pixel distance between the picture point and space length.

Because the picture plane of camera is long and wide limited, demarcate pole clearance from camera lens during less than 1 meter when one dimension, can't form three points complete clearly as.Therefore, adopt and carry out emulation experiment, the situation when one dimension demarcation pole length conformance criteria is not satisfied in checking.Demarcate thing with one dimension and be positioned at z=0.2 rice, h=0 rice is example, table 2 is presented at when not satisfying consistent the constraint, during the scope of the angle of demarcating bar when one dimension at 0 °-30 °, remote point, the distance relation of physical length and the distance of corresponding diagram picture point pixel distance have occurred and has concerned inconsistent phenomenon less than the pixel distance of proximal points apart from intermediate point apart from the pixel distance of intermediate point.

Table 2 is listed when one dimension is demarcated pole clearance and do not satisfied the design criteria scope from the scope of camera lens, increases with angle, and the pixel distance that one dimension is demarcated bar remote point and intermediate point may wrong coupling phenomenon occur less than proximal points apart from the pixel distance of intermediate point.Therefore, one dimension is demarcated bar and is carried out infrared camera group timing signal, must consider the distance relation of three labels of one dimension demarcation bar, makes that demarcating bar at one dimension satisfies the design criteria that one dimension is demarcated bar brandishing of space in the scope.See that " Figure of description " is shown in Figure 4, do not satisfy the consistent one dimension demarcation thing corresponding diagram picture point that retrains apart from situation, as seen be presented at 0 ° to 50 ° scope pixel distance of angle and the inconsistent phenomenon of one dimension marking rod label space length.

Table 2 does not satisfy consistent constraint criterion, concerns between the distance of one dimension demarcation thing and the picture point

In sum: guarantee that brandishing the one dimension label in the space can make three labels become clear and separated image, then the length of one dimension demarcation thing is proper in the 0.25m left and right sides.If the one dimension marking rod needs freely to brandish, the distance range of mark object point then:

$z_{\min }>0.25m---\left(41\right)$

Have according to the one dimension scaling criterion:

$\frac{1}{d_1}-\frac{1}{d_2}>8m>\frac{2}{z_{\min }}---\left(42\right)$

The character of inequality has:

$d_1<\frac{1}{8}m,d_2<\frac{d_1}{1-2d_1}=\frac{1}{6}m---\left(43\right)$

Determine that according to this scope label is apart from d ₁=0.087m, d ₂=0.163m is proper, demarcates in the brandishing of thing at one dimension like this, can form the image of clear and easy differentiation.After determining the mutual alignment of three labels, the design one dimension is demarcated thing.A label is fixed on the top that at first is fixed on one dimension demarcation thing, is fixing second label apart from first label 0.163m place then, is fixing the 3rd label at second label 0.087m place of distance at last.After three labels were determined, one dimension was demarcated bar and is also completed.According to theoretical proof, She Ji three labels can utilize distance condition to carry out the image coordinate coupling like this, finally finish camera calibration.

Claims (4)

1. provide a kind of one dimension to demarcate the thing design criteria, and use this criterion design one dimension to demarcate the bar instrument, it is characterized in that: be fixed on the straight straight-bar by three labels, utilize the mutual alignment of three labels, mate the corresponding relation of three label images in the different cameral video image.

2. the instrument demarcated of a kind of polyphaser according to claim 1, its design criteria is: the mutual alignment of three gauge points is to determine by following expression formula,

$\frac{1}{d_1}-\frac{1}{d_2}>\frac{2}{z_{\min }}$

D wherein ₁, d ₂Two end points are established d to the distance of intermediate point on the expression straight-bar ₂＞d ₁, z _MinRefer to one dimension demarcate bar in the process of brandishing from the nearest distance of each camera.

3. the instrument demarcated of a kind of polyphaser according to claim 1 is characterized in that: three labels are can simply identification on camera image, can be based on Infrared or ordinary ray identification; During the motion of one dimension marking rod, three labels on the marking rod are fixed, and move with marking rod.

4. claim 1 and follow-up calibration step, namely the camera set fundamental matrix is found the solution, the camera confidential reference items are found the solution, the outer ginseng of camera set is found the solution, and has the camera model parameter global optimization adjustment of distortion factor, and the equationof structure group is found the solution around the inside and outside ginseng of camera set and is calculated.

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