CN1851752A - Dual video camera calibrating method for three-dimensional reconfiguration system - Google Patents

Abstract

The present invention provides plane-calibrating object based on twin camera calibrating method. Said method completely marks out video camera system inside and outside parameter, mainly having imaging centre, distortion parameter, effective focal length and external parameter. Said calibrating board has array distributed sign dot, utilizing digital image center section located 16 points to construct orthogonal 2 groups of parallel straight lines, after obtaining a pair of vanishing point, to obtain vector from optical center to above-mentioned 2 vanishing points, and utilizing its vertical relation to obtain imaging centre quadrature equation, simultaneous plurality of quadrature equation to obtain imaging centre. Said invention utilizes a group of collateral lines projecting constraint to solve distortion parameter, said method also utilizes calibration dot and constraint condition to list a set of linear equations, through one-dimensional search to solve distortion parameter. Said invention also Utilizes two-step method to solve external parameter and effective focal length.

Description

Double-camera calibrating method in the three-dimensional reconfiguration system

Technical field

The present invention relates to the demarcation problem of the twin camera in the vision system, relate in particular to double-camera calibrating method in a kind of three-dimensional reconfiguration system.

Background technology

One of basic task of computer vision is taken the image that obtains from video camera, calculates the three-dimensional information of object in the visual field, comes thus three-dimensional body is rebuild and discerned.The three-dimensional geometric information of body surface point and its mutual relationship between the respective point on the image are that the process of setting up this geometric model is actual to be exactly the solution procedure of camera parameters by the decision of the imaging model of video camera.Therefore, the demarcation to camera parameters is the prerequisite and the key of this modeling process.Solution procedure to camera parameters is called camera calibration.

Document " Image Processing; Analysis; and Machine Vision " (M.Sonka, V.Hlavac, R.Boyle, International Thomson Publishing, 1998) set forth a kind of comparatively general video camera imaging model in, this imaging model can be described with following formula:

$\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]=\mathrm{\λA}\left[\begin{array}{cc}R& T\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]$

Wherein, X, Y, Z are the spatial point coordinates of demarcating thing, and x, y are the two-dimensional points coordinates on image, and R, T are the external parameter of video camera, have defined video camera respectively in three-dimensional attitude and position, $A=\left[\begin{array}{ccc}f& s& x_0\\ 0& f& y_0\\ 0& 0& 1\end{array}\right]$ Be intrinsic parameters of the camera, comprise the master apart from f, pixel scale factor s, center position (x ₀, y ₀).

Camera calibration is exactly a process of calculating video camera external parameter and inner parameter.The camera calibration technology roughly can be divided into two classes: traditional camera marking method and camera self-calibration method.

In recent years, video camera obtained very big progress from calibration algorithm, delivered a considerable amount of documents, the some of them algorithm has obtained comparatively widely to use.But because poor with respect to traditional calibration algorithm precision, be not suitable for accuracy of detection being required very high occasion such as three-dimensionalreconstruction etc. from calibration algorithm.

Traditional calibration algorithm has also obtained using comparatively widely, has also obtained effect preferably simultaneously.Document " Aversatile camera calibration technique for high accuracy 3D machine vision metrology usingoff-the-shelf TV cameras and lenses " (Tsai R Y.IEEE Robotics Automation for example, 1987,3 (4): disclose a kind of utilize radial alignment to retrain to obtain external parameter, focal length and the linear solution of distortion once radially pages324-344).This method iteration parameter is less, and initial value preferably can be provided automatically, and it is fast to find the solution speed, has considered the radial distortion of camera lens simultaneously, and precision is higher.Shortcoming is in this method, and the horizontal spacing of sensitization unit and longitudinal pitch are considered to known in the ccd array, imaging center are not revised.

Summary of the invention

The invention provides and a kind ofly can carry out double-camera calibrating method in the three-dimensional reconfiguration system of complete demarcation, have the simple advantage of method the parameter of video camera.

The present invention adopts following technical scheme:

Double-camera calibrating method in a kind of three-dimensional reconfiguration system comprises: the demarcation of the demarcation of imaging center, the demarcation of distortion parameter and external parameter and effective focal length is characterized in that:

(1) demarcation of imaging center:

Scaling board is taken, obtained digital picture, this scaling board has the sign round dot by array distribution, utilizes 16 points that are positioned at the digital picture center section, tries to achieve a pair of vanishing point V ₁, V ₂, utilize on the scaling board by orthogonal 2 groups of parallel lines of constituting of sign round dot, obtain by photocentre to above-mentioned 2 vanishing point V ₁, V ₂Vector, and utilize its vertical relation to obtain about imaging center (u ₀, v ₀) the quadrature equation:

(u ₁-u ₀)(u ₂-u ₀)+(v ₁-v ₀)(v ₂-v ₀)+f ²＝0；

Repeat above-mentioned steps, obtain other 2 couples of vanishing point V respectively ₃, V ₄And V ₅, V ₆And corresponding two about imaging center (u ₀, v ₀) the quadrature equation:

(u ₃-u ₀) (u ₄-u ₀)+(v ₃-v ₀) (v ₄-v ₀)+f ²=0 reaches

(u ₅-u ₀)(u ₆-u ₀)+(v ₅-v ₀)(v ₆-v ₀)+f ²＝0，

Above-mentioned three equations of simultaneous are found the solution and are obtained imaging center (u ₀, v ₀);

(2) demarcation of distortion parameter

Use one group of sign round dot on the parallel lines that are positioned on the scaling board, and utilize parallel lines projection intersection point (x on the picture plane _c, y _c) constraint condition and distortion model, obtain one group and cross intersection point (x _c, y _c) straight-line equation:

Y-y _c=k _i(x-x _c) (i=1,2 ..., N), k wherein _iBe the slope of i bar straight line,

Above-mentioned straight-line equation group is combined into: AW=B

Wherein

Solve by least square method: W=(AA ^t) ^-1A ^tB, wherein, A and B matrix are the functions about distortion factor d, and then obtain W=[A (d) A ^t(d)] ^-1A ^t(d) B (d) utilizes variable step-size search method search distortion factor d in the one-dimensional space, when $\left|\right|\stackrel{\‾}{\mathrm{AW}}-B\left|\right|=\underset{d}{\min }\left|\right|\mathrm{AW}-B\left|\right|$ The time, the d value is distortion factor;

Above-mentioned step-length adopts following method to determine: the distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel, generally speaking, this has reached the limit of the bearing accuracy in the monumented point center of circle, and therefore further search is nonsensical.

(3) demarcate external parameter and effective focal length with two-step approach.

Compared with prior art, the present invention has following advantage:

The present invention is mainly used in the various application scenarios of twin camera being demarcated real-time based on the plane reference plate.Utilize each parameter of calibration algorithm calibrating camera of this patent, mainly contain following advantage:

(1) this patent algorithm has more intactly marked each parameter of desirable video camera, comprise imaging center, distortion factor, effective focal length, attitude parameter and translation parameters, mark the distortion parameter of camera lens simultaneously, the follow-up image that photographs can carry out distortion in images according to this parameter and proofread and correct.

(2) computing in this patent algorithm is linear operation, does not use iteration, nonlinear operation such as recalls, so computing velocity is fast, can be applied to various to the demanding occasion of real-time.

(3) all used plane reference object to demarcate in this patent algorithm, plane reference object is three-dimensional demarcate thing have make simple, the precision advantages of higher, this has just reduced in the calibration process the dependence of high-precision calibrating piece, has simplified calibration process.

Description of drawings

Fig. 1 scaling board figure.

Fig. 2 vanishing point forms schematic diagram.

Fig. 3 searches for the process flow diagram of distortion parameter.

Fig. 4 depth model synoptic diagram.

Fig. 53 D scanning system structural drawing.

Fig. 6 parameter calibration process flow diagram.

Embodiment

Double-camera calibrating method in a kind of three-dimensional reconfiguration system comprises: the demarcation of the demarcation of imaging center, the demarcation of distortion parameter and external parameter and effective focal length is characterized in that:

(1) demarcation of imaging center:

Scaling board is taken, obtained digital picture, this scaling board has the sign round dot by array distribution, utilizes 16 points that are positioned at the digital picture center section, tries to achieve a pair of vanishing point V ₁, V ₂, utilize on the scaling board by orthogonal 2 groups of parallel lines of constituting of sign round dot, obtain by photocentre to above-mentioned 2 vanishing point V ₁, V ₂Vector, and utilize its vertical relation to obtain about imaging center (u ₀, v ₀) the quadrature equation:

(u ₁-u ₀)(u ₂-u ₀)+(v ₁-v ₀)(v ₂-v ₀)+f ²＝0；

Repeat above-mentioned steps, obtain other 2 couples of vanishing point V respectively ₃, V ₄And V ₅, V ₆And corresponding two about imaging center (u ₀, v ₀) the quadrature equation:

(u ₃-u ₀) (u ₄-u ₀)+(v ₃-v ₀) (v ₄-v ₀)+f ²=0 reaches

(u ₅-u ₀)(u ₆-u ₀)+(v ₅-v ₀)(v ₆-v ₀)+f ²＝0，

Above-mentioned three equations of simultaneous are found the solution and are obtained imaging center (u ₀, v ₀);

(2) demarcation of distortion parameter

Use one group of sign round dot on the parallel lines that are positioned on the scaling board, and utilize parallel lines projection intersection point (x on the picture plane _c, y _c) constraint condition and distortion model, obtain one group and cross intersection point (x _c, y _c) straight-line equation:

Y-y _c=k _i(x-x _c) (i=1,2 ..., N), k wherein _iBe the slope of i bar straight line,

Above-mentioned straight-line equation group is combined into: AW=B

Wherein

Solve by least square method: W=(AA ^t) ^-1A ^tB, wherein, A and B matrix are the functions about distortion factor d, and then obtain W=[A (d) A ^t(d)] ^-1A ^t(d) B (d) utilizes variable step-size search method search distortion factor d in the one-dimensional space, when $\left|\right|\stackrel{\‾}{\mathrm{AW}}-B\left|\right|=\underset{d}{\min }\left|\right|\mathrm{AW}-B\left|\right|$ The time, the d value is distortion factor;

Above-mentioned step-length adopts following method to determine: the distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel, generally speaking, this has reached the limit of the bearing accuracy in the monumented point center of circle, and therefore further search is nonsensical.

(3) demarcate external parameter and effective focal length with two-step approach.

With reference to the accompanying drawings, specific embodiments of the present invention are made more detailed description:

The present invention utilizes plane reference object---and scaling board carries out the twin camera parameter calibration, and array distribution has round monumented point on the plate, and as Fig. 1, the circle monumented point can be arranged in the straight line that is parallel to each other.Handle by video camera is taken the image that obtains, obtain the picture side's coordinate and the object coordinates of monumented point.Calibration algorithm in this patent utilizes these center of circle data, and camera interior and exterior parameter is demarcated.

Concrete steps are as follows:

(1) demarcation of imaging center

Document " a kind of new hand-held cameras Camera self-calibration based " (Chen Zezhi, Wu Chengke. Chinese image graphics journal, 2003,8 (A version) (3), 241-346) a kind of new video camera Camera self-calibration based based on linear model has been proposed, this method is at first to utilize the character of three-point perspective projection figure, vanishing point and vectorial quadrature to obtain one group of nonlinear equation, is converted into the Solving Linear calibrating parameters then.Adopted cubic block as scaling reference in the document with three-point perspective, and the maximum feasible one-tenth two-point perspectiveness of the plane reference plate that we use in calibration process, this just needs the scaling board image of different angles to remedy this restriction.

Calibration point on our the employed plane reference is array distribution, selects suitable dotted line can form the some groups of straight lines that are parallel to each other.Here we only choose the crosswise spots of array and vertically put and constitute two groups of parallel lines, and simultaneously, these two groups of parallel lines are orthogonal.In shooting process, projection plane and scaling board plane keep certain included angle, make these two groups parallel projections on imaging plane intersect at a point respectively.

(it is the center of circle that these points are positioned at the picture centre to be positioned at the picture point of imaging surface center section, with the length of image and wide 1/3 is in the major and minor axis elliptic region) can will not consider the distortion factor of camera lens, and directly use linear camera model, therefore, this part picture point can satisfy desirable perspective geometry relation.

Ask the vanishing point coordinate

We utilize 16 points being positioned at the digital picture center section (it is the center of circle that these points are positioned at the picture centre, and the length of image and wide 1/3 be that the major and minor axis elliptic region is interior), ask a pair of vanishing point V ₁, V ₂, establish the coordinate of these two vanishing points under the digital picture coordinate system and be respectively (u ₁, v ₁), (u ₂, v ₂).Below with vanishing point (u ₁, v ₁) be example, provide solution procedure.

Horizontal 4 straight lines as shown in the figure intersect at vanishing point (v ₁, v ₁), its straight-line equation can be expressed as:

y-v ₁＝k _i(x-u ₁)(i＝1，2，3，4) (1)

K wherein _iIt is the slope of i bar straight line.Formula (1) facilitation is:

k _ix+v ₁-k _iu ₁＝y

Each calibration point coordinate substitution can be got system of equations:

AW＝B

Wherein A is 16 * 9 matrixes, $A=\left[\begin{array}{ccccccccc}{x}_{11}& 0& 0& 0& 1& -1& 0& 0& 0\\ x_{12}& 0& 0& 0& 1& -1& 0& 0& 0\\ x_{13}& 0& 0& 0& 1& -1& 0& 0& 0\\ x_{14}& 0& 0& 0& 1& -1& 0& 0& 0\\ 0& x_{21}& 0& 0& 1& 0& -1& 0& 0\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ 0& x_{24}& 0& 0& 1& 0& -1& 0& 0\\ 0& 0& x_{31}& 0& 1& 0& 0& -1& 0\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ 0& 0& x_{34}& 0& 1& 0& 0& -1& 0\\ 0& 0& 0& x_{41}& 1& 0& 0& 0& -1\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ \·& \·& \·& \·& \·& \·& \·& \·& \·\\ 0& 0& 0& x_{44}& 1& 0& 0& 0& -1\end{array}\right];$ W length is 9 column vector,

W ^t=[k ₁k ₂k ₃k ₄y _ck ₁x _ck ₂x _ck ₃x _ck ₄x _c]; B length is 16 column vector,

B ^t＝[y ₁₁ y ₁₂ y ₁₃ y ₁₄ y ₂₁ … y ₂₄ y ₃₁ … y ₃₄ y ₄₁ … y ₄₄]。

Solve with least square method:

W＝(AA ^t) ^-1A ^tB

U then ₁=W ₅, $v_1=\frac{W_6+W_7+W_8+W_9}{W_1+W_2+W_3+W_4}.$

Find the solution imaging center

Because it is vertical mutually to walk crosswise the straight line that constitutes with the point of vertically arranging on the scaling board, according to projection theorem, as Fig. 2, photocentre O is to V ₁, V ₂Line OV ₁And OV ₂Also vertical mutually.V ₁, V ₂Coordinate under camera coordinate system is respectively ((u ₁-u ₀), (v ₁-v ₀), f) with ((u ₂-u ₀), (v ₂-v ₀), f), wherein f is the video camera effective focal length, (u ₀, v ₀) be imaging center.

Because

With

Vertical mutually, then have $\stackrel{\‾}{{\mathrm{OV}}_1}\·\stackrel{\‾}{{\mathrm{OV}}_2}=0,$ Therefore can get:

(u ₁-u ₀)(u ₂-u ₀)+(v ₁-v ₀)(v ₂-v ₀)+f ²＝0 (2)

Translation-angle is taken two width of cloth or several scaling board images, is example with two width of cloth here.If corresponding vanishing point is respectively V ₃, V ₄And V ₅, V ₆, then have:

(u ₃-u ₀)(u ₄-u ₀)+(v ₃-v ₀)(v ₄-v ₀)+f ²＝0 (3)

(u ₅-u ₀)(u ₆-u ₀)+(v ₅-v ₀)(v ₆-v ₀)+f ²＝0 (4)

Deduct formula (3) and formula (4) respectively with formula (2):

(u ₁+u ₂-u ₃-u ₄)u ₀+(v ₁+v ₂-v ₃-v ₄)v ₀＝u ₁u ₂-u ₃u ₄+v ₁v ₂-v ₃v ₄ (5)

(u ₁+u ₂-u ₅-u ₆)u ₀+(v ₁+v ₂-v ₅-v ₆)v ₀＝u ₁u ₂-u ₅u ₆+v ₁v ₂-v ₅v ₆ (6)

Simultaneous formula (5) and formula (6) can solve imaging center (u ₀, v ₀).

At least need take three width of cloth scaling board images in the said process, often take multiple image in the practical application, can obtain the equation of a plurality of similar formulas (5) and formula (6) like this, can ask the least square solution of system of equations, in this case, finding the solution the stability of data result can be more better.

In the practical application two ccd video cameras are fixed on the top of the shelf by shown in Figure 5.The left and right sides mirror that requires according to calibration algorithm is respectively taken three original scaling board image informations, handles by above-mentioned steps, find the solution the imaging center of left and right sides mirror.Constantly repeat 9 same processes, obtain measurement result table 1:

The calibration result of table 1 left and right sides mirror imaging center

	Left side mirror		Right mirror
					Cx	Cy	Cx	Cy
	1 2	370.263 368.872	322.793 321.661	357.514 359.714					322.313 323.400

3 4 5 6 7 8 9 10

367.771 368.190 368.887 369.771 372.918 370.555 370.991 371.530

321.578 321.122 321.935 322.180 322.841 322.946 322.320 323.146

361.981 360.401 360.005 361.529 359.170 359.289 360.796 359.574

323.389 322.829 322.681 323.289 323.275 320.736 321.651 322.164

(2) demarcation of distortion parameter

Because there is distortion in camera lens, has certain skew between the image point position on the image that the shooting of video camera is obtained and the position of ideal image point, the computer vision that accuracy requirement is higher is used, must revise this class side-play amount.Distortion model has been described the mathematical relation between distortional point and the ideal point, can carry out certain correction to distortional point by this mathematical model, and in fact the calibration point of distortion parameter is exactly to determine corresponding distortion model.

x _i＝(u _i-u ₀)(1+dr ²)

y _i＝(v _i-v ₀)(1+dr ²)

Wherein, r ²=(u _i-u ₀) ²+ (v _i-v ₀) ²

This patent proposes the constraint that a kind of projection that utilizes one group of parallel lines intersects at a point, find the solution distortion parameter, this method has been used simultaneously and has been positioned at one group of sign round dot on the line that is parallel to each other, utilize parallel lines listing one group of linear equation, find the solution distortion parameter by linear search as the constraint condition that meets at any of the projection on the plane.

If the straight line that world coordinates exists the N bar to be parallel to each other, there is M in each straight line _i(i=1,2 ... N) individual monumented point, the ideal image point coordinate of j point is (x on the i bar straight line _Ij, y _Ij), the distortion picture point is coordinate (u _Ij, v _Ij), have:

x _ij＝(u _ij-u ₀)(1+dr ²)

y _ij＝(v _ij-v ₀)(1+dr ²)

Wherein, r ²=(u _Ij-u ₀) ²+ (v _Ij-v ₀) ²

If the intersection point of each straight line is (x _c, y _c), then the The Representation Equation of each straight line is:

y-y _c＝k _i(x-x _c)(i＝1，2，…，N)

K wherein _iIt is the slope of i bar straight line.Satisfy following equation between the ideal image point:

AW＝B

Wherein

Solve by least square method:

W＝(AA ^t) ^-1A ^tB

Each non-constant element of A and B matrix is that the ideal coordinates value by calibration point constitutes, and the ideal coordinates value is to carry out revised result by the distortional point coordinate figure through distortion model.Therefore, after having selected parallel lines and corresponding calibration point, can think that A and B matrix are the functions about distortion factor d, correspondingly:

W＝[A(d)A ^t(d)] ^-1A ^t(d)B(d)

Utilize variable step-size search method search distortion factor d in the one-dimensional space, make:

$\left|\right|\stackrel{\‾}{\mathrm{AW}}-B\left|\right|=\underset{d}{\min }\left|\right|\mathrm{AW}-B\left|\right|$

At this moment d is the distortion parameter that we will find the solution.Concrete steps are as follows:

1) region of search can just elect (10 as ^-6, 10 ^-6), at first with 10 ^-7Be step-length, search for the d as a result of this time search ⁽¹⁾

2) with interval (d ⁽¹⁾-10 ^-7, d ⁽¹⁾+ 10 ^-7) be the region of search, with 10 ^-8Be step-length, search for the d as a result of this time search ⁽²⁾

3) with interval (d ⁽²⁾-10 ^-8, d ⁽²⁾+ 10 ^-8) be the region of search, with 10 ^-9Be step-length, search for the d as a result of this time search ⁽³⁾

d ⁽³⁾Be the distortion parameter d that is found the solution, see accompanying drawing 3.

The distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel, generally speaking, this has reached the limit of the bearing accuracy in the monumented point center of circle, and therefore further search is nonsensical.

In the practical application two ccd video cameras are fixed on the top of the shelf by shown in Figure 5.The left and right sides mirror that requires according to calibration algorithm is respectively taken an original scaling board image information, handles by above-mentioned steps, find the solution the distortion factor of left and right sides mirror.Constantly repeat 9 same processes, only take piece image at every turn, obtain distortion factor table 2 as a result:

The calibration result of table 2 left and right sides mirror distortion parameter

Sequence number	Left side mirror distortion parameter (10-5)	Right mirror distortion parameter (10-5)
			1	0.0049	0.0056
2	0.0048	0.0059

3	0.0052	0.0063
			4	0.0051	0.0053
5	0.0052	0.0050
			6	0.0053	0.0062
7	0.0052	0.0062
			8	0.0052	0.0062
9	0.0051	0.0059
			10	0.0056	0.0059

(3) demarcation of external parameter and effective focal length

Document " A Versatile Camera Calibration Technique for High-Accuracy 3D Machine VisionMetrology Using Off-the Shelf TV Cameras and Lenses " (Tsai R Y, IEEE Journal of Roboticsand Automation, 1987, RA-3 (4): 323-344)

Propose a kind of calibration algorithm that is called as two-step approach, it mainly is to utilize the restriction of radial parallel constraint to solve the attitude parameter of video camera and two translational components except that depth factor in the first step.Utilize the iterative depth factor, distortion parameter and effective focal length in second step.Used the first step algorithm in the document in this patent, and for the step of second in document algorithm, because it has taked interative computation, rapidity and stability all can't guarantee, in addition, owing to marked distortion parameter in this patent, so directly utilize the depth model of video camera that depth factor and effective focal length are demarcated.And then use depth model and find the solution degree of depth translational component and effective focal length.

As Fig. 4, to cross object point P and make plane parallel in imaging plane, this plane hands over optical axis in P _o, and

With

The x that is parallel to camera coordinate system respectively _cAnd y _cAxle, P _oP _xAnd P _oP _yRespectively with PP _xAnd PP _yVertical mutually, then because plane P P _xP _oP _yParallel with imaging plane, then at rectangular pyramid o _c-PP _xP _oP _yIn, satisfy following geometric relationship:

$\frac{\mathrm{op}}{P_{0}P}=\frac{o_{c}o}{o_c{P}_o}=\frac{{\mathrm{oP}}_x}{P_o{P}_x}=\frac{{\mathrm{oP}}_y}{P_o{P}_y}$

That is:

$\frac{f}{z_c}=\frac{x}{x_c}=\frac{y}{y_c}$

(x _c, y _c, z _c) be the coordinate figure of any object point P under camera coordinate system, establishing this coordinate figure under world coordinate system is (x _w, y _w, 0), then have:

$\left|\begin{array}{c}{x}_c=r_1{x}_w+r_2{y}_w+t_x\\ z_c=r_7{x}_w+r_8{y}_w+t_z\end{array}\right.$

Put in order:

$[r_1{x}_w+r_2{y}_w+t_x-x]\left[\begin{array}{c}f\\ t_z\end{array}\right]=x(r_7{x}_w+r_8{y}_w)$

Select the calibration point more than 2, can obtain video camera degree of depth translational component and effective focal length.As can be seen from the above equation, we should avoid scaling board vertical with camera optical axis when demarcating degree of depth translational component, promptly need to guarantee a certain size angle between imaging plane and the scaling board plane, get 20 °～30 ° usually; In addition, for improving the correctness of calibration result, should there be certain degree of depth level each other in the punctuate of choosing, can select calibration point according to the tilt condition of scaling board in the practical application.

In the practical application two ccd video cameras are fixed on the top of the shelf by shown in Figure 5.The left and right sides mirror that requires according to calibration algorithm is respectively taken an original scaling board image information, handles by above-mentioned steps, find the solution relative position parameter, relative attitude parameter and the effective focal length of left and right sides mirror.Constantly repeat 9 times, only take piece image at every turn, obtaining external parameter is that attitude parameter and location parameter see Table 3, and effective focal length sees Table 4.

Table 3 left and right sides mirror relative attitude and location position result

The effective focal length calibration result of table 4 left and right sides mirror

	Left side mirror effective focal length	Right mirror effective focal length
			1	-1259.93	-1316.00
2	-1265.06	-1308.64
			3	-1257.48	-1313.32
4	-1268.89	-1320.23
			5	-1258.77	-1316.15
6	-1293.62	-1307.40
			7	-1279.61	-1314.23
8	-1284.73	-1308.23
			9	-1268.60	-1311.27
10	-1258.59	-1309.62

Whole calibrating procedure is carried out according to the flow process in the accompanying drawing 6, demarcates imaging center, distortion factor, attitude parameter, location parameter and effective focal length successively.

Claims (1)

1, double-camera calibrating method in a kind of three-dimensional reconfiguration system comprises: the demarcation of the demarcation of imaging center, the demarcation of distortion parameter and external parameter and effective focal length is characterized in that:

(1) demarcation of imaging center:

Scaling board is taken, obtained digital picture, this scaling board has the sign round dot by array distribution, utilizes 16 points that are positioned at the digital picture center section, tries to achieve a pair of vanishing point V ₁, V ₂, utilize on the scaling board by orthogonal 2 groups of parallel lines of constituting of sign round dot, obtain by photocentre to above-mentioned 2 vanishing point V ₁, V ₂Vector, and utilize its vertical relation to obtain about imaging center (u ₀, v ₀) the quadrature equation:

(u ₁-u ₀)(u ₂-u ₀)+(v ₁-v ₀)(v ₂-v ₀)+f ²＝0；

Repeat above-mentioned steps, obtain other 2 couples of vanishing point V respectively ₃, V ₄And V ₅, V ₆And corresponding two about imaging center (u ₀, v ₀) the quadrature equation:

(u ₃-u ₀) (u ₄-u ₀)+(v ₃-v ₀) (v ₄-v ₀)+f ²=0 reaches

(u ₅-u ₀)(u ₆-u ₀)+(v ₅-v ₀)(v ₆-v ₀)+f ²＝0，

Above-mentioned three equations of simultaneous are found the solution and are obtained imaging center (u ₀, v ₀);

(2) demarcation of distortion parameter

Use one group of sign round dot on the parallel lines that are positioned on the scaling board, and utilize parallel lines projection intersection point (x on the picture plane _c, y _c) constraint condition and distortion model, obtain one group and cross intersection point (x _c, y _c) straight-line equation:

Y-y _c=k _i(x-x _c) (i=1,2 ..., N), k wherein _iBe the slope of i bar straight line,

Above-mentioned straight-line equation group is combined into: AW=B

Wherein

Solve by least square method: W=(AA ^t) ^-1A ^tB, wherein, A and B matrix are the functions about distortion factor d, and then obtain W=[A (d) A ^t(d)] ^-1A ^t(d) B (d) utilizes variable step-size search method search distortion factor d in the one-dimensional space, when $\left|\right|\stackrel{\‾}{\mathrm{AW}}-B\left|\right|=\underset{d}{\min }\left|\right|\mathrm{AW}-B\left|\right|$ The time, the d value is distortion factor;

Above-mentioned step-length adopts following method to determine: the distortion parameter value of camera lens is all smaller, and the region of search can just elect (10 as ^-6, 10 ^-6), when the precision of distortion parameter reaches 10 ^-9The time, the correction precision of pixel has been reached about 0.02 pixel, generally speaking, this has reached the limit of the bearing accuracy in the monumented point center of circle, and therefore further search is nonsensical.

(3) demarcate external parameter and effective focal length with two-step approach.

Images