CN101329764B - Method for positioning video camera using two arbitrary coplane circles - Google Patents

Abstract

The invention relates to a method for calibrating a camera by any two coplanar circles, and two non-concyclic centre coplanar circles are used as the calibration objects. A clear image is taken by the camera for the calibration objects, to define the equations of two elliptical shadows in the images and solve the coordinates of the image points of the focoids. The image point coordinates of the focoids and the shadow equations of absolute secondary curves are utilized to define the focal distance of the camera; a world coordinate system is set up, with the center of any of the two circles as the origin, and Z axis is parallel with the normal direction of the plane of the two circles. A rotation matrix is defined according to the relation between blanking points, blanking lines and the elliptical shadows; the solved position, of the world coordinate system, under the camera coordinate system is the right translation vector. The method of the invention can easily and conveniently define all variable parameters every time when the camera is calibrated, can realize the wholly automatic calibration, reduce calculation errors arisen by human intervention, and is particularly suitable for non-contact industrial inspection and the vision-based independent navigation system.

Description

Adopt two any coplane circles to carry out the method for camera calibration

Technical field

The present invention relates to a kind of method that adopts two any coplane circles to carry out camera calibration, can determine parameters such as focal length of camera, rotation matrix and translation vector exactly.The invention belongs to advanced field of measuring technique, be particularly useful in the computer stereo vision camera calibration, non-contact industrial detection and based on the autonomous navigation system of vision.

Background technology

The purpose of camera calibration is to adopt specific demarcation thing to determine the inside and outside parameter of video camera.Camera calibration is the basic demand of obtaining three-dimensional information in the computer vision field from two dimensional image, is to finish many vision work necessary procedure.Along with popularizing of video camera, many non-vision professional persons need a kind of simple and easy, scaling method helps them to finish the work relevant with vision flexibly.Camera calibration is based on the basis of the non-contact measurement and the independent navigation of machine vision.Because circle has easy detection and anti-advantage such as block, it is often used as demarcates thing and comes calibrating camera.

Utilizing a plurality of circles to carry out aspect the camera calibration, people have done a large amount of work, and have obtained some achievements.Recent two algorithm (P.Gurdjos that above coplane circle is demarcated that propose, P.Sturm, and Y.H.Wu, " Euclidean structure from N 〉=2 parallel circles:theory and algorithms; " in Proc.Eur.Conf.on Computer Vision, pp.238-252, IEEE (2006)) needs the different reference object image of at least three width of cloth, relate generally to the calculating of intrinsic parameters of the camera, and ignored the calculating of video camera external parameter to a certain extent.Yet work is crucial to the external parameter of video camera to computer vision, for example the definite needs of independent navigation and three-dimensional attitude of object.In addition, in the middle of the application of reality, the position of video camera is often change, and respective focal is also and then adjusted, and other inner parameter of video camera, as aspect ratio, inclination factor and principal point almost remain unchanged.Now also there is method to propose to adopt two any coplane circles to carry out camera calibration (Q.Chen, H.Wu, and T.Wada, " Camera calibration with two arbitrary coplanarcircles, " in Proc.Eur.Conf.on Computer Vision, pp.521-532, IEEE (2004)), but this is a kind of method based on the iteration optimum, and convergence depends on suitable initialization condition very much, and does not have clear and definite proposition how algorithm to be carried out initialization.This method is the angle from cartesian geometry in addition, needs quite complicated equation to describe the oblique cone body of being determined by photocentre and oval image.Therefore, at known invariant parameter: aspect ratio, under the condition of inclination factor and principal point, a kind of simple and easy stable method that can determine focal length of camera and external parameter fully has bigger actual application value.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, propose a kind of method that adopts two any coplane circles to carry out camera calibration, can determine focus of camera and external parameter easily, and can realize full automatic calibration, need not man-machine interaction.

Above-mentioned purpose of the present invention is achieved through the following technical solutions: the demarcation thing that the present invention adopts is two, and the coplane of the concyclic heart is not round arbitrarily.To demarcate thing and be positioned in the video camera ken, and take the demarcation thing, obtain a width of cloth picture rich in detail with video camera; Detect the border of two oval images in the image, and utilize the boundary pixel point to simulate two elliptic equations; Two elliptic equations that utilization simulates are obtained the corresponding image point position of two groups of focoid in the image, thereby obtain the picpointed coordinate of two groups of different focoid; Utilize the picpointed coordinate of these two groups of focoid and drop shadow curve's equation of absolute conic to obtain focal length of camera; According to the shadow point that disappears, the relation between hachure and the oval image of disappearing, determine rotation matrix, obtain translation vector according to the singularity of the coordinate system of being set up at last, finish camera parameters and demarcate.

Measuring method involved in the present invention comprises following concrete steps:

1. at first make and demarcate thing.Demarcation thing of the present invention is two, and the coplane of the concyclic heart is not round arbitrarily.

2. take to demarcate thing with video camera, obtain the reference object image that a width of cloth has two oval images, guarantee that clear and each circle of imaging all surpasses one-third of the area and blocks.

3. utilize the canny operator, detect the border of each oval image on the reference object image respectively, thereby obtain two groups of point sets that constitute by oval image boundary pixel; Utilize this two groups of point sets respectively, simulate the equation of two oval images.

4. utilize two oval image equations that simulate, in complex domain, solve their intersecting point coordinate, promptly get the picpointed coordinate i of two groups of focoid _n, j _n, n=1,2, i wherein ₁And j ₁, i ₂And j ₂Be conjugate pair.

5. utilize the projection equation of absolute conic and the picpointed coordinate of focoid to solve focus of camera.

6. set up world coordinate system, initial point any center of circle in two circles, the Z axle is parallel with the normal direction on two round planes, place.Obtain the equation of the hachure that disappears by the picpointed coordinate of focoid, utilize the shadow point that disappears, the restriction relation between hachure and the oval image equation of disappearing, determine rotation matrix.

7. the coordinate of initial point under camera coordinate system that solves world coordinate system is translation vector.So far, finish Camera calibration.

Compare with existing method, the present invention only needs a width of cloth to demarcate the image of thing, can determine the inside and outside parameter that the shift in position with video camera changes easily, and can realize full automatic calibration, need not man-machine interaction, reduced the measuring error that artificial intervention causes.The present invention be particularly useful in the computer stereo vision camera calibration, non-contact industrial detection and based on the autonomous navigation system of vision.

Description of drawings

Fig. 1 carries out the synoptic diagram of camera calibration for adopting two any coplane circles.

Fig. 2 carries out the demarcation thing synoptic diagram that camera calibration adopted for two any coplane circles of employing.

Embodiment

In order to understand the present invention better, technical scheme of the present invention is described in further detail below in conjunction with drawings and Examples.

Figure 1 shows that the perspective view of demarcation thing on the plane of delineation that the present invention proposes.Two any circles that are used to demarcate are in plane π, and OXYZ is a camera coordinate system, O _wX _wY _wZ _wBe world coordinate system, wherein O _wNow (equally in the drawings on the center of circle, the right) on the center of circle that justify on the left side in the drawings, Z _wAxle is parallel with the normal direction of plane π.If the intrinsic parameter matrix of video camera is K, then according to pin-hole model, (u wherein ₀, v ₀) expression principal point position, f ₁/ f ₂Be aspect ratio, s is an inclination factor, and these all are invariant parameters, is known in the present invention.Other has f ₁=fm _x, f ₂=fm _y, wherein f is a focus of camera, m _xAnd m _yBe respectively the pixel count of x and y direction epigraph coordinate unit distance, m _xAnd m _yBe known parameters.

Fig. 2 is a demarcation thing synoptic diagram of the present invention.Two circles can be tangent, overlap, mutually disjoint on same plane, but all not concyclic heart.

Describe the implementation step of the inventive method below in detail:

1. at first make and demarcate thing.On a smooth object, draw two circles arbitrarily, notice that the center of circle is not in same point.The coplane of the concyclic heart is not round as demarcating thing arbitrarily with these two.

2. will demarcate thing and entirely be placed in the FOV (Field of View) of video camera, and take with video camera and demarcate thing, obtain the reference object image that a width of cloth has two oval images.Must guarantee that imaging is clear, and each circle there are not all 1/3rd above areas to block.

3. utilize the canny operator, detect the border of each oval image in the reference object image respectively, thereby obtain two groups of point sets that constitute by oval image boundary pixel.Utilize this two groups of point sets respectively, simulate the equation of two oval images, with the Matrix C of oval image _nExpression, n=1 wherein, 2.Concrete method is referring to (A.W.Fitzgibbon, M.Pilu, and R.B.Fisher, " Direct Least-SquaresFitting of Ellipses ", IEEE Trans.Pattern Analysis and MachineIntelligence, vol.14, no.2, pp.239-256).

4. utilize the equation of two oval images, in complex domain, solve their intersecting point coordinate, promptly get the picpointed coordinate i of two groups of focoid _n, j _n, n=1,2, i wherein ₁And j ₁, i ₂And j ₂Be conjugate pair.

5. utilize the projection equation of absolute conic and the picpointed coordinate of focoid to solve focus of camera.Because the picture point of focoid promptly has in the projection of absolute conic

With

ω=(KK wherein ^T) ^-1=K ^-TK ^-1Projection equation for absolute conic.Have only a unknown parameter f among the K, obviously can solve focus of camera f.

6. determine rotation matrix: rotation matrix R=[r ₁, r ₂, r ₃], r wherein _n, n=1,2,3 is the n column vector of rotation matrix.In order to eliminate the uncertainty of world coordinate system direction, assumed conditions

(0?0?1)·r ₃≥0，(1?0?0)·r ₁≥0。(1)

At first obtain the equation l of the hachure that disappears by the picpointed coordinate of focoid _∞Utilize again plane π normal direction the shadow point that disappears, restriction relation (R.Hartley and A.Zisserman between hachure and the oval image equation disappears, Multiple View Geometry in Computer Vision, Cambridge Univ.Press (2000)) Kr ₃∝ ω ^*l _∞, can determine

$r_3=s_1\frac{K^{-1}{\mathrm{\ω}}^{*}{l}_{\∞}}{\left|\right|K^{-1}{\mathrm{\ω}}^{*}{l}_{\∞}\left|\right|}---\left(2\right)$

S wherein ₁Be undetermined symbol ,+or-.

Utilize relational expression

$\left\{\begin{array}{c}{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="H2008100412167E00011.png"\; state="\{\{state\}\}">p</figure-callout>}}_1={\mathrm{<figure-callout\; id="1"\; label="Kt"\; filenames="H2008100412167E00011.png"\; state="\{\{state\}\}">Kt</figure-callout>}}_1\&Proportional;{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="H2008100412167E00011.png"\; state="\{\{state\}\}">C</figure-callout>}}_1^{*}{l}_{\&infin;}\\ p_2={\mathrm{Kt}}_2\&Proportional;C_2^{*}{l}_{\&infin;}\end{array}\right.,---\left(3\right)$

Wherein, t _n, n=1,2 are circle Q _n, n=1, the coordinate of 2 the center of circle under camera coordinate system, p _n, n=1,2 are circle Q _n, n=1, the coordinate of the picture point in 2 the center of circle under camera coordinate system.

Utilize formula Kr ₁∝ l * l _∞, l=p wherein ₁* p ₂Axis of symmetry for image.

Can get ${\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2008100412167E00011.png"\; state="\{\{state\}\}">r</figure-callout>}}_1=s_2\frac{K^{-1}(l\&times;l_{\&infin;})}{\left|\right|K^{-1}(l\&times;l_{\&infin;})\left|\right|}---\left(4\right)$

S wherein ₂Be undetermined symbol ,+or-.

Comprehensively (1), (2), (4) formula, can be unique determine s ₁, s ₂Thereby can calculate rotation matrix R=[r ₁r ₃* r ₁r ₃].

7. determine translation vector: owing to, solve this center of circle and be translation vector at the coordinate of camera coordinate system with the center of circle of arbitrary circle in two circles initial point as world coordinate system.

Concrete steps are as follows:

The i of unit _n, j _n, i.e. i _n, j _nThe 4th element of vector is 1.The quafric curve envelope that can degenerate

R wherein ₃₃Be r ₃The 3rd element.

Utilize relational expression

R wherein ₁And R ₂Be respectively round Q ₁And Q ₂Radius, C ₁ ^*With ₂ ^*Be respectively round Q ₁And Q ₂The antithesis quafric curve of oval image.

Calculate (C _∞' ^*, C ₁ ^*) generalized eigenvalue, can obtain a unique nonzero eigenvalue, be k ₁, in like manner can get k ₂Know C _∞' ^*-k ₁C ₁ ^*And C _∞' ^*-k ₂C ₂ ^*Getting order is 1, thereby has

$\left\{\begin{array}{c}\left(\frac{t_1}{R_1}\right){\left(\frac{t_1}{R_1}\right)}^T=K^{-1}(C_{\&infin;}^{\&prime;*}-k_1{\mathrm{<figure-callout\; id="1"\; label="C"\; filenames="H2008100412167E00011.png"\; state="\{\{state\}\}">C</figure-callout>}}_1^{*})K^{-T}\\ \left(\frac{t_2}{R_2}\right){\left(\frac{t_2}{R_2}\right)}^T=K^{-1}(C_{\mathrm{\&omega;}}^{\&prime;*}-k_2{C}_2^{*})K^{-T}\end{array}\right.$

Obvious t ₁/ R ₁And t ₂/ R ₂Obtain from following formula easily.T again ₂=Dr ₁+ t ₁, wherein D is two distances between the center of circle.Utilize following relation again

$\frac{R_2}{R_1}\frac{t_2}{R_2}=\frac{D}{R_1}{\mathrm{<figure-callout\; id="1"\; label="r"\; filenames="H2008100412167E00011.png"\; state="\{\{state\}\}">r</figure-callout>}}_1+\frac{t_1}{{\mathrm{<figure-callout\; id="1"\; label="R"\; filenames="H2008100412167E00011.png"\; state="\{\{state\}\}">R</figure-callout>}}_1}$

Easily estimate R ₂/ R ₁And D/R ₁If obviously the distance between known any one radius of a circle or two centers of circle can be obtained translation vector t ₁Perhaps t ₂(initial point of world coordinate system is O ₁The time, then be t ₁The initial point of world coordinate system is O ₂The time, then be t ₂).

So far, the parameter calibration of video camera finishes.

Claims (1)

1. two any coplane circles of an employing carry out the method for camera calibration, it is characterized in that comprising following concrete steps:

1) the coplane of the concyclic heart is not round as demarcating thing arbitrarily with two;

2) take to demarcate thing with video camera, obtain the reference object image that a width of cloth has two oval images, guarantee that clear and each circle of imaging all surpasses one-third of the area and blocks;

3) utilize the canny operator, detect the border of each oval image on the reference object image respectively, thereby obtain two groups of point sets that constitute by oval image boundary pixel, utilize this two groups of point sets respectively, simulate the equation of two oval images;

4) utilize the equation of two oval images, in complex domain, solve their intersecting point coordinate, promptly get the picpointed coordinate i of two groups of focoid _n, j _n, n=1,2, i wherein ₁And j ₁, i ₂And j ₂Be conjugate pair;

5) utilize the projection equation of absolute conic and the picpointed coordinate of focoid to solve focus of camera;

6) set up world coordinate system, initial point any center of circle in two circles, the Z axle is parallel with the normal direction on two round planes, place; Assumed conditions (0 0 1) r ₃〉=0, (1 0 0) r ₁〉=0; Obtain the equation l of the hachure that disappears by the picpointed coordinate of focoid _∞, utilize again plane π normal direction the shadow point that disappears, restriction relation Kr between hachure and the oval image equation disappears ₃∝ ω ^*l _∞, determine

Utilize relational expression

And Kr ₁∝ l * l _∞,

And r ₂=r ₃* r ₁Thereby, obtain rotation matrix R=[r ₁, r ₂, r ₃];

S wherein ₁, s ₂For symbol+or ^-K is the intrinsic parameter matrix of video camera, ω ^*=KK ^TDual graph picture for absolute conic; t _n, n=1,2 are circle Q _n, n=1, the coordinate of 2 the center of circle under camera coordinate system, p _n, n=1,2 are circle Q _n, n=1, the coordinate of the picture point in 2 the center of circle under camera coordinate system, l=p ₁* p ₂Axis of symmetry for image;

7) coordinate of initial point under camera coordinate system that solves world coordinate system is translation vector; So far, finish Camera calibration.

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