CN100595790C - Video camera parameter calibration method by adopting single circle as marker - Google Patents

Abstract

The invention relates to a calibration method for the intrinsic parameters of a camera by adopting a single circle as a calibration object; the method comprises the following steps that: first, threedifferent images of a calibration object are shot by using a camera; then an image point location of a circular point of each image is identified; by utilizing the image point of the three groups of the circular points, projection curve equation of absolute conic is fitted; finally, all intrinsic parameters of the camera are calculated in a way linearly, including a principal point location, aspect ratio and tilt factor. The method of the invention can identify all intrinsic parameter of the camera once, and can realize automatic calibration and reduce calculation error caused by human intervention, and is particularly applicable to a non-contact type industrial inspection and an autonomous navigation system based on vision.

Description

Adopt single circle for demarcating the camera intrinsic parameter scaling method of thing

Technical field

The present invention relates to a kind ofly adopt single circle, be particularly useful for non-contact industrial detection and based on the autonomous navigation system of vision for demarcating the camera intrinsic parameter scaling method of thing.The invention belongs to advanced field of measuring technique.

Background technology

The purpose of demarcating in the video camera is to adopt specific demarcation thing to determine intrinsic parameters of the camera, and it 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 circle to carry out aspect the camera calibration, people have done a large amount of work, and have obtained some achievements.Meng Xiaoqiao has proposed to come by the straight line in the center of circle with single circle and cluster method (the X.Meng and Z.Hu of calibrating camera intrinsic parameter, A New Easy Camera Calibration Technique Basedon Circular Points, Pattern Recognition, vol.36, no.5, pp.1155-1164,2003), but this method needs many straight lines of match, and not only precision is low but also operation is quite complicated, is unfavorable for realizing full automatic calibration.Afterwards, Wu Yihong etc. have proposed to carry out with two coplane circles the method (Y.Wu of camera calibration, H.Zhu and Z.Hu, Camera Calibration from Quasi-Affine Invarianceof Two parallel Circles, Proc.European Conf.Computer Vision, vol.1, pp.190-202,2004).Meanwhile, Korea S J.S.Kim etc. has proposed to come with two concentric circless the method (J.S.Kim of calibrating camera, P.Grudjos, and I.S.Kweon, Geometric andAlgebraic Constraints of Projected Concentric Circles and TheirApplication to Camera Calibration, IEEE Trans.On PAMI, vol.27, no.4,2005).Above-mentioned two kinds of methods are simpler than the method that Meng Xiaoqiao proposes, but they need to utilize two circles as demarcating thing, and are equally quite inconvenient.Therefore, research and propose a kind of method that need not man-machine interaction and can accurately determine the whole intrinsic parameters of video camera (comprising the principal point position, aspect ratio and inclination factor) and have bigger using value.

Summary of the invention

The objective of the invention is at the deficiencies in the prior art, propose a kind of camera intrinsic parameter scaling method that adopts single circle for the demarcation thing, can determine whole intrinsic parameters of video camera 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 present invention adopts single circle for demarcating thing.Be placed on three different positions with demarcating thing, and take the demarcation thing, obtain the different image of three width of cloth with video camera; To each width of cloth image, detect the border of oval image, and utilize the boundary pixel point to simulate elliptic equation; Detect the subpoint in the center of circle in each width of cloth image; Utilize corresponding restriction relation, obtain the image point position of focoid in each width of cloth image respectively, thereby obtain the picture point homogeneous coordinates of three groups of different focoid; Utilize the picture point homogeneous coordinates of these three groups of focoid to simulate drop shadow curve's equation of absolute conic; Utilize this equation and corresponding constraint condition to determine the intrinsic parameter of video camera, demarcate thereby finish camera intrinsic parameter.

Method of the present invention comprises following concrete steps:

1, at first makes the demarcation thing.On a blank sheet of paper, draw a circle.In order to handle conveniently, draw a little bullet at circle centre position, its radius is about 5 millimeters.To be painted with round blank sheet of paper then and be close to smooth body surface, and constitute and demarcate thing.

2, will demarcate thing and successively be placed on three different positions, and all take in each position and demarcate thing, thereby obtain the different reference object image of three width of cloth with oval image with video camera.All imaging is clear and do not have and obviously to block need to guarantee each width of cloth image.

3, utilize the canny operator, detect the border of oval image in every width of cloth image respectively, thereby obtain three groups of point sets that constitute by oval image boundary pixel.Utilize this three groups of point sets respectively, simulate oval image matrix C _n, n=1,2,3.Simultaneously, calculate the center of gravity p of little bullet view field on every width of cloth image _n, n=1,2,3.

4, calculate oval image matrix C _nThe antithesis Matrix C _n ^*Utilize following formula:

$k{C}_n^{*}=(i_n{j}_n^T+j_n^T{i}_n)-p_n{p}_n^T,$

Obtain the homogeneous coordinates i of the picture point of focoid on the n width of cloth figure by the method for matrix decomposition _nAnd j _n, n=1,2,3, thus obtain the homogeneous coordinates of the picture point of three groups of focoid.

5, utilize the homogeneous coordinates of the picture point of these three groups of focoid to simulate the equation ω of drop shadow curve of absolute conic.

6, calculate the inverse matrix ω of ω ^-1, utilize formula ω ^-1=KK ^T, decomposite the intrinsic parameter matrix K of video camera, thereby obtain whole intrinsic parameters of video camera, finish the intrinsic parameter of video camera and demarcate.

Compare with existing method, the present invention can be easy and be determined all intrinsic parameters of video camera exactly, comprises the principal point position, aspect ratio and inclination factor, and can realize full automatic calibration, reduced the measuring error that artificial intervention causes.The present invention is particularly useful for non-contact industrial detection and based on the autonomous navigation system of vision.

Description of drawings

Fig. 1 is the synoptic diagram of camera intrinsic parameter scaling method of the present invention.

The demarcation thing synoptic diagram that Fig. 2 is adopted for camera intrinsic parameter scaling method of the present invention.

Embodiment

In order to understand the present invention better, technical scheme of the present invention is explained in 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.Among Fig. 1, OXYZ is a camera coordinate system, and ouv is for being the image coordinate system of unit with the pixel.The round S that is used to demarcate is in plane π.Its circle centre position has a radius to be about 5 millimeters bullet Q, and the center of gravity of its view field on image is p.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.

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

1, at first makes the demarcation thing.Circle of iso-surface patch on a blank sheet of paper, and draw a radius at its circle centre position and be about 5 millimeters little bullet, will be painted with round blank sheet of paper then and be close to smooth body surface, constitute and demarcate thing.

2, will demarcate thing and successively be placed on three different positions, and all take the image that a width of cloth is demarcated thing in each position, thereby obtain the different reference object image of three width of cloth with oval image with video camera.All imaging is clear and do not have and obviously to block to guarantee each width of cloth image.

3, utilize the canny operator, detect the border of oval image in every width of cloth image respectively, thereby obtain three groups of point sets that constitute by oval image boundary pixel.Utilize this three groups of point sets respectively, simulate the Matrix C of the oval image of expression _n, n=1 wherein, 2,3.(concrete method is referring to A.W.Fitzgibbon, M.Pilu, andR.B.Fisher, " Direct Least-Squares Fitting of Ellipses ", IEEE Trans.Pattern Analysis and Machine Intelligence, vol.14, no.2, pp.239-256).Simultaneously, calculate the center of gravity of the view field of little bullet on every width of cloth image, be designated as p _n, n=1,2,3.

4, calculate oval image matrix C respectively _nThe antithesis Matrix C _n ^*If the homogeneous coordinates of the picture point of the focoid on this width of cloth figure are i _nAnd j _n, they all are three dimensional vectors, the homogeneous coordinates of putting on the expression plane.

Utilize following formula:

Wherein k is a scale factor, is unknown number, vectorial i _nAnd j _nBe unknown number, three rank real symmetric matrix C _n ^*Be known, three dimensional vector p _nAlso be known, n=1 wherein, 2,3.

Concrete grammar is:

Calculate (p _np _n ^T, C _n ^*) generalized eigenvalue, can obtain a unique nonzero eigenvalue, be designated as k ₀So, the envelope that constitutes by the picture point of focoid

Utilize svd, can calculate the homogeneous coordinates i of the picture point of focoid _nAnd j _n(concrete grammar referring to P.Gurdjos, P.Sturm and Y.H.Wu, Euclidean Structure from N 〉=2 Parallel Circles:Theory and Algorithms, Proc.ECCV, part I, pp.238-252,2006).

5, obtain after the homogeneous coordinates of picture point of focoid of three width of cloth images, can simulate the ω of projection equation of absolute conic.Concrete grammar is:

Because the picture point of focoid then has in the projection of absolute conic:

$i_n^T{\mathrm{\ωi}}_n=0,$ $j_n^T{\mathrm{\ωj}}_n=0,n=\mathrm{1,2,3}.$

6 equations of simultaneous can solve ω at an easy rate.

6, utilize the ω of projection equation of absolute conic, can calculate principal point position (u ₀, v ₀), aspect ratio f ₁/ f ₂With inclination factor s.

Detailed process is:

Obtain the inverse matrix ω of ω ^-1,

Order ${\mathrm{\ω}}^{-1}=\left[\begin{array}{ccc}{m}_1& m_2& m_3\\ m_2& m_4& m_5\\ m_3& m_5& m_6\end{array}\right].$

Because ${\mathrm{\ω}}^{-1}={\mathrm{KK}}^T=\left[\begin{array}{ccc}{f}_1^2+s^2+u_0^2& f_{2}s+u_0{v}_0& u_0\\ f_{2}s+u_0{v}_0& f_2^2+v_0^2& v_0\\ u_0& v_0& 1\end{array}\right],$

Can solve: u ₀=m ₃/ m ₆, v ₀=m ₅/ m ₆, $f_2=\sqrt{m_4-v_0^2},$ $s=\frac{m_2-u_0{v}_0}{f_2},$ $f_1=\sqrt{m_1-u_0^2-s^2}.$

So far, all intrinsic parameters of video camera are demarcated and are finished.

Claims (1)

1. one kind is adopted single circle for demarcating the camera intrinsic parameter scaling method of thing, it is characterized in that comprising the steps:

1) on a blank sheet of paper, draw a circle, and draw a radius at the home position place is 5 millimeters little bullet, will be painted with round blank sheet of paper then and be close to smooth body surface, constitute and demarcate thing;

2) will demarcate thing and successively be placed on three different positions, and all take demarcate thing with video camera in each position, thereby obtain the different reference object image with oval image of three width of cloth, all imaging is clear and do not have and obviously block to guarantee each width of cloth image;

3) utilize the canny operator, detect the border of oval image in every width of cloth image respectively, thereby obtain three groups of point sets that constitute by oval image boundary pixel; Utilize this three groups of point sets respectively, simulate oval image matrix C _n, n=1,2,3; Simultaneously, calculate the center of gravity p of little bullet view field on every width of cloth image _n, n=1,2,3;

4) calculate oval image matrix C _nThe antithesis Matrix C _n ^*Utilize following formula:

${\mathrm{kC}}_n^{*}=(i_n{j}_n^T+j_n^T{i}_n)-p_n{p}_n^T,$

Obtain the homogeneous coordinates i of the picture point of focoid on the n width of cloth figure by the method for matrix decomposition _nAnd j _n, n=1,2,3, thus obtain the homogeneous coordinates of the picture point of three groups of different focoid; K is a scale factor in the formula;

5) utilize the homogeneous coordinates of the picture point of these three groups of focoid to simulate the ω of projection equation of absolute conic; Because the picture point of focoid then has in the projection of absolute conic:

$i_n^T{\mathrm{\ωi}}_n=0,$ $j_n^T{\mathrm{\ωj}}_n=0,$ n＝1，2，3；

6 equations of simultaneous solve ω;

6) calculate the inverse matrix ω of ω ^-1, order ${\mathrm{\ω}}^{-1}=\left[\begin{array}{ccc}{m}_1& m_2& m_3\\ m_2& m_4& m_5\\ m_3& m_5& m_6\end{array}\right];$

According to ${\mathrm{\ω}}^{-1}={\mathrm{KK}}^T=\left[\begin{array}{ccc}{f}_1^2+s^2+u_0^2& f_{2}s+u_0{v}_0& u_0\\ f_{2}s+u_0{v}_0& f_2^2+v_0^2& v_0\\ u_0& v_0& 1\end{array}\right],$ K is the confidential reference items of video camera

Matrix number;

Calculate principal point position (u ₀, v ₀), aspect ratio f ₁/ f ₂With inclination factor s; Wherein, u ₀=m ₃/ m ₆, v ₀=m ₅/ m ₆, $f_2=\sqrt{m_4-v_0^2},$ $s=\frac{m_2-u_0{v}_0}{f_2},$ $f_1=\sqrt{m_1-u_0^2-s^2};$ Thereby obtain whole intrinsic parameters of video camera, finish the intrinsic parameter of video camera and demarcate.

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