CN106127737A - A kind of flat board calibration system in sports tournament is measured - Google Patents

Abstract

A kind of flat board calibration system in sports tournament is measured, native system uses planar graph standardizition.Plane reference method is exactly to utilize multiple imaging plane to be analyzed the position of target, selects suitable imaging plane that target is carried out the determination of position.The first step, with the video camera of two different azimuth in left and right to demarcating thing and being calibrated thing and shoot and obtain image；Second step, after the image obtaining two, left and right video camera processes, therefrom extracts characteristic point and mates, and then obtaining inner parameter and the external parameter of video camera；3rd step, utilizes the measuring principle of two kinds of methods, by characteristic point and the inside and outside parameter of video camera, is calculated and is calibrated thing and is positioned at three-dimensional information.Tradition scaling method and plane gridiron pattern scaling method having been carried out contrast experiment, has used plane gridiron pattern standardizition higher than the precision using conventional three-dimensional space framework standardizition, relative error is less.

Description

A kind of flat board calibration system in sports tournament is measured

Technical field

The video camera three dimensions that the present invention relates to be applied in sports tournament is demarcated, and belongs to sport scene measurement Research neck Territory, particularly relates to the portable calibration system of the three-dimensional camera shooting in a kind of physical culture.

Background technology

Video analysis is research means conventional in sports and scientific research, by can be at not shadow to the parsing of motor technique image On the premise of ringing normal play and training, obtain kinematics parameters during athlete's more truly.Video camera is carried out standard True three dimensions demarcation is the premise of video analysis.In current researches on exercise biomechanics field both domestic and external, current physical culture The main scaling method used of the research of scientific research field is that traditional cameras based on three radial framework is demarcated, then will mark The 2-D data determined is after direct linear transformation (Direct Linear Transformation, DLT), it is thus achieved that three-dimensional seat Mark data.

Generally using fixing standard card cage to demarcate the video camera used in measure field, it is radial It is made up of eight detachable mark posts.

This method has bigger limitation in actual applications, especially carries out timing signal at competition and training scene, These limit can be more prominent, and limitation is as follows:

First the calibration range measured reality is limited, it is impossible to effectively demarcate grand movement project, even Sometimes cause measuring because of the particularity of in-situ match camera site；Secondly along with the growth of the time of use, framework can be because of The former increase thus resulting in measurement error such as self-deformation；The most this framework is the heaviest, carries inconvenience, in physical culture In-situ match is wasted time and energy when installing；Finally also need to manually the labelling point of framework is identified at timing signal, thus can be big Increase and add the time of demarcation.Sports Scientific Research is exerted a certain influence by problem above, it is therefore desirable to a kind of new method Substitute traditional 3 D stereo framework to demarcate, to reach purpose convenient, fast at timing signal, effective.

Summary of the invention

The present invention uses planar graph standardizition.Plane reference method is exactly to utilize multiple imaging plane to enter the position of target Row is analyzed, and selects suitable imaging plane that target is carried out the determination of position.The imaging of each plane is different, due to often The imaging of individual plane all in motion, so finding certain several point in needing the plane between video camera and target, divides Imaging law between analysis target and video camera, then demarcates target according to this rule.Due to the demarcation to object Can be put by these and be affected, along with the continuous motion of target, between video camera and target, the point in plane will get more and more, Thus the accuracy of object demarcation is more and more higher, thus provide reliable Informational support for camera calibration, and can subtract The cost of few camera calibration, improves the efficiency of demarcation.Comparing 3 D stereo standardizition, the degree of accuracy of plane reference is higher, Time used by demarcation is relatively short, will not deform upon after long-time use, and easy to carry, and cost is relatively low, thus flat Face standardizition is worthy to be popularized in gym survey research field.

Camera model

The process of three-dimensional reconstruction needs to obtain data by video camera, it is therefore desirable to the work first checking on video camera is former Reason.

By video camera, the point in three dimensions can be mapped on imaging plane i.e. two dimensional image, wherein maps Relation can represent with matrix.

$\left[\begin{array}{c}x\\ y\end{array}\right]=M\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]---\left(1\right)$

Wherein (x, y)^tFor the point in video camera imaging plane, (X, Y, Z)^tFor the point in three dimensions, compare two dimensional image Information is a many depth information Z.Matrix M represents the mapping relations matrix between three-dimensional information and two-dimensional signal.

Mapping relations matrix M between three-dimensional information and two-dimensional signal is defined as camera parameters, and each parameter in M is by reality Testing and calculating determines, the process solving each parameter is referred to as camera calibration.For solving the transformation relation of each element of above-mentioned matrix, need Set up the geometry imaging model of video camera.Pinhole camera modeling, is also called linear model, is also the while of being the simplest Conventional camera imaging model.

Pinhole camera modeling

In video camera imaging geometric model, need to relate to following three coordinate system:

1) image coordinate system: the pixel coordinate system in units of pixel set up by image origin.The abscissa u of pixel and Vertical coordinate v be respectively this pixel the columns of pixel in the picture and line number.s_xAnd s_yRepresent one pixel of digital picture respectively Length and width, namely physical length.As determined s_xAnd s_yJust can obtain the image coordinate represented with physical unit (such as millimeter) System.In the pinhole camera modeling of Fig. 1, x_sc_sy_sCoordinate system is image coordinate system, and the plane at image coordinate system place is referred to as into Image plane.Point p is a pixel on imaging plane.

2) camera coordinate system: unlike image coordinate system, camera coordinate system is three-dimensional system of coordinate.Initial point is for taking the photograph Camera photocentre, z_cAxle is camera optical axis, with imaging plane perpendicular, x_cWith y_cAxle respectively with the transverse and longitudinal coordinate axes of image coordinate system Parallel.Camera coordinates only represents the coordinate relation within video camera, thus unrelated with camera position.In Fig. 1, O_cx_cy_cz_c Coordinate system is camera coordinate system.Point p_cFor in three dimensions point, its imaging point is a some p on imaging plane.

3) world coordinate system: owing to camera coordinate system can only describe the coordinate relation within video camera, so also needing to Introduce a coordinate system representing camera position, namely world coordinate system.World coordinate system choose typically all in order to Calculate or represent convenient, so being not fixing.When binocular or many mesh are rebuild, select one of them camera coordinates System is world coordinate system, also selects object of reference to set up world coordinate system.World coordinate system is a three-dimensional system of coordinate, and its initial point is O_w, coordinate axes is respectively x_w, y_w, z_w。

Coordinate in pixel for unit image coordinate system (u, v)^TBeing pixel coordinate, unit is pixel rather than thing Reason length coordinate.Physical length coordinate (x is needed the when of use_s, y_s)^T, then use formula (2) to calculate.

$u=\frac{x_s}{s_x}+u_0,v=\frac{y_s}{s_y}+v_0---\left(1\right)$

Wherein, u₀And v₀It it is picture centre side-play amount.Because the image coordinate system initial point in units of pixel is usually image The upper left corner, and during image coordinate system in units of physical length, typically using imaging plane with optical axes crosspoint as initial point, this The coordinate of individual intersection point is (u₀, v₀)^t, it is possible to use u₀And v₀Be given as side-play amount.Formula (1) writes out by homogeneous coordinates form As follows:

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{s_x}& 0& u_0\\ 0& \frac{1}{s_y}& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_s\\ y_s\\ 1\end{array}\right]---\left(2\right)$

According further to similar triangle theory, obtain under camera coordinate system, the spatial point coordinate corresponding to imaging point With image coordinate system coordinate conversion relation:

$\frac{1}{z_c}\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\end{array}\right]=\frac{1}{f}\left[\begin{array}{c}{x}_s\\ y_s\\ 1\end{array}\right]---\left(3\right)$

Wherein f is video camera Jiao's length, i.e. photocentre O_cTo imaging plane x_sc_sy_sDistance.According to formula (1), by formula (3) it is expressed as follows by homogeneous coordinates:

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{s_x}& 0& u_0\\ 0& \frac{1}{s_y}& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}f& 0& 0& 0\\ 0& f& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\\ 1\end{array}\right]---\left(4\right)$

Camera coordinate system is all to use physical length unit with world coordinate system, and transformation relation between the two can be used Spin matrix R and vector t describes.In world coordinate system space, the coordinate of 1 P is (x_w, y_w, z_w, 1)^T, in camera coordinates Coordinate under Xi is (x_c, y_c, z_c, 1)^T, then then there is a following relation:

$\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\\ 1\end{array}\right]=\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]---\left(5\right)$

Wherein, spin matrix R is the orthogonal matrices of 3 × 3, and t is the translation vector of 3 × 1, and O is the null vector of 1 × 3.

Coordinate relation in the image coordinate system that coordinate points from world coordinate system is corresponding is derived with (5) according to formula (4):

$\begin{array}{c}{z}_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{s_x}& 0& u_0\\ 0& \frac{1}{s_y}& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}f& 0& 0& 0\\ 0& f& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]\\ =\left[\begin{array}{cccc}{\mathrm{\α}}_x& 0& u_0& 0\\ 0& {\mathrm{\α}}_y& v_0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]=M_I{M}_{E}X=MX\end{array}---\left(6\right)$

Wherein, α_x=f/s_x, α_y=f/s_y, M is 3 × 4 matrixes, referred to as projection matrix；M as can be seen from the above equation_ICompletely by α_x、α_y、u₀、v₀Determining, above-mentioned parameter is the most relevant with video camera internal structure, and unrelated with camera position attitude external factor, Therefore it is referred to as inner parameter, is called for short internal reference；M_EDetermined, therefore relative to the position and attitude of world coordinate system by video camera completely It is referred to as the external parameter of video camera, is called for short outer ginseng.Camera calibration just determines that the process of the inside and outside parameter of video camera.

Camera calibration

Camera calibration is the first step of three-dimensional reconstruction, obtains camera interior and exterior parameter and camera lens by camera calibration Distortion parameter.Calibration process is extremely important, if demarcating the result obtained not accurately, reconstruction below can be affected by the biggest. General scaling method has DLT method, Tsai calibrating method, Zhang Zhengyou standardizition.Zhang Zhengyou standardizition, demarcates also known as gridiron pattern Method, is the scaling method being widely recognized as and using in current field.The process demarcated needs the chess to a known dimensions parameter Dish lattice plane carries out multi-angle and takes pictures, and utilizes the multiple image obtained to solve camera parameters, as shown in Figure 3.

Make u=(u, v, 1)^T, X=(x_w, y_w, z_w, 1)^T, formula (6) is carried out following rewriting:

$z_{c}u=\left[\begin{array}{ccc}{\mathrm{\α}}_x& 0& u_0\\ 0& {\mathrm{\α}}_y& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cc}R& t\end{array}\right]X=A\left[\begin{array}{cc}R& t\end{array}\right]X---\left(7\right)$

Wherein A is the Intrinsic Matrix of 3 × 3 matrixes, i.e. video camera.[R t] is the outer parameter of 3 × 4 matrixes, i.e. video camera Matrix, including translation vector (3 × 1 matrix) and spin matrix (3 × 3 matrix).Simplified formula is as follows:

z_cU=HX (8)

Wherein H=A [r₁ r₂T], it is 3 × 3 matrixes.This is because gridiron pattern used is plane, choose world coordinate system z_w=0, the most remaining r of rotating vector₁And r₂Two column vectors.H is referred to as homography matrix, this matrix represent in three dimensions The transformation relation between point and video camera imaging Plane-point in one plane.Picture point on imaging plane is chosen tessellated Internal angle point, its coordinate obtains by the way of image procossing, and three dimensions point coordinates determines according to gridiron pattern dimensional parameters.This Sample, the corresponding homography matrix of every pictures.

Homography matrix is represented with three column vector form, and in order to have more universality, adds scaling factor, Then have:

H=[h₁ h₂ h₃]=λ A [r₁ r₂ t] (9)

Wherein λ is exactly the scaling factor added.Owing to R is spin matrix, it is unit orthogonal matrix, therefore r₁And r₂ It is mutually orthogonal.A is camera intrinsic parameter matrix, is reversible, has:

$h_1^T{A}^{-T}{A}^{-1}{h}_2=0---\left(10\right)$

$h_1^T{A}^{-T}{A}^{-1}{h}_1=h_2^T{A}^{-T}{A}^{-1}{h}_2---\left(11\right)$

Order:

$B=A^{-T}{A}^{-1}=\left[\begin{array}{ccc}{B}_{11}& B_{12}& B_{13}\\ B_{21}& B_{22}& B_{23}\\ B_{31}& B_{32}& B_{33}\end{array}\right]---\left(12\right)$

Because B matrix is a symmetrical matrix, so representing with 6 dimensional vectors again:

B=(B₁₁, B₁₂, B₂₂, B₁₃, B₂₃, B₃₃)^T (13)

The i-th column vector making H-matrix is:

h_i=(h_i1, h_i2, h_i3)^T (14)

Then have:

$h_i^T{\mathrm{Bh}}_j=v_{ij}^{T}b---\left(15\right)$

Wherein:

v_ij=[h_i1h_j1, h_i1h_j2+h_i2h_j1, h_i2h_j2, h_i3h_j1+h_i1h_j3, h_i3h_j2+h_i2h_j3, h_i3h_j3]^T (16)

Finally, obtain according to intrinsic parameter restrictive condition (10), (11):

$\left[\begin{array}{c}{v}_{12}^T\\ {\left(v_{11}-v_{22}\right)}^T\end{array}\right]b=0---\left(17\right)$

H in intrinsic parameter restrictive condition₁And h₂Tried to achieve by homography matrix.Homography matrix H is 3 × 3 matrixes, has 9 ginsengs Number, one of them is scale factor, it is only necessary to solve 8 parameters.The corresponding homography matrix in each visual field, it is only necessary to provide four Individual angle point information can solve, and the x and y coordinates of each angle point provides an equation.Visible, every corresponding two equations of photo Group, camera intrinsic parameter has 5 unknown numbers, can try to achieve more than 3 photos as long as providing.When demarcation image of taking pictures is more Time, use row literary composition Burger-Ma Kuaerte iterative algorithm to be optimized and solve.

After solving b vector, solve camera intrinsic parameter matrix A according to (10) reverse.

After solving matrix A, and then calculate the outer parameter of video camera:

$\begin{array}{c}{r}_1={\mathrm{\λA}}^{-1}{h}_1\\ r_2={\mathrm{\λA}}^{-1}{h}_2\\ r_3=r_1\×r_2\\ t={\mathrm{\λA}}^{-1}{h}_3\end{array}---\left(18\right)$

Pass through process above, it is possible to solve the inside and outside parameter of video camera, the most just can obtain distortion parameter.

Accompanying drawing explanation

Fig. 1 pinhole camera modeling

Fig. 2 image coordinate system

Fig. 3 demarcates gridiron pattern used

Fig. 4 plane reference system forms

Fig. 5 plane reference Technology Roadmap

Fig. 6 overall flow figure

Detailed description of the invention

As Figure 4-Figure 6, three dimensions calibration system based on planar graph is mainly made up of following sections: homemade Plane reference plate, video camera (at least two), calibration software and notebook computer.

The first step, with the video camera of two different azimuth in left and right to demarcating thing and being calibrated thing and shoot and obtain image；The Two steps, after the image obtaining two, left and right video camera processes, therefrom extract characteristic point and mate, and then obtaining The inner parameter of video camera and external parameter；3rd step, utilizes the measuring principle of two kinds of methods, by characteristic point and video camera Inside and outside parameter, is calculated and is calibrated thing and is positioned at three-dimensional information.

Plane gridiron pattern is demarcated

Video camera putting position and camera parameters arrange identical with traditional method, respectively to standard one-metre spingboard, plane Gridiron pattern scaling board shoots, and individually shoots several by two, left and right video camera the most respectively and be placed in picture centre during shooting The image of gridiron pattern scaling board different angles, shoot several gridiron pattern scaling boards by left and right two machine more different simultaneously The image of angle and the image of diverse location moves in spatial dimension standard one-metre spingboard, carry out image to the image after shooting Processing, automatically extract image characteristic point by self-organizing system and mate with scaling board characteristic point, system obtains left and right automatically Camera intrinsic parameter and outer parameter, carry out binocular calibration after obtaining corresponding Parameter File, show that gridiron pattern scaling board is each The length of grid and the difference of full-length and the distributed data of reconstruction length, utilize software to obtain two, left and right video cameras and clap After taking the photograph the two-dimensional projection's coordinate information corresponding to standard one-metre spingboard four terminal A, B, C, D of picture, can be obtained by system reconstructing Four terminal A of one-metre spingboard, the D coordinates value of B, C, D, thus by calculate can obtain three-dimensional reconstruction between AB, CD away from From.

Under the shooting distance of five meters, ten meters and 30 meters, to tradition scaling method and plane gridiron pattern scaling method Carry out contrast experiment, rebuild by carrying out standard one-metre spingboard demarcating, its result rebuild is carried out trueness error and compares.

Experiment measurement distance is when five meters, ten meters and 30 meters, to one-metre spingboard 3 D stereo framework and plane gridiron pattern Scaling board two kinds is demarcated thing and is demarcated respectively, chooses actual measured value calibrated to one-metre spingboard and carries out group with standard value absolute error Between variation analysis.As shown in table 1 below, two kinds of meansigma methodss demarcating many groups reconstructed results that thing measurement obtains are compared.

1 two kinds of table demarcates measured value and the group difference of standard value absolute error under three kinds of shooting distances of thing

Note: N is shooting group number, and absolute error average, standard deviation unit are mm

Use independent sample T inspection, compare 3 D stereo framework demarcation different with plane gridiron pattern two kinds thing to one-metre spingboard Measured value and the difference of standard value absolute error.Result shows, plane gridiron pattern demarcates the test knot comparing 3 D stereo framework Really error is less, and assay shows have significant differences (P < 0.01), i.e. demarcates under three kinds of shooting distances, uses Plane gridiron pattern standardizition is higher than the precision using conventional three-dimensional space framework standardizition, and relative error is less.

Claims (2)

1. the flat board calibration system in sports tournament is measured, it is characterised in that:

Native system uses planar graph standardizition；Plane reference method is exactly to utilize multiple imaging plane to carry out the position of target point Analysis, selects suitable imaging plane that target is carried out the determination of position；The imaging of each plane is different, due to each flat The imaging in face all in motion, so finding certain several point in needing the plane between video camera and target, analyzes mesh Imaging law between mark and video camera, then demarcates target according to this rule；Owing to the demarcation of object can be subject to The impact put to these, along with the continuous motion of target, between video camera and target, the point in plane will get more and more, thus The accuracy that object is demarcated is more and more higher, thus provides reliable Informational support for camera calibration, and can reduce and take the photograph The cost of camera calibration, improves the efficiency of demarcation；Comparing 3 D stereo standardizition, the degree of accuracy of plane reference is higher, demarcates Time used is relatively short, will not deform upon after long-time use, and easy to carry, and cost is relatively low, so plane mark Method of determining is worthy to be popularized in gym survey research field；

Camera model

The process of three-dimensional reconstruction needs to obtain data by video camera, it is therefore desirable to first check on the operation principle of video camera；

By video camera, the point in three dimensions can be mapped on imaging plane i.e. two dimensional image, wherein mapping relations Can represent with matrix；

$\left[\begin{array}{c}x\\ y\end{array}\right]=M\left[\begin{array}{c}X\\ Y\\ Z\end{array}\right]---\left(1\right)$

Wherein (x, y)^tFor the point in video camera imaging plane, (X, Y, Z)^tFor the point in three dimensions, compare two-dimensional image information Many depth information Z；Matrix M represents the mapping relations matrix between three-dimensional information and two-dimensional signal；

Mapping relations matrix M between three-dimensional information and two-dimensional signal is defined as camera parameters, each parameter in M by testing and Calculating determines, the process solving each parameter is referred to as camera calibration；For solving the transformation relation of each element of above-mentioned matrix, need to set up The geometry imaging model of video camera；Pinhole camera modeling, is also called linear model, is also the most frequently used while of being the simplest Camera imaging model；

Pinhole camera modeling

In video camera imaging geometric model, need to relate to following three coordinate system:

1) image coordinate system: the pixel coordinate system in units of pixel set up by image origin；The abscissa u of pixel and vertical seat Mark v be respectively this pixel the columns of pixel in the picture and line number；s_xAnd s_yRepresent the length of one pixel of digital picture respectively And width, namely physical length；As determined s_xAnd s_yJust can obtain the image coordinate system represented with physical unit；Pinhole camera In model, x_sc_sy_sCoordinate system is image coordinate system, and the plane at image coordinate system place is referred to as imaging plane；Point p is that imaging is put down A pixel on face；

2) camera coordinate system: unlike image coordinate system, camera coordinate system is three-dimensional system of coordinate；Initial point is video camera Photocentre, z_cAxle is camera optical axis, with imaging plane perpendicular, x_cWith y_cAxle is parallel with the transverse and longitudinal coordinate axes of image coordinate system respectively； Camera coordinates only represents the coordinate relation within video camera, thus unrelated with camera position；O_cx_cy_cz_cCoordinate system is shooting Machine coordinate system；Point p_cFor in three dimensions point, its imaging point is a some p on imaging plane；

3) world coordinate system: owing to camera coordinate system can only describe the coordinate relation within video camera, so also needing to introduce One coordinate system representing camera position, namely world coordinate system；Choosing typically all in order to calculate of world coordinate system Or represent convenient, so being not fixing；When binocular or many mesh are rebuild, one of them camera coordinate system is selected to be World coordinate system, also selects object of reference to set up world coordinate system；World coordinate system is a three-dimensional system of coordinate, and its initial point is O_w, Coordinate axes is respectively x_w, y_w, z_w；

Coordinate in pixel for unit image coordinate system (u, v)^TBeing pixel coordinate, unit is pixel rather than physical length Coordinate；Physical length coordinate (x is needed the when of use_s, y_s)^T, then use formula (2) to calculate；

$u=\frac{x_s}{s_x}+u_0,v=\frac{y_s}{s_y}+v_0---\left(1\right)$

Wherein, u₀And v₀It it is picture centre side-play amount；Because the image coordinate system initial point in units of pixel is usually a left side for image Upper angle, and during image coordinate system in units of physical length, typically using imaging plane with optical axes crosspoint as initial point, this is handed over The coordinate of point is (u₀, v₀)^t, it is possible to use u₀And v₀Be given as side-play amount；Formula (1) with homogeneous coordinates form write out as Under:

$\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{s_x}& 0& u_0\\ 0& \frac{1}{s_y}& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_s\\ y_s\\ 1\end{array}\right]---\left(2\right)$

According further to similar triangle theory, obtain under camera coordinate system, the spatial point coordinate corresponding to imaging point and figure As coordinate system coordinate conversion relation:

$\frac{1}{z_c}\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\end{array}\right]=\frac{1}{f}\left[\begin{array}{c}{x}_s\\ y_s\\ 1\end{array}\right]---\left(3\right)$

Wherein f is video camera Jiao's length, i.e. photocentre O_cTo imaging plane x_sc_sy_sDistance；According to formula (1), formula (3) is used Homogeneous coordinates are expressed as follows:

$z_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{s_x}& 0& u_0\\ 0& \frac{1}{s_y}& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}f& 0& 0& 0\\ 0& f& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\\ 1\end{array}\right]---\left(4\right)$

Camera coordinate system is all to use physical length unit with world coordinate system, and transformation relation between the two can be with rotating Matrix R and vector t describes；In world coordinate system space, the coordinate of 1 P is (x_w, y_w, z_w, 1)^T, under camera coordinate system Coordinate be (x_c, y_c, z_c, 1)^T, then then there is a following relation:

$\left[\begin{array}{c}{x}_c\\ y_c\\ z_c\\ 1\end{array}\right]=\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]---\left(5\right)$

Wherein, spin matrix R is the orthogonal matrices of 3 × 3, and t is the translation vector of 3 × 1, and O is the null vector of 1 × 3；

Coordinate relation in the image coordinate system that coordinate points from world coordinate system is corresponding is derived with (5) according to formula (4):

$\begin{array}{c}{z}_c\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}\frac{1}{s_x}& 0& u_0\\ 0& \frac{1}{s_y}& v_0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{cccc}f& 0& 0& 0\\ 0& f& 0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]\\ =\left[\begin{array}{cccc}{\mathrm{\&alpha;}}_x& 0& u_0& 0\\ 0& {\mathrm{\&alpha;}}_y& v_0& 0\\ 0& 0& 1& 0\end{array}\right]\left[\begin{array}{cc}R& t\\ 0^T& 1\end{array}\right]\left[\begin{array}{c}{x}_w\\ y_w\\ z_w\\ 1\end{array}\right]=M_I{M}_{E}X=MX\end{array}---\left(6\right)$

Wherein, α_x=f/s_x, α_y=f/s_y, M is 3 × 4 matrixes, referred to as projection matrix；M as can be seen from the above equation_ICompletely by α_x、α_y、 u₀、v₀Determining, above-mentioned parameter is the most relevant with video camera internal structure, and unrelated with camera position attitude external factor, therefore claims For inner parameter, be called for short internal reference；M_EDetermined, because referred to herein as taking the photograph relative to the position and attitude of world coordinate system by video camera completely The external parameter of camera, is called for short outer ginseng；Camera calibration just determines that the process of the inside and outside parameter of video camera；

Camera calibration

Camera calibration is the first step of three-dimensional reconstruction, obtains camera interior and exterior parameter and lens distortion by camera calibration Parameter；Calibration process is extremely important, if demarcating the result obtained not accurately, reconstruction below can be affected by the biggest；General Scaling method have DLT method, Tsai calibrating method, Zhang Zhengyou standardizition；Zhang Zhengyou standardizition, also known as gridiron pattern standardizition, It it is the scaling method being widely recognized as and using in current field；The process demarcated needs the gridiron pattern to a known dimensions parameter Plane carries out multi-angle and takes pictures, and utilizes the multiple image obtained to solve camera parameters；

Make u=(u, v, 1)^T, X=(x_w, y_w, z_w, 1)^T, formula (6) is carried out following rewriting:

$z_{c}u=\left[\begin{array}{ccc}{\mathrm{\&alpha;}}_x& 0& u_0\\ 0& {\mathrm{\&alpha;}}_y& v_0\\ 0& 0& 1\end{array}\right]\&lsqb;\begin{array}{cc}R& t\end{array}\&rsqb;X=A\&lsqb;\begin{array}{cc}R& t\end{array}\&rsqb;X---\left(7\right)$

Wherein A is the Intrinsic Matrix of 3 × 3 matrixes, i.e. video camera；[R t] is the outer parameter square of 3 × 4 matrixes, i.e. video camera Battle array, including translation vector (3 × 1 matrix) and spin matrix (3 × 3 matrix)；Simplified formula is as follows:

z_cU=HX (8)

Wherein H=A [r₁ r₂T], it is 3 × 3 matrixes；This is because gridiron pattern used is plane, choose world coordinate system z_w= 0, the most remaining r of rotating vector₁And r₂Two column vectors；H is referred to as homography matrix, and this matrix represents in three dimensions at one The transformation relation between point and video camera imaging Plane-point in plane；Picture point on imaging plane chooses tessellated inside Angle point, its coordinate obtains by the way of image procossing, and three dimensions point coordinates determines according to gridiron pattern dimensional parameters；So, The corresponding homography matrix of every pictures；

Homography matrix is represented with three column vector form, and in order to have more universality, adds scaling factor, then Have:

H=[h₁ h₂ h₃]=λ A [r₁ r₂ t] (9)

Wherein λ is exactly the scaling factor added；Owing to R is spin matrix, it is unit orthogonal matrix, therefore r₁And r₂It it is phase The most orthogonal；A is camera intrinsic parameter matrix, is reversible, has:

$h_1^T{A}^{-T}{A}^{-1}{h}_2=0---\left(10\right)$

$h_1^T{A}^{-T}{A}^{-1}{h}_1=h_2^T{A}^{-T}{A}^{-1}{h}_2---\left(11\right)$

Order:

$B=A^{-T}{A}^{-1}=\left[\begin{array}{ccc}{B}_{11}& B_{12}& B_{13}\\ B_{21}& B_{22}& B_{23}\\ B_{31}& B_{32}& B_{33}\end{array}\right]---\left(12\right)$

Because B matrix is a symmetrical matrix, so representing with 6 dimensional vectors again:

B=(B₁₁, B₁₂, B₂₂, B₁₃, B₂₃, B₃₃)^T (13)

The i-th column vector making H-matrix is:

h_i=(h_i1, h_i2, h_i3)^T (14)

Then have:

$h_i^T{\mathrm{Bh}}_j=v_{ij}^{T}b---\left(15\right)$

Wherein:

v_ij=[h_i1h_j1, h_i1h_j2+h_i2h_j1, h_i2h_j2, h_i3h_j1+h_i1h_j3, h_i3h_j2+h_i2h_j3, h_i3h_j3]^T (16)

Finally, obtain according to intrinsic parameter restrictive condition (10), (11):

$\left[\begin{array}{c}{v}_{12}^T\\ {(v_{11}-v_{22})}^T\end{array}\right]b=0---\left(17\right)$

H in intrinsic parameter restrictive condition₁And h₂Tried to achieve by homography matrix；Homography matrix H is 3 × 3 matrixes, has 9 parameters, One of them is scale factor, it is only necessary to solve 8 parameters；The corresponding homography matrix in each visual field, it is only necessary to provide four Angle point information can solve, and the x and y coordinates of each angle point provides an equation；Visible, every corresponding two equation group of photo, Camera intrinsic parameter has 5 unknown numbers, can try to achieve more than 3 photos as long as providing；When demarcation take pictures image more time, adopt It is optimized with row literary composition Burger-Ma Kuaerte iterative algorithm and solves；

After solving b vector, solve camera intrinsic parameter matrix A according to (10) reverse；

After solving matrix A, and then calculate the outer parameter of video camera:

$\begin{array}{c}{r}_1={\mathrm{\&lambda;A}}^{-1}{h}_1\\ r_2={\mathrm{\&lambda;A}}^{-1}{h}_2\\ r_3=r_1\&times;r_2\\ t={\mathrm{\&lambda;A}}^{-1}{h}_3\end{array}---\left(18\right)$

Pass through process above, it is possible to solve the inside and outside parameter of video camera, the most just can obtain distortion parameter.

A kind of flat board calibration system in sports tournament is measured the most according to claim 1, it is characterised in that: based on The three dimensions calibration system of planar graph is mainly made up of following sections: homemade plane reference plate, video camera, demarcation are soft Part and notebook computer；

The first step, with the video camera of two different azimuth in left and right to demarcating thing and being calibrated thing and shoot and obtain image；Second step, After the image obtaining two, left and right video camera processes, therefrom characteristic point extracted and mate, and then obtaining shooting The inner parameter of machine and external parameter；3rd step, utilizes the measuring principle of two kinds of methods, inside and outside characteristic point and video camera Parameter, is calculated and is calibrated thing and is positioned at three-dimensional information；

Plane gridiron pattern is demarcated

Video camera putting position and camera parameters arrange identical with traditional method, respectively to standard one-metre spingboard, plane chessboard Lattice scaling board shoots, and individually shoots several chesses being placed in picture centre by two, left and right video camera the most respectively during shooting The image of dish lattice scaling board different angles, shoots several gridiron pattern scaling board different angles by left and right two machine more simultaneously Image and the image of diverse location moves in spatial dimension standard one-metre spingboard, the image after shooting is carried out at image Reason, automatically extracts image characteristic point by self-organizing system and mates with scaling board characteristic point, and system is automatically obtained left and right and taken the photograph Camera intrinsic parameter and outer parameter, carry out binocular calibration after obtaining corresponding Parameter File, draw each lattice of gridiron pattern scaling board The length of son and the difference of full-length and the distributed data of reconstruction length, utilize software to obtain the video cameras shooting of two, left and right After two-dimensional projection's coordinate information corresponding to the standard one-metre spingboard of picture four terminal A, B, C, D, one can be obtained by system reconstructing Rice four terminal A of plate, the D coordinates value of B, C, D, thus by calculating the three-dimensional reconstruction distance that can obtain between AB, CD；

Under the shooting distance of five meters, ten meters and 30 meters, tradition scaling method and plane gridiron pattern scaling method are carried out Contrast experiment, rebuilds by carrying out standard one-metre spingboard demarcating, its result rebuild is carried out trueness error and compares.