CN106097300A - A kind of polyphaser scaling method based on high-precision motion platform - Google Patents
A kind of polyphaser scaling method based on high-precision motion platform Download PDFInfo
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Abstract
A kind of polyphaser scaling method based on high-precision motion platform of the present invention, in whole working region, it is fixed on the scaling board on high-precision motion platform by object stage and can do the linear movements such as the most known rotation translation, it is thus achieved that scaling board pose under world coordinate system.Scaling board moves under the control of high-precision motion platform, it is made to occur in the visual field of certain camera or multiple camera, image shot by camera, with corresponding point under image coordinate system to coordinate under searching world coordinate system, finally use global optimization approach, one piece solves each camera parameter, overcome existing scaling method and need the camera in multicamera system is demarcated one by one the poor efficiency of existence, there are the shortcomings such as bigger cumulative error or the trouble designing specific demarcation parts, achieve the disposable demarcation that multicamera system is overall, there is extremely important engineer applied be worth, complete high-precision calibrating and three-dimensional reconstruction.Measurement process is simple, and calibration result is accurate, improves work efficiency.
Description
Technical field
The present invention relates to the multicamera system in computer vision field, a kind of based on high-precision motion platform
Polyphaser scaling method.
Background technology
Multicamera system is fairly common at computer vision field, as answered at 3D reconstruction, motion-captured, multi-view point video etc.
In with, it is often necessary to various different cameral, light source, the multicamera system of composition of storage device.Multicamera system is demarcated, the most really
The inside and outside parameter of each camera fixed, is the multicamera system important step that carries out that reliable efficient operation is indispensable.
In the past, multicamera system was demarcated and was typically used two ways: (1) uses tradition demarcation mode, but these demarcate thing
Exist and self block, it is impossible to observe demarcation thing from multiple visual angles simultaneously, thus cannot disposably demarcate multicamera system, only
Can demarcate the most two-by-two, finally be transformed under the same coordinate system, it is achieved global calibration.Owing to relating to various coarse seat
, there is bigger cumulative error in mark conversion；And need the camera in multicamera system is demarcated one by one, extremely inefficient.(2) set
Put and specifically demarcate thing, make in polyphaser calibration process its around solid fixed-axis rotation or static, owing to special sign thing does not exists
Self blocks, and polyphaser can shoot simultaneously, demarcates together.But it is difficult and the most general to demarcate thing design comparison in actual use
All over property, poor practicability and calibrated parameters precision are low.When the overlapping region, the visual field of any two camera is little or does not the most weigh
Time folded, above two method is the most helpless.
Summary of the invention
For problems of the prior art, the present invention provides a kind of polyphaser based on high-precision motion platform to demarcate
Method, on the premise of ensureing operation high efficiency, improves stated accuracy.
The present invention is to be achieved through the following technical solutions:
A kind of polyphaser scaling method based on high-precision motion platform, comprises the steps,
Step 1, initializes polyphaser calibration system, and described polyphaser calibration system includes object stage and high-precision motion
Platform, and at least two camera；All cameras are evenly arranged in the top of object stage, and the view-finder of camera is all towards loading
Platform, fixed placement scaling board on object stage, the motion of high-precision motion platform courses object stage；Described high-precision motion platform
Having 6 and above degree of freedom, displacement accuracy reaches the motion platform of 0.1mm；
Step 2, sets up world coordinate system on the scaling board of initial pose, and chooses at least five demarcation on scaling board
Point, obtains the world coordinates of all fixed points；
Step 3, by the control of high-precision motion platform, moves to next pose by scaling board from a upper pose, and makes
Scaling board is filled into and does not shoots two width scaling boards in one or more Current camera visuals field of different positions and pose hypograph；
Step 4, one or more Current camera carry out image acquisition respectively, and obtain mark the scaling board under current pose
Determine the image coordinate of at least five fixed point corresponding point on image that step 2 in plate is chosen and the world on world coordinate system
Coordinate；
Step 5, repeats step 3 and 4 until each camera at least shoots two width scaling boards image under different positions and pose；
All camera inside and outside parameter are carried out global calibration by step 6, use all marks that step 4 is obtained by Global Algorithm
The image coordinate of fixed point is optimized with the relation of its world coordinates, determines the accurate calibrating parameters of each camera.
Preferably, in step 2, the scaling board of initial pose is positioned at the visual field of any one or more camera.
Preferably, time during scaling board is filled into corresponding camera fields of view so that in shooting image, region shared by scaling board accounts for one
More than Ban.
Preferably, when solving the world coordinates of fixed point, it is assumed that scaling board coordinate system overlaps with stage coordinate system, if
Misaligned, mutually convert through vector operation.
Preferably, when scaling board is shot by multiple cameras simultaneously, the visual field of described multiple cameras is overlapping, and
Overlapping region, the visual field can photograph whole scaling boards.
Preferably, scaling board uses gridiron pattern scaling board, and under initial attitude, any one point of scaling board is sat as the world
Mark system initial point Ow, mutually perpendicular two borders of scaling board are XwAxle and YwAxle, ZwVertical and scaling board plane.
Preferably, when all cameras carry out the shooting timing signal to scaling board successively, comprise the following steps that,
Step 1), initialize polyphaser calibration system, described polyphaser calibration system includes object stage and high accuracy fortune
Moving platform, and at least two camera；All cameras are evenly arranged in the top of object stage, and the view-finder of camera is all towards load
Thing platform, fixed placement scaling board on object stage, the motion of high-precision motion platform courses object stage；Described high-precision motion is put down
Platform has 6 and above degree of freedom, and displacement accuracy reaches the motion platform of 0.1mm；
Step 2), at initial pose (R0,T0) scaling board on set up world coordinate system Ow-XwYwZw, its initial point OwFor mark
Determine the point that on plate, any one is fixing；And choose n fixed point, wherein, n is positive integer, and n >=5；The coordinate of n fixed point
It is respectively (X01,Y01,0),(X02,Y02,0)…(X0n,Y0n,0)；
Step 3), by the control of high-precision motion platform, by scaling board from a upper pose (Ri-1,Ti-1) move to next
Pose (Ri,Ti), make scaling board be filled into the Current camera visual field not shooting two width scaling boards at different positions and pose hypograph
In；
Step 4), Current camera is to current pose (Ri,TiScaling board under) carries out image acquisition respectively, and obtains demarcation
Step 1 in plate) n fixed point the choosing image coordinate of corresponding point on image is respectively (ui1,vi1),(ui2,vi2)…
(uin,vin) and world coordinates (Xi1,Yi1,Zi1),(Xi2,Yi2,Zi2)…(Xin,Yin,Zin)；
Step 5), repeat step 3) and 4) until two width scaling boards figure under different positions and pose at least clapped by each camera
Picture, the m that have taken altogether under m scaling board pose opens image；
Step 6), all cameras are photographed the picpointed coordinate of corresponding point in image and carries out global calibration, use the overall situation to calculate
Method is to step 4) all corresponding point of obtaining to being optimized, determine the accurate calibrating parameters of each camera.
Further, in step 3) in, scaling board next pose (Ri,Ti) obtained by equation below,
(Ri,Ti)=(R(i-1)i*Ri-1,R(i-1)i*Ti-1+T(i-1)i)
Wherein, (Ri-1,Ti-1) it is a upper pose；(R(i-1)i,T(i-1)i) for this motion before and after scaling board position relationship, it is possible to
By reading the gain of parameter that high-precision motion platform moves.
Further, by step 4) in obtain the fixed point image coordinate (u that the image coordinate of i-th camera is fastenedi1,
vi1),(ui2,vi2)…(uin,vin) with fixed point based on coordinate (X under world coordinate systemi1,Yi1,Zi1),(Xi2,Yi2,Zi2)…
(Xin,Yin,Zin) corresponding relation；In step 6) in the inner parameter of all cameras and external parameter are carried out global calibration；Its
In,
(Xi1,Yi1,Zi1)=(X01,Y01,Z01)*Ri+Ti,(Xi2,Yi2,Zi2)(X02,Y02,0)*Ri+Ti,…,
(Xin,Yin,Zin)(X0n,Y0n,0)*Ri+Ti。
Further, step 6) in the comprising the following steps that of global optimization,
WithFor object function, the gridiron pattern calibration algorithm equation proposed with Zhang Zhengyou as model,
Method of least square or other optimized algorithms is used to calculate each camera inside and outside parameter；Wherein, QijIt is that jth fixed point is in i-th
Picture point value of calculation on pose, xijIt is jth fixed point picture point measured value on i-th pose, d (Qij,xij) it is QijWith
xijBetween norm；
Outer ginseng (the R of each camera obtained1,T1),(Rn,Tn) ... it is respectively each camera coordinates relative to step 2) choosing
The position relationship of the world coordinate system taken, then kth camera is (R about the outer ginseng of first camerak1,Tk1), wherein (Rk1,
Tk1)=(-Rk*R1,-Rk*T1-Tk)。
Compared with prior art, the present invention has a following useful technique effect:
The present invention is in whole working region, and being fixed on the scaling board on high-precision motion platform by object stage can do
The linear movements such as the most known rotation translation, it is thus achieved that scaling board pose under world coordinate system.Scaling board is in high accuracy fortune
Move under the control of moving platform so that it is occur in the visual field of certain camera or multiple camera, image shot by camera, find the world
With corresponding point under image coordinate system to coordinate under coordinate system, finally using global optimization approach, one piece solves each camera
Parameter, overcome existing scaling method need the camera in multicamera system is demarcated one by one existence poor efficiency, have the most tired
Long-pending error or design the shortcoming such as trouble of specific demarcation parts, it is achieved that the disposable demarcation that multicamera system is overall, has pole
Its important engineer applied is worth, and completes high-precision calibrating and three-dimensional reconstruction.High-precision measurement can be carried out and automatically control
Ability, measures process simple, and calibration result is accurate, effectively raises work efficiency.And when multiple magazine generations
Time mobile, this multicamera system needs to re-scale.
Accompanying drawing explanation
Fig. 1 is the application layout schematic diagram of the polyphaser calibration system described in present example.
Fig. 2 be described in present example in method as a example by first camera calibration calibration process schematic diagram.
Fig. 3 is the flow chart of method described in present example.
In Fig. 1: gridiron pattern scaling board 1, collected by camera controller 2, multicamera system 3, each camera fields of view 4, in high precision
Motion platform controller 5.
Detailed description of the invention
Below in conjunction with specific embodiment, the present invention is described in further detail, described in be explanation of the invention and
It not to limit.
Multicamera system usually requires that video camera or photographing unit are from multiple angle shot objects.When object or person to be reconstructed exist
The image of synchronization difference viewing angle, utilizes the calibration result of multicamera system can calculate object or person to be reconstructed
Three-dimensional information, it is achieved the targets such as capturing movement.Thus demarcating is the most basic and most important step of this system.The camera of the present invention
Layout structure uses general multicamera system structure, and installation site and attitude to polyphaser do not have particular/special requirement；As
Shown in Fig. 1, the layout schematic diagram of multicamera system calibration system in this preferred embodiment, scaling board moving range is multicamera system
Working area, i.e. all field of vision of camera.
Gridiron pattern scaling board 1 is positioned at each camera fields of view 4 of multicamera system 3, and gridiron pattern scaling board 1 passes through object stage
Being fixed on the moving component of high-precision motion platform, such as mechanical arm, under the control of controller 5, the motion of moving component will
Gridiron pattern scaling board 1 is driven to do identical motion in working area；Multicamera system 3 is under the control of collected by camera controller 2
Shooting is the image demarcating parts 1 of motion in its working region, for the demarcation to multicamera system 3.
The scaling method that the present invention proposes mainly includes the kinematic parameter obtaining scaling board, obtains the image of scaling board, figure
As input, from image, extract index point image coordinate structural map picture point correspondence and utilize the overall situation or nonlinear optimization algorithm excellent
Change the steps such as calibration result, it should illustrate to control to demarcate with high-precision motion platform controller in whole calibration process
Plate, does not allow manual toggle or touches scaling board.The gridiron pattern scaling board 1 used in this preferred embodiment, the chessboard on scaling board
Lattice summit can easily identify, as index point.Illustrating as it is shown on figure 3, shoot image one by one with camera, concrete steps are such as
Under.
Step 1, initializes multicamera system calibration system.Wherein polyphaser caliberating device based on high-precision motion platform
In apply high-precision motion platform, described high-precision motion platform refers to have 6 and above degree of freedom, displacement essence
The degree motion platform up to 0.1mm, the high-precision motion platform such as including high accuracy The Cloud Terrace, high-accuracy mechanical arm.Motion platform can
To drive scaling board to do the motion of various known trajectory in working region.
Step 2, as shown in (1) of Fig. 3, with initial pose (R0,T0) the scaling board upper left corner be world coordinate system initial point
Ow, mutually perpendicular two borders of scaling board are XwAxle and YwAxle, ZwVertical and scaling board plane；Scaling board is chosen n >=5
Fixed point, it is in initial pose (R when scaling board0,T0) time coordinate under world coordinate system be respectively (X01,Y01,0),
(X02,Y02,0),…,(X0n,Y0n,0)；In this preferred embodiment, during the world coordinate system of location, the initial pose of scaling board can be
The optional position of working area, but in view of the simple period demarcated, first move scaling board so that it is fill first camera as far as possible
The visual field.Choosing current pose is initial pose；Fixed point on scaling board can randomly select, it is also possible to selects easily calculating
N point, but this n is put on scaling board to be evenly distributed on, and n can not be The more the better less than 5.
Step 3, as shown in (2) of Fig. 3, scaling board in working area from a pose (Ri-1,Ti-1) move to next bit
Appearance (Ri,Ti), make scaling board fill kth camera fields of view as far as possible；Owing to scaling board is fixed on high-precision motion platform, at this
Scaling board position relationship (R before and after motion(i-1)i,T(i-1)i) can be by reading the essence that the parameter that move of high-precision motion platform obtain
Really represent, so (Ri,Ti)=(R(i-1)i*Ri-1,R(i-1)i*Ti-1+T(i-1)i).Scaling board is filled camera fields of view and is referred to captured
Image in scaling board should at least account for 1/2nd of image.
Because big scaling board is due to the problem made in technique, plate surface evenness is the highest, has a strong impact on stated accuracy；Institute
The scaling board used with the present invention is the classical little scaling board of gridiron pattern, and the known (gridiron pattern of geological information between fixed point
Size is known) and scaling board kinematic parameter known (using the motion of high-precision motion platform courses scaling board), scaling board is by carrying
Thing platform is secured firmly to above moving component, and motion platform kinematic geometry information is identical, the most just with scaling board kinematic geometry information
It is that the coordinate system of scaling board should overlap with the coordinate system of high-precision motion platform, if misaligned again through a certain amount of vector
Computing calculates and converts.Operator can control scaling board by the motion of high-precision motion platform controller control moving component
Rigid motion.After motion every time, whole scaling board should fill up whole camera fields of view as far as possible.
Step 4, as shown in (3) of Fig. 3, kth camera is to current pose (Ri,TiScaling board under) carries out image acquisition,
And obtain n fixed point picpointed coordinate (u of corresponding point on image that step 2 in scaling board is choseni1,vi1),(ui2,vi2)…
(uin,vin)；Fixed point image coordinate (the u that the image coordinate of kth camera is fastened can be obtainedi1,vi1),(ui2,vi2)…
(uin,vin) and scaling board fixed point coordinate (X under world coordinate systemi1,Yi1,Zi1),(Xi2,Yi2,Zi2)…(Xin,Yin,Zin)
Corresponding relation, in step 6 outside the interior participation of all cameras ginseng global calibration；Wherein,
(Xi1,Yi1,Zi1)=(X01,Y01,Z01)*Ri+Ti,(Xi2,Yi2,Zi2)(X02,Y02,0)*Ri+Ti,…,
(Xin,Yin,Zin)(X0n,Y0n,0)*Ri+Ti；.
When finding scaling board fixed point corresponding point in the picture, if certain or multiple point are difficult to find that, can be used it
He puts replacement or ignores this point, but must ensure number n >=5 a little and be evenly distributed.In order to improve camera parameter
Precision, each camera preferably shoots the image of scaling board under multiple pose, finds fixed point.And many poses includes various angle as far as possible
Degree, i.e. straight-on camera, scaling board be positioned at image upper left, upper in, upper right, centre, lower-left, lower in, bottom right and toward upper and lower, left and right
Rotation.
Step 5, as shown in (4) of Fig. 3, repeats step 3 with step 4 until each camera at least shoots two width scaling boards and exists
Image under different positions and pose, the m that have taken altogether under m scaling board pose opens image；
Step 6, as shown in (5) of Fig. 3, overall situation hi-Fix, it is all right that step 3 is obtained by employing Global Algorithm
Should put being optimized, determine the accurate calibrating parameters of each camera.
Global optimization approach withFor object function, wherein QijIt is that jth fixed point is in i-th
Picture point value of calculation on pose, xijIt is jth fixed point picture point measured value on i-th pose, d (Qij,xij) it is QijWith
xijBetween norm；The gridiron pattern calibration algorithm equation proposed with Zhang Zhengyou, as model, uses method of least square or other iteration
Optimized algorithm solves the internal reference of each camera and outer ginseng Ri,TiMatrix, then kth camera about the outer ginseng of first camera is
(Rk1,Tk1), wherein (Rk1,Tk1)=(-Rk*R1,-Rk*T1-Tk)。
If scaling board fills certain 2 or multiple camera fields of view under a certain pose of the present invention simultaneously, multiple cameras can be same
Time shooting scaling board image under current pose, simultaneously find scaling board fixed point the corresponding point on image.When multiple
Magazine one when being moved, this multicamera system needs to re-scale.
As in figure 2 it is shown, as a example by first camera calibration, the pose conversion in the calibration process of other cameras: Fig. 2 is described
The lower right corner is the image coordinate system O-UV set up.Fig. 2 lower left corner is first the camera coordinates system O set upc1-Xc1Yc1Zc1.Fig. 2
The upper left corner is the world coordinate system O that scaling board is set up under initial posew-XwYwZw.Scaling board is in the control of high-precision motion platform
The 1st world coordinate system O is set up after being moved to certain position by initial pose under systemw1-Xw1Yw1Zw1, Fig. 2 upper right corner, this moves
Procedure parameter (R01,T01) directly or indirectly can be obtained by high-precision motion platform.Just can get after global calibration process
First camera coordinates system and the position relationship (R of world coordinate system1,T1)。
Claims (10)
1. a polyphaser scaling method based on high-precision motion platform, it is characterised in that comprise the steps,
Step 1, initializes polyphaser calibration system, and described polyphaser calibration system includes that object stage and high-precision motion are put down
Platform, and at least two camera；All cameras are evenly arranged in the top of object stage, and the view-finder of camera is all towards loading
Platform, fixed placement scaling board on object stage, the motion of high-precision motion platform courses object stage；Described high-precision motion platform
Having 6 and above degree of freedom, displacement accuracy reaches the motion platform of 0.1mm；
Step 2, sets up world coordinate system on the scaling board of initial pose, and chooses at least five fixed point on scaling board,
Obtain the world coordinates of all fixed points；
Step 3, by the control of high-precision motion platform, moves to next pose by scaling board from a upper pose, and makes demarcation
Plate is filled into and does not shoots two width scaling boards in one or more Current camera visuals field of different positions and pose hypograph；
Step 4, one or more Current camera carry out image acquisition respectively, and obtain scaling board the scaling board under current pose
The image coordinate of at least five fixed point corresponding point on image that middle step 2 is chosen and the world on world coordinate system sit
Mark；
Step 5, repeats step 3 and 4 until each camera at least shoots two width scaling boards image under different positions and pose；
All camera inside and outside parameter are carried out global calibration by step 6, use all fixed points that step 4 is obtained by Global Algorithm
The relation of image coordinate and its world coordinates be optimized, determine the accurate calibrating parameters of each camera.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 1, it is characterised in that step
In rapid 2, the scaling board of initial pose is positioned at the visual field of any one or more camera.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 1, it is characterised in that mark
Determine plate when being filled in corresponding camera fields of view so that in shooting image, region shared by scaling board accounts for more than half.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 1, it is characterised in that
When solving the world coordinates of fixed point, it is assumed that scaling board coordinate system overlaps with stage coordinate system, if misaligned, through vector
Computing mutually converts.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 1, it is characterised in that when
When scaling board is shot by multiple cameras simultaneously, the visual field of described multiple cameras is overlapping, and can in overlapping region, the visual field
Photograph whole scaling boards.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 1, it is characterised in that mark
Determining plate and use gridiron pattern scaling board, under initial attitude, any one point of scaling board is as world coordinate system initial point Ow, scaling board
Mutually perpendicular two borders are XwAxle and YwAxle, ZwVertical and scaling board plane.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 1, it is characterised in that when
All cameras carry out the shooting timing signal to scaling board successively, comprise the following steps that,
Step 1), initialize polyphaser calibration system, described polyphaser calibration system includes that object stage and high-precision motion are put down
Platform, and at least two camera；All cameras are evenly arranged in the top of object stage, and the view-finder of camera is all towards loading
Platform, fixed placement scaling board on object stage, the motion of high-precision motion platform courses object stage；Described high-precision motion platform
Having 6 and above degree of freedom, displacement accuracy reaches the motion platform of 0.1mm；
Step 2), at initial pose (R0,T0) scaling board on set up world coordinate system Ow-XwYwZw, its initial point OwFor on scaling board
Any one fixing point；And choose n fixed point, wherein, n is positive integer, and n >=5；The coordinate of n fixed point is respectively
(X01,Y01,0),(X02,Y02,0)…(X0n,Y0n,0)；
Step 3), by the control of high-precision motion platform, by scaling board from a upper pose (Ri-1,Ti-1) move to next pose
(Ri,Ti), make scaling board be filled into and do not shoot two width scaling boards in a Current camera visual field of different positions and pose hypograph；
Step 4), Current camera is to current pose (Ri,TiScaling board under) carries out image acquisition respectively, and obtains in scaling board
Step 1) n fixed point the choosing image coordinate of corresponding point on image is respectively (ui1,vi1),(ui2,vi2)…(uin,vin)
And world coordinates；
Step 5), repeat step 3) and 4) until two width scaling boards image under different positions and pose at least clapped by each camera, altogether
The m that have taken under m scaling board pose opens image；
Step 6), all cameras are photographed the picpointed coordinate of corresponding point in image and carries out global calibration, use Global Algorithm pair
Step 4) all corresponding point of obtaining to being optimized, determine the accurate calibrating parameters of each camera.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 7, it is characterised in that
Step 3) in, scaling board next pose (Ri,Ti) obtained by equation below,
(Ri,Ti)=(R(i-1)i*Ri-1,R(i-1)i*Ti-1+T(i-1)i)
Wherein, (Ri-1,Ti-1) it is a upper pose；(R(i-1)i,T(i-1)i) for this motion before and after scaling board position relationship, it is possible to pass through
Read the gain of parameter that high-precision motion platform moves.
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 7, it is characterised in that logical
Cross in step 4) in obtain the fixed point image coordinate (u that the image coordinate of i-th camera is fastenedi1,vi1),(ui2,vi2)…
(uin,vin) with fixed point based on coordinate (X under world coordinate systemi1,Yi1,Zi1),(Xi2,Yi2,Zi2)…(Xin,Yin,Zin) right
Should be related to；In step 6) in the inner parameter of all cameras and external parameter are carried out global calibration；Wherein,
(Xi1,Yi1,Zi1)=(X01,Y01,Z01)*Ri+Ti, (Xi2,Yi2,Zi2)(X02,Y02,0)*Ri+Ti,…,
(Xin,Yin,Zin)(X0n,Y0n,0)*Ri+Ti。
A kind of polyphaser scaling method based on high-precision motion platform the most according to claim 7, it is characterised in that
Step 6) in the comprising the following steps that of global optimization,
WithFor object function, the gridiron pattern calibration algorithm equation proposed with Zhang Zhengyou, as model, uses
Method of least square or other optimized algorithms calculate each camera inside and outside parameter；Wherein, QijIt is that jth fixed point is at i-th pose
On picture point value of calculation, xijIt is jth fixed point picture point measured value on i-th pose, d (Qij,xij) it is QijWith xijIt
Between norm；
Outer ginseng (the R of each camera obtained1,T1),(Rn,Tn) ... it is respectively each camera coordinates relative to step 2) choose
The position relationship of world coordinate system, then kth camera is (R about the outer ginseng of first camerak1,Tk1), wherein (Rk1,Tk1)=
(-Rk*R1,-Rk*T1-Tk)。
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