CN107481290A - Camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine - Google Patents
Camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine Download PDFInfo
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Abstract
The present invention relates to field of visual inspection, to realize camera internal parameter high-precision calibrating and distortion compensation.The technical solution adopted by the present invention is, camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine, step 1 determines the method for solving of traditional camera imaging model parameters, the camera internal parameter that goes out in step 1 of data scaling that is gathered according to step 2 simultaneously compensates according to the distortion formula of step 1, and step 3 is to establish model database according to remaining image deformation amount after step 1 and step 2 carry out demarcation and distortion compensation to carry out distortion compensation again.Present invention is mainly applied to vision-based detection occasion.
Description
Technical field
The present invention relates to field of visual inspection, is related to high-precision calibrating method and the realization of camera internal parameter.Specifically
Say, be related to camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine.
Background technology
The demarcation of camera is the pith in vision measurement system, and the precision of camera calibration directly affects vision survey
The precision of amount system.The demarcation of camera can trace back to 1919[4], first mould for proposing centrifugal distortion of A.Conrady
Type, hereafter there are many effective methods to put forward, can substantially be divided into three classes：Linear calibration's method, it is nonlinear calibration method, linear
With non-linear combination scaling method.
Linear Camaera Calibrating Method determines calibrating parameters by solving linear equation, and advantage is that calculating speed is fast, and shortcoming is that do not have
The distortion of consideration camera lens, the number of unknown number are generally more than the free degree that image point position changes, it is impossible to meet the inside ginseng of camera
Number is restrictive, and more sensitive to noise, convergence is also bad[12].Direct linear transformation[8]Be by Abdal-Aziz and
Itd is proposed at the beginning of the Karara70 ages, feature is that algorithm is simple, and precision is not high.
Nonlinear calibration method is based on the nonlinear mathematical model established between unknown quantity and known quantity.Pass through iterative
Object function, such a method can reach very high precision, but calculating is more complicated, if initial solution value is unreasonable, just
Correct result can not be obtained.Document [9,10,11,18,19] belongs to such method.The self-calibrating method of camera is only by more
Corresponding relation between width picture is demarcated[13,14,15,16], flexibility is strong, has a wide range of application, but robustness is not high.
Belong to the method that linear processes are combined using more method at present.The part in the calibration process of camera
Linear equation solution has been used, has also used nonlinear iteration optimization.Advantage is to simplify to calculate and have higher precision.
The two-step method based on radial constraint that Tsai is proposed is most representative[6,7], realizing for algorithm is relatively easy, can pass through iteration
The optimization of parameters is realized, but only considered radial distortion, it is necessary to which nonlinear optimization, distortion compensation precision are not high enough.
Positive friend proposes the flexible camera calibration method of comparison[17], restriction relation is established using the chess and card trrellis diagram of several different postures, profit
Distortion factor is solved with linear equation, is optimized using non-linear.Some later researchers are not high for distortion compensation precision
The problem of propose radial distortion, centrifugal distortion, thin prism distortion etc. mathematical modeling[1,2,3,5,12,19], improve to a certain extent
The compensation precision of camera distortion, but for large-sized vision measurement system distortion compensation precision still can not meet need
Will.Traditional scaling method demarcation thing used is the plane characteristic pattern of delineation mostly, and space multistory feature information extraction is less, carries
Take characteristic point imaging typically can only covering part imaging surface, be difficult to realize whole imaging surface covering.
A kind of camera high-precision calibrating based on three coordinate measuring machine and abnormal is proposed based on the above present Research present invention
Become compensation method.
The content of the invention
For overcome the deficiencies in the prior art, it is contemplated that realizing camera internal parameter high-precision calibrating and distortion compensation.
The technical solution adopted by the present invention is that camera high-precision calibrating and distortion compensation method, step 1 based on three coordinate measuring machine are true
Determine the method for solving of traditional camera imaging model parameters, gone out according to the data scaling that step 2 gathers in the camera in step 1
Portion's parameter simultaneously compensates according to the distortion formula of step 1, step 3 be step 1 and step 2 carry out demarcation and distortion compensation it
The distortion compensation of model database progress again is established according to remaining image deformation amount afterwards, specifically：
The method that step 1 determines new camera calibration and distortion compensation
Ideal coordinates system is established according to national forest park in Xiaokeng, due to various distortion, actual image planes during actual imaging be present
Coordinate system is converted to preferable image coordinates system by rotation, around xiThe anglec of rotation of axle is θ, around yiThe anglec of rotation of axleTangentially
Distortion is represented with this rotation transformation, according to original image point coordinates, rotation angle θ,And single order radial distortion coefficient is
k1, second order rank coefficient of radial distortion is k2, world coordinate system is ow-xwywzw, camera coordinate system oc-xcyczc, preferable image planes
Coordinate system is o-xiyi, actual image coordinates system is o-xryr.Point P is actual object point, piFor ideal image point, prFor actual imaging
Point, pdFor the imaging point with radial distortion, using o as origin, the reference axis x based on preferable image coordinates systemi,yiAnd camera
Optical axis establishes coordinate system o-zcxiyi, then:
prPixel coordinate in actual imaging areal coordinate system is (ur,vr), using the actual image coordinates of size Expressing as
(xr0,yr0), point prIn coordinate system o-zcxiyiIn coordinate be (xr,yr,zr), principal point pixel in actual imaging areal coordinate system
Coordinate is (cx,cy), dx,dyRespectively imaging surface unit pixel is in x and y directions size, unit：Mm, wherein pixel coordinate list
Position is pixel, and other coordinate units are mm：
Because the inclination angle in actual imaging face and ideal image face is smaller, spin matrix RcDo following processing
pdIn camera coordinate system oc-xcyczcIn imager coordinate be (xd,yd, f),
piThe resonable coordinate being thought of as in image coordinates system is (xi,yi), in xiRadial distortion compensation rate in direction is δkx, in yi
Radial distortion compensation rate in direction is δky,
xi=xd+δkx yi=yd+δky
According to pinhole imaging system principle, point p is in camera coordinate system oc-xcyczcLower coordinate is (xc,yc,zc)
Object function f is established according to formula (5), (6), (7) and rotation translation matrix R, Tai,fbi
faiPart I be to become the x that converses through R, T by the space coordinates of calibration pointcF is multiplied by, Part II is by reality
Border image coordinates (xr0,yr0) ask to obtain (x by formula (3), (5), (6)d+δkx) calibration point space coordinates is multiplied by by R, T change conversion
The zc gone out, should be equal by both formulas (7), fbiPart I be to become the y that converses through R, T by the space coordinates of calibration pointc
F is multiplied by, Part II is by actual image coordinates (xr0,yr0) ask to obtain (y by formula (3), (5), (6)d+δky) it is multiplied by calibration point
Space coordinates becomes the z conversed by R, Tc, similarly they also should be equal, is then used as target letter using the quadratic sum of its difference
Number, the according to target minimum requirement of function determine the optimum value of R, T, f and distortion factor, wherein coordinate system ow-xwywzwTo coordinate system
oc-xcyczcSpin matrix R be：
Camera coordinate system is to world coordinate system rotation transformation：It is first about xcThe axle anglec of rotation is α, secondly surrounds ycAxle
The anglec of rotation is β, finally around zcThe axle anglec of rotation is γ, corresponding translation vector T=[tx ty tz]T, world coordinate system ow-
xwywzwWith camera coordinate system oc-xcyczcConversion relational expression is：
Due to principal point coordinate (cx,cy) and rotation angle θ,Part component can be mutual during same objective function optimization
Influence, the loop iteration optimization of optimizing application algorithm Levenberg-Marquardt progress in two steps, the first step optimized coefficients α, β,
γ,tx,ty,tz,f,dx, k1,k2,cx,cy, coefficient k1,k2Initial value is 0, principal point coordinate (cx,cy) initial value is imaging surface
Center pixel coordinate, dxFor camera producer set-point, α initial values are 0.5 π, and beta, gamma initial value is all 0, tx,ty,tzInitial value is
The estimate obtained using other instruments, θ,Initial value be 0, object function F0For：
The f that second step substitutes into the result that the first step optimizes in formula (8) as known quantityai,fbi, optimization object function F1Ask
Untwist rotational angle theta,Their initial value is 0.
The rotation angle θ obtained,Formula (8) is substituted into again together as known quantity and first step result, optimizes F0, so follow
Ring iterative is untill meeting certain threshold accuracy；
Step 2 three coordinate measuring machine gathered data
A circular luminous point is fixed above three coordinate measuring machine gauge head, has planned the traveling of three coordinate measuring machine in advance
Path, make camera face three coordinate measuring machine, control three coordinate measuring machine often runs a position after suitable time-delay waits, phase
Machine program automatically extracts luminous point imaging center subpixel coordinates, then preserves the seat of imaging center coordinate and three coordinate measuring machine
Mark；
Step 3 distortion data storehouse compensates
(1) distortion data storehouse is established
Distortion data storehouse compensated by distortion model after the grid that forms of imaging point and corresponding mesh point residual distortion
Compensation rate is formed, and the residual distortion amount for imaging point after compensating distortion model is further compensate for, distortion residual volume difx,
difyIt is by ideal image point image coordinates (xi,yi) and the corresponding imaging point image coordinates (x after distortion model compensatesif,
yif) ask difference to obtain, ideal image point image coordinates (xi,yi) it is the demarcation point coordinates (x provided by measuring machinew,yw,zw) and rotation
Torque battle array R, translation matrix T, focal length f are tried to achieve by formula (13), take middle cutting plane b2Corresponding to interior after distortion model compensates
Mesh point of the imaging point as distortion data storehouse, all mesh points form a complete careful grid, and grid point coordinates
(xif,yif) and corresponding difx,difyDistortion data storehouse is established together,
difx=xi-xif
dify=yi-yif (14)
(2) compensation rate interpolation arithmetic
Node to be compensated is carried out zonule positioning in the grid in distortion data storehouse again after distortion model compensates first,
Four points nearest apart from node to be compensated in grid are determined, then find out the distortion compensation amount of four respective directions
difx,dify, finally carry out bilinear interpolation compensation.
Compensation rate interpolation arithmetic in an example, calculates xiDirection distortion compensation amount step is coordinate system o-xiyiFor picture
Areal coordinate system, the residual distortion compensation rate of mesh point be exactly corresponding to perpendicular to plane oxiyiLine segment length, point P are compensation point,
A, B, C, D are four mesh points of range points P recently, line segment AA in grid1,BB1,CC1,DD1Length be point A, B, C, D pairs
Answer xiThe residual distortion compensation rate in direction.Line segment EE1,FF1Length be corresponding interpolation point E, F residual distortion compensation rate,
Line segment PP1Length be the point P to be solved residual distortion compensation rate difPx,
Similarly obtain yiThe distortion compensation amount dif of direction of principal axis coordinatePy。
In step 2, in order to obtain spatial information of the luminous point in more opening position, in camera coverage prismatoid space
It is interior, plan three cutting planes respectively from the near to the remote apart from camera, in order to reduce the influence of temperature error, calibration of camera preferably exists
Laboratory is carried out, and reduces the gathered data time as far as possible, avoids relative position between three dimensions benchmark and equipment from changing,
Cutting plane b1With cutting plane b3100 positions are planned respectively；It is middle truncated simultaneously for more Accurate Calibration camera internal parameter
Face b2Plan more multiple positions.
In the step 3 of an example, the u of grid to mean breadth be 24.07 pixels, v to equispaced be 20.01
Individual pixel；Middle b210000 points of planning in cutting plane n, 100 data point positions are planned in other two sections respectively.
The features of the present invention and beneficial effect are：
1st, influence camera imaging distortion parameters have been taken into full account, have derived camera imaging parameter calibration and distortion compensation
Model.
2nd, the present invention can effectively improve the calibration of camera precision of camera.
3rd, the present invention can largely improve the distortion compensation effect of camera, especially for some lens distortions not
It is more preferable that application effect is carried out in the case of rule.
4th, the present invention acquires the multiple standard points in space based on three coordinate measuring machine and demarcated, with bigger flexible
Property.
5th, multiple imaging points of the invention cover whole imaging surface substantially, ensure that the essence of camera calibration and distortion compensation
Degree.
6th, it is high and simple and easy to establish database application linear compensation distortion precision.
Brief description of the drawings：
Fig. 1 actual imagings and ideal image model.
Fig. 2 actual scene figures.
Fig. 3 gathered datas space schematic diagram.
Fig. 4 gathers point range.
Fig. 5 linear interpolations.
Embodiment
The present invention realizes that camera internal parameter high-precision calibrating and distortion are mended to overcome the shortcomings of existing scaling method
Repay.Mainly including the following steps, wherein step 1 theoretically determines the method for solving of traditional camera imaging model parameters,
The camera internal parameter that goes out in step 1 of data scaling that is gathered according to step 2 simultaneously compensates according to the distortion formula of step 1,
Step 3 is to establish model data according to remaining image deformation amount after step 1 and step 2 carry out demarcation and distortion compensation
Storehouse, step 4 are the distortion compensations that the model database established according to step 3 carries out again linear interpolation.
The method that step 1 determines new camera calibration and distortion compensation
Ideal coordinates system is established according to national forest park in Xiaokeng, as shown in Fig. 1 solid black lines.Exist during due to actual imaging each
Kind distortion, black dotted lines shown in Fig. 1 are exactly actual imaging face and optical axis.As can be seen from Figure 1 actual imaging face and it is preferable into
There is certain inclination angle between image planes.Actual image coordinates system is converted to preferable image coordinates system by rotation, around xiAxle
The anglec of rotation is θ, around yiThe anglec of rotation of axleTangential distortion can be represented with this rotation transformation[4], document [4] is according to original
Begin imaging point coordinates, rotation angle θ,And single order radial distortion coefficient is k1, second order rank coefficient of radial distortion is k2, derive
Ideal image point coordinates, based in demarcation thing on straight line multiple points be still under ideal image it is conllinear solve θ,
k1,k2.Camera calibration and distortion model penalty method before of the present invention are namely based on this model.
World coordinate system is ow-xwywzw, camera coordinate system oc-xcyczc, preferable image coordinates system is o-xiyi, it is real
Border image coordinates system is o-xryr.Point P is actual object point, piFor ideal image point, prFor actual imaging point, pdFor with radially abnormal
The imaging point of change.Using o as origin, the reference axis x based on preferable image coordinates systemi,yiAnd camera optical axis establishes coordinate system o-
zcxiyi。
Theory deduction:
In Fig. 1, prPixel coordinate in actual imaging areal coordinate system is (ur,vr), with the actual image planes of size Expressing
Coordinate is (xr0,yr0).Point prIn coordinate system o-zcxiyiIn coordinate be (xr,yr,zr), principal point is in actual imaging areal coordinate system
Middle pixel coordinate is (cx,cy), dx,dyRespectively imaging surface unit pixel is in x and y directions size, unit：mm.Wherein pixel
The unit of coordinate is pixel, and other coordinate units are mm.
Because the inclination angle in actual imaging face and ideal image face is smaller, spin matrix RcFollowing processing can be done
pdIn camera coordinate system oc-xcyczcIn imager coordinate be (xd,yd,f)。
piThe resonable coordinate being thought of as in image coordinates system is (xi,yi), in xiRadial distortion compensation rate in direction is δkx, in yi
Radial distortion compensation rate in direction is δky。
xi=xd+δkx yi=yd+δky
According to pinhole imaging system principle, point p is in camera coordinate system oc-xcyczcLower coordinate is (xc,yc,zc)。
Object function f is established according to formula (5), (6), (7) and rotation translation matrix R, Tai,fbi。
Fai Part I is to become the x conversed through R, T by the space coordinates of calibration pointcBe multiplied by f, Part II be by
Actual image coordinates (xr0,yr0) ask to obtain (x by formula (3), (5), (6)d+δkx) calibration point space coordinates is multiplied by by R, T conversion
The zc calculated, should be equal by both formulas (7).fbiPart I be by calibration point space coordinates through R, T become converse
ycF is multiplied by, Part II is by actual image coordinates (xr0,yr0) ask to obtain (y by formula (3), (5), (6)d+δky) it is multiplied by calibration point
Space coordinates becomes the z conversed by R, Tc, similarly they also should be equal, is then used as target letter using the quadratic sum of its difference
Number, the according to target minimum requirement of function determine the optimum value of R, T, f and distortion factor.Wherein coordinate system ow-xwywzwTo coordinate system
oc-xcyczcSpin matrix R be：
Camera coordinate system is to world coordinate system rotation transformation：It is first about xcThe axle anglec of rotation is α, secondly surrounds ycAxle
The anglec of rotation is β, finally around zcThe axle anglec of rotation is γ.Corresponding translation vector T=[tx ty tz]T, world coordinate system ow-
xwywzwWith camera coordinate system oc-xcyczcConversion relational expression is：
Due to principal point coordinate (cx,cy) and rotation angle θ,Part component can be mutual during same objective function optimization
Influence.According to document [6] dyIt need not optimize, optimizing application algorithm Levenberg-Marquardt is carried out in two steps herein
Loop iteration optimizes, first step optimized coefficients α, beta, gamma, tx,ty,tz,f,dx,k1,k2,cx,cy, coefficient k1,k2Initial value is 0,
Principal point coordinate (cx,cy) initial value be imaging surface center pixel coordinate, dxFor camera producer set-point, camera coordinates herein
For position relationship between system and world coordinate system as shown in figure 1, α initial values are 0.5 π, beta, gamma initial value is all 0, tx,ty,tzInitially
Be worth for using other instruments obtain estimate, θ,Initial value be 0.Object function F0For：
The f that second step substitutes into the result that the first step optimizes in formula (8) as known quantityai,fbi, optimization object function F1Ask
Untwist rotational angle theta,Their initial value is 0.
The rotation angle θ obtained,Formula (8) is substituted into again together as known quantity and first step result, optimizes F0, so follow
Ring iterative is untill meeting certain threshold accuracy.
Step 2 three coordinate measuring machine gathered data
What the method for the present invention was realized based on three-dimensional coordinates measurement machine platform, three coordinate measuring machine operation positioning precision compares
Height, three dimensions point spacing and distribution can be neatly planned, can be used in the vision measurement of various different measurement ranges
System, the datum quantity of scope and pitch needed for formation, a large amount of three-dimensional references calibration points can be extracted, and camera phase can be adjusted
Point cloud imaging is covered whole camera imaging face substantially for the position and attitude of three coordinate measuring machine, can extract more more comprehensively
Three-dimensional feature information, imaging plane can be divided into more careful grid, realize the more comprehensive phase of higher precision
Machine is demarcated and distortion compensation.The model of the three coordinate measuring machine used in experiment：global classic SR 07.10.07.
The three coordinate measuring machine of independent development[20]Control software POSCOM, camera driver and POSCOM are integrated.
A circular luminous point is fixed above three coordinate measuring machine gauge head, as shown in Fig. 2 having planned the traveling of three coordinate measuring machine in advance
Path, makes camera face three coordinate measuring machine, and POSCOM control three coordinate measuring machines often run a position through suitable time-delay etc.
After, camera programm automatically extracts luminous point imaging center subpixel coordinates, then preserves imaging center coordinate and three coordinates are surveyed
The coordinate of amount machine.
In order to obtain spatial information of the luminous point in more opening position, in camera coverage prismatoid space, such as Fig. 3 institutes
Show and planned three cutting planes respectively from the near to the remote apart from camera.In order to reduce the influence of temperature error, calibration of camera is suitable
Carried out in the preferable laboratory of temperature conditionss, and reduce the gathered data time as far as possible, avoided between three dimensions benchmark and equipment
Relative position changes, cutting plane b1With cutting plane b3100 positions are planned respectively；Simultaneously for more Accurate Calibration camera
Inner parameter, middle cutting plane b2More multiple positions such as 100 × 100 are planned, overall gathered data needs small more than 2
When.
Step 3 distortion data storehouse compensates
(1) distortion data storehouse is established
The grid and correspond to the residual of mesh point that imaging point after distortion data storehouse is compensated by distortion model herein forms
Remaining distortion compensation amount composition, the residual distortion amount for imaging point after compensating distortion model are further compensate for.Distort residual volume
difx,difyIt is by ideal image point image coordinates (xi,yi) and the corresponding imaging point image coordinates after distortion model compensates
(xif,yif) ask difference to obtain.Ideal image point image coordinates (xi,yi) it is the demarcation point coordinates (x provided by measuring machinew,yw,zw)
Tried to achieve with spin matrix R, translation matrix T, focal length f by formula (13).Take middle cutting plane b2Mended corresponding to interior by distortion model
Mesh point of the rear imaging point as distortion data storehouse is repaid, all mesh points form a complete careful grid, and grid scope is such as
In Fig. 4 shown in N1, and grid point coordinates (xif,yif) and corresponding difx,difyDistortion data storehouse is established together.
difx=xi-xif
dify=yi-yif (14)
In Fig. 4, stain represents the boundary point of grid in distortion data storehouse in N1, wherein the rectangular area surrounded is exactly
Imaging point distribution in distortion data storehouse, 10000 mesh points are distributed with the range of this, it can be seen that point cloud imaging from N1
Substantially whole imaging surface is covered, compensation point will carry out the positioning of grid cell domain in this rectangle, and the u of grid is to mean breadth
24.07 pixels, v to equispaced be 20.01 pixels；Black asterisk represents control point cloud in three coordinate measuring machine in N2
Distribution under coordinate system, middle b210000 points are planned in cutting plane n, 100 data have been planned in other two sections respectively
Point position.
(2) compensation rate interpolation arithmetic
Node to be compensated is carried out zonule positioning in the grid in distortion data storehouse again after distortion model compensates first,
Four points nearest apart from node to be compensated in grid are determined, then find out the distortion compensation amount of four respective directions
difx,dify, it is last to carry out bilinear interpolation compensation as shown in Figure 5.To calculate xiIllustrated exemplified by the distortion compensation amount of direction,
Coordinate system o-xiyiFor image coordinates system, the residual distortion compensation rate of mesh point be exactly corresponding to perpendicular to plane oxiyiLength along path
Degree.Point P is compensation point, and A, B, C, D are four mesh points that range points P is nearest in grid.Line segment AA1,BB1,CC1,DD1Length
Degree is that point A, B, C, D correspond to xiThe residual distortion compensation rate in direction.Line segment EE1,FF1Length be corresponding interpolation point E, F's
Residual distortion compensation rate.Line segment PP1Length be the point P to be solved residual distortion compensation rate difPx。
Y can similarly be obtainediThe distortion compensation amount dif of direction of principal axis coordinatePy。
The present invention is further described with instantiation below in conjunction with the accompanying drawings.
Step 1：It is determined that solve camera imaging model.Ideal coordinates system is established according to national forest park in Xiaokeng, as Fig. 1 black is real
Shown in line.Due to various distortion during actual imaging be present, dotted line shown in Fig. 1 is exactly actual imaging face and optical axis.Can be with from Fig. 1
Finding out has certain inclination angle between actual imaging face and ideal image face.Actual image coordinates system is converted to ideal by rotation
Image coordinates system, the anglec of rotation be θ andTangential distortion can be represented with this rotation transformation[4], document [4] according to it is original into
Picpointed coordinate, rotation angle θ,And coefficient of radial distortion k1,k2Ideal image point coordinates is derived, based on one in demarcation thing
On straight line multiple points be still under ideal image it is conllinear solve θ,k1,k2.Camera calibration before of the present invention and
Distortion model penalty method is namely based on this model.
World coordinate system is ow-xwywzw, camera coordinate system oc-xcyczc, preferable image coordinates system is o-xiyi, it is real
Border image coordinates system is o-xryr.Point P is actual object point, piFor ideal image point, prFor actual imaging point, pdFor with radially abnormal
The imaging point of change.Using o as origin, the reference axis x based on preferable image coordinates systemi,yiAnd camera optical axis establishes coordinate system o-
zcxiyi。
The method that step 2 determines new camera calibration and distortion compensation
Theory deduction:
In Fig. 1, prPixel coordinate in actual imaging areal coordinate system is (ur,vr), with the actual image planes of size Expressing
Coordinate is (xr0,yr0).Point prIn coordinate system o-zcxiyiIn coordinate be (xr,yr,zr), principal point is in actual imaging areal coordinate system
Middle pixel coordinate is (cx,cy), dx,dyRespectively imaging surface unit pixel is in x and y directions size, unit：mm.Wherein pixel
The unit of coordinate is pixel, and other coordinate units are mm.
Because the inclination angle in actual imaging face and ideal image face is smaller, spin matrix RcFollowing processing can be done
pdIn camera coordinate system oc-xcyczcIn imager coordinate be (xd,yd,f)。
piThe resonable coordinate being thought of as in image coordinates system is (xi,yi), in xiRadial distortion compensation rate in direction is δkx, in yi
Radial distortion compensation rate in direction is δky。
xi=xd+δkx yi=yd+δky
According to pinhole imaging system principle, point p is in camera coordinate system oc-xcyczcLower coordinate is (xc,yc,zc)。
Object function f is established according to formula (5), (6), (7) and rotation translation matrix R, Tai,fbi。
faiPart I be to become the x that converses through R, T by the space coordinates of calibration pointcF is multiplied by, Part II is by reality
Border image coordinates (xr0,yr0) ask to obtain (x by formula (3), (5), (6)d+δkx) calibration point space coordinates is multiplied by by R, T change conversion
The z gone outc, should be equal by both formulas (7).fbiPart I be to become the y that converses through R, T by the space coordinates of calibration pointc
F is multiplied by, Part II is by actual image coordinates (xr0,yr0) ask to obtain (y by formula (3), (5), (6)d+δky) it is multiplied by calibration point
Space coordinates becomes the z conversed by R, Tc, similarly they also should be equal, is then used as target letter using the quadratic sum of its difference
Number, the according to target minimum requirement of function determine the optimum value of R, T, f and distortion factor.Wherein coordinate system ow-xwywzwTo coordinate system
oc-xcyczcSpin matrix R be：
Camera coordinate system is to world coordinate system rotation transformation：It is first about xcThe axle anglec of rotation is α, secondly surrounds ycAxle
The anglec of rotation is β, finally around zcThe axle anglec of rotation is γ.Corresponding translation vector T=[tx ty tz]T, world coordinate system ow-
xwywzwWith camera coordinate system oc-xcyczcConversion relational expression is：
Due to principal point coordinate (cx,cy) and rotation angle θ,Part component can be mutual during same objective function optimization
Influence.According to document [6] dyIt need not optimize, optimizing application algorithm Levenberg-Marquardt is carried out in two steps herein
Loop iteration optimizes, first step optimized coefficients α, beta, gamma, tx,ty,tz,f,dx,k1,k2,cx,cy, coefficient k1,k2Initial value is 0,
Principal point coordinate (cx,cy) initial value be imaging surface center pixel coordinate, dxFor camera producer set-point, camera coordinates herein
For position relationship between system and world coordinate system as shown in figure 1, α initial values are 0.5 π, beta, gamma initial value is all 0, tx,ty,tzInitially
Be worth for using other instruments obtain estimate, θ,Initial value be 0.Object function F0For：
The f that second step substitutes into the result that the first step optimizes in formula (8) as known quantityai,fbi, optimization object function F1Ask
Untwist rotational angle theta,Their initial value is 0.
The rotation angle θ obtained,Formula (8) is substituted into again together as known quantity and first step result, optimizes F0, so follow
Ring iterative is untill meeting certain threshold accuracy.
Step 3 three coordinate measuring machine gathered data
What the method for the present invention was realized based on three-dimensional coordinates measurement machine platform, three coordinate measuring machine operation positioning precision compares
Height, three dimensions point spacing and distribution can be neatly planned, can be used in the vision measurement of various different measurement ranges
System, the datum quantity of scope and pitch needed for formation, a large amount of three-dimensional references calibration points can be extracted, and camera phase can be adjusted
Point cloud imaging is covered whole camera imaging face substantially for the position and attitude of three coordinate measuring machine, can extract more more comprehensively
Three-dimensional feature information, imaging plane can be divided into more careful grid, realize the more comprehensive phase of higher precision
Machine is demarcated and distortion compensation.The model of the three coordinate measuring machine used in experiment：global classic SR 07.10.07.
The three coordinate measuring machine of independent development[20]Control software POSCOM, camera driver and POSCOM are integrated.
A circular luminous point is fixed above three coordinate measuring machine gauge head, as shown in Fig. 2 having planned the traveling of three coordinate measuring machine in advance
Path, makes camera face three coordinate measuring machine, and POSCOM control three coordinate measuring machines often run a position through suitable time-delay etc.
After, camera programm automatically extracts luminous point imaging center subpixel coordinates, then preserves imaging center coordinate and three coordinates are surveyed
The coordinate of amount machine.
In order to obtain spatial information of the luminous point in more opening position, in camera coverage prismatoid space, such as Fig. 3 institutes
Show and planned three cutting planes respectively from the near to the remote apart from camera.In order to reduce the influence of temperature error, calibration of camera is suitable
Carried out in the preferable laboratory of temperature conditionss, and reduce the gathered data time as far as possible, avoided between three dimensions benchmark and equipment
Relative position changes, cutting plane b1With cutting plane b3100 positions are planned respectively；Simultaneously for more Accurate Calibration camera
Inner parameter, middle cutting plane b2More multiple positions such as 100 × 100 are planned, overall gathered data needs small more than 2
When.The present invention is not limited to the number of collection point.
Step 4 distortion data storehouse compensates
(1) distortion data storehouse is established
The grid and correspond to the residual of mesh point that imaging point after distortion data storehouse is compensated by distortion model herein forms
Remaining distortion compensation amount composition, the residual distortion amount for imaging point after compensating distortion model are further compensate for.Distort residual volume
difx,difyIt is by ideal image point image coordinates (xi,yi) and the corresponding imaging point image coordinates after distortion model compensates
(xif,yif) ask difference to obtain.Ideal image point image coordinates (xi,yi) it is the demarcation point coordinates (x provided by measuring machinew,yw,zw)
Tried to achieve with spin matrix R, translation matrix T, focal length f by formula (13).Take middle cutting plane b2Mended corresponding to interior by distortion model
Mesh point of the rear imaging point as distortion data storehouse is repaid, all mesh points form a complete careful grid, and grid scope is such as
In Fig. 4 shown in N1, and grid point coordinates (xif,yif) and corresponding difx,difyDistortion data storehouse is established together.
difx=xi-xif
dify=yi-yif (14)
In Fig. 4, stain represents the boundary point of grid in distortion data storehouse in N1, wherein the rectangular area surrounded is exactly
Imaging point distribution in distortion data storehouse, 10000 mesh points are distributed with the range of this, it can be seen that point cloud imaging from N1
Substantially whole imaging surface is covered, compensation point will carry out the positioning of grid cell domain in this rectangle, and the u of grid is to mean breadth
24.07 pixels, v to equispaced be 20.01 pixels；Black asterisk represents control point cloud in three coordinate measuring machine in N2
Distribution under coordinate system, middle b210000 points are planned in cutting plane n, 100 data have been planned in other two sections respectively
Point position.
(2) compensation rate interpolation arithmetic
Node to be compensated is carried out zonule positioning in the grid in distortion data storehouse again after distortion model compensates first,
Four points nearest apart from node to be compensated in grid are determined, then find out the distortion compensation amount of four respective directions
difx,dify, it is last to carry out bilinear interpolation compensation as shown in Figure 5.To calculate xiIllustrated exemplified by the distortion compensation amount of direction,
Coordinate system o-xiyiFor image coordinates system, the residual distortion compensation rate of mesh point be exactly corresponding to perpendicular to plane oxiyiLength along path
Degree.Point P is compensation point, and A, B, C, D are four mesh points that range points P is nearest in grid.Line segment AA1,BB1,CC1,DD1Length
Degree is that point A, B, C, D correspond to xiThe residual distortion compensation rate in direction.Line segment EE1,FF1Length be corresponding interpolation point E, F's
Residual distortion compensation rate.Line segment PP1Length be the point P to be solved residual distortion compensation rate difPx。
Y can similarly be obtainediThe distortion compensation amount dif of direction of principal axis coordinatePy。
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Claims (4)
1. a kind of camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine, it is characterized in that, step 1 determines to pass
The method for solving of system camera imaging model parameters, the camera internal that the data scaling gathered according to step 2 goes out in step 1 are joined
Number simultaneously compensates according to the distortion formula of step 1, and step 3 is the root after step 1 and step 2 carry out demarcation and distortion compensation
The distortion compensation of model database progress again is established according to remaining image deformation amount, specifically：
Camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine, step 1 determine traditional camera imaging model
The method for solving of parameters, the camera internal parameter that goes out in step 1 of data scaling gathered according to step 2 and according to step 1
Distortion formula compensate, step 3 be step 1 and step 2 carry out demarcation and distortion compensation after according to remaining imaging
Amount of distortion establishes the distortion compensation of model database progress again, specifically：
The method that step 1 determines new camera calibration and distortion compensation
Ideal coordinates system is established according to national forest park in Xiaokeng, due to various distortion, actual image coordinates during actual imaging be present
System is converted to preferable image coordinates system by rotation, around xiThe anglec of rotation of axle is θ, around yiThe anglec of rotation of axleTangential distortion
Represented with this rotation transformation, according to original image point coordinates, rotation angle θ,And single order radial distortion coefficient is k1, two
Rank rank coefficient of radial distortion is k2, world coordinate system is ow-xwywzw, camera coordinate system oc-xcyczc, preferable image coordinates
It is for o-xiyi, actual image coordinates system is o-xryr.Point P is actual object point, piFor ideal image point, prFor actual imaging point,
pdFor the imaging point with radial distortion, using o as origin, the reference axis x based on preferable image coordinates systemi,yiAnd camera optical axis
Establish coordinate system o-zcxiyi, then:
prPixel coordinate in actual imaging areal coordinate system is (ur,vr), using the actual image coordinates of size Expressing as (xr0,
yr0), point prIn coordinate system o-zcxiyiIn coordinate be (xr,yr,zr), principal point pixel coordinate in actual imaging areal coordinate system is
(cx,cy), dx,dyRespectively imaging surface unit pixel is in x and y directions size, unit：Mm, wherein pixel coordinate unit are pictures
Element, other coordinate units are mm：
Because the inclination angle in actual imaging face and ideal image face is smaller, spin matrix RcDo following processing
pdIn camera coordinate system oc-xcyczcIn imager coordinate be (xd,yd, f),
piThe resonable coordinate being thought of as in image coordinates system is (xi,yi), in xiRadial distortion compensation rate in direction is δkx, in yiDirection footpath
It is δ to distortion compensation amountky,
xi=xd+δkx yi=yd+δky
According to pinhole imaging system principle, point p is in camera coordinate system oc-xcyczcLower coordinate is (xc,yc,zc)
Object function f is established according to formula (5), (6), (7) and rotation translation matrix R, Tai,fbi
faiPart I be to become the x that converses through R, T by the space coordinates of calibration pointcF is multiplied by, Part II is by actual picture
Areal coordinate (xr0,yr0) ask to obtain (x by formula (3), (5), (6)d+δkx) it is multiplied by what calibration point space coordinates conversed by R, T change
zc, should be equal by both formulas (7), fbiPart I be to become the y that converses through R, T by the space coordinates of calibration pointcIt is multiplied by
F, Part II are by actual image coordinates (xr0,yr0) ask to obtain (y by formula (3), (5), (6)d+δky) it is multiplied by the demarcation space of points
Coordinate becomes the z conversed by R, Tc, similarly they also should be equal, then using the quadratic sum of its difference as object function,
The according to target minimum requirement of function determines the optimum value of R, T, f and distortion factor, wherein coordinate system ow-xwywzwTo coordinate system oc-
xcyczcSpin matrix R be：
Camera coordinate system is to world coordinate system rotation transformation：It is first about xcThe axle anglec of rotation is α, secondly surrounds ycAxle rotates
Angle is β, finally around zcThe axle anglec of rotation is γ, corresponding translation vector T=[tx ty tz]T, world coordinate system ow-
xwywzwWith camera coordinate system oc-xcyczcConversion relational expression is：
Due to principal point coordinate (cx,cy) and rotation angle θ,Part component can influence each other during same objective function optimization,
The loop iteration optimization of optimizing application algorithm Levenberg-Marquardt progress in two steps, first step optimized coefficients α, beta, gamma,
tx,ty,tz,f,dx,k1,k2,cx,cy, coefficient k1,k2Initial value is 0, principal point coordinate (cx,cy) initial value be imaging surface center
Pixel coordinate, dxFor camera producer set-point, α initial values are 0.5 π, and beta, gamma initial value is all 0, tx,ty,tzInitial value is utilization
The estimate that other instruments obtain, θ,Initial value be 0, object function F0For：
The f that second step substitutes into the result that the first step optimizes in formula (8) as known quantityai,fbi, optimization object function F1Solve rotation
Rotational angle theta,Their initial value is 0.
The rotation angle θ obtained,Formula (8) is substituted into again together as known quantity and first step result, optimizes F0, so circulate and change
In generation, is untill meeting certain threshold accuracy；
Step 2 three coordinate measuring machine gathered data
A circular luminous point is fixed above three coordinate measuring machine gauge head, has planned the traveling road of three coordinate measuring machine in advance
Footpath, make camera face three coordinate measuring machine, control three coordinate measuring machine often runs a position after suitable time-delay waits, camera
Program automatically extracts luminous point imaging center subpixel coordinates, then preserves the seat of imaging center coordinate and three coordinate measuring machine
Mark；
Step 3 distortion data storehouse compensates
(1) distortion data storehouse is established
Distortion data storehouse compensated by distortion model after the grid that forms of imaging point and corresponding mesh point residual distortion compensation
Amount composition, the residual distortion amount for imaging point after compensating distortion model are further compensate for, distortion residual volume difx,difyIt is
By ideal image point image coordinates (xi,yi) and the corresponding imaging point image coordinates (x after distortion model compensatesif,yif) ask
Difference obtains, ideal image point image coordinates (xi,yi) it is the demarcation point coordinates (x provided by measuring machinew,yw,zw) and spin matrix
R, translation matrix T, focal length f are tried to achieve by formula (13), take middle cutting plane b2The interior corresponding imaging point after distortion model compensates
As the mesh point in distortion data storehouse, all mesh points form a complete careful grid, and grid point coordinates (xif,
yif) and corresponding difx,difyDistortion data storehouse is established together,
difx=xi-xif
dify=yi-yif (14)
(2) compensation rate interpolation arithmetic
Node to be compensated is carried out zonule positioning in the grid in distortion data storehouse again after distortion model compensates first, it is determined that
Go out four points nearest apart from node to be compensated in grid, then find out the distortion compensation amount dif of four respective directionsx,
dify, finally carry out bilinear interpolation compensation.
2. camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine as claimed in claim 1, its feature
It is that compensation rate interpolation arithmetic in an example, calculates xiDirection distortion compensation amount step is coordinate system o-xiyiSat for image planes
Mark system, the residual distortion compensation rate of mesh point are exactly corresponding perpendicular to plane oxiyiLine segment length, point P are compensation point, A, B,
C, D are four mesh points of range points P recently, line segment AA in grid1,BB1,CC1,DD1Length be that point A, B, C, D correspond to xiSide
To residual distortion compensation rate.Line segment EE1,FF1Length be corresponding interpolation point E, F residual distortion compensation rate, line segment PP1
Length be the point P to be solved residual distortion compensation rate difPx,
Similarly obtain yiThe distortion compensation amount dif of direction of principal axis coordinatePy。
3. camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine as claimed in claim 1, its feature
It is, in step 2, in order to obtain spatial information of the luminous point in more opening position, in camera coverage prismatoid space, distance
Camera plans three cutting planes respectively from the near to the remote, and in order to reduce the influence of temperature error, calibration of camera is preferably in laboratory
Carry out, and reduce the gathered data time as far as possible, avoid relative position between three dimensions benchmark and equipment from changing, cutting plane
b1With cutting plane b3100 positions are planned respectively；Simultaneously for more Accurate Calibration camera internal parameter, middle cutting plane b2Rule
Draw more multiple positions.
4. camera high-precision calibrating and distortion compensation method based on three coordinate measuring machine as claimed in claim 1, its feature
Be, in the step 3 of an example, the u of grid to mean breadth be 24.07 pixels, v to equispaced be 20.01 pictures
Element；Middle b210000 points of planning in cutting plane n, 100 data point positions are planned in other two sections respectively.
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