CN104048601B - Complete imaging mapping method based on coordinate transform - Google Patents
Complete imaging mapping method based on coordinate transform Download PDFInfo
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Abstract
The present invention relates to the complete imaging mapping method based on coordinate transform, and it includes pose of camera centering and the undistorted focal plane of image, and mapping mathematical model is established backward；The pose of camera centering carries out vision pose detection using using video camera to 2D calibrating templates in detection platform, obtain the angle of inclination of camera optical axis and detection platform, the angle of pitch and deflection angle of double freedom precise adjusting device are adjusted on this basis, it is final to ensure camera optical axis perpendicular to detection platform；When mapping mathematical model is built upon camera optical axis perpendicular to detection plane backward described image is undistorted focal plane on the basis of acquired image.Mapping method structure, be coordinate position mapping relations from projection plane to imaging plane i.e. reflection method backward.It is simple, reasonable that the mapping method of the present invention is conceived, and its energy individual element produces output image, will not produce calculating waste problem and be easy to the application of high-precision interpolation algorithm.
Description
Technical field
The present invention relates to a kind of complete imaging mapping method, more particularly to a kind of complete imaging mapping based on coordinate transform
Method.
Background technology
Vision detection technology suffers from being widely applied in the every field of industry at present, the measurement hand based on machine vision
Section and method have also obtained quick development, but the vision measurement research to physical dimension is concentrated mainly on to micro-structure or chi
Very little smaller parts, it is main reason is that CCD device Pixel-level relative accuracy is only 10 at present-3The order of magnitude, and vision system
Unite between Polaroid imaging region and detection resolution inversely.When carrying out image measurement to small items, due to
Visual field is smaller, can accordingly improve the resolving power of image measurement to improve measurement accuracy；And for larger or slender parts geometry
The comprehensive detection of size, because resolution ratio is not high so as to causing accuracy of detection can not meet in the complete image of Polaroid acquisition
Application request.
Can solve the measurement of large-size part vision according to breaking the whole up into parts, collecting zero again for whole complete imaging basic thought
Contradiction between middle visual field and image resolution ratio, document 1【The machine of the large scale machine components such as He Boxia, Zhang Zhisheng, Xu Sun Hao
Device vision high-precision measuring method.China Mechanical Engineering, 2,009 20 (1)】Carried for the machine components with bar shaped grain surface
Go out the sequence image calibration method based on textural characteristics, but to the random detection pair of smooth surface or surface texture
As helpless, its application field is extremely limited.
Document 2【Precision size detection algorithm researchs of the such as Liu Lingyun, Luo Min based on image mosaic, manufacturing technology and machine
Bed, 2012,11】It is middle that image mosaic technology is applied in vision measurement, image projection is established using calibrating camera mode
Model, it is proposed that the merging algorithm for images based on pose conversion realizes the accuracy registration between image, and is driven by positioner
Video camera precise transformation pose obtains image sequence, and the experimental verification algorithm has higher splicing precision.By the sequence of collection
Image is mapped to the committed step that same datum plane is the stitching algorithm after eliminating distortion, but due in the algorithm not to shooting
Machine external parameter is any limitation as, and the mathematical modeling for focal plane mapping that the image established is undistorted is complex.
The mathematical modeling for focal plane mapping that image employed in document 2 is undistorted as shown in accompanying drawing one, wherein, { C } is
Camera coordinate system during actual imaging, { C ' } are undistorted virtual video camera coordinate system, its Xc ', Yc ' axle respectively with world coordinates
It is the same orientation of respective shaft of { W }.Then mapping point (u ', v ')TWith actual imaging coordinate (u, v)TMeet following relation：
R in above formulaij(i=1,2,3；J=1,2,3,4) the corresponding element for being matrix M in video camera pinhole imaging system mathematical modeling
Element.Due to mapping relations formula (1) represent be from imaging plane to projection plane coordinate position mapping, belong to and map forward
Method, it is that gray-level interpolation algorithm is considerably complicated used by obtaining projection plane point position gray value in specific implementation, this undoubtedly increases
Add the details degeneration of the calculating time overhead of computer CPU and image more obvious.
The content of the invention
The present invention is to solve existing complete imaging mapping method complexity, adds the calculating time of computer CPU
Expense and the details of image degenerate the problems such as more obvious and propose it is a kind of can individual element produce output image, will not produce
Calculate waste problem and be easy to the complete imaging mapping method based on coordinate transform of the application of high-precision interpolation algorithm.
The present invention is achieved by the following technical solutions：
The mapping method of the above-mentioned complete imaging based on coordinate transform, it includes pose of camera centering, the shooting
Seat in the plane appearance centering is built upon video camera and is arranged on by means of a double freedom precise adjusting device above measurement plane, and it is wrapped
Include following steps：
1) video camera shoots multiple image to the target plane of different positions and pose, by each characteristic point on target and its image
Corresponding points relation application plane reference method between corresponding picture point, optimize the accurate inside ginseng for obtaining video camera of search
Number；
2) target is lain in measurement plane, world coordinate system { W is set using target plane as X/Y plane1}；
3) video camera is reused to target planar imaging, by characteristic point on target and its picture point corresponding relation, has been demarcated
Video camera internal reference world coordinate system { W is drawn according to pinhole imaging system formula1Relative to the description of camera coordinate system { C } pose
Homogeneous transform matrixTo the homogeneous transform matrixIt is fixed around camera coordinate system { C } to carry out Euler's angular transformation acquisition
The RPY angles of axle x-y-z rotations；
4) respective angles that the coordinate system { C } measured by treating rotates successively relative to two axles of Y, the Z of its own, which are less than, to be set
When determining threshold epsilon, the vertical centering of video camera is completed；Otherwise pitching and the deflection angle of double freedom precise adjusting device are suitably adjusted,
Return to step 3) again to target imaging measurement.
The complete imaging mapping method based on coordinate transform, wherein, the mapping method also include establish image without
Distort focal plane mapping mathematical model backward；
The foundation of described image is undistorted focal plane mapping mathematical model backward is carried out based on the pose of camera,
Point P { X in measurement plane when initially setting up camera optical axis perpendicular to measurement planew,Yw,0}TWith image coordinate (u, v)TIt
Between actual imaging mathematical modeling, then establish imaging mathematical modelings of the same point P in virtual video camera in measurement plane, then
Finally establish the mathematical modeling that the undistorted focal plane of image maps backward.
The complete imaging mapping method based on coordinate transform, wherein, the imaging mathematical modulo in the virtual video camera
Type is built upon camera coordinate system { C ' } and world coordinate system { W1Under the premise of posture identical, pass that its mathematical modeling meets
It is that formula is：
In above-mentioned formula (4), f, Sx、SyFor video camera internal reference；ZC'Thrown for photocentre in virtual video camera coordinate system { C ' } Z axis
Shadow, determined by picture resolution δ set on projection plane；u0′、v0' it is coordinate of the optical centre in mapping graph picture.
The complete imaging mapping method based on coordinate transform, wherein, described image is undistorted, and focal plane maps backward
The relational expression of satisfaction is：
In above-mentioned formula (5), ξ, f, Sx、Sy、u0、v0For video camera internal reference；α、ZCTo join outside video camera, wherein ZC=cpz-
H, h are target thicknesses, and α is α obtained by Euler's angular transformation during centering；u0′、v0' it is seat of the optical centre in mapping graph picture
Mark；ZC′Project in virtual video camera coordinate system { C ' } Z axis for photocentre, determined by picture resolution δ set on projection plane.
The complete imaging mapping method based on coordinate transform, wherein, described image resolving power δ is along row or column direction
Size representated by single pixel, it meets relational expression：
That is ZC′=f δ (6)；
In above-mentioned formula (6), Hei、WidFor the length/width of mapping area on projection plane；Row、ColFor mapping graph as
Row/column；F is video camera internal reference focal length；ZC′Projected for photocentre in virtual video camera coordinate system { C ' } Z axis.
Beneficial effect：
Complete imaging mapping method of the invention based on coordinate transform is simple, reasonable, wherein, pose of camera aligning method
It is that vision pose detection is carried out to 2D calibrating templates in detection platform using video camera, obtains camera optical axis and detection platform
Angle of inclination, the angle of pitch and deflection angle of double freedom precise adjusting device are adjusted on this basis, finally ensures camera light
Axle is perpendicular to detection platform.
Meanwhile using the coordinate position mapping relations from projection plane to imaging plane, establish the undistorted focal plane of image
Mapping mathematical model backward, this reflection method backward will not produce calculate waste problem and conveniently using high-precision interpolation algorithm come
Realize.
Brief description of the drawings
Fig. 1 is that the undistorted focal plane of image of the complete imaging mapping method of the invention based on coordinate transform maps number backward
Learn model schematic.
Embodiment
As shown in figure 1, the complete imaging mapping method of the invention based on coordinate transform, it includes：
First, the centering of pose of camera
1) video camera shoots multiple image to the target plane of different positions and pose, by each characteristic point on target and its image
Corresponding points relation application plane reference method between corresponding picture point, optimize the accurate inside ginseng for obtaining video camera of search
Number.
2) target is lain in measurement plane, world coordinate system { W is set using target plane as X/Y plane1}。
3) video camera is reused to target planar imaging, by characteristic point on target and its picture point corresponding relation, has been demarcated
Video camera internal reference world coordinate system { W is drawn according to pinhole imaging system formula (1)1Retouched relative to camera coordinate system { C } pose
The homogeneous transform matrix statedTo the matrixEuler's angular transformation acquisition is carried out around camera coordinate system { C } according to formula (2)
The RPY angles of fixing axle x-y-z rotations.
In above-mentioned formula (2), (cpx、cpy、cpz) it is coordinate system { W1Coordinate of the origin in coordinate system { C }；α、β、γ
The respective angles rotated successively relative to tri- axles of X, Y, the Z of its own for coordinate system { C }, wherein, X, Y, Z of coordinate system { C }
Three axles distinguish after corresponding rotation alpha, β, γ with coordinate system { W1Same orientation.
4) when measured β, γ angle is less than given threshold ε, the vertical centering of video camera is completed.Otherwise appropriate adjustment is double certainly
Pitching and deflection angle by degree precise adjusting device, return to step 3) again to target imaging measurement.
2nd, the undistorted focal plane of image mapping mathematical model backward is established
As shown in figure 1, the foundation of the undistorted focal plane of image mapping mathematical model backward is based on above-mentioned position for video camera
Appearance, specifically first that the optical axis of video camera is vertical with measurement plane holding all the time, then actual imaging mathematical modeling is represented by：
In above-mentioned formula (3), f, Sx、Sy、u0、v0For video camera internal reference；ZC, α be video camera outside join, wherein ZC=cpz- h, h
For target thicknesses, α is α obtained by Euler's angular transformation during centering；
Similarly, same point P { X in measurement planew,Yw,0}TIn virtual video camera (virtual video camera coordinate system { C ' } and generation
Boundary's coordinate system { W } same to posture) in be imaged when with picture point (u, v)TBetween meet relational expression：
In above-mentioned formula (4), f, Sx、SyFor video camera internal reference；ZC'Thrown for photocentre in virtual video camera coordinate system { C ' } Z axis
Shadow, determined by picture resolution δ set on projection plane；u′0、v0' it is coordinate of the optical centre in mapping graph picture；
The mathematical modeling that then the undistorted focal plane of image maps backward can be reduced to：
In above-mentioned formula (5), ξ, f, Sx、Sy、u0、v0For video camera internal reference；α、ZCTo join outside video camera, wherein ZC=cpz-
H, h are target thicknesses, and α is α obtained by Euler's angular transformation during centering；u′0、v0' it is seat of the optical centre in mapping graph picture
Mark；ZC′Projected for photocentre in virtual video camera coordinate system { C ' } Z axis, by picture resolution δ set on projection plane (along row
Or the size representated by column direction single pixel) determine；
Wherein,That is ZC′=f δ (6)；
In above-mentioned formula (6), Hei、WidFor the length/width of mapping area on projection plane；Row、ColFor mapping graph as
Row/column；F is video camera internal reference focal length；ZC′Projected for photocentre in virtual video camera coordinate system { C ' } Z axis.
Complete imaging mapping method of the invention based on coordinate transform is simple, reasonable, wherein, pose of camera aligning method
It is that vision pose detection is carried out to 2D calibrating templates in detection platform using video camera, obtains camera optical axis and detection platform
Angle of inclination, the angle of pitch and deflection angle of double freedom precise adjusting device are adjusted on this basis, finally ensures camera light
Axle is perpendicular to detection platform.
Meanwhile using the coordinate position mapping relations from projection plane to imaging plane, establish the undistorted focal plane of image
Mapping mathematical model backward, this reflection method backward will not produce calculate waste problem and conveniently using high-precision interpolation algorithm come
Realize.
Claims (5)
1. a kind of mapping method of the complete imaging based on coordinate transform, it is characterised in that described including pose of camera centering
Pose of camera centering is built upon video camera and is arranged on by means of a double freedom precise adjusting device above measurement plane,
It comprises the following steps：
1) video camera shoots multiple image to the target plane of different positions and pose, corresponding on its image by each characteristic point on target
Picture point between corresponding points relation application plane reference method, optimize the accurate inner parameter for obtaining video camera of search；
2) target is lain in measurement plane, world coordinate system { W is set using target plane as X/Y plane1}；
3) video camera is reused to target planar imaging, by characteristic point on target and its picture point corresponding relation, taking the photograph of having demarcated
Camera internal reference draws world coordinate system { W according to pinhole imaging system formula1Relative to the homogeneous of camera coordinate system { C } pose description
Transformation matrixTo the homogeneous transform matrixEuler's angular transformation acquisition is carried out around camera coordinate system { C } fixing axle x-
The RPY angles of y-z rotations；
4) treat that the respective angles that measured coordinate system { C } rotates successively relative to two axles of Y, the Z of its own are less than setting threshold
During value ε, the vertical centering of video camera is completed；Otherwise pitching and the deflection angle of double freedom precise adjusting device are suitably adjusted, is returned
Step 3) is again to target imaging measurement.
2. the complete imaging mapping method based on coordinate transform as claimed in claim 1, it is characterised in that the mapping method
Also include establishing the undistorted focal plane of image mapping mathematical model backward；
The foundation of described image is undistorted focal plane mapping mathematical model backward is carried out based on the pose of camera, i.e., first
Point P { X in measurement plane when first establishing camera optical axis perpendicular to measurement planew,Yw,0}TWith image coordinate (u, v)TBetween
Actual imaging mathematical modeling, imaging mathematical modelings of the same point P in virtual video camera in measurement plane is then established, then finally
Establish the mathematical modeling that the undistorted focal plane of image maps backward.
3. the complete imaging mapping method based on coordinate transform as claimed in claim 2, it is characterised in that the virtual shooting
Imaging mathematical modeling in machine is built upon virtual video camera coordinate system { C ' } and world coordinate system { W1Posture identical premise
Under, the relational expression that its mathematical modeling meets is：
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In above-mentioned formula (4), f, Sx、SyFor video camera internal reference；ZC'Projected for photocentre in virtual video camera coordinate system { C ' } Z axis, by
Set picture resolution δ is determined on projection plane；u′0、v′0For coordinate of the optical centre in mapping graph picture.
4. the complete imaging mapping method based on coordinate transform as claimed in claim 2, it is characterised in that described image is without abnormal
Become focal plane map backward the relational expression of satisfaction into：
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In above-mentioned formula (5), ξ, f, Sx、Sy、u0、v0For video camera internal reference；α、ZCTo join outside video camera, wherein ZC=cpz- h, h are
Target thicknesses,cpzProjected for Z axis of the arbitrfary point in target plane in camera coordinate system { C }, α is Eulerian angles change during centering
Change gained α；(u ', v ') is that the image coordinate (u, v) of actual imaging is mapped to the image coordinate of corresponding points in virtual image；u′0、
v′0For coordinate of the optical centre in mapping graph picture；ZC′Projected for photocentre in virtual video camera coordinate system { C ' } Z axis, by projecting
Set picture resolution δ is determined in plane.
5. the complete imaging mapping method based on coordinate transform as described in claim 3 or 4, it is characterised in that described image
Resolving power δ is that it meets relational expression along the size representated by the single pixel of row or column direction：
That is ZC′=f δ (6)；
In above-mentioned formula (6), Hei、WidFor the length/width of mapping area on projection plane；Row、ColFor mapping graph picture row/
Row；F is video camera internal reference focal length；ZC′Projected for photocentre in virtual video camera coordinate system { C ' } Z axis.
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