CN102564348A - Systematic geometric demarcation method for reflection three-dimensional measurement of stripe - Google Patents

Systematic geometric demarcation method for reflection three-dimensional measurement of stripe Download PDF

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CN102564348A
CN102564348A CN2012100000981A CN201210000098A CN102564348A CN 102564348 A CN102564348 A CN 102564348A CN 2012100000981 A CN2012100000981 A CN 2012100000981A CN 201210000098 A CN201210000098 A CN 201210000098A CN 102564348 A CN102564348 A CN 102564348A
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display device
stripe
striped
reflection
systematic
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苏显渝
肖永亮
陈文静
刘元坤
张启灿
向立群
曹益平
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Sichuan University
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Sichuan University
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Abstract

The invention discloses a systematic geometric demarcation method for reflection three-dimensional measurement of a stripe, and relates to systematic geometric demarcation during the three-dimensional appearance measurement of an object with a mirror reflection characteristic. As a stripe display device appears in a viewing field range of a video camera indirectly, the conventional systematic geometric demarcation process is fulfilled by adopting a method of sticking a marking point on a plane mirror. However, the physical coordinates of the marking point are required to be pre-measured through other precision measurement means. To solve the problem, the systematic geometric demarcation method adopts the scheme that the operation of sticking the marking point on the plane mirror is eliminated, the stripe on the stripe display device is reflected three times by the plane mirror, and analysis and linear calculation are conducted on the coordinates of the characteristic point and the imaging point of the stripe, so that the original value evaluation of the systematic geometric demarcation process is fulfilled; and then the evaluation result is optimized by adopting bundle adjustment, so as to obtain the final systematic geometric demarcation result. The systematic geometric demarcation method has the advantages of simplicity and flexibility; and only a plane mirror with a proper size is required for fulfilling the systematic geometric demarcation of the reflection three-dimensional measurement of the stripe. The systematic geometric demarcation method provides an efficient systematic demarcation way for phase position measurement deflection methods, stripe reflection photogrammetric survey and like which are based on stripe reflection three-dimensional measuring methods, thereby having a wide application prospect.

Description

The system geometric calibration method of streak reflex three-dimensional measurement
Technical field
The present invention relates to the measuring three-dimensional morphology with specular reflective characteristics object, especially for the system geometric calibration of streak reflex three-dimensional measurement, belong to advanced optics manufacture and detection technique field.
Background technology
Structured light projection, which obtains object dimensional face shape, has the advantages that quick measurement of full field, measurement accuracy are higher, has been widely used in the three-dimensional measurement on diffusing reflection surface.For the three-dimensional measurement of specular reflection surface, according to streak reflex characteristic, G. Hausler (M. C.Knauer, J. Kaminski, and G. Hausler. Phase measuring deflectometery: a new approach to measure specular freeform surfaces, Proc. SPIE, 2004, 5457:366 ~ 376) propose to utilize phase measurement deviation art, utilize gradient integral measurement mirror shape；M. Petz(M. Petz, R. Tutsch, Reflection grating photogrammetry:A technique for absolute shape measurement of specular free-form surfaces, Proc. SPIE, 5869,2005) propose that reflecting grating is photogrammetric, using light triangle intersection measurement mirror shape.The technological difficulties of above two measuring method are system geometric calibration.Due to striped display device（For example：Liquid crystal display）The bar graph of upper display is not occurred directly in the field range of video camera, the geometry pose completed using the level crossing of labelling point between video camera and display device is needed to estimate, but the mark point coordinates pasted on level crossing must be measured by other precision measurement methods in advance.It is obvious that mark point, which is measured, can increase time of measuring and measurement cost.Effectively simple system geometric calibration how is carried out, is one of difficult point of streak reflex three-dimensional measurement.
The content of the invention
In order to effectively be simply done the geometric calibration of streak reflex three-dimension measuring system, herein using the bar graph calibrating camera in level crossing reflection strip display device and the geometry pose of striped display device, without the labelling point on level crossing.Directly the streak reflex in striped display device is no less than 3 times using level crossing and reflection strip figure is received with fixed video camera.First according to mirror image figure of the streak feature point in level crossing in striped display device the position orientation relation between video camera and mirror image bar graph is assessed with it in the image coordinate in video camera imaging face；Then according to the equivalence of two kinds of explanations of reflective projection imaging model, i.e. video camera is imaged to the mirror image striped imaging in level crossing with the virtual video camera in level crossing to the striped in striped display device, it is linear to resolve video camera and the pose of striped display device according to video camera and no less than 3 position orientation relations of mirror image striped graph evaluation；Finally by the use of reflective projection imaging model as cost function, bundle adjustment optimization is completed.
Brief description of the drawings
Fig. 1 is reflective projection imaging model
Streak feature point distribution in Fig. 2 striped display devices；
Fig. 3,4,5 are distributed for the characteristic point and re-projection of mirror image bar graph.Wherein "+" represents mirror image features' point；" O " represents the re-projection of linear algorithm；" " represents the re-projection after bundle adjustment.  
Embodiment
The present invention is further illustrated with reference to the accompanying drawings and examples.Fig. 1 describes the reflective projection imaging model of streak reflex three-dimensional measurement.Striped display device（By taking liquid crystal display LCD as an example）It is respectively defined as with the coordinate system of video cameraWith
Figure 483091DEST_PATH_IMAGE002
.Streak reflex three-dimension measuring system geometric calibration is to determine
Figure 770984DEST_PATH_IMAGE001
With
Figure 533404DEST_PATH_IMAGE002
Between geometrical relationship, typically pass through spin matrix
Figure 652669DEST_PATH_IMAGE003
And translation vectorRepresent.Reflective projection imaging model can be sketched：First, LCD is transformed under camera coordinate system；Then by LCD to level crossing mirror image；Finally, its mirror image is imaged in video camera imaging face.Characteristic point on LCD
Figure 381646DEST_PATH_IMAGE005
Mirror point on level crossing
Figure 885439DEST_PATH_IMAGE006
Homogeneous coordinates formulation be
                
Figure 859212DEST_PATH_IMAGE007
 (1)
Figure 921583DEST_PATH_IMAGE008
It is normal direction of the level crossing under camera coordinate system,
Figure 246385DEST_PATH_IMAGE009
It is distance of the level crossing to video camera.Then, mirror point
Figure 288291DEST_PATH_IMAGE006
It is imaged by nonlinear imaging model in video camera imaging face.LCD coordinate systems are right-handed system, then, its mirror image is left-handed system.Assuming that nonlinear imaging Model Abstraction is mathe-matical map function
Figure 382149DEST_PATH_IMAGE010
, its image coordinate
Figure 615422DEST_PATH_IMAGE011
For
 (2)
Therefore, in reflective projection imaging model, it is contemplated that the lens distortion of video camera, pin-hole model is no longer only considered.From reflective projection imaging model, free mirror-reflection pose assessment refers to knownWith
Figure 283797DEST_PATH_IMAGE011
, calculate
Figure 189437DEST_PATH_IMAGE003
With
Figure 721787DEST_PATH_IMAGE004
.The process of streak reflex three-dimension measuring system geometric calibration is divided into two steps：The first step is linear solution；Second step is bundle adjustment Optimization Solution parameter.The first step：Order
Figure 105495DEST_PATH_IMAGE013
, another of reflective projection imaging model be construed to：By video camera to level crossing mirror image into virtual video camera, this virtual video camera pair
Figure 173945DEST_PATH_IMAGE005
Point imaging.By actual imaging dot image coordinate
Figure 250485DEST_PATH_IMAGE011
To level crossing mirror image into
Figure 293569DEST_PATH_IMAGE014
, according to the pose assessment algorithm based on horizontal control point,
Figure 480968DEST_PATH_IMAGE014
With
Figure 403925DEST_PATH_IMAGE005
The pose between virtual video camera coordinate system and world coordinate system can be assessed
Figure 651366DEST_PATH_IMAGE015
With
Figure 158309DEST_PATH_IMAGE016
.Due to the symmetry of imaging, two kinds of reflective projection imaging model explain there is equivalence, can obtain
Figure 149399DEST_PATH_IMAGE017
(3)
It can obtain
Figure 926862DEST_PATH_IMAGE015
,
Figure 345205DEST_PATH_IMAGE003
With
Figure 73864DEST_PATH_IMAGE016
,
Figure 868645DEST_PATH_IMAGE018
Between fundamental relation
                                     
Figure 500614DEST_PATH_IMAGE019
  (4)
According to equation (4), 3 mirrored images calculating are at least needed
Figure 89859DEST_PATH_IMAGE003
With
Figure 571393DEST_PATH_IMAGE004
.Level crossing is arbitrarily turned an angle, 3 mirrored images just can be obtained.To every a pair of mirrored images,
Figure 904286DEST_PATH_IMAGE020
, make unit vector
Figure 390762DEST_PATH_IMAGE021
With
Figure 416487DEST_PATH_IMAGE022
,
Figure 683520DEST_PATH_IMAGE023
It is vertical, then
Figure 53059DEST_PATH_IMAGE024
, can obtain
Figure 659621DEST_PATH_IMAGE025
 (5)
Therefore,
Figure 856247DEST_PATH_IMAGE026
Characteristic value is for 1 characteristic vector
Figure 282680DEST_PATH_IMAGE027
.According to the cross product of characteristic vector, the normal vector of mirror can be calculated
,
Figure 182558DEST_PATH_IMAGE029
, (6)
Then, 3 spin matrixs
Figure 463815DEST_PATH_IMAGE031
It can be solved according to equation (4),
Figure 440736DEST_PATH_IMAGE032
.It is muting ideally,
Figure 756311DEST_PATH_IMAGE031
Should be equal.But in fact, due to noise,
Figure 294739DEST_PATH_IMAGE031
And it is unequal, then need to be averaging spin matrix.Order
Figure 695765DEST_PATH_IMAGE033
, then spin matrix average out to
Figure 476377DEST_PATH_IMAGE034
 (7)
Remaining parameter
Figure 912037DEST_PATH_IMAGE035
Linear equation can be built according to equation (3) to solve
Figure 355788DEST_PATH_IMAGE036
 (8)
So far, the system geometrical relationship of streak reflex three-dimension measuring system
Figure 509689DEST_PATH_IMAGE003
With
Figure 828413DEST_PATH_IMAGE004
It can be solved by 3 secondary flat mirror reflecting linears.Second step：Linear solution is generally to noise-sensitive, and bundle adjustment can be by right
Figure 180896DEST_PATH_IMAGE003
﹑
Figure 795549DEST_PATH_IMAGE018
﹑,
Figure 795046DEST_PATH_IMAGE038
Adjust simultaneously, make the re-projection error of reflective projection minimum.According to the problem of specific, it is necessary to build cost function and the optimization of bundle adjustment pose is completed under Levenberg-Marquardt algorithms, the structure of its cost function is based on reflective projection imaging model.Due to
Figure 438254DEST_PATH_IMAGE037
,Simply intermediate variable, in order to reduce adjustment parameter, makes
Figure 352301DEST_PATH_IMAGE039
, spin matrixRepresented by three parameter procedures of Rodrigues matrixes, meet the unit property of orthogonality of spin matrix.Accordingly, it would be desirable to which the number of parameters of adjustment is total up to 15.Assuming that
Figure 841368DEST_PATH_IMAGE040
Have in reflective projection image
Figure 561937DEST_PATH_IMAGE041
Individual characteristic point, can build altogether
Figure 646568DEST_PATH_IMAGE042
Individual equation.According to equation (1) and (2), cost function is configured to
                 
Figure 612250DEST_PATH_IMAGE043
 (9)
Figure 731515DEST_PATH_IMAGE044
Bundle adjustment
Figure 622986DEST_PATH_IMAGE045
Belong to typical nonlinear least square method, using linear solution as initial value, by changing blocking factor
Figure 460492DEST_PATH_IMAGE046
Carry out the descent direction of control algolithm, its correction
Figure 26602DEST_PATH_IMAGE047
 (10)
Wherein,
Figure 374DEST_PATH_IMAGE048
To represent adjustment parameter
Figure 564211DEST_PATH_IMAGE003
﹑﹑
Figure 429454DEST_PATH_IMAGE049
Vector,For
Figure 258049DEST_PATH_IMAGE051
For adjustment parameterJacobian matrix.The realization of bundle adjustment is mathematically required
Figure 211017DEST_PATH_IMAGE052
, i.e.,
Figure 159381DEST_PATH_IMAGE053
.When
Figure 65020DEST_PATH_IMAGE054
When, picture point
Figure 98835DEST_PATH_IMAGE006
With the pose of camera coordinate system
Figure 246658DEST_PATH_IMAGE015
With
Figure 315108DEST_PATH_IMAGE016
Typical P3P problems are evaluated as, there is multi-solution.But, P4P and P5P poses assessment algorithm can be met
Figure 391648DEST_PATH_IMAGE015
With
Figure 647180DEST_PATH_IMAGE016
Resolving, ensure that again progress bundle adjustment optimization
Figure 598693DEST_PATH_IMAGE003
With.On the other hand, bundle adjustment belongs to Local Optimization Algorithm, it is desirable to provide the higher initial value of precision makes cost function finally restrain, linear solution as optimization initial driving.Therefore, the points for participating in resolving are more,
Figure 831409DEST_PATH_IMAGE055
With
Figure 574237DEST_PATH_IMAGE004
Initial precision can be higher, the equation of bundle adjustment can be more,
Figure 565326DEST_PATH_IMAGE055
WithOptimization precision also can be higher.In embodiment, two-dimensional strip is shot using JAI CV-A50 B/W cameras, the resolution ratio of video camera is 640 × 480 pixels, and Pixel Dimensions are
Figure 283105DEST_PATH_IMAGE056
m；Striped is shown using Philips 170S87 liquid crystal displays, resolution ratio is 1024 × 1280 pixels, and the point spacing of display is 0.264 mm.Fig. 2 is the streak feature point distribution on liquid crystal display.Using level crossing to the streak reflex 3 times on liquid crystal display, mirror image bar graph such as Fig. 3 of camera record, shown in 4,5.Wherein "+" represents mirror image features' point；" O " represents the re-projection of linear algorithm；" " represents the re-projection after bundle adjustment.As shown in table 1, the pose result of actual demarcation is actual re-projection error
Figure 778809DEST_PATH_IMAGE057
,
Re-projection error variance (the unit of the reflective projection of table 1：Pixel)
  Fig. 3 Fig. 4 Fig. 5
Horizontal direction 0.083 0.091 0.087
Vertical direction 0.074 0.082 0.074

Claims (5)

1. a kind of system geometric calibration method for streak reflex three-dimensional measurement, it is characterised in that:Calibrating camera and striped display device not directly in its field range（For example：Liquid crystal display）Between geometry position orientation relation；The two-dimentional sine streak reflection shown in striped display device is not less than 3 times using level crossing, the mirror image and record of fixed video camera to striped in level crossing；According to the image coordinate of streak feature point coordinates in striped display device He its imaging point, the geometry position orientation relation between calibrating camera and striped display device.
2. described two-dimentional sine streak is required according to right 1, it is characterised in that：The form of two-dimensional strip image writes program by computer, and the pixel size of its image is consistent with the resolution ratio of striped display device, it is included on the display screen of striped display device；With reference to the equation and the point spacing of striped display device of design bar graph, plane phase target can be built.
3. described image characteristic point is required according to right 1, it is characterised in that：The bar graph of camera record is handled using Fourier analysis, wrapped phase is obtained, takes its phase zero points to be characterized a little, and according to the sub-pixel positioning of the linear character of phase progress image characteristic point.
4. described level crossing is required according to right 1, it is characterised in that：One piece of level crossing, it is not necessary to stick any mark point in the above.
5. the video camera according to being required right 1 and the geometry position orientation relation not directly between its field range intra-striate display device are demarcated, it is characterised in that：According to the bar graph record not less than 3 secondary reflection projection imagings, using plane multiple spot pose assessment algorithm, the position orientation relation of 3 or more than 3 in striped display device between striped mirror image in video camera and level crossing is resolved；Utilize the position orientation relation linear solution video cameras of 3 or more than 3 and the geometry position orientation relation of striped display device；Finally optimize calibration result using bundle adjustment.
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Application publication date: 20120711