CN108986171A - Camera lens heat affecting error compensating method in vision measurement system - Google Patents
Camera lens heat affecting error compensating method in vision measurement system Download PDFInfo
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Abstract
Camera lens heat affecting error compensating method belongs to Computer Vision Detection and field of image detection in vision measurement system of the present invention, in particular to for camera lens heat affecting error compensating method in the two CCD camera measure system under high temperature heat radiation environment.This method is in two CCD camera measure system, binocular camera shoots scaling board image under varying temperature environment, it is analyzed according to characteristic point image shift and solves migration model structure, principal point offset error and camera lens thermal distoftion error coefficient initial value are solved respectively, the accurate solution of all parameters is carried out by LM optimization algorithm, compensation is modified to the picture point offset error as caused by camera lens thermal deformation, obtains accurate image characteristic point picpointed coordinate.Compensation method is modified compensation to distorted image by the heat affecting error compensation model established, and realizes the accurate recovery of distorted image, the measuring precision significantly improves, to ensure that the accurate measurement under hot environment to object geometry parameter.
Description
Technical field
The invention belongs to Computer Vision Detection and field of image detection, in particular under high temperature heat radiation environment
Two CCD camera measure system in camera lens heat affecting error compensating method.
Background technique
A kind of Binocular vision photogrammetry non-contact measurement method high as strong real-time, measurement accuracy, is widely used in
The numerous areas such as industrial detection, target identification, especially during real-time measurement large forgings is forged and pressed in terms of hot geometric dimension
With incomparable advantage.Many scholars have carried out a large amount of research around how obtaining high-precision measurement result, however
Current main research work concentrates on the matching precision of the stated accuracy and characteristic point that improve camera system, and has ignored forging
Influence of the high temperature heat radiation to measuring system itself precision.Existing vision measurement system usually exists when measuring high-temperature forging
After completing measuring system calibration, i.e., on-line measurement is carried out to forging geometric parameter, the precision of measuring system is not carried out real-time
Calibration, may cause in measurement process, and acquisition image is influenced and distorting transformation by forging heat radiation, and characteristic point shifts,
The increase of measuring system measurement error is eventually led to, Measurement reliability is difficult to ensure.Current common correlative study such as Jilin University Zhao
It is firm et al. in paper " hot forging structural light three-dimensional measuring technique " China Mechanical Engineering, 2006 (s1): proposed in 134-137.
A kind of hot forging structural light three-dimensional measuring technique, acquired using imaging sensor projected using optical grating projection device it is to be measured
The white light fringe image of body surface is concentrated mainly on nearly feux rouges and infrared light this characteristic according to high-temperature forging radiation spectrum,
Filtering out for red spectral band interference light is realized using digital filtering, and then obtains the image of tested high-temperature forging.Measuring system exists
It only needs 5s that characteristic parameter within the scope of 1m × 0.8m can be realized in laboratory to measure.But program measurement range is limited, and does not examine
There are heat affecting stripped deviations when worry measurement.
Summary of the invention
The technical problem to be solved by the present invention is to overcome the shortcomings of existing accuracy compensation technology, surveyed at forging scene
Amount system, which is influenced by heat, causes image fault that measurement system error is caused to increase, and invents the hot shadow of camera lens in a kind of vision measurement system
Ring error compensating method.In two CCD camera measure system, it is contemplated that acquisition image, which is influenced by heat, leads to image fault deformation, spy
Sign point coordinate the problem of shifting, the present invention establish at camera lens temperature and image different location picpointed coordinate offset error it
Between numerical relationship model.When by analysis camera lens different temperatures, different location processing ideal point coordinate and practical picture in image
Error variation between point coordinate, establishes error compensation model, is compensated by lot of experimental data regression analysis
Each penalty coefficient in model, the final accurate compensation for realizing picture point offset error in image under different temperatures, obtains accurate
Image characteristic point picpointed coordinate reduces the heat affecting error of measuring system.
The technical solution adopted by the present invention is that camera lens heat affecting error compensating method, feature in a kind of vision measurement system
It is, this method is in two CCD camera measure system, and binocular camera shoots scaling board image under varying temperature environment, according to feature point diagram
As shift analysis and migration model structure is solved, solves principal point offset error and camera lens thermal distoftion error coefficient initial value respectively, is led to
The accurate solution that LM optimization algorithm carries out all parameters is crossed, benefit is modified to the picture point offset error as caused by camera lens thermal deformation
It repays, obtains accurate image characteristic point picpointed coordinate；Specific step is as follows for method:
Step 1 is using scaling board image under binocular camera shooting varying temperature environment
First using scaling board image under binocular camera shooting varying temperature environment, 24 characteristic point conducts in image are extracted respectively
Object is analyzed, the temperature for drawing 24 characteristic points increases front and back characteristic point offset comparison diagram, draws entire image overall offset amount
Image shift spirogram after figure and removal image overall offset amount, is made that according to 24 characteristic point coordinate shift figures in measurement model
Error curve；Hundred groups or more the picture point migrated images shot using two heating and cooling cycles stage, the error deviation extracted
Picpointed coordinate carries out analytical calculation, the offset rule of characteristic point when analyzing camera lens temperature change；
In order to further appreciate that rule that image characteristic point offset varies with temperature, and extracted four at picture centre respectively
A characteristic point (9,10,15,16) is also known as principal point and four Thursday characteristic points (1,6,19,24) as analysis object, analyzes camera lens
When temperature change, the offset rule of this 8 characteristic points, the temperature for drawing 8 characteristic points increases front and back characteristic point offset comparison diagram
And curve of deviation figure；
Analyser head surface temperature increase after in image each characteristic point drift condition, in the temperature rise period with camera lens surface
Temperature raised feature point coordinate is integrally presented to be deviated to v to increase, u to reduced direction, and exhausted relative to initial picpointed coordinate
Offset is gradually increased；In temperature-fall period direction with the temperature rise period almost on the contrary, absolute offset values are gradually reduced；However it is dropping
Track when thermophase picpointed coordinate deviating track is increased with temperature is not overlapped, this shows that camera lens is led in lifting thermophase thermal deformation
Cause picture point offset rule not identical；Therefore, there is different picture points to deviate rule for temperature rise period and temperature-fall period, in conjunction with secondary
Heating and cooling phase characteristic picture point deviates law-analysing it is found that two temperature rise periods of camera lens and two temperature-fall period picture point offset rules
With repeatability, and from picture point overall offset amount, analysis know in camera lens temperature distortion rear image point offset to be sat with principal point
Based on error caused by mark deviates；Camera lens temperature change causes feature picture point offset error to be by principal point offset error and camera lens heat
Distortion error composition, and this two errors are mutually indepedent, influence from each other there is no direct, camera lens is in heating and the rank that cools down
Section its error deviation rule is similar and different；
Step 2 solves migration model structure according to the characteristic point image shift of shooting
Build the experimental model comprising target complete characteristic point, by the coordinate shift error curve of all characteristic points it is found that
The error band that 24 characteristic point offset coordinates are formed at the same temperature is lens distortion introducing picture point offset error, and with temperature
The offset for changing each picture point globality is to generate offset by principal point coordinate to cause；Therefore, respectively with two margin of error Δ u, Δ v come
It indicates, picture point offset error model caused by final camera lens thermal deformation is expressed as:
Wherein, u ', v ' are picture point actual coordinate, and u, v are picture point initial coordinate, δu1、δv1The offset introduced for principal point offset
Error, δu2、δv2Respectively camera lens thermal distoftion introduces error；
The margin of error due to caused by lens distortion follows the bigger rule of the margin of error remoter from optical center, center in figure
The picture point offset that place's picture point generates in temperature changing process is based on principal point offset error, therefore, not with this four points
The mean approximation of synthermal lower offset is considered image overall offset amount；By the way of fitting of a polynomial, principal point is solved
Offset error varies with temperature curve；Lifting thermophase picture point curve of deviation is subjected to piecewise fitting, wherein Δ u is in heating and cooling
Phase change curve uses the available ideal fitting result of 3 rank multinomials, and in the variation of lifting thermophase for Δ v
Curve only needs second order polynomial both available ideal fitting results, is formula (2) based on this principal point offset error model
It is shown:
Wherein, a1、b1、c1、d1、a2、b2、c2It for principal point heat affecting offset error coefficient, is returned by lot of experimental data
Analyze 7 obtained penalty coefficients；
For the error that camera lens thermal distoftion introduces, picture point offset form meets radial distortion and the superimposed knot of tangential distortion
Fruit, therefore the distortion model is also to form camera lens thermal distoftion error model by camera lens first order radial distortion and second order centrifugal distortion, with
Conventional camera lens itself distortion difference is that three distortion factors to be asked not are constant, but changes with camera lens temperature change
, camera lens thermal distoftion error model indicates are as follows:
Wherein,(u0,v0) be camera principal point
Coordinate；k1For radial distortion parameter, p1、p2For centrifugal distortion parameter, k1、p1、p2Three distortion parameters are and temperature variation Δ T
Related function, three distortion parameters are characterized respectively by three second order polynomials with variation function, are expressed from the next respectively:
Wherein, e1、f1、g1、h1、j1、q1、l1、m1、n1The coefficient of respectively three distortion parameter polynomial fittings；
Step 3 solves principal point offset error and camera lens thermal distoftion error coefficient initial value respectively
Parameter is solved for 15 bands are co-existed in two in picture point offset error model, respectively 7 principal point offsets are missed
Poor coefficient a1、b1、c1、d1、a2、b2、c2With 9 camera lens thermal distoftion error coefficient e1、f1、g1、h1、j1、q1、l1、m1、n1；For ginseng
Number Solve problems, first substitute into formula (2) and formula (3) in formula (1), wherein Δ u and Δ v under different temperatures respectively
And principal point offset error deltau1、δv1It is known；Therefore, Δ u and Δ v after removal principal point offset influences are that camera lens thermal distoftion causes
Error, Δ u and Δ v after another removal principal point influences respectively are equal to δu2And δv2To acquire three under different temperatures distortion
Parameter Variation, 9 error compensation coefficient initial values for finally finding out three distortion parameters are respectively e1、f1、g1、h1、j1、q1、
l1、m1、n1；
Public affairs are substituted into respectively using 7 initial values of principal point offset error coefficient and 9 initial values of camera lens thermal distoftion error coefficient
Formula (1) finds out theoretical offset (the Δ u of feature picture point under different temperaturesI,ΔvI) and theoretical offset picpointed coordinate (uI,vI),
Wherein, uI=Δ uI+ u, vI=Δ vI+v；Each characteristic point actual shifts rear image point is found out by picture point actual shifts coordinate (u ', v ')
World coordinates (the X acquiredW1,YW1,ZW1), the theoretical offset coordinates (u being calculated by compensation modelI,vI) find out each characteristic point
Theoretical calculation obtains the object point world coordinates (X after picture point offset coordinatesW2,YW2,ZW2)；
Step 4 carries out the accurate solution of all parameters by LM optimization algorithm
World coordinates (X is obtained with theoretical calculationW1,YW1,ZW1) and actually obtain world coordinates (XW2,YW2,ZW2) point-to-point transmission
Apart from minimum optimization aim, each system of error compensation model is carried out by Levenberg-Marquardt (LM) optimization algorithm
Several accurate solutions.Optimization object function is as follows:
The error deviation picpointed coordinate arrived extracted using the picture point migrated image of two heating and cooling cycles stage shooting into
Row calculates, and the error compensation model that binocular image is obtained after the calculating of Levenberg-Marquardt (LM) optimization algorithm is each
A coefficient；
Step 5 is modified to there is picture point offset error caused by camera lens thermal deformation
After completing the calculating to each penalty coefficient of picture point offset error compensation model and solving, deviated using theoretical error
When temperature change can be calculated in calculation formula in image each picture point theoretical error offset, theoretical error calculations of offset is public
Formula is as follows:
Wherein, ui、viFor coordinate after picture point compensation, u ', v ' are picture point actual shifts coordinate, can be distinguished according to temperature change
Find out δu1、δv1、δu2、δv2This four margins of error, to obtain coordinate (u after picture point error compensationi,vi)；
It is missed using the theoretical offset that image picture point under different temperatures is calculated in the camera lens temperature variation data of experiment acquisition
Difference, and then the picture point offset error as caused by camera lens thermal deformation is modified, respectively left and right camera lens thermal deformation causes
Picpointed coordinate before and after picture point offset error compensation；According to the picpointed coordinate comparison of compensation front and back, picture point compensation model is accurately retouched
Stating camera lens thermal deformation leads to picture point offset rule, is modified to picture point offset error under different temperatures.
The beneficial effects of the invention are as follows in vision measurement high temp objects, pattern distortion is caused to be distorted for environment heat affecting
The problem of causing measurement accuracy to reduce is modified compensation to distorted image by the heat affecting error compensation model of foundation, drop
The low heat affecting error of measuring system, realizes the accurate recovery of distorted image, to ensure that determinand under hot environment
The accurate measurement of body geometry parameter.
Detailed description of the invention
Fig. 1 is 24 characteristic point positions and reference numeral in uncalibrated image.Wherein, 1-24 is respectively the 24th feature of 1-
Point.
Fig. 2 is that camera lens surface temperature increases front and back characteristic point offset comparison diagram, and Fig. 3 is whole for image characteristic point before and after temperature rise
Spirogram is deviated, Fig. 4 is image characteristic point offset spirogram after removal image overall offset amount, wherein represents 24 in three figures
Characteristic point offset amplify 50 times after as a result, 1- it is rectangular indicate temperature increase before each characteristic point position, 2- triangle indicate
Temperature increases the offset of each characteristic point at 20 DEG C.
Fig. 5 is comparison diagram before and after experimental reconstruction error compensation.Wherein, abscissa-picture sequence numbers, ordinate-reconstruction error
(mm)。
Fig. 6 is camera lens thermal deformation error compensation flow chart.
Specific embodiment
Below with reference to the specific implementation that the present invention will be described in detail of technical solution and attached drawing.
Fig. 1 is 24 characteristic point positions and reference numeral in uncalibrated image, and 1-24 is respectively the 24th characteristic point of 1-.Fig. 6
For camera lens thermal deformation error compensation flow chart, specific step is as follows for method:
Firstly, to understand the rule that image characteristic point offset varies with temperature, respectively with 24 characteristic points in image
To analyze object, when analyzing camera lens temperature change, the offset rule of characteristic point as shown in Figure 2,3, 4, represents 24 in three figures
A picture point offset amplifies the result after 50 times.Making error curve according to 24 characteristic point coordinate shifts in measurement model can
To know, the error band that characteristic point offset coordinates are formed at the same temperature is lens distortion introducing picture point offset error, and with temperature
The offset for changing each picture point globality is caused by principal point coordinate shift.It analyzes in conjunction with error theory it is found that lens distortion causes
Picture point offset and image entirety picture point deviate to be independent from each other between the picture point offsets of the two types, therefore respectively with two
A margin of error indicates, obtains shown in picture point offset error model caused by camera lens thermal deformation such as formula (1).
On the other hand, there is larger difference in view of lifting thermophase picture point offset change curve, for lifting thermophase
Picture point curve of deviation carries out piecewise fitting.Wherein, ideal is obtained using 3 rank multinomials in heating and cooling phase change curve to Δ u
Fitting result, ideal fitting result obtained using second order polynomial in the change curve of lifting thermophase to Δ v, thus
To shown in principal point offset error model such as formula (2).Wherein, a1、b1、c1、d1、a2、b2、c2For principal point heat affecting offset error system
Number, is 7 penalty coefficients obtained by lot of experimental data regression analysis.
It is also superimposed by radial distortion and tangential distortion as a result, therefore thermal distoftion mould since camera lens thermal distoftion introduces error
Type is also to be made of camera lens first order radial distortion and second order centrifugal distortion, and relevant parameter is become with camera lens temperature change
Change, the error model of camera lens thermal distoftion is obtained, as shown in formula (3).
Formula (2) and formula (3) are substituted into formula (1) respectively, wherein the Δ u under different temperatures becomes in lifting thermophase
Change curve and use the available ideal fitting result of 3 rank multinomials, and Δ v is only needed in the change curve of lifting thermophase
Second order polynomial both available ideal fitting result, based on shown in this principal point offset error model such as formula (2):
Lifting thermophase picture point curve of deviation is subjected to piecewise fitting, two forging cycle period lifting thermophase curves are quasi-
The results are shown in Table 1 for conjunction.
1 picture point curve of deviation fitting result of table
Δ u and Δ v after removing principal point offset influence are error caused by camera lens thermal distoftion, respectively another removal principal point shadow
Δ u and Δ v after sound are equal to δu2And δv2.The system of 7 compensation in compensation model is obtained by lot of experimental data regression analysis
Number, then based on the feature constraint of formula (4) to the coefficient e of three distortion parameter polynomial fittings1、f1、g1、h1、j1、q1、l1、m1、
n1It solves respectively.Three distortion parameter changing rules under different temperatures are acquired, 9 errors of three distortion parameters are finally found out
Penalty coefficient initial value is respectively e1=1.23-8、f1=5.34-10、g1=2.07-13、h1=1.69-7、j1=1.43-9、q1=
8.65-13、l1=5.27-8、m1=1.98-9、n1=3.73-13。
Public affairs are substituted into respectively using 7 initial values of principal point offset error coefficient and 9 initial values of camera lens thermal distoftion error coefficient
Formula (1), so as to find out the theoretical offset of feature picture point and theoretical offset picpointed coordinate v under different temperaturesI=Δ vI+v。
World coordinates (the X that each characteristic point actual shifts rear image point acquires can be found out by picture point actual shifts coordinate at this timeW1,YW1,ZW1),
Theoretical offset coordinates (the u being calculated simultaneously by compensation modelI,vI) find out each characteristic point theoretical calculation obtain picture point offset sit
Object point world coordinates (X after markW2,YW2,ZW2).And world coordinates (X is obtained with theoretical calculationW1,YW1,ZW1) and must actually be born
Boundary coordinate (XW2,YW2,ZW2) the minimum optimization aim of distance between two points, pass through Levenberg-Marquardt (LM) optimization algorithm
Carry out the accurate solution of error compensation model parameter.Shown in optimization object function such as formula (6).
It is sat using the error deviation picture point arrived that 148 groups of picture point migrated images of two heating and cooling cycles stage shooting extract
Mark is calculated, and obtains each coefficient of error compensation model of right image after the calculating of LM optimization algorithm.Similarly left image is each
A error coefficient can also optimize, and Fig. 5 is comparison diagram before and after experimental reconstruction error compensation.Calculating acquires, and acquires after final optimization pass
The each penalty coefficient of left images it is as shown in table 2.
Live heat radiation environment is forged using the simulation established in laboratory, real-time measurement camera lens temperature change works as camera lens
At 0.5 DEG C of the every variation of temperature, one group of characteristic image is acquired；Experiment two forging cycle periods of acquisition, experiment collect 148 groups altogether
Characteristic image, after proposing compensation method using the present invention, 8 characteristic points (1,6,9,10,15,16,19,24) in two groups of experiments
Offset error is carried out after error compensation model is corrected according to formula (6), and camera lens thermal deformation picture point offset error is substantially reduced, such as
Shown in table 3.
Each coefficient solving result of 2 error compensation model of table
Distribution compares before and after table 3 tests picture point error compensation
It is mended according to picture point distribution before and after experiment picture point error compensation it is found that implementing camera lens thermal deformation picture point offset error
After repaying, picture point offset caused by camera lens temperature change has obtained effective containment, the either maximum image surrounding of offset
The characteristic point at place or four characteristic points at picture centre, after the compensation of offset error amount in addition to Individual features point, base
Originally it can be reduced within 0.5 pixel × 0.5 pixel, see attached drawing 5.According to the reconstruction error comparison of compensation front and back it is found that in image
Characteristic point three-dimensional reconstruction error is reduced to 0.1mm from maximum 1mm, and measurement error reduces 90% after compensation, to become for temperature
Change high-precision videographic measurment under environment to provide the foundation.
The thermal deformation errors model obtained using experimental calculation, to the left and right camera lens thermal deformation as caused by thermal deformation
Lead to the picpointed coordinate before and after picture point offset error compensation, the picpointed coordinate after finally obtaining high-accuracy compensation.
Claims (1)
1. camera lens heat affecting error compensating method in a kind of vision measurement system, which is characterized in that this method is surveyed in binocular vision
In amount system, scaling board image under varying temperature environment is shot with binocular camera, mould is deviated according to characteristic point image shift analysis and solution
Type structure solves principal point offset error and camera lens thermal distoftion error coefficient initial value respectively, carries out all ginsengs by LM optimization algorithm
Several accurate solutions is modified compensation to the picture point offset error as caused by camera lens thermal deformation, obtains accurate characteristics of image
Point picpointed coordinate；Specific step is as follows for method:
Step 1 is using scaling board image under binocular camera shooting varying temperature environment
First using scaling board image under binocular camera shooting varying temperature environment, 24 characteristic points in image are extracted respectively and are used as analysis
Object, draw 24 characteristic points temperature increase front and back characteristic point offset comparison diagram, draw entire image overall offset spirogram and
Image shift spirogram after removal image overall offset amount, is made that error according to 24 characteristic point coordinate shift figures in measurement model
Curve；Hundred groups or more the picture point migrated images shot using two heating and cooling cycles stage, the error deviation picture point extracted
Coordinate carries out analytical calculation, the offset rule of characteristic point when analyzing camera lens temperature change；In order to further appreciate that image characteristic point
The rule that offset varies with temperature extracts four characteristic points (9,10,15,16), also known as principal point at picture centre respectively, and
Four Thursday characteristic points (1,6,19,24) are analysis object, when analyzing camera lens temperature change, the offset rule of this 8 characteristic points,
The temperature for drawing 8 characteristic points increases front and back characteristic point offset comparison diagram and curve of deviation figure；
Analyser head surface temperature increase after in image each characteristic point drift condition, in the temperature rise period with camera lens surface temperature
Raised feature point coordinate is integrally presented to be deviated to v to increase, u to reduced direction, and absolutely inclined relative to initial picpointed coordinate
Shifting amount is gradually increased；In temperature-fall period direction with the temperature rise period almost on the contrary, absolute offset values are gradually reduced；However in cooling rank
Track when section picpointed coordinate deviating track is increased with temperature is not overlapped, this shows that camera lens leads to picture in lifting thermophase thermal deformation
Point offset rule is not identical；Therefore, there is different picture points to deviate rule for temperature rise period and temperature-fall period, in conjunction with secondary lifting
Thermophase feature picture point offset law-analysing is it is found that two temperature rise periods of camera lens and two temperature-fall period picture point offset rules have
Repeatability, and analysis knows in camera lens temperature distortion rear image point offset to be inclined with principal point coordinate from picture point overall offset amount
Based on error caused by moving；Camera lens temperature change causes feature picture point offset error to be by principal point offset error and camera lens thermal distoftion
Error composition, and this two errors are mutually indepedent, influence from each other there is no direct, camera lens heating and temperature-fall period its
Error deviation rule is similar and different；
Step 2 solves migration model structure according to the characteristic point image shift of shooting
The experimental model comprising target complete characteristic point is built, by the coordinate shift error curve of all characteristic points it is found that same
The error band that 24 characteristic point offset coordinates are formed at a temperature of one is that lens distortion introduces picture point offset error, and varies with temperature
The offset of each picture point globality is to generate offset by principal point coordinate to cause；Therefore, respectively with two margin of error Δ u, Δ v come table
Show, picture point offset error model caused by final camera lens thermal deformation is expressed as:
Wherein, u ', v ' are picture point actual coordinate, and u, v are picture point initial coordinate, δu1、δv1For principal point offset introduce offset error,
δu2、δv2Respectively camera lens thermal distoftion introduces error；
The margin of error due to caused by lens distortion follows the bigger rule of the margin of error remoter from optical center, picture at center in figure
The picture point offset that generates in temperature changing process of point is based on principal point offset error, therefore, with this four points not equality of temperature
The mean approximation for spending lower offset is considered image overall offset amount, by the way of fitting of a polynomial, solves principal point offset
Error varies with temperature curve；Lifting thermophase picture point curve of deviation is subjected to piecewise fitting, wherein Δ u is in lifting thermophase
Change curve obtains ideal fitting result using 3 rank multinomials, and only needs for Δ v in the change curve of lifting thermophase
It wants second order polynomial both to obtain ideal fitting result, is shown in formula (2) based on this principal point offset error model:
Wherein, a1、b1、c1、d1、a2、b2、c2It for principal point heat affecting offset error coefficient, is obtained by lot of experimental data regression analysis
7 penalty coefficients arrived；
For camera lens thermal distoftion introduce error, picture point offset form meet radial distortion and tangential distortion it is superimposed as a result,
Therefore the distortion model is also to form camera lens thermal distoftion error model by camera lens first order radial distortion and second order centrifugal distortion, with routine
Camera lens itself distortion difference is that three distortion factors to be asked not are constant, but changes, mirror with camera lens temperature change
Head thermal distoftion error model indicates are as follows:
Wherein,(u0,v0) be camera principal point coordinate；
k1For radial distortion parameter, p1、p2For centrifugal distortion parameter, k1、p1、p2Three distortion parameters are related with temperature variation Δ T
Function, three distortion parameters with variation function characterized respectively by three second order polynomials, be expressed from the next respectively:
Wherein, e1、f1、g1、h1、j1、q1、l1、m1、n1The coefficient of respectively three distortion parameter polynomial fittings；
Step 3 solves principal point offset error and camera lens thermal distoftion error coefficient initial value respectively
Parameter, respectively 7 principal point offset error systems are solved for 15 bands are co-existed in two in picture point offset error model
Number a1、b1、c1、d1、a2、b2、c2With 9 camera lens thermal distoftion error coefficient e1、f1、g1、h1、j1、q1、l1、m1、n1；It is asked for parameter
Solution problem first substitutes into formula (2) and formula (3) in formula (1) respectively, wherein Δ u and Δ v and master under different temperatures
Point offset error δu1、δv1It is known；Therefore, Δ u and Δ v after removal principal point offset influences are to miss caused by camera lens thermal distoftion
Difference, Δ u and Δ v after another removal principal point influences respectively are equal to δu2And δv2To acquire three distortion parameters under different temperatures
Changing rule, 9 error compensation coefficient initial values for finally finding out three distortion parameters are respectively e1、f1、g1、h1、j1、q1、l1、m1、
n1；
Formula is substituted into respectively using 7 initial values of principal point offset error coefficient and 9 initial values of camera lens thermal distoftion error coefficient
(1), theoretical offset (the Δ u of feature picture point under different temperatures is found outI,ΔvI) and theoretical offset picpointed coordinate (uI,vI),
In, uI=Δ uI+ u, vI=Δ vI+v；Each characteristic point actual shifts rear image point is found out by picture point actual shifts coordinate (u ', v ') to ask
World coordinates (the X obtainedW1,YW1,ZW1), the theoretical offset coordinates (u being calculated by compensation modelI,vI) find out each characteristic point reason
By the object point world coordinates (X after picture point offset coordinates is calculatedW2,YW2,ZW2)；
Step 4 carries out the accurate solution of all parameters by LM optimization algorithm
World coordinates (X is obtained with theoretical calculationW1,YW1,ZW1) and actually obtain world coordinates (XW2,YW2,ZW2) distance between two points
Minimum optimization aim carries out the accurate of each coefficient of error compensation model by Levenberg-Marquardt optimization algorithm
It solves；Optimization object function is as follows:
Using the picture point migrated image of two heating and cooling cycles stage shooting extract to error deviation picpointed coordinate counted
It calculates, obtains each coefficient of error compensation model of binocular image after the calculating of LM optimization algorithm；
Step 5 is modified the picture point offset error as caused by camera lens thermal deformation
After completing the calculating to each penalty coefficient of picture point offset error compensation model and solving, theoretical error calculations of offset is utilized
When temperature change is calculated in formula in image each picture point theoretical error offset, theoretical error calculations of offset formula are as follows:
Wherein, ui、viFor coordinate after picture point compensation, u ', v ' are picture point actual shifts coordinate, find out δ respectively according to temperature changeu1、
δv1、δu2、δv2This four margins of error, to obtain coordinate (u after picture point error compensationi,vi)；
The theoretical offset error of image picture point under different temperatures is calculated using the camera lens temperature variation data of experiment acquisition, into
And the picture point offset error as caused by camera lens thermal deformation is modified, respectively left and right camera lens thermal deformation leads to picture point
Picpointed coordinate before and after offset error compensation；According to the picpointed coordinate comparison of compensation front and back, picture point compensation model accurately describes mirror
Head thermal deformation leads to picture point offset rule, is modified to picture point offset error under different temperatures.
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