CN107726975B - A kind of error analysis method of view-based access control model stitching measure - Google Patents
A kind of error analysis method of view-based access control model stitching measure Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
- G01B11/005—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates coordinate measuring machines
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N21/00—Investigating or analysing materials by the use of optical means, i.e. using sub-millimetre waves, infrared, visible or ultraviolet light
- G01N21/84—Systems specially adapted for particular applications
- G01N21/88—Investigating the presence of flaws or contamination
- G01N21/93—Detection standards; Calibrating baseline adjustment, drift correction
Abstract
A kind of error analysis method of view-based access control model stitching measure of the present invention belongs to computer vision measurement technical field, is related to a kind of error analysis method of view-based access control model stitching measure.This method is based on laser tracker and binocular vision system carries out stitching measure, multiple common points are arranged in its public view field first, binocular camera acquisition image and the pixel coordinate for extracting image, laser tracker acquire the coordinate of each common point simultaneously, this coordinate value is under world coordinate system.Calculate an influence for the external parameter matrix of pixel error extracted, coordinate value error influence and point coordinate value error influence in coordinate pair point visual coordinate system under under world coordinate system of the error of outer ginseng matrix on point under world coordinate system is calculated again, finally finds out composition error of the tested point under world coordinate system.This method analytic process is simple, and error propagation chain is clear；The layout for optimizing common point according to the error analysis improves the overall precision of measuring system.
Description
Technical field
The invention belongs to computer vision measurement technical fields, are related to a kind of error analysis side of view-based access control model stitching measure
Method
Background technique
With the continuous improvement of the components manufacture level such as aerospace field, auto industry, essence of the people to components
Degree requires higher and higher.The measurement method traditional for these components includes three coordinate machine method, laser radar method, indoor GPS
Method etc., the machine vision method developed in recent years are also answered extensively due to having many advantages, such as that non-contact, measuring speed is fast, precision is high
For aerospace and auto industry field.This method is asked by extracting the pixel coordinate of image shot by camera a little sits in vision
Mark is lower three-dimensional coordinate, then using the transition matrix of visual coordinate system to world coordinate system by point under visual coordinate system three
Dimension coordinate is converted to world coordinate system, and DATA REASONING splicing is completed.There are error when being extracted due to the pixel coordinate of point, this
Error will directly affect coordinate value of the maximal end point under world coordinate system, that is, influence measurement accuracy a little, therefore mentioning about point
The research for taking error to influence final three-dimensional coordinate has weight for the quality for improving Instrument measuring precision and guarantee components
The meaning wanted.
By literature search, Chinese invention patent number: CN 104729534 A, Tan Qimeng, Li Jingdong, Hu Chengwei et al. invention
" the monocular vision error measuring system and limits of error quantization method of cooperative target " patent of invention propose a kind of monocular vision
Error measuring system, analyze calibration of camera internal parameters error, visual indicia point three dimensional space coordinate value obtain error and its
Two-dimensional coordinate position error in tag image is capable of the source of view measurement error, has important meaning for Error Tracing &
Justice, but in the patent and these errors are not specified to the quantitative effect relationship of the three-dimensional coordinate error of maximal end point.Chinese invention
A kind of patent No.: " stereoscopic vision relative measurement system mistake of CN 106323337 A, Liu Zongming, Zhang Yu, Cao Shuqing et al. invention
The patent of invention detailed analysis of poor analysis method " image characteristics extraction precision, focal length stated accuracy, rotation and translation matrix mark
Determine the composition error that precision measures space three-dimensional target point, but only analyzes the error of vision measurement system itself, it can not
When for large parts vision stitching measure, the error analysis of whole system.
Summary of the invention
The present invention to overcome the shortcomings of existing technologies, invents a kind of error analysis method of view-based access control model stitching measure, should
Pixel extraction error is described in detail to each influence for calculating link error, quantitatively by the solution procedure of point coordinate in method
The pixel extraction error that analyzes the precision of maximal end point three-dimensional coordinate under world coordinate system is influenced, calculation formula is simple, easily
In realization, analysis and raising and system layout for vision splicing system precision are of great significance.
The technical solution adopted by the present invention is that a kind of error analysis method of view-based access control model stitching measure, characterized in that should
Method is based on laser tracker and binocular vision system carries out stitching measure, and multiple common points are arranged in its public view field, double
Mesh camera acquisition image and the pixel coordinate for extracting image, the pixel error that quantitative analysis is extracted sit point under world coordinate system
The influence of scale value error；The picture extracted is calculated according to the three-dimensional reconstruction formula of visual coordinate point and Formula of Coordinate System Transformation first
The influence of the plain external parameter matrix of error, the error for then calculating outer parameter matrix miss coordinate value of the point under world coordinate system
Difference, which influences and put the error of coordinate under visual coordinate system, influences coordinate value error of the point under world coordinate system, finally finds out
Composition error of the tested point under world coordinate system；Specific step is as follows for this method:
The first step builds the binocular vision splicing measuring systems based on laser tracker, establishes coordinate system；
Firstly, left and right camera 3,5 is separately fixed on left and right camera support 2,4, then respectively by left and right camera support
It is fixed in the crossbeam arranged on left and right sides of tripod 1；Using the optical center of left camera 3 as the origin of local coordinate system, camera imaging is flat
The u direction in face is the direction x, and optical axis direction is z-axis direction, establishes right-handed coordinate system；Connection is mounted on swashing on laser turntable
Optical tracker system gauge head 8 establishes laser tracker coordinate system as global coordinate system；It is arranged on measured object 6 in public view field
Multiple common points 7 acquire image by binocular camera, and extract the pixel coordinate of image, pass through the reconstruction formula of binocular vision point
The coordinate a little under visual coordinate system is acquired, laser tracker acquires the coordinate of each common point simultaneously, this coordinate value is alive
Under boundary's coordinate system, seek visual coordinate system to world coordinate system transition matrix；
The random error of second step visual coordinate system to world coordinate system transition matrix calculates
1) error that pixel extraction error a little causes a little three-dimensional coordinate under visual coordinate system is calculated first；
By the pixel coordinate (u of known left and right camera1,v1) and (u2,v2) and calibration result, three-dimensional a little is calculated
Coordinate (xv,yv,zv):
Wherein(u01,v01) it is left phase
The principal point coordinate of machine, (u02,v02) be right camera principal point coordinate, fx1、fy1For the equivalent focal length of left camera, fx2、fy2For right phase
The equivalent focal length of machine,For the transition matrix parameter of left camera to right camera.According to above-mentioned Three-dimensional Gravity
Formula is built, when extracting pixel in the picture there are when error, this pixel error will be transmitted to a little by formula (1) in vision
On three-dimensional coordinate under coordinate system, it is located at u1、v1、u2、v2The error of extraction pixel on direction is respectivelyAnd it is irrelevant, then the coordinate value under visual coordinate system is about the covariance for proposing a pixel error
Matrix Cxyz:
Cxyz=JDuv·JT (2)
Wherein, J is the covariance matrix of a little coordinate pair pixel error under visual coordinate system, DuvFor pixel error itself
Covariance matrix,
2) influence of the error of the common point coordinate under computation vision coordinate system to transition matrix
Common point is obtained after the coordinate of visual coordinate system, needs to acquire visual coordinate using three or three or more points
It is the transition matrix to world coordinate system, if taking n (n >=3, n ∈ N) a common point, common point is sat in visual coordinate system and the world
Coordinate under mark system is expressed asWithI=1,2 ... n, Two coordinate system
Transfer algorithm are as follows:
Wherein
For the spin matrix of visual coordinate system to world coordinate system, ψ, θ and φ are respectively the rotation angle around x-axis, y-axis and z-axis,For the translation matrix of visual coordinate system to world coordinate system, two matrixes share 6 unknown parameters.Above-mentioned formula is again
It can be write as:
Since the measurement of common point is there are error,In order to acquire optimal transition matrix, should make each
It is aValue take minimum, enableIndicate transition matrix parameter vector,Indicate common point under visual coordinate system
Coordinate parameters vector, therefore following objective function is constructed to acquire transition matrix:
To set up above-mentioned formula, the derivation about conversion parameter is carried out to f (RT, PC), derivative value should be 0, it may be assumed that
Above-mentioned formula is the implicit function about RT and PC, i.e. existence function relationship between RT and PC, RT=f (PC), according to
Implicit function differentiation rule has:
Other than parameter RT about the covariance matrix for mentioning point tolerance be expressed as CRT:
CRT=GCxyz·GT (8)
Wherein G is local derviation of the parameter RT to PC.
The error calculation of third step tested point coordinate value under world coordinate system
After acquiring outer parameter matrix, tested point can be acquired under visual coordinate system by following formula in world coordinate system
Coordinate value:
Wherein Pwm is three-dimensional coordinate of the tested point under world coordinate system, Pwm=[xwm,ywm,zwm]T, Pvm is tested point
Three-dimensional coordinate under visual coordinate system, Pvm=[xvm,yvm,zvm]T, but since tested point Pvm is under visual coordinate system
Coordinate and transition matrixAll there is error, and mutually indepedent, therefore it should be sought respectively, the alive boundary of tested point is sat
Mark is the error of lower coordinate value；
1) the outer parameter matrix error caused by the coordinate under the alive boundary's coordinate system of tested point of
According to the parameter of the external parameter matrix of formula (9)Carry out derivation:
Wherein, H is the local derviation of tested point parameter outside the coordinate pair under world coordinate system, then tested point is in world coordinate system
Under coordinate for outer parameter matrix covariance matrix indicate are as follows:
CPRT=HCRT·HT (11)
Therefore, coordinate of the tested point under world coordinate system is expressed as about the error of outer parameter:
ERT=trace (CPRT) (12)
Wherein, trace (CPRT) representing matrix CPRTMark；
2) three-dimensional coordinate error caused by being extracted under visual coordinate system as pixel is under the alive boundary's coordinate system of tested point
Coordinate caused by error
Three-dimensional coordinate Pvm=[x according to formula (9) to tested point under visual coordinate systemvm,yvm,zvm]TCarry out derivation:
The then association side of three-dimensional coordinate of the tested point in the coordinate under world coordinate system for tested point under visual coordinate system
Poor matrix is expressed as:
CPvm=LCxyz·LT (14)
Therefore, the errors table of coordinate of the tested point in the coordinate under world coordinate system about tested point under visual coordinate system
It is shown as:
EPvm=trace (CPvm) (15)
Composition error EP is that coordinate of the above-mentioned tested point under world coordinate system is being regarded about outer parameter matrix and tested point
Feel the sum of the error of coordinate under coordinate system, it may be assumed that
EP=ERT+EPvm。 (16)
The beneficial effects of the invention are as follows can quantitative analysis pixel extraction error to point in visual coordinate system and world coordinates
It is the influence of lower coordinate value and the influence to transition matrix error, accurately indicates the precision of different location point；Analytic process
Simply, error propagation chain is clear；The layout that common point can be optimized according to the error analysis improves the whole essence of measuring system
Degree.
Detailed description of the invention
Attached drawing 1 is the systematic schematic diagram of view-based access control model stitching measure.Wherein, 1- tripod, the left camera support of 2-, the left phase of 3-
Machine, the right camera support of 4-, the right camera of 5-, 6- measured object, 7- common point, 8- laser tracker gauge head；OWXWYWZWWorld coordinates
System, OVXVYVZVLocal coordinate system, RV WVisual coordinate system is to world coordinate system spin matrix, TV WVisual coordinate system sits to the world
Mark system translation matrix.
Attached drawing 2 is view-based access control model stitching measure error analysis flow chart.
Specific embodiment
With reference to the accompanying drawing with the technical solution specific embodiment that the present invention will be described in detail.
Embodiment 1 builds the binocular vision splicing measuring systems as shown in Fig. 1 based on laser tracker first, swashs
Optical tracker system gauge head 8 selects Leica AT960MR, measurement range 1-20m.Left camera 3 and right camera 5 select VC-12MC-M,
Resolution ratio 3072*4096, highest frame frequency 60Hz.And binocular vision system is demarcated using gridiron pattern, the camera mark of acquisition
It is as follows to determine parameter: left principal point for camera coordinate value u01=2140.397824, v01=1510.250152；Equivalent focal length fx1=
6447.987913 fy1=6454.015281；Right principal point for camera coordinate value u02=2124.090030, v02=1526.184441,
Equivalent focal length fx2=6417.044403, fy2=6420.363610 and left camera to right camera transition matrixIn the public view field of laser tracker and vision measurement system
Arrange that 9 common points, vision measurement system acquire public point image and any point image, it is alive that laser tracker measures common point
Then coordinate value under boundary's coordinate system is analyzed the error at any point, detailed process is as follows for method:
The random error of first step visual coordinate system to world coordinate system transition matrix calculates
1) error that pixel extraction error a little causes a little three-dimensional coordinate under visual coordinate system is calculated first
Pixel extraction is carried out to the image that camera is shot, obtains the left and right pixel coordinate of all points , and utilize
These coordinate values under visual coordinate system are calculated in formula (1)Picture is set according to experiment condition
Element extracts errorIt is equal and is equal to 0.5, then acquire each point in vision using formula (2)
Covariance matrix under coordinate systemWherein
2) influence of the error of common point coordinate to transition matrix under computation vision coordinate system
9 common points are taken, the coordinate under visual coordinate system and world coordinate system is expressed asWithI=1,2 ... n establish least square objective function according to formula (3)
F (RT, PC) solves to obtain ψ=0.580206, θ=0.306834, φ=- 2.343679, t1=2982.129371, t2=
330.777454, t3=-1482.893136, according to formula (5) visual coordinate system to world coordinate system transition matrixWithRetain all ginsengs in formula (6)
Number establishes the implicit function about function RT=f (PC), and obtains RT according to implicit function differentiation rule, that is, formula (7) and lead to PC
Then number substitutes into the covariance matrix that outer parameter RT is calculated using formula (8) for all known numeric values
Second step tested point coordinate value error calculation under world coordinate system
After acquiring outer parameter covariance matrix, the coordinate of outer parameter matrix and tested point under visual coordinate system is calculated separately
It is worth the influence to the coordinate value under the alive boundary's coordinate system of tested point.
1) outer parameter matrix error caused by the coordinate under the alive boundary's coordinate system of tested point
Its pixel coordinate is shot and extracted to tested point, and pixel coordinate is (u1,v1)=(3215.06,
434.58), (u2,v2)=(2895.27,375.02), and formula (11) are substituted into, tested point is calculated in world coordinates
System under coordinate for outer parameter matrix covariance matrixTo CPRTIt asks
Mark obtains coordinate of the tested point under world coordinate system for the error E of outer parameter matrixRT=0.1221.
2) three-dimensional coordinate error caused by being extracted under visual coordinate system as pixel is under the alive boundary's coordinate system of tested point
Coordinate caused by error
The pixel coordinate of the tested point is substituted into formula (2) to the error matrix for calculating its coordinate under visual coordinate systemIt substitutes into formula (14), and substitutes into outer parameter matrix and acquire tested point in world's seat
The covariance matrix of three-dimensional coordinate of the coordinate for tested point under visual coordinate system under mark systemTo CPvmMark is sought, coordinate of this under world coordinate system is obtained and exists about point
The error E of coordinate under visual coordinate systemPvm=0.0571.
Finally coordinate of the above-mentioned tested point acquired under world coordinate system is being regarded about outer parameter matrix and tested point
Feel that the error of the coordinate under coordinate system is summed according to formula (16), the error for obtaining tested point is EP=0.1792.
Embodiment can in the hope of any tested point in the coordinate under world coordinate system caused by pixel extraction error
Error, the precision for the analysis measurement point that can be quantified are of great significance for the layout of common point, raising system accuracy.
Claims (1)
1. a kind of error analysis method of view-based access control model stitching measure, characterized in that this method is based on laser tracker and binocular
Vision system carries out stitching measure, builds binocular vision system first, multiple common points, binocular phase are arranged in its public view field
Machine acquisition image and the pixel coordinate for extracting image, the pixel error that quantitative analysis is extracted coordinate value under world coordinate system to point
The influence of error；The pixel error pair extracted is calculated according to the three-dimensional reconstruction formula of visual coordinate point and Formula of Coordinate System Transformation
The influence of outer parameter matrix, then the error of outer parameter matrix is calculated on the coordinate value error influence put under world coordinate system and point
Error of coordinate under visual coordinate system influences coordinate value error of the point under world coordinate system, exists finally, finding out tested point
Composition error under world coordinate system；Specific step is as follows for this method:
The first step builds the binocular vision splicing measuring systems based on laser tracker, establishes coordinate system；
Firstly, left and right camera (3,5) is separately fixed on left and right camera support (2,4), then respectively by left and right camera support
It is fixed in the crossbeam arranged on left and right sides of tripod (1)；Using the optical center of left camera (3) as the origin of visual coordinate system, camera at
As plane u direction be the direction x, optical axis direction be z-axis direction, establish visual coordinate system OVXVYVZV；Connection is mounted on laser
Laser tracker gauge head (8) on turntable, establishes laser tracker coordinate system as world coordinate system OWXWYWZW；In public view
Multiple common points (7) are arranged on measured object (6) in, image are acquired by binocular camera, and extract the pixel coordinate of image, are led to
The reconstruction formula for crossing binocular vision point acquires coordinate a little under visual coordinate system, and laser tracker acquires each common point simultaneously
Coordinate, this coordinate value be under world coordinate system, using least square method acquire visual coordinate system to world coordinate system turn
Change matrix；
The random error of second step visual coordinate system to world coordinate system transition matrix calculates
1) error that pixel extraction error a little causes a little three-dimensional coordinate under visual coordinate system is calculated first；
By the pixel coordinate (u of known left and right camera1,v1) and (u2,v2) and calibration result, three-dimensional coordinate a little is calculated
(xv,yv,zv):
Wherein(u01,v01) be left camera master
Point coordinate, (u02,v02) be right camera principal point coordinate, fx1、fy1For the equivalent focal length of left camera, fx2、fy2For right camera etc.
Focal length is imitated,For the transition matrix parameter of left camera to right camera；It is public according to above-mentioned three-dimensional reconstruction
Formula, when extracting pixel in the picture there are when error, this pixel error will be transmitted to a little by formula (1) in visual coordinate
On three-dimensional coordinate under system, it is located at u1、v1、u2、v2The error of extraction pixel on direction is respectivelyAnd it is irrelevant, then the coordinate value under visual coordinate system is about the covariance for proposing a pixel error
Matrix Cxyz:
Cxyz=JDuv·JT (2)
Wherein, J is the covariance matrix of a little coordinate pair pixel error under visual coordinate system, DuvFor the association of pixel error itself
Variance matrix,
2) influence of the error of the common point coordinate under computation vision coordinate system to transition matrix
Common point is obtained after the coordinate of visual coordinate system, needs to acquire visual coordinate system using three or three or more points and arrive
The transition matrix of world coordinate system, if taking n (n >=3, n ∈ N) a common point, common point is in visual coordinate system and world coordinate system
Under coordinate be expressed asWithThe conversion of Two coordinate system
Algorithm are as follows:
WhereinFor view
Coordinate system is felt to the spin matrix of world coordinate system, ψ, θ and φ are respectively the rotation angle around x-axis, y-axis and z-axis,For
To the translation matrix of world coordinate system, two matrixes share 6 unknown parameters for visual coordinate system, and above-mentioned formula can be write as again:
Since the measurement of common point is there are error,In order to acquire optimal transition matrix, each should be madeValue take minimum, enableIndicate transition matrix parameter vector,Indicate common point under visual coordinate system
Coordinate parameters vector, therefore following objective function is constructed to acquire transition matrix:
To set up above-mentioned formula, the derivation about conversion parameter is carried out to f (RT, PC), derivative value should be 0, it may be assumed that
Above-mentioned formula is the implicit function about RT and PC, i.e. existence function relationship between RT and PC, RT=f (PC), according to hidden letter
Number Rule for derivation has:
Other than parameter RT about the covariance matrix for mentioning point tolerance be expressed as CRT:
CRT=GCxyz·GT (8)
Wherein G is local derviation of the parameter RT to PC；
The error calculation of third step tested point coordinate value under world coordinate system
After acquiring outer parameter matrix, tested point can be acquired under visual coordinate system by following formula in the coordinate of world coordinate system
Value:
Wherein Pwm is three-dimensional coordinate of the tested point under world coordinate system, Pwm=[xwm,ywm,zwm]T, Pvm is that tested point is regarding
Feel the three-dimensional coordinate under coordinate system, Pvm=[xvm,yvm,zvm]T, but the coordinate due to tested point Pvm under visual coordinate system
And transition matrixAll there is error, and mutually indepedent, therefore it should be sought respectively to the alive boundary's coordinate system of tested point
The error of lower coordinate value；
1) the outer parameter matrix error caused by the coordinate under the alive boundary's coordinate system of tested point of
According to the parameter of the external parameter matrix of formula (9)Carry out derivation:
Wherein, H is the local derviation of tested point parameter outside the coordinate pair under world coordinate system, then tested point is under world coordinate system
Coordinate indicates the covariance matrix of outer parameter matrix are as follows:
CPRT=HCRT·HT (11)
Therefore, coordinate of the tested point under world coordinate system is expressed as about the error of outer parameter:
ERT=trace (CPRT) (12)
Wherein, trace (CPRT) representing matrix CPRTMark；
2) three-dimensional coordinate error caused by being extracted under visual coordinate system as pixel is to the seat under the alive boundary's coordinate system of tested point
Error caused by mark
Three-dimensional coordinate Pvm=[x according to formula (9) to tested point under visual coordinate systemvm,yvm,zvm]TCarry out derivation:
The then covariance square of three-dimensional coordinate of the tested point in the coordinate under world coordinate system for tested point under visual coordinate system
Matrix representation are as follows:
CPvm=LCxyz·LT (14)
Therefore, the error of coordinate of the tested point in the coordinate under world coordinate system about tested point under visual coordinate system indicates
Are as follows:
EPvm=trace (CPvm) (15)
Composition error EP is that coordinate of the above-mentioned tested point under world coordinate system is sat about outer parameter matrix and tested point in vision
The sum of the error of coordinate under mark system, it may be assumed that
EP=ERT+EPvm (16)。
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