CN106323337B - A kind of stereoscopic vision relative measurement system error analysis method - Google Patents
A kind of stereoscopic vision relative measurement system error analysis method Download PDFInfo
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Abstract
The invention discloses a kind of stereoscopic vision relative measurement system error analysis methods, comprise the following steps: S1, establish the space three-dimensional target point measurement model of stereoscopic vision relative measurement system；S2 analyzes the image characteristics extraction precision of stereoscopic vision relative measurement system；S3 analyzes the focal length stated accuracy of stereoscopic vision relative measurement system；S4 analyzes the spin matrix stated accuracy of stereoscopic vision relative measurement system；S5 analyzes the translation vector stated accuracy of stereoscopic vision relative measurement system；S6 measures synthetical error analysis to the space three-dimensional target point of stereoscopic vision relative measurement system.The present invention can be analyzed from spin matrix and translation vector stated accuracy between focal length stated accuracy, vertical vision camera pair.
Description
Technical field
The present invention relates to spacecraft super close distance relative measurement techniques, particularly belong to a kind of stereoscopic vision relative measurement system
Error analysis method.
Background technique
By in-orbit service, the in-orbit service aircraft that can use advantage of lower cost carries out failure member to inert satellite
The replacement of device restores the function of satellite, or carries out fuel make up, prolongs its service life.And in-orbit service task is completed,
Primarily on condition that can find target in super close distance viability, and the relative status information for obtaining target is supplied to control system
System completes corresponding control task.Therefore, spacecraft super close distance relative measurement technique is the success for carrying out in-orbit service task
Whether key technology.
Vertical vision relative measurement is to utilize two cameras from different perspectives while obtaining target image, is based on image characteristic point
Parallax, the three-dimensional geometric information of target signature, including azimuth information and range information are obtained according to trigonometry principle.Stereopsis
Feel the performance of relative measurement system mainly with camera properties and parameter, between two cameras spatial position and measured point and measurement be
The position of system is related.In actual application, once system calibrating, must just keep relatively fixed, focal length, the camera of camera
Between baseline and orientation cannot all change, so, can maximum journey concerning it to the optimization design of system structure parameter
Degree plays the key of measurement performance.
Summary of the invention
The object of the present invention is to provide a kind of stereoscopic vision relative measurement system error analysis methods, not only only give figure
Influence as feature extraction precision to measurement accuracy, also respectively from spin matrix between focal length stated accuracy, vertical vision camera pair
It is analyzed with translation vector stated accuracy, and has finally obtained the survey of stereoscopic vision relative measurement system space three-dimensional target point
Measure the analytical expression of error analysis.
In order to achieve the goal above, the present invention is achieved by the following technical solutions:
A kind of stereoscopic vision relative measurement system error analysis method, which is characterized in that comprise the following steps:
S1 establishes the space three-dimensional target point measurement model of stereoscopic vision relative measurement system；
S2 analyzes the image characteristics extraction precision of stereoscopic vision relative measurement system；
S3 analyzes the focal length stated accuracy of stereoscopic vision relative measurement system；
S4 analyzes the spin matrix stated accuracy of stereoscopic vision relative measurement system；
S5 analyzes the translation vector stated accuracy of stereoscopic vision relative measurement system；
S6 measures synthetical error analysis to the space three-dimensional target point of stereoscopic vision relative measurement system.
The stereoscopic vision relative measurement system is the first stereo vision camera and the second solid of horizontal symmetrical setting
Vision camera.
In the step S1, if the first stereo vision camera o-xyz is located at the origin of world coordinate system and without spin,
Image coordinate system is Ol-XlYl, effective focal length f1, the second stereo vision camera coordinate system is or-xryrzr, image seat
Mark system is Or-XrYr, effective focal length fr, had by camera Perspective transformation model:
O-xyz coordinate system and or-xryrzrMutual alignment relation between coordinate system can pass through space conversion matrix MlrTable
It is shown as:
Mlr=[R T]
In formula,Respectively o-xyz coordinate system and or-xryrzrRotation between coordinate system
Translation transformation vector between matrix and its origin, it is known that, for the spatial point in o-xyz coordinate system, 2 camera image planes points it
Between corresponding relationship are as follows:
ρrIt is expressed as a nondimensional scale factor.
Then have, space objective point coordinate in step S1 are as follows:
Stereoscopic vision relative measurement system is simplified, it is assumed that fl=fr=f, while the first stereo vision camera and
Two stereo vision camera horizontal symmetricals are placed, it may be assumed that
Obtain following abbreviation equation:
Spatial point in the step S2 determines forward error in the picture point difference that a pair of of stereo vision camera projects.
Measurement error of the image characteristics extraction precision to objective point in the step S2 are as follows:
Wherein d is actual range, and f is camera focus, and Δ x is picture point changes in coordinates small quantity.
Measurement error of the step S3 mid-focal length algnment accuracy to objective point are as follows:
Wherein Δ f is focal length variations small quantity.
The step S4 specifically: according to the relationship between Eulerian angles and spin matrix, describe spin matrix, analysis rotation
Measurement error of the stated accuracy of corner to objective point, measurement of the stated accuracy of the rotation angle to objective point
Error are as follows:
Wherein Δ r is that attitude angle changes small quantity, gmaxIntermediate function derivation maximum value.
Measurement error of the translation vector stated accuracy to objective point in the step S5 are as follows:Wherein Δ txChange small quantity for horizontal direction translation vector.
The step S6 specifically: establish composition error TRANSFER MODEL, analyze stereoscopic vision relative measurement system error
Composition error, the composition error are as follows:
Compared with prior art, the present invention having the advantage that
For the present invention relative to traditional error analysis method, the present invention not only only gives image characteristics extraction precision to survey
The influence of accuracy of measurement, also respectively from spin matrix and translation vector stated accuracy between focal length stated accuracy, vertical vision camera pair
It is analyzed, and has finally obtained the resolution table of stereoscopic vision relative measurement system space three-dimensional target point analysis of measurement errors
Up to formula.The achievement has important directive significance to the design and engineer application of stereoscopic vision relative measurement system system.
Detailed description of the invention
Fig. 1 is a kind of schematic diagram of stereoscopic vision relative measurement system of the present invention；
Distance change schematic diagram of the Fig. 2 between stereoscopic vision relative measurement system of the present invention and measured target.
Specific embodiment
The present invention is further elaborated by the way that a preferable specific embodiment is described in detail below in conjunction with attached drawing.
A kind of stereoscopic vision relative measurement system error analysis method, comprises the following steps:
S1 establishes the space three-dimensional target point measurement model of stereoscopic vision relative measurement system；
S2 analyzes the image characteristics extraction precision of stereoscopic vision relative measurement system；
S3 analyzes the focal length stated accuracy of stereoscopic vision relative measurement system；
S4 analyzes the spin matrix stated accuracy of stereoscopic vision relative measurement system；
S5 analyzes the translation vector stated accuracy of stereoscopic vision relative measurement system；
S6 measures synthetical error analysis to the space three-dimensional target point of stereoscopic vision relative measurement system.
Above-mentioned stereoscopic vision relative measurement system is the stereo vision camera of a pair of of horizontal symmetrical setting.
It is located at the origin of world coordinate system and without spin as shown in Figure 1, setting the first stereo vision camera o-xyz, image
Coordinate system is Ol-XlYl, effective focal length f1, second camera coordinate system is or-xryrzr, image coordinate system Or-XrYr, effectively burnt
Away from for fr, had by camera Perspective transformation model:
O-xyz coordinate system and or-xryrzrMutual alignment relation between coordinate system can pass through space conversion matrix MlrTable
It is shown as:
Mlr=[R T]
In formula,Respectively o-xyz coordinate system and or-xryrzrRotation between coordinate system
Translation transformation vector between matrix and its origin.It is found that for the spatial point in o-xyz coordinate system, 2 camera image planes points it
Between corresponding relationship are as follows:
r1 r2 r3…r9Indicate the element of spin matrix, tx ty tzIt is expressed as the element of translation vector, ρrIt is expressed as a nothing
The scale factor of dimension.
According to above-mentioned, have, space objective point coordinate in step S1 are as follows:
It is thus known that focal length fl,frWith spatial point in the magazine image coordinate in left and right, as long as finding out spin matrix R peace
Moving vector T can be obtained by the three dimensional space coordinate of testee point.
Rational Simplification is carried out to stereoscopic vision relative measurement system, it is assumed that fl=fr=f, while two stereo vision cameras
Horizontal symmetrical is placed, it may be assumed that
For Stereo Vision Measurement System, z is main error for compared to x and y to error, thus the present invention
The influence that each factor of selective analysis generates z to error obtains following abbreviation equation:
Spatial point in above-mentioned steps S2 determines forward error in the picture point difference that a pair of of stereo vision camera projects,
When measured target is remoter apart from camera, two picture point coordinate differences of projection are smaller, and the error of resolving is bigger, meanwhile, two phases
Image difference between machine is with apart from relevant, and distance is remoter, and image difference is smaller.
Z to error determined by spatial point in the picture point difference that two cameras project, got in measured target apart from camera
When remote, two picture point coordinate difference (X of projectionr-Xl) smaller, the error of resolving is bigger.Assuming that X '=Xr-Xl, then solution formula
It reforms into:
The precision variation of z caused by Δ X slight error is analyzed upper formula derivation.
Here the image difference between two cameras be with apart from relevant, it is assumed that d is actual range, then exists:
So having, measurement error of the image characteristics extraction precision to objective point in above-mentioned step S2 are as follows:
Wherein d is actual range, and f is camera focus, and Δ x is that picture point changes in coordinates is small
Amount.
In the step S3, the focal length value that camera optical system is individually demarcated cannot be used directly to carry out stereoscopic vision
Measurement uses, because therefore, it is necessary to specific devices there is no the installation error in view of that may introduce after assembling with detector
Focal length value after re-scaling optical system and imaging detector assembly with algorithm, analyzes focal length stated accuracy to objective
Point measurement error bring influences.
The focal length value that camera lens is individually demarcated cannot be used directly to carry out the calculating of vision measurement, because not considering
Installation error with that may introduce after detector assembly, the coke of camera lens is re-scaled therefore, it is necessary to specific device and algorithm
Away from value, but calibration result still includes certain calibration error.Next by analysis focal length algnment accuracy to measurement error
It influences.
FormulaIt is available to f derivation:
By formula:
Thus, formula (2) is readily modified as
Wherein Δ f is focal length variations small quantity.
Formula (3) is measurement error of the focal length algnment accuracy to objective point
In the step S4, during stereo-visiuon measurement, stand between vision camera pair known to rotation relationship conduct
Condition.The rotation angle and origin relative coordinate values demarcated between two measurement cameras by some standard feature points.But
There is a certain error in practical calibration process, and the rotation angle between two cameras is indicated with spin matrix, there is 9 unknown numbers,
But only three degree of freedom, i.e. pitch angle, yaw angle, roll angle between two cameras, according to Eulerian angles and spin matrix it
Between relationship, describe spin matrix, analyze measurement error of the stated accuracy to objective point of rotation angle.
During stereoscopic vision relative measurement, posture is as known conditions between two measurement cameras.Pass through some marks
Quasi- characteristic point (known distance, it is known that null point coordinate value) is come the rotation angle and origin relative coordinate demarcated between two measurement cameras
Value.But in practical calibration process, there is a certain error, below by the rotation angle of analysis calibration and translation accuracy of measurement to survey
Measuring error bring influences.Rotation angle between two cameras indicates there are 9 unknown numbers with spin matrix, but only there are three
Freedom degree, i.e. pitch angle, yaw angle, roll angle between two cameras.For simplifying the analysis, it is assumed here that caused due to calibration
Three angle errors it is identical.Then according to the relationship between Eulerian angles and spin matrix, spin matrix are as follows:
R, T are substituted into formulaIt can then obtain:
When spin matrix does not have error, true value are as follows:
Then error:
Since actual error is smaller, when posture calibrated error is 0.05 ° between two cameras, appearance between two cameras
State calibrated error is smaller, therefore denominator (X in above formularXl+XrYl-fYl-f2) Δ r be much smaller than Xrf-XlF can be ignored.
Then formulaIt can be rewritten as:
Image difference is converted into distance, then formulaIt can be rewritten as:
It enables:
G=XrXl+XrYl-fYl-f2
Seek the extreme value of function g, it is assumed that the detector resolution that we select is h*w, and picture dot is having a size of pix, then Xr,Xl
And Yr,YlValue range is respectively
By formulaSubstitute into formula g=XrXl+XrYl-fYl-f2It is then available:
Respectively to X in above formulalAnd YlLocal derviation is sought, analytic function is most worth, it obtains:
According to analysis it is found that Xr,XlAnd Yr,YlStationary point not in value range, therefore, most value on two boundaries, i.e.,
So measurement error of the stated accuracy of rotation angle to objective point are as follows:Wherein Δ
R is that attitude angle changes small quantity, gmaxIntermediate function derivation maximum value.
In the S5, during stereo-visiuon measurement, positional relationship is found between vision camera pair as known conditions,
The positional relationship demarcated between two measurement cameras by some standard feature points, but there are one in practical calibration process
Fixed error, the positional relationship between two cameras indicate there are 3 unknown numbers, but typically only consider with translation vector
The single positional relationship of horizontal direction, herein under the premise of analyze translation vector stated accuracy to objective point measurement error
Bring influences.
Mainly in the x direction due to two camera baselines, not distance is substantially thought in the direction y and z, in practical calculating
X is affected to measurement error to the precision of calibration in the process, and thus, our Main Analysis are by txStated accuracy is to final measurement
As a result influence, enables tx=t 'x+Δt。
Wherein txInclude certain error, formulaIn to txDerivation, available:
Equally, picture point difference is converted into distance, then available translation vector stated accuracy is to objective point
Measurement error:
Wherein Δ txChange small quantity for horizontal direction translation vector.
Above-mentioned step S6 specifically: in influence stereoscopic vision relative measurement system space three-dimensional target point measurement model
After each component is analysed item by item, composition error TRANSFER MODEL is established, analyzes the synthesis of stereoscopic vision relative measurement system error
Error,
According to formula of error transmission:
Composition error can be obtained:
In conclusion a kind of stereoscopic vision relative measurement system error analysis method of the present invention, not only only gives image
Influence of the feature extraction precision to measurement accuracy, also respectively from spin matrix between focal length stated accuracy, vertical vision camera pair and
Translation vector stated accuracy is analyzed, and has finally obtained the measurement of stereoscopic vision relative measurement system space three-dimensional target point
The analytical expression of error analysis.
It is discussed in detail although the contents of the present invention have passed through above preferred embodiment, but it should be appreciated that above-mentioned
Description is not considered as limitation of the present invention.After those skilled in the art have read above content, for of the invention
A variety of modifications and substitutions all will be apparent.Therefore, protection scope of the present invention should be limited to the appended claims.
Claims (7)
1. a kind of stereoscopic vision relative measurement system error analysis method, which is characterized in that comprise the following steps:
S1 establishes the space three-dimensional target point measurement model of stereoscopic vision relative measurement system；
S2 analyzes the image characteristics extraction precision of stereoscopic vision relative measurement system；
S3 analyzes the focal length stated accuracy of stereoscopic vision relative measurement system；
S4 analyzes the spin matrix stated accuracy of stereoscopic vision relative measurement system；
S5 analyzes the translation vector stated accuracy of stereoscopic vision relative measurement system；
S6 measures synthetical error analysis to the space three-dimensional target point of stereoscopic vision relative measurement system；The stereoscopic vision
Relative measurement system is the first stereo vision camera and the second stereo vision camera of horizontal symmetrical setting；
Measurement error of the image characteristics extraction precision to objective point in the step S2 are as follows:
Wherein d is actual range, and f is camera focus, and Δ x is picture point changes in coordinates small quantity.
2. stereoscopic vision relative measurement system error analysis method as described in claim 1, which is characterized in that the step
In S1, if the first stereo vision camera o-xyz is located at the origin of world coordinate system and without spin, image coordinate system Ol-
XlYl, effective focal length f1, the second stereo vision camera coordinate system is or-xryrzr, image coordinate system Or-XrYr, have
Effect focal length is fr, had by camera Perspective transformation model:
O-xyz coordinate system and or-xryrzrMutual alignment relation between coordinate system can pass through space conversion matrix MlrIt indicates
Are as follows:
Mlr=[R T]
In formula,Respectively o-xyz coordinate system and or-xryrzrSpin matrix between coordinate system and
Translation transformation vector between its origin, it is known that, pair for the spatial point in o-xyz coordinate system, between 2 camera image planes points
It should be related to are as follows:
ρrIt is expressed as a nondimensional scale factor；
Then have, space objective point coordinate in step S1 are as follows:
Stereoscopic vision relative measurement system is simplified, it is assumed that fl=fr=f, while the first stereo vision camera and second is stood
Body vision camera horizontal symmetrical is placed, it may be assumed that
Obtain following abbreviation equation:
3. stereoscopic vision relative measurement system error analysis method as described in claim 1, which is characterized in that the step S2
In the picture point difference that projects in a pair of of stereo vision camera of spatial point determine forward error.
4. stereoscopic vision relative measurement system error analysis method as described in claim 1, which is characterized in that the step S3
Measurement error of the mid-focal length algnment accuracy to objective point are as follows:
Wherein Δ f is focal length variations small quantity.
5. stereoscopic vision relative measurement system error analysis method as described in claim 1, which is characterized in that the step
S4 specifically: according to the relationship between Eulerian angles and spin matrix, describe spin matrix, analyze the stated accuracy of rotation angle to three
Tie up the measurement error of target point, the measurement error of the stated accuracy of the rotation angle to objective point are as follows:
Wherein Δ r is that attitude angle changes small quantity, gmaxIntermediate function derivation maximum value.
6. stereoscopic vision relative measurement system error analysis method as described in claim 1, which is characterized in that the step
Measurement error of the translation vector stated accuracy to objective point in S5 are as follows:
Wherein Δ txChange small quantity for horizontal direction translation vector.
7. stereoscopic vision relative measurement system error analysis method as described in claim 1, which is characterized in that the step
S6 specifically: establish composition error TRANSFER MODEL, analyze the composition error of stereoscopic vision relative measurement system error, described is comprehensive
Close error are as follows:
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