CN105354853B - Two-step method based on non-coplanar control straight line imaging demarcation camera parameter - Google Patents
Two-step method based on non-coplanar control straight line imaging demarcation camera parameter Download PDFInfo
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- CN105354853B CN105354853B CN201510854425.3A CN201510854425A CN105354853B CN 105354853 B CN105354853 B CN 105354853B CN 201510854425 A CN201510854425 A CN 201510854425A CN 105354853 B CN105354853 B CN 105354853B
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Abstract
The present invention relates to a kind of two-step method based on non-coplanar control straight line imaging demarcation camera parameter.The demarcation of linear dimensions and the calculating of aberration coefficients are carried out using linear feature.Its key step is as follows：（1）Extraction control straight line imaging features point, is fitted graph line；（2）Camera linear dimensions is calculated using graph line and control straight line；（3）Re-projection imaging is carried out to control straight line；（4）Aberration coefficients are calculated using re-projection straight line, intrinsic parameter and actual image point；（5）Correct actual image point；（6）Revised picture point again restrain by fitting a straight line, loop iteration to result；（7）Circulation calculates aberration coefficients again after terminating.The present invention is prevalent in shooting scene in view of linear feature, and linear feature has the advantage more stable, extraction accuracy is higher compared to point feature, it is proposed that the method demarcated using linear feature to camera parameter, Method And Principle is simple, is easily achieved, convenient and practical, precision is preferable.
Description
Technical field
The invention belongs to computer vision field and videographic measurment field, is related to one kind and utilizes linear feature to carry out camera ginseng
The method of several demarcation.
Background technology
It is that computer vision and shooting are surveyed that the information such as three-dimensional structure, the measurement of testee are obtained from two-dimensional image information
One of basic task of amount.And from two-dimensional image information recover testee three-dimensional information be testee imaging inverse mistake
Journey, this inverse process needs the corresponding relation between the three-dimensional information of clear and definite two-dimensional image information and testee, i.e., clearly by picture
The parameter of machine is come the camera imaging model that describes, namely the demarcation of camera parameter.In videographic measurment, point feature, which is prevalent in, to be taken the photograph
In image field scape, the two-step method that camera parameter calibration is carried out based on point feature is more conventional, but linear feature is also generally deposited
In scene is imaged, and linear feature has the advantages of more stable, extraction accuracy is higher compared to point feature, therefore is imaging
Algorithm based on linear feature demarcation camera parameter in measurement is also study hotspot.It is typically based on the two-step method of linear feature
In, the first step carries out fitting a straight line to the point in control straight line imaging, obtains ideal line parameter, and then it is linear to demarcate camera
Parameter；Graph line with distortion is fitted to conic section and carries out aberration coefficients with ideal image straight line simultaneous by second step
Solve, what this step actually obtained be by conic fitting into straight line and ideal line between aberration coefficients, and non-band
There are the actual image point of distortion and the aberration coefficients of ideal line.
The content of the invention
The invention provides a kind of linear feature information of generally existing in scene based on shooting to carry out camera parameter calibration
Method, this method require space control straight line it is non-coplanar.Method mainly divides two parts, when the demarcation of camera linear dimensions,
The demarcation of camera parameter is realized using the imaging relations of non-coplanar control straight line and its straight line of image formation；Second, actual image point and ideal
The solution of aberration coefficients between straight line.
The present invention adopts the following technical scheme that：
The demarcation of camera parameter, its specific steps are realized using the imaging relations of non-coplanar control straight line and its straight line of image formation
Including：Multiple linear feature points from image after extraction control straight line imaging, carry out fitting a straight line, obtain graph line system
Number, then using controlling straight line parameter to demarcate camera linear dimensions with graph line coefficient, control straight line is subjected to re-projection and obtained
To ideal line coefficient, simultaneous intrinsic parameter, control straight line parameter and distortion picture point calculate aberration coefficients, then with the aberration resolved
Coefficient amendment distorts picture point, and fitted figure as straight line coefficient, restrain, and finally calculates aberration again by such loop iteration to result again
Coefficient.
1st, it is fitted graph line
Multiple characteristic points from image after extraction control straight line imaging, multiple characteristic points are carried out with least square method
Fitting a straight line, obtain graph line coefficient；
2nd, do not consider aberration, camera linear dimensions is calculated using graph line coefficient and control straight line parameter
The expression-form for controlling straight line to use two sides to intersect, will control straight line parameterWith figure
As straight line coefficientFollowing two equations are obtained by imaging relations simultaneous:To cross a certain flat of control straight line
The parameter in face；To cross the parameter of another plane of control straight line；Control what straight line can be intersected with two planes
Form provides, i.e.,Simultaneous gets up to represent a control straight line.
The expression-form for controlling straight line to use two sides to intersect
Graph line form is
Projection matrix
Project to obtain by perspective
By coordinate nonhomogeneousization
Graph line equation is substituted into obtain
Will control
Y, Z in linear equation represent to obtain with X
Above formula is substituted into arrange to obtain
For following two equation equal sign
Left end simplify expression；
Want above formula establishment coefficient to set up for any X, F, G are 0, obtain following formula
In general, variable replacement thus is carried out to above formulaObtain
On intermediate variableEquation.One control straight line can list two equations, and a plurality of control straight line can be listed
System of linear equations, with least square solution system of linear equations, obtain intermediate variable, then byObtain projection matrix,,, decompose projection matrixObtain camera linear dimensions：Picture
Principal point, equivalent focal length, Eulerian angles, translation vector。
Parameter declaration：
To cross the parameter of a certain plane of control straight line；
To cross the parameter of another plane of control straight line；
Control straight line can be provided with the form that two planes intersect, i.e.,Simultaneous gets up can
To represent a control straight line.
Represent the point on control straight line；
For projection matrix,For the element of projection matrix；
To correspond to Points on Straight Line on the plane of delineationIdeal image point coordinate；
To correspond to Points on Straight Line on the plane of delineationThe actual image point coordinate for having distortion；
It is picture point homogeneous coordinates form than the row factor；
For following two equation equal sign
Left end simplify expression；
For principal point；
For equivalent focal length；
For Eulerian angles；
For translation vector；
For aberration coefficients；
Aberration on respectively x, y direction；
For the normalized image coordinate of ideal image point；
For the normalized image coordinate of actual image point；
3rd, re-projection is carried out to control straight line using linear dimensions
According to projection imaging relation straight line will be controlled to carry out re-projection as ideal line：
By following formula：
Graph line coefficient is put forward to obtain by arrangement：
Graph line, only two frees degree, therefore graph line can be solved by above formula equation group
Coefficient, as ideal image straight line coefficient.
4th, aberration coefficients, the step are calculated using re-projection straight line, intrinsic parameter and actual image point（4）Using throwing again
Shadow straight line coefficient, by step（2）Obtained intrinsic parameter, the fact characteristic point of extraction and control straight line parameter, which is combined, carries out solution picture
Poor coefficient, rather than using ideal image point or fitting conic section, be specially：
Aberration model is
WhereinFor actual image point,For ideal image point,For aberration coefficients,、For equivalent Jiao of camera
Away from.
For normalized image coordinate.
Aberration is the normalization coordinate definition with ideal image point herein, but in physical condition, we can not clearly know
The accurate coordinates of road ideal image point, in two-step method iteration, because actual image point is constantly corrected and gradually in ideal image point, thus
Also it is equivalent to gradually in defining aberration model with ideal image point, thus actual image point normalizing consistent with actual aberration model
Change the aberration of coordinate definition：
Bring its aberration model into ideal image linear equation, arrange
A point on straight line can list an equation on aberration coefficients, and multiple points on straight line can be listed accordingly
System of linear equations, aberration coefficients are obtained with least square solution system of linear equations。
5th, amendment distortion picture point
After obtaining aberration coefficients, aberration coefficients are substituted into aberration model
To actual image pointIt is modified.
6th, graph line is fitted again, and loop iteration solves camera linear dimensions
Fitting a straight line, repeat step are re-started to revised picture point（1）, loop iteration is stable to result, exits and follows
Ring.
7th, aberration coefficients are solved again
Because during loop iteration, the actual image point being corrected moves closer to ideal image point, is thus followed for the last time
The difference coefficient that ring obtainsZero should be leveled off to, so needing to recalculate aberration coefficients.At the same time, due to being corrected
Picture point afterwards moves closer to ideal image point, can use the picture point of last amendment as ideal image point, extraction obtain without
The picture point of amendment is crossed as actual image point, substitute into aberration model and arrange to obtain：
One point can list two equations on aberration coefficients, and multiple spot can list corresponding system of linear equations, fortune
Final aberration coefficients are obtained with least square solution system of linear equations。
The present invention is prevalent in shooting scene in view of linear feature, and linear feature is more steady with respect to point feature
Calmly, precision is higher, and Method And Principle is simple, is easily achieved, and precision is preferable.
Brief description of the drawings
Fig. 1 is this method flow chart.
Embodiment
The invention provides a kind of linear feature information of generally existing in scene based on shooting to carry out camera parameter calibration
Method, this method require space control straight line it is non-coplanar.Method mainly divides two parts, when the demarcation of camera linear dimensions,
Second, the solution of the aberration coefficients between actual image point and ideal line.It is multiple straight after extraction control straight line imaging from image
Line feature point, fitting a straight line is carried out, obtains graph line coefficient, then using controlling straight line parameter and graph line coefficient to demarcate
Camera linear dimensions, control straight line is then subjected to re-projection and obtains ideal line coefficient, simultaneous intrinsic parameter, control straight line parameter
Aberration coefficients are calculated with distortion picture point, then with the aberration coefficients amendment distortion picture point resolved, fitted figure is as straight line coefficient again,
Such loop iteration to result restrains, and finally calculates aberration coefficients again.
Claims (6)
1. based on the two-step method of non-coplanar control straight line imaging demarcation camera parameter, using the mark of linear feature progress linear dimensions
Fixed and aberration coefficients calculating, it is characterised in that multiple characteristic points first from image after extraction control straight line imaging, carry out
Fitting a straight line, graph line coefficient is obtained, then to demarcate camera linear as straight line coefficient using straight line parameter and fitted figure is controlled
Parameter, then re-projection control straight line, aberration coefficients are calculated using re-projection straight line, intrinsic parameter and actual image point, then with solution
The aberration coefficients amendment distortion picture point of calculation, is fitted graph line, such loop iteration, specific steps include again：
(1) characteristic point after straight line imaging is controlled on image is extracted, fitting a straight line is carried out and obtains graph line coefficient,
(2) camera linear dimensions is demarcated with graph line coefficient and control straight line parameter,
(3) linear dimensions re-projection straight line is utilized,
(4) aberration coefficients are calculated using re-projection straight line, intrinsic parameter and actual image point,
(5) amendment distortion picture point,
(6) graph line is fitted again, and loop iteration to result is restrained, and fitting a straight line is re-started to revised picture point, weight
Multiple step (1), loop iteration is stable to result, exits circulation,
(7) aberration coefficients are calculated again.
2. the two-step method according to claim 1 based on non-coplanar control straight line imaging demarcation camera parameter, its feature exist
In the step (2) is demarcated with graph line coefficient and control straight line parameter to camera linear dimensions, is specially：
The expression-form for controlling straight line to use two sides to intersect is straight with image by control straight line parameter A, B, C, D, A ', B ', C ', D '
Linear system number a, b, c obtain following two equations by imaging relations simultaneous:
The expression-form for controlling straight line to use two sides to intersect
Graph line form is
Projection matrix
Project to obtain by perspective
By coordinate nonhomogeneousization
Graph line equation is substituted into obtain
a(m0X+m1Y+m2Z+m3)+b(m4X+m5Y+m6Z+m7)+c(m8X+m9Y+m10Z+m11)=0
Y, Z in linear equation will be controlled to represent to obtain with X
Above formula is substituted into arrange to obtain
F (M, A, B, C, D, A', B', C', D') X+G (M, A, B, C, D, A', B', C', D')=0
Want above formula establishment coefficient to set up for any X, F, G are 0, obtain following formula
m11=Tz＞ 0, variable replacement thus is carried out to above formulaObtain intermediate variable siEquation
One control straight line can list two equations, and a plurality of control straight line can list system of linear equations, with least square method
System of linear equations is solved, obtains intermediate variable si, then by siProjection matrix M is obtained,mi=m11×
si(i=0,1 ..., 10), decompose projection matrix M and obtain camera linear dimensions：Principal point Cx,Cy, equivalent focal length Fx,Fy, Eulerian angles
Ax,Ay,Az, translation vector Tx,Ty,Tz；Parameter declaration：
A, B, C, D were the parameter for a certain plane for controlling straight line；
A ', B ', C ', D ' were the parameter for another plane for controlling straight line；
Control straight line can be provided with the form that two planes intersect, i.e. A, B, C, D, A ', B ', C ', D ' simultaneous gets up can be with table
Show a control straight line；
X, Y, Z represent the point on control straight line；
M is projection matrix, mi(i=0 ..., 11) is the element of projection matrix；
To correspond to Points on Straight Line X, Y, Z ideal image point coordinate on the plane of delineation；
X, y are the actual image point coordinate for having distortion for corresponding to Points on Straight Line X, Y, Z on the plane of delineation；
It is picture point homogeneous coordinates form than the row factor；
F (M, A, B, C, D, A', B', C', D'), G (M, A, B, C, D, A', B', C', D') are a left side for following two equation equal sign
End simplifies expression；
Cx,CyFor principal point；
Fx,FyFor equivalent focal length；
Ax,Ay,AzFor Eulerian angles；
Tx,Ty,TzFor translation vector；
k0~k4For aberration coefficients；
δx,δyAberration on respectively x, y direction；
For the normalized image coordinate of ideal image point；
xd,ydFor the normalized image coordinate of actual image point.
3. the two-step method according to claim 1 based on non-coplanar control straight line imaging demarcation camera parameter, its feature exist
In the step (3) carries out re-projection to control straight line using linear dimensions and is specially：
According to projection imaging relation straight line will be controlled to carry out re-projection as ideal line：
By following formula：
Graph line coefficient is put forward to obtain by arrangement：
Graph lineOnly two frees degree, therefore graph line coefficient can be solved by above formula equation group
A, b, c, as ideal image straight line coefficient.
4. the two-step method according to claim 1 based on non-coplanar control straight line imaging demarcation camera parameter, its feature exist
In, the step (4) using re-projection straight line coefficient, the intrinsic parameter obtained by step (2), extraction fact characteristic point and
Control straight line parameter, which is combined, to be carried out solving aberration coefficients k0~k4, rather than using ideal image point or conic section is fitted, specifically
For：
Aberration model is
Wherein x, y are actual image point,For ideal image point, k0~k4For aberration coefficients, Fx、FyFor camera equivalent focal length,
For normalized image coordinate
Aberration is the normalization coordinate definition with ideal image point herein, but in physical condition, we can not clearly know reason
Imagine the accurate coordinates of point, in two-step method iteration, due to actual image point constantly corrected and gradually in ideal image point, thus also
Equivalent to gradually in defining aberration model with ideal image point, consistent with actual aberration model, thus actual image point normalization is sat
Demarcate the aberration of justice：
Bring its aberration model into ideal image linear equationArrange
A point on straight line can list an equation on aberration coefficients, and multiple points on straight line can list corresponding linear
Equation group, aberration coefficients k is obtained with least square solution system of linear equations0~k4。
5. the two-step method according to claim 1 based on non-coplanar control straight line imaging demarcation camera parameter, its feature exist
In step (5) the amendment distortion picture point is specially：
After obtaining aberration coefficients, aberration coefficients are substituted into aberration model
Actual image point x, y are modified.
6. the two-step method according to claim 1 based on non-coplanar control straight line imaging demarcation camera parameter, its feature exist
In the step (7) solves aberration coefficients k again0~k4Specially：
Because during loop iteration, the actual image point being corrected moves closer to ideal image point, is thus circulated for the last time
The difference coefficient k arrived0~k4Zero should be leveled off to, so needing to recalculate aberration coefficients, at the same time, after being corrected
Picture point moves closer to ideal image point, can use the picture point of last amendment as ideal image pointExtraction is obtained without amendment
Picture point as actual image point x, y, substitute into aberration model and arrange to obtain：
One point can list two equations on aberration coefficients, and multiple spot can list corresponding system of linear equations, with minimum
Square law solution system of linear equations obtains final aberration coefficients k0~k4。
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| CN113077517B (en) * | 2020-01-03 | 2022-06-24 | 湖南科天健光电技术有限公司 | Spatial light measurement system calibration device and method based on light beam straight line characteristics |
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| CN104156974A (en) * | 2014-09-05 | 2014-11-19 | 大连理工大学 | Camera distortion calibration method on basis of multiple constraints |
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| CN103148865A (en) * | 2013-01-17 | 2013-06-12 | 天津大学 | Camera model standardization method and standardization device |
| CN104156974A (en) * | 2014-09-05 | 2014-11-19 | 大连理工大学 | Camera distortion calibration method on basis of multiple constraints |
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