CN106157322B - A kind of camera installation site scaling method based on plane mirror - Google Patents
A kind of camera installation site scaling method based on plane mirror Download PDFInfo
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Abstract
The invention discloses a kind of camera installation site scaling method based on plane mirror, belongs to the photogrammetry technical field of optical system.The present invention calculates pose initial value of the 1-dimension drone in camera coordinate system according to Cross ration invariability, and obtain the optimal solution of target pose by minimum re-projection error the following steps are included: 1-dimension drone is put before camera repeatedly；Mirror surface normal vector and camera optical center are calculated to mirror surface distance using closed solutions method；Then the optimal solution of plane mirror pose is obtained by reflecting re-projection error minimum；After mirror plane pose determines, in conjunction with the transformational relation of camera coordinate system and platform virtual image coordinate system, the transformational relation between camera coordinate system and platform real image coordinate system is acquired, completes the calibration of camera installation parameter.The present invention does not need to know target motion and camera posture information in advance, and least twice placement position can acquire mirror surface posture, and realization is simple and convenient, is particularly suitable for the occasion that camera and mirror surface are in a fixed position.
Description
Technical field
The invention belongs to the photogrammetry technical fields of optical system, specifically a kind of for measuring camera installation
The method of position.
Background technique
In vision measurement application, it is pose of the target in camera coordinate system that camera, which directly measure obtain, however perhaps
More measurement tasks are the relative poses of platform where measuring target and camera, it is therefore necessary to installation position of the camera on platform
It sets and is demarcated, so that information of the target in camera coordinate system is transformed into platform coordinate system.In numerous applications, as
Platform where machine is not in camera visual field, therefore camera can not directly observe platform where it.
In addition, there are also hand and eye calibrating method, full filed methods etc. for camera installation site scaling method.Full filed method is needed by one
Platform assists camera, constructs two groups of control points, wherein one group is laid on measurement camera mounting platform, and this group of control point is in platform
Known to coordinate in coordinate system；Another group of control points layout is in the field range of measurement camera.This two groups of control points are all auxiliary
It helps in the field range of camera.The method requires auxiliary camera to have larger field, causes its spatial resolution relatively low, influences
Stated accuracy.Auxiliary camera in above-mentioned calibration process can use total station, laser tracker and theodolite etc., these high-precisions
3-D measuring apparatus price, use cost is high, is unfavorable for large-scale promotion use.
Summary of the invention
The purpose of the present invention is for the platform in camera installation site parameter calibration as where camera can not observe it
And bring calibration is difficult, proposes a kind of camera installation site scaling method based on plane mirror.If the position of known plane mirror
The appearance information and platform virtual image is in camera visual field, can be calculated the transformational relation of camera coordinate system and platform coordinate system.
Camera installation site scaling method based on plane mirror proposed by the invention keeps the opposite of camera and plane mirror
Then position relationship executes following steps:
Step 1,1-dimension drone is put between camera and plane mirror repeatedly, each placement position is different；Camera shooting
Characteristic point real image when each secondary position on 1-dimension drone and its characteristic point virtual image in mirror surface；It obtains target real image and target is empty
The pose of picture.
If it is P that i-th, which puts space coordinate of j-th of the characteristic point of target in camera coordinate system { C },i,j, corresponding image
Coordinate is pi,j；If i-th puts the virtual image of j-th of characteristic point of target, the space coordinate in { C } isCorresponding image is sat
It is designated asWherein, i=1 ..., M, j=1 ..., N, M are the number of putting of 1-dimension drone, and M is the positive integer greater than 2, N mono-
The characteristic point quantity that dimension target is possessed.
Step 2, determine mirror surface normal vector n and camera optical center to mirror surface distance l；
Mirror reflecting matrixWherein, S=S-1, H=I -2nnT, H is Householder matrix, is indicated
The reflection that determinant is -1 rotates, and I indicates unit matrix；
Matrix H is solved by orthogonal forced consistency problem, then acquires mirror surface normal vector n；
Distance l is sought according to the following formula:
Step 3, by seeking following re-projection error functional minimum value, mirror surface normal vector and camera optical center are obtained to mirror
Identity distance from optimal value.
The re-projection error functionWherein, function argument Ω=(n, l),Indicate the image coordinate of re-projection characteristic point, d () is indicated as the distance between two points in plane.
Step 4, it determines the transformational relation between camera coordinate system and platform coordinate system, completes the calibration of camera installation site.
Camera observes the virtual image of the mounting platform in mirror surface by plane mirror, to acquire camera coordinate system { C } and flat
Transformational relation R between platform virtual image coordinate system { B ' }B′C,tB′C；Then result step 3 obtained substitutes into following formula, acquires camera seat
Transformational relation R between mark system { C } and platform real image coordinate system { B }BC,tBC；
The advantages and positive effects of the present invention are:
(1) scaling method of the invention does not need to know target motion and camera posture information in advance；Least twice is put
Position can acquire mirror surface posture, complete the calibration of camera installation parameter, realize simple and convenient；
(2) scaling method of the invention haves no need to change the posture of camera and plane mirror, is particularly suitable for camera and mirror surface
The occasion being in a fixed position.
Detailed description of the invention
Fig. 1 is the overall step schematic diagram of the camera installation site scaling method the present invention is based on plane mirror；
When Fig. 2 is that i-th is put, 1-dimension drone real image and the target virtual image are as the perspective view in plane；
When Fig. 3 is that i-th is put, mirror-reflection schematic diagram；
Fig. 4 is that the transformational relation of camera coordinate system { C }, platform real image coordinate system { B } and platform virtual image coordinate system { B ' } shows
It is intended to；
Fig. 5 is mirror plane pose evaluated error: (a) EnRoot-mean-square error；(b)ElRoot-mean-square error；(c)EqIt is square
Root error.
Specific embodiment
Below in conjunction with drawings and examples, the present invention is described in further detail.
A kind of camera installation site scaling method based on plane mirror proposed by the present invention, process is as shown in Figure 1, demarcating
When, keep the relative positional relationship of camera and plane mirror constant.Each specific implementation step is as follows.
Step 1: the pose of 1-dimension drone is estimated.
As shown in Fig. 2, the real image of target and the virtual image are in camera visual field.OcxcyczcFor camera coordinate system, it is denoted as { C }.
Camera model uses perspective projection model, spatial point P=[X, Y, Z]TWith corresponding picture point p=[u, v]TThere is following relationship:
Wherein, s is scale factor, and K is Intrinsic Matrix, fxAnd fyFor equivalent focal length, (u0,v0) it is image principal point coordinate.
Step 1.1, the intrinsic parameter calibration for completing camera, are considered as Fixed constant, and camera and plane mirror for camera intrinsic parameter
Posture remain unchanged in the process；
Step 1.2 puts 1-dimension drone M times, and each placement position is different, and target real image and the target virtual image are all in picture
In machine visual field, to obtain the image of target real image and the target virtual image when putting every time；M is the positive integer greater than 2.
When step 1.3, calculating are put every time, the pose of target real image and the target virtual image；
As shown in Fig. 2, Pi,jWithI-th placement position is respectively indicated, j-th of characteristic point of target and its virtual image are at { C }
In space coordinate, pi,jWithRespectively corresponding image coordinate, wherein i=1 ..., M, j=1 ..., N.M is 1-dimension drone
Put number, the characteristic point quantity that N is possessed by 1-dimension drone.Three characteristic points of 1-dimension drone are shown in Fig. 2.
When i-th is put, real target and empty target can be respectively by Pi,1,diWithIt uniquely determines, diWithIt respectively indicates
Corresponding 1-dimension drone direction vector.
Pi,1,diInitial value obtained according to the Cross ration invariability of perspective projection, and by seeking re-projection error function f
The minimum value of (Ω) obtains Pi,1,diOptimal value:
Wherein, Ω=(Pi,1,di) it is variable to be optimized,θiWithRespectively
For diRelative to the Eulerian angles of { C }, θiFor the angle of site,For azimuth, d () is indicated as the distance between two points in plane,Table
The image coordinate for showing re-projection characteristic point, meets following formula:
Wherein, s is scale factor, and L is the spacing of adjacent characteristic point.
Similarly, it is obtained according to the Cross ration invariability of perspective projectionInitial value, by seeking re-projection error letter
Several minimum values can acquireOptimal value.
Step 2: the closed solution of Calculation Plane mirror pose.
As shown in Fig. 2, before camera { C } is located at plane mirror, plane mirror can be unique by its mirror surface normal vector n and with { C } distance l
It determines.Spatial point P on mirror plane, and if only if:
nTP=l (4)
Mirror reflecting matrix can be expressed from the next:
Wherein, S=S-1, H=I -2nnTIt .H is Householder matrix, the reflection for indicating that determinant is -1 rotates.I table
Show three-dimensional unit matrix.
Point P and corresponding virtual image pointThere is following relationship:
Step 2.1 calculates mirror plane normal vector n.
When target puts number greater than 2, Householder matrix can be asked by orthogonal forced consistency problem
Solution.The error and E of normal vector may be expressed as:
Wherein, eiIndicate the error of mirror surface normal vector when i-th is put；||·||FFor Frobenius norm,When noise is not present for measured value, E=0.
The optimal estimation value of matrix H is equivalent to so that formula (7) obtains minimum value；According to the property of Householder matrix,
Formula (7) is deployable are as follows:
Wherein,
As it can be seen that E is minimized and is equivalent to tr (Η Δ) and is maximized, therefore solution can be passed throughObtain matrix H
Optimal value.
It is rightSingular value decomposition is carried out, is had:
U and V is the matrix that singular value decomposition obtains.
Matrix D meets:
D=diag (1,1 ,-det (VUT)) (10)
Then work as H=VDUTWhen, formula (7) obtains minimum value.After acquiring matrix H, mirror plane normal vector n is determined therewith.
Step 2.2, the spacing l for calculating mirror plane and camera.
According to formula (6), have:
Then distance l can be calculated by following formula:
Step 3: the iterative solution of Calculation Plane mirror pose.
The plane mirror pose that step 2 obtains is known as closed solution.Closed solution calculating process is succinct, but it is more sensitive to noise.
In this step, the minimum value by seeking re-projection error optimizes closed solution.
According to camera model, have:
Wherein, s is scale factor, and K is Intrinsic Matrix, and I is three-dimensional unit matrix,Indicate the image of re-projection point
Coordinate.
Mirror plane method is obtained using the re-projection error function minimum that Levenberg-Marquardt method seeks following formula
The optimal value of vector n and distance l:
Wherein function argument Ω=(n, l),θ andIt is opposite for normal vector n
In the Eulerian angles of { C }, θ is the angle of site,For azimuth.D () distance between picture point.To acquire normal vector n and distance l
Optimal value, to complete the calibration of plane mirror.
Step 4: calculating the relative pose of camera and platform.
As shown in figure 3, camera observes the virtual image of the mounting platform in mirror surface by plane mirror, to acquire camera coordinate
It is the transformational relation R between { C } and platform virtual image coordinate system { B ' }B′C,tB′C.According to step 3 as a result, camera can be acquired directly
Transformational relation R between coordinate system { C } and platform real image coordinate system { B }BC,tBC, to complete the calibration of camera installation parameter.
Wherein, R indicate spin matrix, t indicate translation vector, subscript B ' C, BC respectively represent camera coordinate system { C } with
Transformational relation, camera coordinate system { C } between platform virtual image coordinate system { B ' } and the transformational relation between platform real image coordinate system { B }.
Embodiment:
Mirror plane pose measurement is the committed step of camera installation parameter calibration.Camera intrinsic parameter fx=fy=995.556, u0
=512 pixels, v0=384 pixels, 1024 pixel of image resolution ratio × 768 pixels.Mirror plane normal vector n=[- 0.5,0,
0.866]T, the distance l=400mm, adjacent characteristic point spacing L=25mm of mirror plane to { C }.
Define mirror surface normal vector error En, mirror surface to optical center range error ElWith re-projection error Eq:
Wherein, ngIndicate the true value of mirror surface normal vector, lgIndicate the true value of camera to mirror surface distance.
Target placement position number M=9, characteristic point quantity N=9.Target position generates at random.Zero-mean, various criterion
The Gaussian noise of difference is added in the image coordinate of characteristic point, from 0 to 1.0 pixel of noise level.For each noise level, carry out
100 times independent experiment calculates En、ElAnd EqRoot-mean-square error.
As shown in figure 5, error linearly becomes larger with noise level, the method for the present invention can effectively optimize plane mirror pose
Closed solution.When noise level is less than 0.5 pixel, the root-mean-square error of normal vector n and distance l be respectively smaller than 0.05 degree and
0.8mm can meet the required precision of common application.
Claims (3)
1. a kind of camera installation site scaling method based on plane mirror, which is characterized in that keep the opposite of camera and plane mirror
Then position relationship executes following steps:
Step 1,1-dimension drone is put between camera and plane mirror repeatedly, each placement position is different；The real image of target and
The virtual image is in camera visual field, characteristic point real image when camera shoots each secondary position on 1-dimension drone and its feature in mirror surface
The point virtual image；Obtain the pose of target real image and the target virtual image；
If it is P that i-th, which puts space coordinate of j-th of the characteristic point of target in camera coordinate system { C },i,j, corresponding image coordinate
For pi,j；If i-th puts the virtual image of j-th of characteristic point of target, the space coordinate in { C } isCorresponding image coordinate isWherein, i=1 ..., M, j=1 ..., N, M are the number of putting of 1-dimension drone, and M is the positive integer more than or equal to 2, N mono-
The characteristic point quantity that dimension target is possessed；
Step 2, determine mirror surface normal vector n and camera optical center to mirror surface distance l；
Mirror reflecting matrixWherein, S=S-1, H=I -2nnT, H is Householder matrix, indicates ranks
The reflection that formula is -1 rotates, and I indicates unit matrix；
Matrix H is solved by orthogonal forced consistency problem, then acquires mirror surface normal vector n；
Distance l is sought according to the following formula:
Step 3, by seeking the minimum value of following re-projection error function f (Ω), mirror surface normal vector and camera optical center are obtained extremely
The optimal value of mirror surface distance completes the calibration of plane mirror；
Wherein, function argument Ω=(n, l),Indicate the image coordinate of re-projection characteristic point, d () is indicated as in plane
Distance between two points；
Step 4, it determines the transformational relation between camera coordinate system and platform coordinate system, completes the calibration of camera installation site；
Camera observes the virtual image of the mounting platform in mirror surface by plane mirror, to acquire camera coordinate system { C } and platform void
As the transformational relation R between coordinate system { B ' }B′C,tB′C；Then result step 3 obtained substitutes into following formula, acquires camera coordinate system
Transformational relation R between { C } and platform real image coordinate system { B }BC,tBC；
2. a kind of camera installation site scaling method based on plane mirror according to claim 1, the step 1 include
Following steps:
Step 1.1, the intrinsic parameter calibration for completing camera, are considered as Fixed constant, and the appearance of camera and plane mirror for camera intrinsic parameter
State remains unchanged in the process；
Step 1.2 puts 1-dimension drone M times, and each placement position is different, and target real image and the target virtual image are all regarded in camera
In, the image of target real image and the target virtual image when putting every time is obtained；
When step 1.3, calculating are put every time, the pose of target real image and the target virtual image；
When i-th is put, real target and empty target are respectively by Pi,1,diWithIt uniquely determines, diFor be real target direction to
Amount,For empty target direction vector；
Pi,1,diWithInitial value obtained according to the Cross ration invariability of perspective projection, then by seeking re-projection error function
Minimum value obtain optimal value；To seek Pi,1,diOptimal value be described as follows:
Re-projection error function f (Ω) are as follows:
Wherein, Ω=(Pi,1,di) it is variable to be optimized,θiWithRespectively diPhase
For the Eulerian angles of { C }, d () is indicated as the distance between two points in plane,Indicate the image coordinate of re-projection characteristic point, it is full
Foot formula:
Wherein, s is scale factor, and L is the spacing of adjacent characteristic point, and K is Intrinsic Matrix.
3. a kind of camera installation site scaling method based on plane mirror according to claim 1, the step 2 include
Following steps:
Step 2.1 calculates mirror plane normal vector n；
When target puts number greater than 2, Householder matrix H is solved by orthogonal forced consistency problem；Mirror surface
The error and E of normal vector indicate are as follows:
Wherein, | | | |FFor Frobenius norm,When noise is not present for measured value, E=
0；diFor the direction vector for being real target,For empty target direction vector；
The optimal estimation value of matrix H is equivalent to so that E obtains minimum value, according to the property of Householder matrix, above formula expansion
Are as follows:
Wherein,
Being minimized E is equivalent to make tr (Η Δ) to be maximized, therefore passes through solutionObtain the optimal of matrix H
Value；
It is rightSingular value decomposition is carried out, is had:
If matrix D meets: D=diag (1,1 ,-det (VUT))；U and V is the matrix that singular value decomposition obtains；
Then work as H=VDUTWhen, E obtains minimum value；After acquiring matrix H, and then determine mirror plane normal vector n；
Step 2.2, the spacing l for calculating mirror plane and camera；
Point P and corresponding virtual image pointThere is following relationship:
According to point P and corresponding virtual image pointRelationship, have:
Then obtain seeking the formula of distance l.
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| CN107808403B (en) * | 2017-11-21 | 2019-04-26 | 韶关学院 | A kind of camera calibration method based on sparse dictionary |
| CN108399640A (en) * | 2018-03-07 | 2018-08-14 | 中国工程物理研究院机械制造工艺研究所 | A kind of speculum relative pose measurement method based on camera calibration |
| CN109215086A (en) * | 2018-08-24 | 2019-01-15 | 深圳市寒武纪智能科技有限公司 | Camera extrinsic scaling method, equipment and system |
| CN113514017B (en) * | 2021-05-06 | 2022-08-16 | 南京理工大学 | Parallel driving mechanism moving platform pose measuring method |
| CN113124821B (en) * | 2021-06-17 | 2021-09-10 | 中国空气动力研究与发展中心低速空气动力研究所 | Structure measurement method based on curved mirror and plane mirror |
| CN114862990B (en) * | 2022-04-22 | 2024-04-30 | 网易（杭州）网络有限公司 | Mirror image parameter acquisition method and device, electronic equipment and storage medium |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103268610A (en) * | 2013-05-23 | 2013-08-28 | 浙江大学 | Unified model of catadioptric omnidirectional camera and calibration method thereof |
| CN104167001A (en) * | 2014-08-27 | 2014-11-26 | 大连理工大学 | Large-visual-field camera calibration method based on orthogonal compensation |
-
2016
- 2016-07-28 CN CN201610609440.6A patent/CN106157322B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103268610A (en) * | 2013-05-23 | 2013-08-28 | 浙江大学 | Unified model of catadioptric omnidirectional camera and calibration method thereof |
| CN104167001A (en) * | 2014-08-27 | 2014-11-26 | 大连理工大学 | Large-visual-field camera calibration method based on orthogonal compensation |
Non-Patent Citations (3)
| Title |
|---|
| A New Mirror-based Extrinsic Camera Calibration Using an Orthogonality Constraint;Takahashi, K.et al.;《Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition》;20120621;第1051-1058页 |
| Mirror-Based Extrinsic Camera Calibration;Hesch, J.A.et al.;《Algorithmic Foundation of Robotics VIII》;20091231;第258-299页 |
| Simple Calibration of Non-overlapping Cameras with a Mirror;Kumar, R.K.et al.;《Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition》;20080628;第1-7页 |
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