CN102930548A - Method for linearly solving camera inner parameter by using two identical intersected ellipses - Google Patents

Method for linearly solving camera inner parameter by using two identical intersected ellipses Download PDF

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CN102930548A
CN102930548A CN2012104654640A CN201210465464A CN102930548A CN 102930548 A CN102930548 A CN 102930548A CN 2012104654640 A CN2012104654640 A CN 2012104654640A CN 201210465464 A CN201210465464 A CN 201210465464A CN 102930548 A CN102930548 A CN 102930548A
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point
ellipses
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picture
camera
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CN102930548B (en
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赵越
余敦来
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Yunnan University YNU
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Abstract

The invention relates to a method for linearly solving camera inner parameters by using two identical intersected ellipses. According to the method, a target drone which is formed by two identical intersected ellipses sharing the same main axis and which is calibrated by a camera is adopted; five images of the target drone are shot in different directions; an ellipse equation is extracted from the images and the intersection points of the two ellipse are solved; end points in the planes of the images in the orthogonal directions are obtained according to the polarity principle and the property of the cross ration of four straight lines; and camera inner parameters are linearly solved by using the end points in the orthogonal directions and the constraint of the images of absolute conics. With the adoption of the target drone in the method, the full-automatic calibration can be implemented, the error caused by the measurement in the calibration process is reduced, and the calibration precision in the calibration process of the camera is improved as the conic is a simpler and more global-oriented element.

Description

Utilize two identical crossing oval linear solution camera intrinsic parameters
Technical field
The invention belongs to the computer research field, relate to a kind of oval template be used to finding the solution camera intrinsic parameter.Utilize on the plane two identical crossing ellipses of main shaft altogether as calibrating template, utilize the character of quafric curve to obtain end point on the pair of orthogonal direction, linearly determine camera intrinsic parameter.
Background technology
One of basic task of computer vision recovers the geological information of object three dimensions from the two-dimensional image information that video camera obtains exactly, thus the geometric configuration of object in identification and the reconstruction of three-dimensional space.Must determine the three-dimensional geometry position of space object point and the mutual relationship between the corresponding point in its image in this process, and this relation is by the geometric model decision of video camera imaging, the parameter of these geometric models is exactly camera parameters.Under most of conditions, these parameters all obtain by experiment, Here it is camera calibration.It generally is divided into tradition and demarcates and certainly demarcate two kinds of methods, which kind of scaling method no matter, and demarcating object all is to adopt some special geometric models, for example: plane square, triangle, circle, space cube and cylinder etc.How setting up the relation relation of certain linearity especially between these geometric models and the camera parameters, is the target that present camera calibration is pursued, and also is one of focus of present computer vision field research.
Although traditional camera marking method can obtain higher precision, calibrating block is made difficulty, is not easy to operation.For this problem document " A flexible new technique for camera calibration ", (Zhengyou Zhang, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1330-1334,2000.) proposed to replace with plane template the method for traditional calibrating block, this method is simple and convenient, cost is low, and can obtain higher precision, but need the physical coordinates of dot matrix on the accurate locating template.Document " Planar conic based camera calibration ", (Changjiang Yang, Fengmei Sun, Zhanyi Hu, In Proceedings of International Conference on Pattern Recognition, vol.1, pp. 555-558,2000.) this method has been done popularization, come calibrating camera with the quafric curve correspondence between image and the template, rather than utilize correspondence between points.Because quafric curve is a kind of primitive of more succinct more globalize, thereby can further improve the stability of method.So solving problem of calibrating with curve is widely studied.Document " A new easy camera calibration technique based on circular points ", (Xiaoqiao Meng, Zhanyi Hu, Pattern Recognition, vol. 36, no. 5, pp. 115-1164,2003.) calibrating template that consists of with a circle and some straight lines by the center of circle proposed, utilize the annulus point to find the solution the method for camera intrinsic parameter, the method is dissolved into the point of the annulus in the projective geometry in the camera calibration first, so the annulus point has become theoretical foundation (Hartley Richard, the Zisserman Andrew of camera self-calibration method, " Multiple view geometry in computer vision ", Cambridge University Press, Cambridge, 2000.).
Circle is special quafric curve on the plane, and circles all on the plane are all by the annulus point.Utilize circle as calibrating template, carry out the method for camera calibration in conjunction with the theory of annulus point and promoted gradually.Document (Yihong Wu, Haijiang Zhu, Zhanyi Hu, Fuchao Wu, " Camera calibration from the quasi-affine invariance of two parallel circles ", In Proceedings of the ECCV, pp. 190-202,2004.) method of demarcating with parallel circle proposed, be that the intersection point of the picture of two parallel circles of annulus point direct solution is finished demarcation according to the intersection point of parallel circle.Document (Yihong Wu, Xinju Li, Fuchao Wu, Zhanyi Hu, " Coplanar circle; quasi-affine invariance and calibration ", Image and Vision Computing, vol. 24, no. 4, pp. 319-326,2006.) position relationship of any two circles on the plane has been discussed, try to achieve the picture of annulus point according to the intersection point of quafric curve in the position relationship computed image of circle.In quafric curve, circle is a very special figure, for general quafric curve clear and definite scaling method is arranged not yet at present, and this paper is on the basis that quafric curve is demarcated, provided in round more generally quafric curve, i.e. oval camera marking method.
Summary of the invention
It is simple to the invention provides a kind of making, widely applicable, the target that is used for finding the solution camera intrinsic parameter of good stability, and this target is comprised of two of common main shaft identical crossing ellipses.In finding the solution the process of camera intrinsic parameter, only need video camera to take 5 intrinsic parameters that 5 width of cloth images just can linear solution go out video camera from different orientation.
The present invention adopts following technical scheme:
The present invention is the target that is used for camera self-calibration that is made of two of common main shaft identical crossing ellipses.Concrete step comprises: extract elliptic equation and find the solution the picture of the intersection point of two ellipses from image, character according to the double ratio of match Principle for Extreme Nodes and Lines and four straight lines of concurrent, draw the end point on the orthogonal directions on the plane of delineation, utilize the constraint linear solution camera intrinsic parameter of the picture of end point on the orthogonal directions and absolute conic.
(1) curvilinear equation in the fitted figure picture
Utilize Edge function in the Matlab program to extract the coordinate of image characteristic point, and simulate ellipse in the image with least-squares algorithm, obtain each elliptic equation on the image.
(2) computed image plane two oval intersection point place straight lines are about the limit of quafric curve
On a plane of world coordinate system, there are altogether two identical ellipses (such as Fig. 1) of main shaft,
Figure 184045DEST_PATH_IMAGE001
Two altogether identical ellipses of main shaft,
Figure 682023DEST_PATH_IMAGE002
The two oval intersection points that intersect.Cross a little
Figure 125773DEST_PATH_IMAGE002
Four tangent lines making respectively two ellipses meet at a little respectively
Figure 341991DEST_PATH_IMAGE003
, because ellipse is symmetric figure,
Figure 224496DEST_PATH_IMAGE003
Two one fix on the principal axis of ellipse, connect
Figure 761001DEST_PATH_IMAGE003
With
Figure 703550DEST_PATH_IMAGE002
Intersect at
Figure 79167DEST_PATH_IMAGE004
Point, namely
Figure 499784DEST_PATH_IMAGE004
Point is
Figure 159305DEST_PATH_IMAGE005
With
Figure 7175DEST_PATH_IMAGE006
The mid point of two line segments.On the picture plane (such as Fig. 2), ellipse
Figure 932406DEST_PATH_IMAGE001
Similarly be
Figure 94397DEST_PATH_IMAGE007
, extract oval marginal point with Matlab, use the least square fitting elliptic curve, oval equation
Figure 421473DEST_PATH_IMAGE007
, be expressed as with matrix of coefficients
Figure 892774DEST_PATH_IMAGE008
, extract the intersection point of two ellipses , cross point
Figure 67721DEST_PATH_IMAGE009
Obtain ellipse Tangent line, four tangent lines intersect at a point in twos and are respectively
Figure 642238DEST_PATH_IMAGE010
Figure 729012DEST_PATH_IMAGE010
It is straight line
Figure 295123DEST_PATH_IMAGE011
About ellipse
Figure 268895DEST_PATH_IMAGE007
Limit, got by cross ratio invariability, the picture of limit still is limit, namely Respectively a little
Figure 282167DEST_PATH_IMAGE003
Picture. With Intersect at The point,
Figure 76018DEST_PATH_IMAGE013
A little
Figure 436461DEST_PATH_IMAGE004
Picture point.
(3) coordinate of the end point on the calculating orthogonal directions
At stencil plane (such as Fig. 1),
Figure 447143DEST_PATH_IMAGE004
It is straight line
Figure 352782DEST_PATH_IMAGE006
With
Figure 448914DEST_PATH_IMAGE005
Mid point, and
Figure 894939DEST_PATH_IMAGE006
With
Figure 212656DEST_PATH_IMAGE005
Orthogonal, establish
Figure 351514DEST_PATH_IMAGE006
The infinity point of direction is
Figure 872625DEST_PATH_IMAGE014
,
Figure 122341DEST_PATH_IMAGE005
The infinity point of direction is
Figure 294565DEST_PATH_IMAGE015
, have
Figure 604324DEST_PATH_IMAGE016
,
Figure 675048DEST_PATH_IMAGE017
, had on picture plane (such as Fig. 2) by cross ratio invariability
Figure 666137DEST_PATH_IMAGE018
,
Figure 505917DEST_PATH_IMAGE019
Wherein
Figure 170598DEST_PATH_IMAGE020
For
Figure 463039DEST_PATH_IMAGE011
The end point of direction,
Figure 320137DEST_PATH_IMAGE021
For
Figure 952107DEST_PATH_IMAGE012
The end point of direction.
(4) find the solution camera intrinsic parameter
Obtain five width of cloth images, gone out 5 intrinsic parameters, i.e. matrixes of video camera by the end point linear solution of orthogonal directions
Figure 603668DEST_PATH_IMAGE022
,
Figure 835935DEST_PATH_IMAGE023
Be the distortion factor of image,
Figure 231144DEST_PATH_IMAGE024
In image coordinate system
Figure 717620DEST_PATH_IMAGE025
Axle and
Figure 805662DEST_PATH_IMAGE026
The scale factor of axle, Be the principal point coordinate, be 5 intrinsic parameters of video camera.
Advantage of the present invention:
(1) this target is made simply, is comprised of two of common main shaft crossing identical ellipses.
(2) physical size of this target do not required, need not to know round position and the world coordinates of each point.
(3) but only need with video camera take from different orientation 5 width of cloth images just linear solution go out 5 intrinsic parameters of video camera.
Description of drawings
Fig. 1 is be used to the target structural representation of finding the solution camera intrinsic parameter.
Fig. 2 is the template imaging plane.
Embodiment
A kind of target be used to finding the solution camera intrinsic parameter, it is to be made of two of common main shaft crossing identical ellipses, such as Fig. 1.Finishing finding the solution of camera intrinsic parameter with this modulation needs through following steps: the experiment pattern that adopts based on the camera marking method of two crossing identical ellipses is any two crossing identical ellipses on the plane, as shown in Figure 1, curvilinear equation in the fitted figure picture, find the solution the plane of delineation two oval intersection point place straight lines about the limit of quafric curve, find the solution the coordinate of the end point on the orthogonal directions, solve camera intrinsic parameter.
Figure 192967DEST_PATH_IMAGE028
Be the intersection point of two ellipses, utilize the method among the present invention that the video camera that is used for experiment is demarcated, concrete steps are as follows:
(1) curvilinear equation in the fitted figure picture
Utilize the Edge function in the Matlab program to extract the coordinate of image characteristic point, and with each the bar curve in the least-squares algorithm fitted figure picture, obtain each bar elliptic curve equation on the image.
(2) computed image plane two oval intersection point place straight lines are about the limit of quafric curve
On a plane of world coordinate system, there are altogether two identical ellipses (such as Fig. 1) of main shaft,
Figure 861846DEST_PATH_IMAGE001
Two altogether identical ellipses of main shaft,
Figure 58472DEST_PATH_IMAGE002
It is the intersection point of two ellipses.Cross a little
Figure 547222DEST_PATH_IMAGE002
Four tangent lines making respectively two ellipses meet at a little respectively
Figure 736764DEST_PATH_IMAGE003
, because ellipse is symmetric figure,
Figure 260149DEST_PATH_IMAGE003
Two one fix on the principal axis of ellipse, connect
Figure 424414DEST_PATH_IMAGE003
With Intersect at
Figure 144425DEST_PATH_IMAGE004
Point, namely
Figure 712197DEST_PATH_IMAGE004
Point is
Figure 312943DEST_PATH_IMAGE005
With
Figure 776285DEST_PATH_IMAGE006
The mid point of two line segments.(such as Fig. 2) extracts oval marginal point with Matlab on the picture plane, uses the least square fitting elliptic curve, obtains
Figure 58362DEST_PATH_IMAGE001
The elliptic equation of picture
Figure 556340DEST_PATH_IMAGE007
, be expressed as with matrix of coefficients , extract the oval intersection point of two pictures
Figure 465576DEST_PATH_IMAGE009
, cross point
Figure 285764DEST_PATH_IMAGE009
About ellipse
Figure 638248DEST_PATH_IMAGE007
Tangent line, four tangent lines intersect at a point in twos and are respectively
Figure 315217DEST_PATH_IMAGE010
Figure 940102DEST_PATH_IMAGE010
It is straight line
Figure 626299DEST_PATH_IMAGE011
About ellipse
Figure 770972DEST_PATH_IMAGE007
Limit, got by cross ratio invariability, the picture of limit still is limit, namely
Figure 884422DEST_PATH_IMAGE010
Respectively a little
Figure 809652DEST_PATH_IMAGE003
Picture. With
Figure 547987DEST_PATH_IMAGE012
Intersect at
Figure 770021DEST_PATH_IMAGE013
The point,
Figure 916969DEST_PATH_IMAGE013
A little Picture point.
(3) coordinate of the end point on the calculating orthogonal directions
At stencil plane (such as Fig. 1),
Figure 310571DEST_PATH_IMAGE004
It is straight line With
Figure 603329DEST_PATH_IMAGE005
Mid point, and With
Figure 392480DEST_PATH_IMAGE005
Orthogonal, establish
Figure 18633DEST_PATH_IMAGE006
The infinity point of direction is
Figure 77856DEST_PATH_IMAGE014
,
Figure 447657DEST_PATH_IMAGE005
The infinity point of direction is
Figure 603832DEST_PATH_IMAGE015
, have
Figure 587838DEST_PATH_IMAGE016
,
Figure 196673DEST_PATH_IMAGE017
, had on picture plane (such as Fig. 2) by cross ratio invariability ,
Figure 52951DEST_PATH_IMAGE019
Wherein
Figure 207858DEST_PATH_IMAGE020
For
Figure 303990DEST_PATH_IMAGE011
The end point of direction,
Figure 15594DEST_PATH_IMAGE021
For The end point of direction.
(4) find the solution camera intrinsic parameter
Obtain five width of cloth images, gone out 5 intrinsic parameters, i.e. matrixes of video camera by the end point linear solution of orthogonal directions
Figure 222901DEST_PATH_IMAGE022
,
Figure 730630DEST_PATH_IMAGE023
Be the distortion factor of image,
Figure 245925DEST_PATH_IMAGE024
In image coordinate system
Figure 168882DEST_PATH_IMAGE025
Axle and The scale factor of axle,
Figure 283786DEST_PATH_IMAGE027
It is the principal point coordinate.
Embodiment
The present invention proposes and utilize two crossing identical ellipses that are total to arbitrarily main shaft on the plane as the linear intrinsic parameter of determining video camera of target.The experiment module structural representation that the present invention adopts as shown in Figure 1.The below makes more detailed description with an example to embodiment of the present invention.
The experiment pattern that adopts based on the camera marking method of two of common main shaft crossing identical ellipses is any two crossing identical ellipses of main shaft altogether on the plane, as shown in Figure 1.
Figure 2012104654640100002DEST_PATH_IMAGE029
Be the intersection point of two ellipses, utilize the method among the present invention that the video camera that is used for experiment is demarcated, concrete steps are as follows:
(1) drop shadow curve's equation of ellipse in the fitted figure picture
The image resolution ratio that the present invention adopts is 640 * 480 pixels, take from different directions several experiment pictures with video camera, choose comparatively clearly picture of five width of cloth, read in image, utilize function among the Matlab to extract the coordinate of image characteristic point, and with each the bar curve in the least-squares algorithm fitted figure picture, obtain curvilinear equation
Figure 2012104654640100002DEST_PATH_IMAGE030
Calculate the ellipse on five width of cloth images
Figure 2012104654640100002DEST_PATH_IMAGE031
, its matrix of coefficients is
Figure 2012104654640100002DEST_PATH_IMAGE032
, as follows:
The matrix of coefficients of two ellipses is respectively on the first width of cloth image:
Figure 2012104654640100002DEST_PATH_IMAGE033
；
Figure 2012104654640100002DEST_PATH_IMAGE034
。
The matrix of coefficients matrix of two ellipses of the second width of cloth image is respectively:
Figure 2012104654640100002DEST_PATH_IMAGE035
；
Figure 2012104654640100002DEST_PATH_IMAGE036
。
The matrix of coefficients matrix of two ellipses of the 3rd width of cloth image is respectively:
Figure 2012104654640100002DEST_PATH_IMAGE037
；
Figure 2012104654640100002DEST_PATH_IMAGE038
。
The matrix of coefficients matrix of two ellipses of the 4th width of cloth image is respectively:
Figure 2012104654640100002DEST_PATH_IMAGE039
；
Figure 2012104654640100002DEST_PATH_IMAGE040
。
The matrix of coefficients matrix of two ellipses of the 5th width of cloth image is respectively:
Figure 2012104654640100002DEST_PATH_IMAGE041
；
Figure 2012104654640100002DEST_PATH_IMAGE042
。
(2) end point on the computed image planar quadrature direction
On a plane of world coordinate system, there are altogether two crossing identical ellipses (such as Fig. 1) of main shaft,
Figure 2012104654640100002DEST_PATH_IMAGE043
,
Figure 2012104654640100002DEST_PATH_IMAGE044
Two altogether identical ellipses of main shaft, ,
Figure 2012104654640100002DEST_PATH_IMAGE046
It is the intersection point of two ellipses.If straight line
Figure 2012104654640100002DEST_PATH_IMAGE047
On infinity point be respectively Cross a little
Figure 855686DEST_PATH_IMAGE045
,
Figure 633149DEST_PATH_IMAGE046
Four tangent lines making respectively two ellipses meet at a little respectively
Figure 2012104654640100002DEST_PATH_IMAGE049
, , establish straight line
Figure 300760DEST_PATH_IMAGE047
On infinity point be respectively Because ellipse is symmetric figure,
Figure 387981DEST_PATH_IMAGE049
,
Figure 347847DEST_PATH_IMAGE050
Two one fix on the principal axis of ellipse, connect
Figure 999408DEST_PATH_IMAGE049
,
Figure 966096DEST_PATH_IMAGE050
With
Figure 361305DEST_PATH_IMAGE045
,
Figure 175678DEST_PATH_IMAGE046
Intersect at Point, namely
Figure 202857DEST_PATH_IMAGE004
Point is With
Figure 260516DEST_PATH_IMAGE006
The mid point of two line segments.
Simultaneous on the picture plane
Figure 2012104654640100002DEST_PATH_IMAGE051
Solving Equations solve intersection point
Figure 191563DEST_PATH_IMAGE009
Coordinate be respectively
Figure 2012104654640100002DEST_PATH_IMAGE052
With
Figure 2012104654640100002DEST_PATH_IMAGE053
, subscript represents respectively
Figure 132843DEST_PATH_IMAGE002
Corresponding picture, homogeneous coordinates are
Figure 2012104654640100002DEST_PATH_IMAGE054
, i.e. mistake
Figure 2012104654640100002DEST_PATH_IMAGE055
Two tangential equations of two curves of point are:
Figure 2012104654640100002DEST_PATH_IMAGE056
， （1）
Figure 2012104654640100002DEST_PATH_IMAGE057
， （2）
Namely cross
Figure 2012104654640100002DEST_PATH_IMAGE058
Two tangential equations of point are respectively:
Figure 2012104654640100002DEST_PATH_IMAGE059
， （3）
Figure 2012104654640100002DEST_PATH_IMAGE060
。（4）
Simultaneous equations (1), (3) get the intersection point of two straight lines
Figure 2012104654640100002DEST_PATH_IMAGE061
Coordinate
Figure 2012104654640100002DEST_PATH_IMAGE062
,
Figure 384701DEST_PATH_IMAGE061
For
Figure 908087DEST_PATH_IMAGE011
About curve
Figure 2012104654640100002DEST_PATH_IMAGE063
Limit, be NThe picture of point.Simultaneous equations (2), (4) For
Figure 10035DEST_PATH_IMAGE011
About curve
Figure 2012104654640100002DEST_PATH_IMAGE065
Limit, be The picture of point.Process
Figure 2012104654640100002DEST_PATH_IMAGE067
Straight line be:
Figure 2012104654640100002DEST_PATH_IMAGE068
（5）
Cross The straight-line equation of point is:
Figure 2012104654640100002DEST_PATH_IMAGE069
（6）
Simultaneous equations (5), (6)
Figure 2012104654640100002DEST_PATH_IMAGE070
With Intersection point
Figure 416593DEST_PATH_IMAGE013
Coordinate
For End point on the direction
Figure 667631DEST_PATH_IMAGE020
Find the solution, we can utilize equally
Figure 12025DEST_PATH_IMAGE004
Be Mid point, existing: , because
Figure 2012104654640100002DEST_PATH_IMAGE073
Picture point be respectively
Figure 2012104654640100002DEST_PATH_IMAGE074
, existing projective transformation keeps cross ratio invariability to have:
Figure 2012104654640100002DEST_PATH_IMAGE075
,
Figure 78387DEST_PATH_IMAGE006
End point on the direction
Figure DEST_PATH_IMAGE076
,
Figure DEST_PATH_IMAGE077
,
Figure DEST_PATH_IMAGE078
Because Point is
Figure 39094DEST_PATH_IMAGE005
Mid point, so
Figure DEST_PATH_IMAGE079
Harmonic conjugates, namely
Figure DEST_PATH_IMAGE080
, again because
Figure DEST_PATH_IMAGE081
Be respectively
Figure DEST_PATH_IMAGE082
Picture point.Because
Figure DEST_PATH_IMAGE083
, solve
Figure 516212DEST_PATH_IMAGE005
The end point of direction
Figure DEST_PATH_IMAGE084
Coordinate
Figure DEST_PATH_IMAGE085
, wherein
Figure DEST_PATH_IMAGE086
,
Figure DEST_PATH_IMAGE087
. the data point of substitution five width of cloth images is found the solution the end point of orthogonal directions
Figure DEST_PATH_IMAGE088
, wherein
Figure DEST_PATH_IMAGE089
Expression 1 to 5 width of cloth image, as follows:
End point on the first width of cloth figure orthogonal directions:
Figure DEST_PATH_IMAGE090
;
Figure DEST_PATH_IMAGE091
。
The coordinate of the end point on the second width of cloth figure orthogonal directions:
;
。
The coordinate of the end point on the 3rd width of cloth figure orthogonal directions:
Figure DEST_PATH_IMAGE094
;
Figure DEST_PATH_IMAGE095
。
End point coordinate on the 4th width of cloth figure orthogonal directions:
Figure DEST_PATH_IMAGE096
;
Figure DEST_PATH_IMAGE097
。
The coordinate of the end point on the 5th width of cloth figure orthogonal directions:
Figure DEST_PATH_IMAGE098
;
Figure DEST_PATH_IMAGE099
。
(3) solve camera intrinsic parameter
The coordinate of the end point on five width of cloth images that obtain through above step on the orthogonal directions can solve linearly the camera intrinsic parameter matrix and is:
Figure DEST_PATH_IMAGE100
Wherein five intrinsic parameters (unit: pixel) be respectively: ,
Figure DEST_PATH_IMAGE102
,
Figure DEST_PATH_IMAGE103
, ,
Figure DEST_PATH_IMAGE105

Claims (1)

1. one kind is utilized two identical crossing oval linear solution camera intrinsic parameters, it is characterized in that utilizing the target on a plane, and this target is to be made of two identical crossing ellipses that are total to main shaft on the plane; At first extract elliptic equation and find the solution the picture of the intersection point of two ellipses from image, character according to the double ratio of match Principle for Extreme Nodes and Lines and four straight lines of concurrent, draw the end point on the orthogonal directions on the plane of delineation, utilize at last 5 intrinsic parameters of constraint linear solution video camera of the picture of end point on the orthogonal directions and absolute conic; Concrete steps comprise: curvilinear equation in the fitted figure picture, and the plane of delineation two oval intersection point place straight lines are found the solution about the limit of quafric curve, and the coordinate of the end point on the orthogonal directions is found the solution, and finds the solution in the camera intrinsic parameter matrix
Figure 2012104654640100001DEST_PATH_IMAGE001
5 parametric solutions;
(1) computed image plane two oval intersection point place straight lines are about the limit of quafric curve
On a plane of world coordinate system, there are altogether two identical ellipses (such as Fig. 1) of main shaft,
Figure 2012104654640100001DEST_PATH_IMAGE002
Two altogether identical ellipses of main shaft,
Figure 2012104654640100001DEST_PATH_IMAGE003
The two oval intersection points that intersect; Cross a little
Figure 343470DEST_PATH_IMAGE003
Four tangent lines making respectively two ellipses meet at a little respectively
Figure 2012104654640100001DEST_PATH_IMAGE004
, because ellipse is symmetric figure,
Figure 462124DEST_PATH_IMAGE004
Two one fix on the principal axis of ellipse, connect
Figure 301904DEST_PATH_IMAGE004
With
Figure 844880DEST_PATH_IMAGE003
Intersect at
Figure 2012104654640100001DEST_PATH_IMAGE005
Point, namely Point is
Figure 2012104654640100001DEST_PATH_IMAGE006
With The mid point of two line segments; On the picture plane (such as Fig. 2), ellipse
Figure 119053DEST_PATH_IMAGE002
Similarly be
Figure 2012104654640100001DEST_PATH_IMAGE008
, extract oval marginal point with the Edge function of Matlab, use the least square fitting elliptic curve, oval equation
Figure 875656DEST_PATH_IMAGE008
, be expressed as with matrix of coefficients
Figure 2012104654640100001DEST_PATH_IMAGE009
Extract the intersection point of two ellipses
Figure 2012104654640100001DEST_PATH_IMAGE010
, cross point
Figure 589534DEST_PATH_IMAGE010
Obtain ellipse
Figure 634851DEST_PATH_IMAGE008
Tangent line, four tangent lines intersect at a point in twos and are respectively
Figure 92377DEST_PATH_IMAGE011
It is straight line About ellipse
Figure 703487DEST_PATH_IMAGE008
Limit, got by cross ratio invariability, the picture of limit still is limit, namely
Figure 791529DEST_PATH_IMAGE011
Respectively a little
Figure 58562DEST_PATH_IMAGE004
Picture;
Figure 340287DEST_PATH_IMAGE012
With
Figure 2012104654640100001DEST_PATH_IMAGE013
Intersect at The point,
Figure 805903DEST_PATH_IMAGE014
A little
Figure 64846DEST_PATH_IMAGE005
Picture point;
(2) coordinate of the end point on the calculating orthogonal directions
At stencil plane (such as Fig. 1), It is straight line
Figure 618504DEST_PATH_IMAGE007
With
Figure 141890DEST_PATH_IMAGE006
Mid point, and
Figure 634051DEST_PATH_IMAGE007
With
Figure 610097DEST_PATH_IMAGE006
Orthogonal, establish
Figure 213117DEST_PATH_IMAGE007
The infinity point of direction is
Figure 2012104654640100001DEST_PATH_IMAGE015
,
Figure 856588DEST_PATH_IMAGE006
The infinity point of direction is
Figure 2012104654640100001DEST_PATH_IMAGE016
, have ,
Figure 2012104654640100001DEST_PATH_IMAGE018
, had on picture plane (such as Fig. 2) by cross ratio invariability
Figure 2012104654640100001DEST_PATH_IMAGE019
, Wherein For The end point of direction,
Figure 2012104654640100001DEST_PATH_IMAGE022
For
Figure 172873DEST_PATH_IMAGE013
The end point of direction;
(3) find the solution camera intrinsic parameter
Obtain five width of cloth images, gone out 5 intrinsic parameters, i.e. matrixes of video camera by the end point linear solution of orthogonal directions
Figure 2012104654640100001DEST_PATH_IMAGE023
,
Figure 2012104654640100001DEST_PATH_IMAGE024
Be the distortion factor of image,
Figure 2012104654640100001DEST_PATH_IMAGE025
In image coordinate system
Figure 2012104654640100001DEST_PATH_IMAGE026
Axle
Figure 2012104654640100001DEST_PATH_IMAGE027
The scale factor of axle,
Figure 2012104654640100001DEST_PATH_IMAGE028
Be the principal point coordinate, be 5 intrinsic parameters of video camera.
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