CN103810697A - Calibration of parabolic refraction and reflection vidicon internal parameters by utilizing four unparallel straight lines in space - Google Patents

Calibration of parabolic refraction and reflection vidicon internal parameters by utilizing four unparallel straight lines in space Download PDF

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CN103810697A
CN103810697A CN201310531024.5A CN201310531024A CN103810697A CN 103810697 A CN103810697 A CN 103810697A CN 201310531024 A CN201310531024 A CN 201310531024A CN 103810697 A CN103810697 A CN 103810697A
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little
hidden
groups
disappearing
parabolic
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赵越
罗欢
李聪
陈旭
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Yunnan University YNU
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Yunnan University YNU
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Abstract

The invention relates to a method for calibrating parabolic refraction and reflection vidicon internal parameters by utilizing an image formed by four unparallel straight lines in a space. The parabolic refraction and reflection image formed by the straight lines in the space is a quadratic curve. The method comprises the steps of firstly extracting images points of the four unparallel straight lines which are not intersected in the space on one point in the image of a parabolic refraction and reflection vidicon, fitting a quadratic curve equation, solving an intersection point of every two curves, and enabling the corresponding intersection points to pass the projection circle center; then calculating 12 groups of orthogonal direction vanishing points in four quadric surface images, utilizing constraint linearity of the vanishing points to solve the parabolic refraction and reflection vidicon internal parameters. By utilizing the method, full-automatic calibration can be achieved, and errors caused by measurement in the calibrating process are decreased. Due to the fact that the straight lines are simple and global-oriented element, the calibrating accuracy in the calibrating process of the parabolic refraction and reflection vidicon is improved.

Description

The image scale of four the not parallel straight lines in space is determined parabolic catadioptric camera intrinsic parameter
Technical field
The invention belongs to computer research field, relate to a kind of for solving the method for parabolic catadioptric camera intrinsic parameter.Utilize in space four not parallel and straight lines of not meeting at any as calibrating template, utilize the character of quafric curve to obtain 12 groups of hidden pictures that disappear a little of orthogonal directions, determine linearly parabolic catadioptric camera intrinsic parameter.
Background technology
One of basic task of computer vision, the two-dimensional image information obtaining from video camera exactly recovers the geological information of object three dimensions, thus the geometric configuration of object in identification and reconstruction of three-dimensional space.Mutual relationship between corresponding point in this process in necessary three-dimensional geometry position and its image of determining space object point, and this relation is determined by the geometric model 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 is generally divided into tradition demarcates and two kinds of methods of self-calibration, no matter which kind of scaling method, and demarcating object is all some special geometric models of employing, for example: plane square, triangle, circle, space cube and cylinder etc.How setting up especially certain the linear relation of relation between these geometric models and camera parameters, is the target that current camera calibration is pursued, and is also one of focus of current computer vision field research.
Parabolic catadioptric video camera is made up of a parabolic minute surface and an orthogonal camera, and visual range is large and keep single view constraint, is modern visual area research focus.Document " Plane-based calibration of central catadioptric cameras ", (S.Gasparini, P.Sturm, J.P.Barreto, IEEE 12th International Conference on Computer Vision, pp. 1195-1202,2009) to use the two dimension pattern plate at reference mark, the point that these reference mark can be angle points, draw or any easily by the point extracting on image, but this method need to solve intrinsic parameter and outer parameter by the method for iteration.Document " Calibration of central catadioptric cameras using a DLT-like approach " (L.Puig, Y.Bastanlar, P.Sturm, J.J.Guerrero, J.Barreto, International journal of Computer Vision, vol.93, pp. 101-114,2011) demarcation based on three-dimensional point is proposed, this method need to be known the position of three-dimensional point on single image.Document " Generic self-calibration of central cameras " (S.Ramalingam, P.Sturm, S.K.Lodha, Computer Vision and Image Understanding, vol. 114, pp. 210-219,2010) a kind of self-calibrating method proposed, without locus and the camera position known a little, but to utilize the corresponding relation of putting on multiple image.
Straight line is the modal geometric element of scene, and the parabolic catadioptric imaging of straight line is generally quafric curve, quafric curve has a lot of good character in camera calibration process, utilize the parabolic refraction and reflection projection of straight line to demarcate, method is simple, thereby just do not need special calibrating template.Document " Paracatadioptric camera calibration " (C.Geyer, K.Daniilidis, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.24, No.5, pp.687-695,2002) with the image calibration parabolic catadioptric video camera of three straight lines.Document " Geometric properties of central catadioptric line images and there application in calibration " (I.P.Barreto, H.Araujo, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.27, No.8, pp.1327-1333,2005) study the geometric properties of rectilinear picture under central catadiotric model, and proposed the scaling method of the central catadiotric system that is applicable to any type.Document " Catadioptric camera calibration using geometric invariants " (X.Ying, Z.Hu, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, No.10, pp.1260-1271,2004) analyzed the relation between catadioptric camera intrinsic parameter and the imaging profile of ball, they utilize the projection of straight line and ball to demarcate, straight line provides three invariants, and ball provides two invariants.
Summary of the invention
The invention provides a kind ofly for solving the method for parabolic catadioptric camera intrinsic parameter, the method is made up of four uneven straight lines in space, and the parabolic catadioptric image of straight line is quafric curve.Solving in the process of parabolic catadioptric camera intrinsic parameter, only need to use parabolic catadioptric video camera to take 5 intrinsic parameters that 1 width image just can linear solution goes out parabolic catadioptric video camera.
The present invention adopts following technical scheme:
The present invention be formed by four uneven straight lines in space for solving the intrinsic parameter of parabolic catadioptric video camera.Concrete step comprises: first extract picture point from the image of parabolic catadioptric video camera, simulate quadratic curve equation and solve the intersection point of every two curves, connect intersection point and then calculate hidden the disappearing a little of 12 groups of orthogonal directionss in four quafric curves, recycle the hidden constraint linear solution parabolic catadioptric camera intrinsic parameter disappearing a little.
1. curvilinear equation in fitted figure picture
Utilize function in Matlab program to extract the coordinate of image characteristic point, and simulate the curve in image with least-squares algorithm, obtain four quadratic curve equations on image.
2. calculate the intersection point of every two quafric curves
If there are four straight lines in space
Figure 2013105310245100002DEST_PATH_IMAGE001
(as Fig. 1), straight line is projected as great circle on unit ball
Figure 2013105310245100002DEST_PATH_IMAGE002
,
Figure DEST_PATH_IMAGE003
, the intersection point of every two circles is designated as
Figure 2013105310245100002DEST_PATH_IMAGE004
with
Figure DEST_PATH_IMAGE005
, wherein
Figure 2013105310245100002DEST_PATH_IMAGE006
Figure DEST_PATH_IMAGE007
Figure 2013105310245100002DEST_PATH_IMAGE008
.Great circle is projected as curve on the catadioptric plane of delineation
Figure DEST_PATH_IMAGE009
, intersection point is respectively
Figure 2013105310245100002DEST_PATH_IMAGE010
with
Figure DEST_PATH_IMAGE011
.Four great circles on unit ball
Figure 2013105310245100002DEST_PATH_IMAGE012
,
Figure DEST_PATH_IMAGE013
,
Figure 2013105310245100002DEST_PATH_IMAGE014
,
Figure DEST_PATH_IMAGE015
for the projection (as Fig. 2) of four, space straight line on unit ball, only consider plane, i.e. a great circle
Figure 351970DEST_PATH_IMAGE012
place plane.
Figure 234476DEST_PATH_IMAGE013
, ,
Figure 93289DEST_PATH_IMAGE015
with
Figure 593541DEST_PATH_IMAGE012
intersection point is respectively
Figure 14158DEST_PATH_IMAGE004
with
Figure 486728DEST_PATH_IMAGE005
,
Figure 2013105310245100002DEST_PATH_IMAGE016
,
Figure DEST_PATH_IMAGE017
.
Figure 2013105310245100002DEST_PATH_IMAGE018
,
Figure DEST_PATH_IMAGE019
,
Figure DEST_PATH_IMAGE020
,
Figure DEST_PATH_IMAGE021
be respectively
Figure 76541DEST_PATH_IMAGE012
,
Figure 1772DEST_PATH_IMAGE013
,
Figure 288397DEST_PATH_IMAGE014
,
Figure 615473DEST_PATH_IMAGE015
imaging (as Fig. 3) on the catadioptric plane of delineation, the intersection point of curve with be respectively
Figure 137087DEST_PATH_IMAGE004
with
Figure 882451DEST_PATH_IMAGE005
projection, just have
Figure 2013105310245100002DEST_PATH_IMAGE022
.
3. calculate 12 groups of hidden disappearing a little of orthogonal directions in four quafric curve imaging planes
Circle on unit ball
Figure DEST_PATH_IMAGE023
meet at respectively six points (as Fig. 2) on unit ball with other three circles, the line of corresponding circle intersection point is circle
Figure 400020DEST_PATH_IMAGE023
diameter, two diameters circle on 4 the adjacent side that forms orthogonal, opposite side is parallel to each other, can determine one group of orthogonal directions, every two groups of three diameters can be determined one group of orthogonal directions, totally three groups.After parabolic catadioptric
Figure 362160DEST_PATH_IMAGE018
,
Figure 928271DEST_PATH_IMAGE019
, ,
Figure 590513DEST_PATH_IMAGE021
be respectively
Figure 977632DEST_PATH_IMAGE012
,
Figure 144171DEST_PATH_IMAGE013
,
Figure 300346DEST_PATH_IMAGE014
,
Figure 720570DEST_PATH_IMAGE015
imaging (as Fig. 3) on the plane of delineation,
Figure 391723DEST_PATH_IMAGE001
imaging.At curve
Figure 565215DEST_PATH_IMAGE018
in the projection at place, can determine altogether three groups of hidden disappearing a little of orthogonal directions.At curve
Figure 638213DEST_PATH_IMAGE019
,
Figure 606169DEST_PATH_IMAGE020
,
Figure 266083DEST_PATH_IMAGE021
in the projection at place, also can determine respectively that the hidden of three groups of orthogonal directionss disappears a little, so, in four imaging planes, have the hidden of 12 groups of orthogonal directionss and disappear a little.
Figure DEST_PATH_IMAGE024
being imaged as of parabolic catadioptric video camera
Figure DEST_PATH_IMAGE025
, in imaging
Figure DEST_PATH_IMAGE026
in,
Figure 836742DEST_PATH_IMAGE026
with
Figure DEST_PATH_IMAGE027
intersection point be
Figure DEST_PATH_IMAGE028
,
Figure 29826DEST_PATH_IMAGE026
with
Figure DEST_PATH_IMAGE029
intersection point be
Figure DEST_PATH_IMAGE030
; Straight line
Figure DEST_PATH_IMAGE031
with
Figure DEST_PATH_IMAGE032
be respectively the excessive round heart the straight line of picture, line correspondence with straight line
Figure DEST_PATH_IMAGE035
meet at a little
Figure DEST_PATH_IMAGE036
, have
Figure DEST_PATH_IMAGE037
; Line correspondence
Figure DEST_PATH_IMAGE038
with straight line meet at a little
Figure DEST_PATH_IMAGE040
, have ,
Figure 548444DEST_PATH_IMAGE036
with
Figure 194189DEST_PATH_IMAGE040
one group of hidden disappearing a little of orthogonal directions exactly; with it is straight line
Figure DEST_PATH_IMAGE044
Figure DEST_PATH_IMAGE045
imaging
Figure 67073DEST_PATH_IMAGE026
on hidden the disappearing a little of one group of orthogonal directions,
Figure DEST_PATH_IMAGE046
with be
Figure DEST_PATH_IMAGE048
Figure 176981DEST_PATH_IMAGE045
imaging
Figure 486739DEST_PATH_IMAGE026
on another group orthogonal directions is hidden disappears a little, totally three groups of hidden disappearing a little of orthogonal directions.Add
Figure DEST_PATH_IMAGE049
Figure DEST_PATH_IMAGE050
picture
Figure 183562DEST_PATH_IMAGE027
,
Figure DEST_PATH_IMAGE051
Figure DEST_PATH_IMAGE052
picture
Figure 299286DEST_PATH_IMAGE020
with
Figure DEST_PATH_IMAGE053
picture
Figure 201383DEST_PATH_IMAGE021
hidden the disappearing a little forming, can obtain 12 groups of hidden disappearing a little altogether.
4. solve parabolic catadioptric camera intrinsic parameter
Use parabolic catadioptric video camera to take 1 width image, the constraint of the picture by the hidden picture disappearing a little of orthogonal directions to absolute conic, linear solution goes out 5 intrinsic parameters, i.e. matrixes of parabolic catadioptric video camera
Figure DEST_PATH_IMAGE055
, wherein for the distortion factor of image, with for focal length,
Figure DEST_PATH_IMAGE059
for principal point coordinate, be 5 intrinsic parameters of parabolic catadioptric video camera.
Advantage of the present invention:
1. this calibrating template is made simply, is made up of four not parallel straight lines that do not meet at any in space.
2. the hidden of 12 groups of orthogonal directionss of the method demand disappears a little, need not ask annulus point and picture centre.
3. need take 5 intrinsic parameters that 1 width image just can linear solution goes out parabolic catadioptric video camera with parabolic catadioptric video camera.
Accompanying drawing explanation
Fig. 1 is the structural representation of four straight lines for solving parabolic catadioptric camera intrinsic parameter.
Fig. 2 is the projection model of four, space straight line on unit ball.
Fig. 3 is four, space straight line imaging plane model under parabolic catadioptric video camera.
Embodiment
For solving a method for parabolic catadioptric camera intrinsic parameter, it be by space four not parallel and do not meet at (as Fig. 1) that any straight line forms.Complete solving of parabolic catadioptric camera intrinsic parameter by this new method and need to pass through following steps: first extract picture point from parabolic catadioptric camera review, simulate quadratic curve equation and solve the intersection point of every two curves, connect hidden the disappearing a little of 12 groups of orthogonal directionss of calculating after intersection point in four planes that every curve forms in unit sphere, recycle the hidden constraint linear solution parabolic catadioptric camera intrinsic parameter disappearing a little.
Concrete steps are as follows:
1. curvilinear equation in fitted figure picture
Utilize Edge function in Matlab program to extract the coordinate of image characteristic point, and simulate the curve in image with least-squares algorithm, obtain four curvilinear equations on image.
2. calculate the intersection point of every two quafric curves
If there are four straight lines in space
Figure 447423DEST_PATH_IMAGE001
(as Fig. 1), straight line is projected as great circle on unit ball
Figure 802181DEST_PATH_IMAGE002
,
Figure 659279DEST_PATH_IMAGE003
, the intersection point of every two circles is designated as
Figure 917347DEST_PATH_IMAGE004
with
Figure 568908DEST_PATH_IMAGE005
, wherein
Figure 676542DEST_PATH_IMAGE006
Figure 71751DEST_PATH_IMAGE007
Figure 682861DEST_PATH_IMAGE008
.Great circle is projected as curve on the catadioptric plane of delineation
Figure 770903DEST_PATH_IMAGE009
, intersection point is respectively
Figure 37936DEST_PATH_IMAGE010
with , wherein
Figure 702452DEST_PATH_IMAGE006
Figure 522247DEST_PATH_IMAGE007
Figure 10998DEST_PATH_IMAGE008
.Four great circles on unit ball
Figure 75906DEST_PATH_IMAGE012
, ,
Figure 825873DEST_PATH_IMAGE014
,
Figure 67498DEST_PATH_IMAGE015
for the projection (as Fig. 2) of four, space straight line on unit ball.Only consider plane, i.e. a great circle
Figure 670518DEST_PATH_IMAGE012
place plane.
Figure 48410DEST_PATH_IMAGE013
,
Figure 212937DEST_PATH_IMAGE014
,
Figure 676279DEST_PATH_IMAGE015
with intersection point is respectively
Figure 580967DEST_PATH_IMAGE004
with
Figure 87035DEST_PATH_IMAGE005
,
Figure 365570DEST_PATH_IMAGE016
, ,
Figure 662876DEST_PATH_IMAGE018
,
Figure 339845DEST_PATH_IMAGE019
, ,
Figure 93004DEST_PATH_IMAGE021
be respectively , ,
Figure 400991DEST_PATH_IMAGE014
,
Figure 625299DEST_PATH_IMAGE015
imaging (as Fig. 3) on the catadioptric plane of delineation, is also
Figure 14692DEST_PATH_IMAGE001
imaging, the intersection point of curve with
Figure 9773DEST_PATH_IMAGE011
be respectively
Figure 37771DEST_PATH_IMAGE004
with
Figure 281671DEST_PATH_IMAGE005
projection, just have
Figure 736923DEST_PATH_IMAGE022
.
3. calculate 12 groups of hidden disappearing a little of orthogonal directions in four planes
Circle on unit ball
Figure 699063DEST_PATH_IMAGE023
with other three circles
Figure 265173DEST_PATH_IMAGE013
,
Figure 363579DEST_PATH_IMAGE014
,
Figure 989733DEST_PATH_IMAGE015
meet at respectively six points (as Fig. 2) on unit ball, the line of corresponding circle intersection point is circle diameter, two diameters circle on 4 the adjacent side that forms orthogonal, opposite side is parallel to each other, can determine one group of orthogonal directions, every two groups of three diameters that six points form can be determined one group of orthogonal directions, totally three groups.After parabolic catadioptric
Figure 41926DEST_PATH_IMAGE018
, ,
Figure 57473DEST_PATH_IMAGE020
,
Figure 728625DEST_PATH_IMAGE021
be respectively
Figure 636539DEST_PATH_IMAGE012
,
Figure 709537DEST_PATH_IMAGE013
,
Figure 677493DEST_PATH_IMAGE014
,
Figure 337406DEST_PATH_IMAGE015
imaging (as Fig. 3) on the plane of delineation, at curve
Figure 49011DEST_PATH_IMAGE018
in the projection at place, can determine three groups of hidden disappearing a little of orthogonal directions, at curve
Figure 242094DEST_PATH_IMAGE019
, ,
Figure 698801DEST_PATH_IMAGE021
in the projection at place,
Figure DEST_PATH_IMAGE060
picture, also can determine respectively that the hidden of three groups of orthogonal directionss disappears a little, so, in four quafric curve imagings, have the hidden of 12 groups of orthogonal directionss and disappear a little.
Figure 276412DEST_PATH_IMAGE024
being imaged as of parabolic catadioptric video camera .In imaging
Figure 633762DEST_PATH_IMAGE026
in,
Figure 993899DEST_PATH_IMAGE026
with
Figure 47306DEST_PATH_IMAGE027
intersection point be
Figure 949403DEST_PATH_IMAGE028
,
Figure 430063DEST_PATH_IMAGE026
with
Figure 50400DEST_PATH_IMAGE029
intersection point be .Straight line
Figure 664101DEST_PATH_IMAGE031
with
Figure 315662DEST_PATH_IMAGE032
be respectively the excessive round heart
Figure 95399DEST_PATH_IMAGE033
the straight line of picture, line correspondence
Figure 54390DEST_PATH_IMAGE034
with straight line meet at a little
Figure 753542DEST_PATH_IMAGE036
, have
Figure 20575DEST_PATH_IMAGE037
; Line correspondence
Figure 281792DEST_PATH_IMAGE038
with straight line
Figure 950671DEST_PATH_IMAGE039
meet at a little
Figure 6352DEST_PATH_IMAGE040
, have
Figure 760681DEST_PATH_IMAGE041
,
Figure 324124DEST_PATH_IMAGE036
with
Figure 847509DEST_PATH_IMAGE040
one group of hidden disappearing a little of orthogonal directions exactly.
Figure 11774DEST_PATH_IMAGE042
with it is straight line
Figure 856420DEST_PATH_IMAGE044
Figure 234311DEST_PATH_IMAGE045
imaging on hidden the disappearing a little of one group of orthogonal directions,
Figure 986815DEST_PATH_IMAGE046
with
Figure 331208DEST_PATH_IMAGE047
be
Figure 625924DEST_PATH_IMAGE048
Figure 397570DEST_PATH_IMAGE045
imaging
Figure 348209DEST_PATH_IMAGE026
on another group orthogonal directions is hidden disappears a little, totally three groups of hidden disappearing a little of orthogonal directions.Add
Figure 293031DEST_PATH_IMAGE049
,
Figure 645515DEST_PATH_IMAGE051
with
Figure 650380DEST_PATH_IMAGE053
the picture forming, can obtain 12 groups of hidden disappearing a little altogether.
4. solve parabolic catadioptric camera intrinsic parameter
Use parabolic catadioptric video camera to take 1 width image, the constraint of the picture by the hidden picture disappearing a little of orthogonal directions to absolute conic, linear solution goes out 5 intrinsic parameters, i.e. matrixes of parabolic catadioptric video camera
Figure 88315DEST_PATH_IMAGE055
, wherein
Figure 341223DEST_PATH_IMAGE056
for the distortion factor of image,
Figure 548213DEST_PATH_IMAGE057
with
Figure 723979DEST_PATH_IMAGE058
for focal length,
Figure 649210DEST_PATH_IMAGE059
for principal point coordinate, be 5 intrinsic parameters of parabolic catadioptric video camera.
Embodiment
The present invention proposes and utilize in space four straight linear not parallel and that do not meet at any to solve the intrinsic parameter of parabolic catadioptric video camera.The experiment module structural representation that the present invention adopts as shown in Figure 1.With an example, embodiment of the present invention are made to more detailed description below.
The experiment pattern that parabolic catadioptric camera marking method based on four straight lines in space adopts be in space four not parallel and do not meet at any straight line, as shown in Figure 1.Article four, straight line is respectively ,
Figure 262911DEST_PATH_IMAGE050
,
Figure 281683DEST_PATH_IMAGE052
,
Figure DEST_PATH_IMAGE061
, utilize the method in the present invention to demarcate the parabolic catadioptric video camera for testing, concrete steps are as follows:
1. fitted figure is as the quadratic curve equation of cathetus projection
The image resolution ratio that the present invention adopts is 245 × 245 pixels, take 1 width experiment picture with parabolic catadioptric video camera, read in image, utilize Edge function in Matlab to extract the coordinate of image characteristic point, and with each curve in least-squares algorithm fitted figure picture, obtain curvilinear equation.Obtain each curve in image
Figure DEST_PATH_IMAGE062
, wherein
Figure DEST_PATH_IMAGE063
, matrix of coefficients
Figure DEST_PATH_IMAGE064
, wherein
Figure 382625DEST_PATH_IMAGE063
for:
Figure DEST_PATH_IMAGE065
，
Figure DEST_PATH_IMAGE066
，
Figure DEST_PATH_IMAGE067
，
Figure DEST_PATH_IMAGE068
。
2. calculate the intersection point of every two quafric curves
If there are four straight lines in space
Figure 535258DEST_PATH_IMAGE001
(as Fig. 1), straight line is projected as great circle on unit ball , , the intersection point of every two circles is designated as
Figure 367188DEST_PATH_IMAGE004
with
Figure 995615DEST_PATH_IMAGE005
, wherein
Figure 297284DEST_PATH_IMAGE006
Figure 985754DEST_PATH_IMAGE007
Figure 107294DEST_PATH_IMAGE008
.Great circle is projected as curve on the catadioptric plane of delineation
Figure 539412DEST_PATH_IMAGE009
, intersection point is respectively
Figure 695587DEST_PATH_IMAGE010
with
Figure 56424DEST_PATH_IMAGE011
, wherein
Figure 665259DEST_PATH_IMAGE006
Figure 573173DEST_PATH_IMAGE007
Figure 646171DEST_PATH_IMAGE008
.Four great circles on unit ball
Figure 614127DEST_PATH_IMAGE012
,
Figure 772576DEST_PATH_IMAGE013
,
Figure 484180DEST_PATH_IMAGE014
,
Figure 411684DEST_PATH_IMAGE015
for four straight lines corresponding to space
Figure 550542DEST_PATH_IMAGE001
projection (as Fig. 2) on unit ball.Only consider plane, i.e. a great circle place plane,
Figure 227695DEST_PATH_IMAGE013
,
Figure 9706DEST_PATH_IMAGE014
,
Figure 319465DEST_PATH_IMAGE015
with
Figure 452506DEST_PATH_IMAGE012
intersection point is respectively
Figure 505913DEST_PATH_IMAGE004
with
Figure 408009DEST_PATH_IMAGE005
, ,
Figure 446690DEST_PATH_IMAGE017
,
Figure 601990DEST_PATH_IMAGE018
,
Figure 296276DEST_PATH_IMAGE019
,
Figure 275734DEST_PATH_IMAGE020
,
Figure 55471DEST_PATH_IMAGE021
be respectively
Figure 512997DEST_PATH_IMAGE012
, ,
Figure 212149DEST_PATH_IMAGE014
,
Figure 479182DEST_PATH_IMAGE015
imaging (as Fig. 3) in parabolic catadioptric camera plane, that is to say imaging, the intersection point of curve with
Figure 901177DEST_PATH_IMAGE011
be respectively
Figure 717823DEST_PATH_IMAGE004
with projection, just have
Figure DEST_PATH_IMAGE069
, wherein
Figure 40537DEST_PATH_IMAGE016
,
Figure 532698DEST_PATH_IMAGE017
.If intersection point homogeneous coordinates are
Figure DEST_PATH_IMAGE070
, there is equation:
Figure DEST_PATH_IMAGE071
，
Figure DEST_PATH_IMAGE072
， （1）
Figure DEST_PATH_IMAGE073
，
Figure DEST_PATH_IMAGE074
, （2）
Figure DEST_PATH_IMAGE075
，
Figure DEST_PATH_IMAGE076
， （3）
Solving equation group (1) (2) (3), can try to achieve curve
Figure 525056DEST_PATH_IMAGE018
with curve
Figure 800179DEST_PATH_IMAGE019
,
Figure 443650DEST_PATH_IMAGE020
,
Figure 345528DEST_PATH_IMAGE021
intersection point with ,
Figure DEST_PATH_IMAGE079
with
Figure DEST_PATH_IMAGE080
,
Figure DEST_PATH_IMAGE081
with
Figure DEST_PATH_IMAGE082
homogeneous coordinates as follows:
Figure DEST_PATH_IMAGE083
,
Figure DEST_PATH_IMAGE084
;
Figure DEST_PATH_IMAGE085
,
Figure DEST_PATH_IMAGE086
;
Figure DEST_PATH_IMAGE087
,
Figure DEST_PATH_IMAGE088
。
In system of equations (1) (2) (3),
Figure DEST_PATH_IMAGE089
,
Figure DEST_PATH_IMAGE090
, , can obtain
Figure 12133DEST_PATH_IMAGE019
with ,
Figure 149777DEST_PATH_IMAGE021
with
Figure 983741DEST_PATH_IMAGE020
with
Figure 934379DEST_PATH_IMAGE021
intersection point:
Figure DEST_PATH_IMAGE092
,
Figure DEST_PATH_IMAGE093
;
Figure DEST_PATH_IMAGE094
,
Figure DEST_PATH_IMAGE095
;
Figure DEST_PATH_IMAGE096
, 。
3. calculate 12 groups of hidden disappearing a little of orthogonal directions in four quadric surfaces
Circle on unit ball
Figure 567617DEST_PATH_IMAGE023
with three circles ,
Figure 920101DEST_PATH_IMAGE014
,
Figure 924966DEST_PATH_IMAGE015
meet at respectively six points (as Fig. 2) on unit ball, corresponding circle
Figure 362901DEST_PATH_IMAGE023
with
Figure 845834DEST_PATH_IMAGE098
with
Figure 318404DEST_PATH_IMAGE023
with
Figure 986846DEST_PATH_IMAGE014
the line of intersection point is two diameters, in two diameter circle, four points can be determined one group of orthogonal directions.After parabolic catadioptric
Figure 198702DEST_PATH_IMAGE018
,
Figure 260199DEST_PATH_IMAGE019
,
Figure 606866DEST_PATH_IMAGE020
, be respectively
Figure 47392DEST_PATH_IMAGE012
,
Figure 291292DEST_PATH_IMAGE098
, ,
Figure 944569DEST_PATH_IMAGE015
imaging (as Fig. 3) on the plane of delineation, is
Figure 510680DEST_PATH_IMAGE001
picture.At curve
Figure 874665DEST_PATH_IMAGE018
in the imaging plane at place, can determine altogether three groups of hidden disappearing a little of orthogonal directions.At curve
Figure 235239DEST_PATH_IMAGE019
,
Figure 684675DEST_PATH_IMAGE020
,
Figure 54476DEST_PATH_IMAGE021
in the imaging plane at place, also can determine respectively that the hidden of three groups of orthogonal directionss disappears a little.So, in four planes, have the hidden of 12 groups of orthogonal directionss and disappear a little.
Figure 7389DEST_PATH_IMAGE023
with
Figure 804444DEST_PATH_IMAGE098
the picture of intersection point
Figure DEST_PATH_IMAGE099
,
Figure DEST_PATH_IMAGE100
,
Figure 36449DEST_PATH_IMAGE023
with
Figure 209941DEST_PATH_IMAGE014
the picture of intersection point is
Figure DEST_PATH_IMAGE101
,
Figure DEST_PATH_IMAGE102
, straight line
Figure DEST_PATH_IMAGE103
with be respectively on the excessive round heart
Figure 313212DEST_PATH_IMAGE033
the straight line of picture, straight line
Figure 35443DEST_PATH_IMAGE034
with
Figure DEST_PATH_IMAGE105
and straight line
Figure 809364DEST_PATH_IMAGE038
with
Figure 674551DEST_PATH_IMAGE039
can determine one group of orthogonal hidden disappearing a little
Figure 875726DEST_PATH_IMAGE036
with
Figure 459154DEST_PATH_IMAGE040
,
Figure 275581DEST_PATH_IMAGE037
,
Figure 260854DEST_PATH_IMAGE041
, be respectively:
Figure DEST_PATH_IMAGE106
，
Figure DEST_PATH_IMAGE107
。
Figure DEST_PATH_IMAGE108
with
Figure DEST_PATH_IMAGE109
,
Figure 757564DEST_PATH_IMAGE046
with
Figure DEST_PATH_IMAGE110
it is curve
Figure 392070DEST_PATH_IMAGE018
the hidden of the another two groups of orthogonal directionss of imaging plane at place disappears a little, can determine that altogether the hidden of three groups of orthogonal directionss disappears a little.Add
Figure 445476DEST_PATH_IMAGE019
,
Figure 285256DEST_PATH_IMAGE020
,
Figure 828233DEST_PATH_IMAGE021
the imaging plane at place can determine that the hidden of 12 groups of orthogonal directionss disappears a little, is respectively altogether:
Figure DEST_PATH_IMAGE111
；
Figure DEST_PATH_IMAGE112
；
Figure DEST_PATH_IMAGE113
；
Figure DEST_PATH_IMAGE114
；
Figure DEST_PATH_IMAGE115
；
Figure DEST_PATH_IMAGE116
；
Figure DEST_PATH_IMAGE117
；
Figure DEST_PATH_IMAGE118
；
Figure DEST_PATH_IMAGE119
；
Figure DEST_PATH_IMAGE120
；
。
4. solve parabolic catadioptric camera intrinsic parameter
Article two, the hidden of orthogonal straight lines disappears a little, is called that pair of orthogonal is hidden to disappear a little.If
Figure DEST_PATH_IMAGE122
mutually orthogonal hidden disappearing a little,
Figure DEST_PATH_IMAGE123
, order
Figure DEST_PATH_IMAGE124
,
Figure DEST_PATH_IMAGE125
represent absolute conic image, and
Figure 556892DEST_PATH_IMAGE125
be symmetric matrix, comprise six unknown quantitys.If
Figure DEST_PATH_IMAGE126
homogeneous coordinates be
Figure DEST_PATH_IMAGE127
:
Figure DEST_PATH_IMAGE128
（4）
A hidden substitution (4) formula that disappears of 12 groups of orthogonal directionss, just can obtain absolute conic
Figure 538624DEST_PATH_IMAGE125
matrix of coefficients.In Matlab, utilize SVD to decompose the Intrinsic Matrix that just can solve linearly parabolic catadioptric video camera
Figure DEST_PATH_IMAGE129
, wherein
Figure 295227DEST_PATH_IMAGE056
for-1.0266,
Figure 946788DEST_PATH_IMAGE057
with
Figure 570535DEST_PATH_IMAGE058
be respectively 246.0921 and 246.8854, for (329.0857,238.8109), be 5 intrinsic parameters of parabolic catadioptric video camera.

Claims (1)

1. utilize the image scale of four not parallel straight lines in space to determine a method for parabolic catadioptric camera intrinsic parameter, it is characterized in that only utilizing vertical element; The parabolic catadioptric image of straight line is quafric curve, first extract picture point from image, matched curve equation also solves the intersection point of every two quafric curves, then calculate hidden the disappearing a little of 12 groups of orthogonal directionss in four quafric curves, recycle the hidden constraint linear solution parabolic catadioptric camera intrinsic parameter to absolute conic disappearing a little; Concrete steps comprise: curvilinear equation in fitted figure picture, the hidden of 12 groups of orthogonal directionss solving in intersection point and four quafric curve imaging planes of every two quafric curves disappears a little, solves in parabolic catadioptric camera intrinsic parameter matrix
Figure 120965DEST_PATH_IMAGE001
deng 5 parameters;
(1) calculate the intersection point of every two quafric curves
If there are four straight lines in space
Figure 764436DEST_PATH_IMAGE002
, straight line is projected as great circle on unit ball
Figure 161919DEST_PATH_IMAGE003
,
Figure 890841DEST_PATH_IMAGE004
, great circle is projected as curve on the catadioptric plane of delineation , intersection point is respectively
Figure 31414DEST_PATH_IMAGE006
with
Figure 865378DEST_PATH_IMAGE007
, wherein
Figure 760839DEST_PATH_IMAGE009
Figure 113323DEST_PATH_IMAGE010
, have
Figure 118188DEST_PATH_IMAGE011
;
(2) calculate 12 groups of hidden disappearing a little of orthogonal directions in four quafric curve imaging planes
Circle on unit ball
Figure 556123DEST_PATH_IMAGE012
meet at respectively six points on unit ball with other three circles, the line of corresponding circle intersection point is circle
Figure 367670DEST_PATH_IMAGE012
diameter, two diameters circle on 4 the adjacent side that forms orthogonal, opposite side is parallel to each other, can determine one group of orthogonal directions, every two groups of three diameters can be determined one group of orthogonal directions, totally three groups; After parabolic refraction and reflection projection
Figure 840239DEST_PATH_IMAGE013
,
Figure 16006DEST_PATH_IMAGE014
,
Figure 941237DEST_PATH_IMAGE015
,
Figure 227861DEST_PATH_IMAGE016
be respectively
Figure 289358DEST_PATH_IMAGE017
,
Figure 636026DEST_PATH_IMAGE018
,
Figure 48553DEST_PATH_IMAGE019
,
Figure 640333DEST_PATH_IMAGE020
imaging on the plane of delineation, at curve
Figure 821916DEST_PATH_IMAGE013
in the projection at place, can determine altogether three groups of hidden disappearing a little of orthogonal directions;
At curve
Figure 73906DEST_PATH_IMAGE014
,
Figure 973729DEST_PATH_IMAGE015
,
Figure 602156DEST_PATH_IMAGE016
In the projection at place, also can determine respectively that the hidden of three groups of orthogonal directions disappears a little, so, in four imaging quadratic surfaces, have the hidden of 12 groups of orthogonal directions and disappear a little; Being imaged as of parabolic catadioptric video camera
Figure 326716DEST_PATH_IMAGE022
, in imaging
Figure 713835DEST_PATH_IMAGE023
In,
Figure 644488DEST_PATH_IMAGE023
With
Figure 535084DEST_PATH_IMAGE024
Intersection point be ,
Figure 3291DEST_PATH_IMAGE023
With
Figure 239100DEST_PATH_IMAGE026
Intersection point be
Figure 249782DEST_PATH_IMAGE027
; Straight line
Figure 280055DEST_PATH_IMAGE028
With
Figure 376187DEST_PATH_IMAGE029
Be respectively the excessive round heart
Figure 651572DEST_PATH_IMAGE030
The straight line of picture, line correspondence
Figure 516760DEST_PATH_IMAGE031
With straight line Meet at a little
Figure 301363DEST_PATH_IMAGE033
, have
Figure 613395DEST_PATH_IMAGE034
; Line correspondence
Figure 598669DEST_PATH_IMAGE035
With straight line
Figure 970744DEST_PATH_IMAGE036
Meet at a little
Figure 41468DEST_PATH_IMAGE037
, have
Figure 661587DEST_PATH_IMAGE038
,
Figure 501367DEST_PATH_IMAGE033
With
Figure 44343DEST_PATH_IMAGE037
One group of hidden disappearing a little of orthogonal direction exactly;
Figure 336784DEST_PATH_IMAGE039
With
Figure 256199DEST_PATH_IMAGE040
It is straight line
Figure 950485DEST_PATH_IMAGE041
Figure 664364DEST_PATH_IMAGE042
Imaging On hidden the disappearing a little of one group of orthogonal direction,
Figure 668671DEST_PATH_IMAGE043
With Be
Figure 367823DEST_PATH_IMAGE045
Figure 634856DEST_PATH_IMAGE042
Imaging
Figure 896073DEST_PATH_IMAGE023
On another group orthogonal direction is hidden disappears a little, totally three groups of hidden disappearing a little of orthogonal direction;Add
Figure 299372DEST_PATH_IMAGE046
Picture
Figure 374962DEST_PATH_IMAGE024
,
Figure 196211DEST_PATH_IMAGE049
Picture
Figure 626055DEST_PATH_IMAGE015
With
Figure 664418DEST_PATH_IMAGE050
Figure 205121DEST_PATH_IMAGE051
Picture
Figure 910909DEST_PATH_IMAGE016
Hidden the disappearing a little forming, can obtain 12 groups of hidden disappearing a little altogether;
(3) solve parabolic catadioptric camera intrinsic parameter
Use parabolic catadioptric video camera to take 1 width image, the constraint of the picture by the hidden picture disappearing a little of orthogonal directions to absolute conic, linear solution goes out 5 intrinsic parameters, i.e. matrixes of parabolic catadioptric video camera
Figure 246075DEST_PATH_IMAGE052
, wherein
Figure 37314DEST_PATH_IMAGE053
for the distortion factor of image,
Figure 116128DEST_PATH_IMAGE054
with
Figure 177887DEST_PATH_IMAGE055
for focal length, for principal point coordinate, be 5 intrinsic parameters of parabolic catadioptric video camera.
CN201310531024.5A 2013-11-01 2013-11-01 Calibration of parabolic refraction and reflection vidicon internal parameters by utilizing four unparallel straight lines in space Pending CN103810697A (en)

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