CN109934879A - Utilize the method for ball and public self-polar triangle calibration parabolic catadioptric video camera - Google Patents
Utilize the method for ball and public self-polar triangle calibration parabolic catadioptric video camera Download PDFInfo
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Abstract
The present invention relates to a kind of methods using ball and public self-polar triangle calibration parabolic catadioptric video camera, comprising: extracts the marginal point and target image marginal point of mirror surface outline projection from 5 width images respectively；According to picture point and its relationship for opening up picture point is obtained to opening up picture point, thus fit ball picture to opening up ball picture；Public self-polar triangle is obtained according to ball picture and to ball picture is opened up, to obtain public pole and polar curve；With ball picture and end point and corresponding polar curve are determined to the positional relationship for opening up ball picture according to public pole, is that ball is regarded as the projection put in the great circle in the center of circle, to obtain the end point in public polar curve direction using unit due to polar curve and ball picture and to the intersection point for opening up ball picture；It obtains in the end point in public pole being orthogonal with the end point on public polar curve according to conjugate value；Finally by the constraint calibrating camera of orthogonal end point and camera intrinsic parameter.
Description
Technical field
The invention belongs to computer vision field, be related to it is a kind of using ball under unit ball projection model to opening up property mark
Determine the method for parabolic catadioptric video camera.
Background technique
Artificial intelligence has more accurately identification, processing, application from 2 dimension images in the demand for development computer of visual field
3 dimension information in space.The calibration of camera chain is a step basic in computer vision research.Scaling method it is accurate
Property, the accuracy of three-dimensional layering manufacture directly in decision computer vision system.Computer calibration is exactly the figure needed using 2 dimensions
As the corresponding 3 dimension space information of information acquisition, corresponding 3 dimension information is such as measured according to image information, obtains object in space
The information such as shape, position, size, athletic posture, it is corresponding just to need to measure the parameter in camera chain, this
The process of measurement is known as the calibration of video camera.The accuracy of camera calibration result directly determines that measurement obtains in 3 dimension spaces
Error between object information and true value, for example need to obtain the coordinate of 3 dimension points in 3 dimension spaces, need to use video camera system
The principal point and focal length of system, the accuracy of principal point and focal length obtained by calibrating determine to obtain the accuracy of 3 dimension points, determine subsequent 3
The accuracy of dimension reconstruct and 3 dimension measurement results.So proposing that accurate reasonable camera marking method has practical application valence
Value.
Most often general unit regards spheric projection model for the imaging model application of central catadiotric video camera, this
A model by document " Catadioptric Projective Geometry ", (Geyer C, Daniilidis K.,
International Journal of Computer Vision, 2001,45 (3): 223-243.) it proposes, and prove this mould
Type is the two steps projection that central catadiotric system imaging process equivalence is that unit regards ball.It is proposed based on Geyer and Daniilidis
Generalized projection model, there are many scaling methods about central catadiotric video camera, distinguishing from calibration type can
To be divided into two classes of self-calibration and calibration.In addition, proposing many marks based on calibration target under central catadiotric camera chain
Determine method: so far, removing document " Catadioptric self-calibration ", (Kang, S.B., In
Proceedings of IEEE International Conference on Computer Vision and Pattern
Recognition, 2000,1:201-207.) and document " Epipolar geometry for central catadioptric
Cameras ", (Sobver T, Pajdla T., International Journal of Computer Vision, 2002,49
(1): outside the method for completing self-calibration based on the corresponding relationship between picture point 23-37.) proposed, demarcating target using entity
It is proposed that the scaling method of central catadiotric video camera can be divided into three classes.The first kind is document " A flexible technique
For accurate omnidirectional camera calibration and structure from motion ",
(Scaramuzza,D.,Martinelli,A.,Siegwart,R.,In Proceedings of IEEE International
Conference on Computer Vision Systems, 2006:45-45.) propose the scaling method based on control point,
By the homography matrix established between the 2 dimension planes of delineation and 3 dimension spaces, the method for algebra completes the calibration of video camera；Second class
For document " Geometric properties of centralcatadioptric line images and their
Application in calibration ", (Barreto J, Araujo H., IEEE Transactions on Pattern
Analysis and Machine Intelligence, 2005,27 (8): 1327-1333.) calibration based on straight line proposed
Method completes camera intrinsic parameter and mirror surface parameter by the geometric properties of the pictures of 3 or 5 straight lines on the image plane
It solves；Third class is document " Catadioptric camera calibration using geometric
Invariants ", (Ying X, Hu Z., IEEE Transactions on Pattern Analysis and Machine
2004,26 (10): Intelligence is put forward for the first time the constraint of ball picture Yu camera intrinsic parameter and offer in 1260-1271.)
Relationship between number.
Document " A calibration method for paracatadioptric camera from sphere
Images ", (Duan H, Wu Y., Pattern Recognition Letters, 2012,33 (6): 677-684.) using empty
Between ball regard the imaging property under spherical model in general unit and complete calibration, on this basis document " Camera
Calibration from the quasi-affine invariance of two parallel circles ", (Wu Y,
Zhu H,Hu Z,et al.,Proc of European Conference of Computer Vision,2004,3021:
190-202.) Spatial Sphere proposed in unit depending on spherical model it is parallel to open up roundlet obtain on the plane of delineation to opening up ball picture
(visual ball picture with to open up ball picture) utilizes and completes calibration to the relationship opened up between ball picture.On the basis of herein, document is utilized
“Camera Calibration Based on the Common Self-polar Triangle of Sphere
Images ", (Haifei H, Hui Z and Yiu ming C., Lecture Notes in Computer Science,
2014.) relationship between public self-polar triangle structure condition and public pole and polar curve obtains 1 end point and corresponding
Polar curve, according to conjugate value obtain be with the end point on public polar curve in the end point in public pole it is orthogonal, thus obtain
5 groups of orthogonal end points are obtained, to complete the calibration of video camera.
Summary of the invention
The present invention provides a kind of production simply, is generally applicable in, and the good Spatial Sphere of stability is that the calibration parabolic of target is rolled over
Reflect the method for video camera.This method by 5 width target figures can linear solution go out 5 intrinsic parameter of video camera
The present invention adopts the following technical scheme:
It is shot from different angles by parabolic catadioptric video camera and obtains 5 width target images.The present invention is by single in space
The method that a ball solves 5 intrinsic parameters of video camera as calibration target, it is characterised in that make full use of target in unit spherical model
Under projected nature: first, respectively from 5 width images extract mirror surface outline projection marginal point and target image marginal point, make
It is fitted with least square method and obtains mirror surface outline projection and the projection of ball picture；Second, relationship for opening up picture point is obtained with it according to picture point
To opening up picture point, thus fit ball picture to opening up ball picture；Third, according to ball picture and to open up ball picture obtain it is public from pole triangle
Shape, to obtain public pole and polar curve.According to public pole and ball picture and end point is determined to the positional relationship for opening up ball picture
And corresponding polar curve, it is that ball is regarded as the throwing put in the great circle in the center of circle using unit due to polar curve and ball picture and to the intersection point for opening up ball picture
Shadow, to obtain the end point in public polar curve direction.End point and public pole in public pole are obtained according to conjugate value
End point on line is orthogonal.Finally by the constraint calibrating camera of orthogonal end point and camera intrinsic parameter.
1. obtaining mirror surface profile and ball image space journey
Based on MATLAB platform, the mirror surface outline projection marginal point and target extracted using least square method from Edge function
Image border point pixel coordinate is to fit mirror surface outline projection equation and ball image space journey.
2. estimation is to opening up ball picture
Under unit ball projection model, imaging of the Spatial Sphere Q under parabolic catadioptric video camera is divided into two steps.The first step, ball Q
Projection is the roundlet S on unit view balln+And Sn-(n=1,2 ..., 5 indicate the n-th width image of shooting), one of them is visible (under
Marking "+" indicates) one invisible (expression of subscript "-"), M+And M-This is corresponded respectively to 2 points on parallel roundlet, and is single
2 endpoints of position view bulb diameter.Unit regards 2 endpoints of bulb diameter as 1 pair of antipodal point, then Sn+With Sn-It is parallel small to opening up for 1 pair
Circle.Second step regards the virtual camera optical center O of ball surface by unitcParallel 1 pair to opening up roundlet Sn+And Sn-Project to image
On plane Π, conic section C is obtainedn+And Cn-, wherein claiming Cn-For visible conic section Cn+To opening up ball picture, subscript "-" with
"+" respectively indicates invisible and as it can be seen that plane of delineation Π and unit view ball centre of sphere OwPlace straight line OcOwVertically.If with OcFor light
The virtual camera Intrinsic Matrix of the heart isWherein fu, fvIt is video camera on u axis and v axis direction
Scale factor, video camera principal point homogeneous coordinates matrix formula p=[u0 v0 1]T, s be the obliquity factor of u axis and v axis direction (also referred to as
Distortion factor), fu,fv,u0,v0, s is 5 intrinsic parameters for needing to solve video camera in calibration process.Using least square method from
The mirror surface outline projection marginal point and target image marginal point pixel coordinate that Edge function extracts fit mirror surface outline projection side
Journey and ball image space journey.If C0For the coefficient matrix of the mirror surface outline projection curve of the 1st width image, Cn+Indicate n-th (n >=5) width figure
The coefficient matrix of ball picture as in, then pass through C0It can get an initial matrix value K of camera intrinsic parameter matrix K0, thus
To absolute conic as the initial value ω of ω0, i.e.,Wherein, ω and camera intrinsic parameter relationship be ω=
K-TK-1.If to ball is opened up as Cn+And Cn-On point be respectivelyWithWherein n=1,2 ... 5, j=1,2 ... N (N >=5) table
Show jth width image, then by initialization intrinsic parameter K0Obtain ω0.Recycle equationPass through imaging pointIt calculates to opening up picture pointSubscript j indicates to clap
The jth width image taken the photograph, subscript n=1,2,3 indicate the n-th of picture point taken, "+,-" respectively indicate it is visible with it is invisible.By throwing
Shadow mapping associativity knows point setTo opening up ball as Cn-On, then point set is fitted by least square methodIt is available to opening up
Ball is as Cn-Equation.
3. public self-polar triangle obtains end point
Spatial Sphere Q obtains 2 disjoint 1 couple of conic section C on the plane of delineation under unit ball projection model+And C-,
It is defined by public self-polar triangle and knows C+With C-Constitute 1 public self-polar triangle Δ mAmBmC, wherein mA,mB,mC3 points of difference
It is correspondingIn feature vector.In 3 vertex, 1 is infinite point, and 2 are located across the polar curve at conic section center
On, the available respective value of method decomposed by SVD, and may determine that at 3 points according to the positional relationship of point and conic section
In end point and the corresponding polar curve by conic section center.
4. harmonic conjugates obtain end point
Roundlet S on unit view ball+On arbitrarily take 1 point M+, by knowing S to opening up property-On there will necessarily be 1 point M-, claim M+
And M-For 1 pair of antipodal point.Then M+With M-Ball centre of sphere O is regarded in unitwFor the great circle O in the center of circleIOn, it keeps tying according to projection mapping element
Invariance is closed, in the effective subpoint O of virtual cameracUnder, 1 couple of antipodal point M+And M-It is right to project 1 pair obtained on plane of delineation Π
Open up picture point m+And m-, OwIt is projected as video camera principal point p, m+And m-In great circle OIPicture OmOn.Wherein, m+And m-With virtually imaging
The effective subpoint O of machinecThe picture point p obtained under projection is conllinear.The end point of corresponding direction is calculated by double ratio harmonic conjugates
(m-m+,p0m∞)=- 1, wherein m∞For straight line m-m+End point on direction.5. the orthogonality of end point
Spatial Sphere Q forms 1 couple of parallel roundlet S on unit view ball+With S-, remember plane ΠSFor parallel S+With S-Plane, then
Disjoint parallel roundlet S+With S-Constitute 1 public self-polar triangle Δ A0B0C0, it is assumed here that C0For infinite point.By pole
With the definition of polar curve, point C0About roundlet S+With S-Polar curve be respectively lS+With lS-, C is known according to round conjugate value property0With
lS+The infinite point in two directions is orthogonal, same C0With lS-The infinite point in two directions is orthogonal, and because S+With S-In parallel, so lS+
With lS-In parallel.Then parallel lines l in projective geometryS+With lS-Intersect at infinite point x∞, then sentence according to straight line is vertical with plane
Fixed condition knows C0Direction is perpendicular to lS+With lS-Place plane Πl, to obtain C0With x∞For 1 group of orthogonal infinite point.Therefore
Public self-polar triangle Δ m on the plane of delineationAmBmCMiddle vertex mA,mB,mCThe end point m of corresponding end point and polar curve direction∞
For 1 group of orthogonal end point, it is denoted as d respectivelyi1And di2, wherein i=1,2 ..., 5 indicate the corresponding end point of the i-th width images.
6. solving parabolic catadioptric camera intrinsic parameter
According to orthogonal end point and absolute conic as the constraint relationship between ωObtain ω.Root again
According to equation ω=K-TK-1Relationship, by Cholesky decompose method obtain camera intrinsic parameter correlation matrix K-1, to K-1It asks
It is inverse to obtain camera intrinsic parameter K.
The invention has the advantages that
(1) target production is simple, only needs 1 ball.
(2) physical size and location information of the target without the concern for ball.
(3) the unobstructed geometric properties of the target itself, which to have in calibration process, enriches complete profile point source.
Detailed description of the invention
Fig. 1 is the target schematic diagram for solving central catadiotric camera intrinsic parameter.
Fig. 2 is projection of the target in parabolic mirror-lens system plane.
Specific embodiment
The present invention provides a kind of methods for solving parabolic catadioptric camera intrinsic parameter, it is by 1 in space
A ball is constituted, such as Fig. 1.It is needed with the calibration that this target completes parabolic catadioptric video camera by following steps: first, from parabolic
5 width images are shot in catadioptric camera chain and therefrom extract the marginal point and target image marginal point of mirror surface outline projection,
It is fitted using least square method and obtains mirror surface outline projection and the projection of ball picture；Second, it is obtained by picture point to opening up picture point, least square
Method fitting is to opening up ball picture；Third obtains public self-polar triangle using ball picture and to ball picture is opened up, to obtain public pole and pole
Line；4th, end point and corresponding polar curve with ball picture and are determined to the positional relationship for opening up ball picture according to public pole, by polar curve
It is that ball is regarded as the projection put in the great circle in the center of circle, to obtain public polar curve direction using unit with ball picture and to the intersection point for opening up ball picture
End point.Camera intrinsic parameter is obtained by the relationship between orthogonal end point and camera intrinsic parameter.Concrete operation step
It is as follows:
1. obtaining mirror surface profile and ball image space journey
The mirror surface outline projection marginal point and target image extracted using least square method from the Edge function in MATLAB
Marginal point pixel coordinate fits mirror surface outline projection equation and ball image space journey.
2. estimation is to opening up ball picture
As shown in Figure 1, the subscript n of conic section is omitted in figure, the Spatial Sphere Q under unit ball projection model is catadioptric in parabolic
The imaging penetrated under video camera is divided into two steps.The first step, ball Q projection are the parallel roundlet S on unit view balln+And Sn-(n=1,2,3
Indicate the n-th width image of shooting), wherein projection centre is that unit regards ball centre of sphere Ow, ball centre of sphere O is regarded with unitwEstablish world's seat
Mark system Ow-xwywzw, M+And M-2 points on respectively parallel roundlet, and be 2 endpoints of unit view bulb diameter, unit regards ball
Two endpoints of diameter are 1 pair of antipodal point, then Sn+With Sn-For to opening up parallel roundlet.Second step regards the void of ball surface by unit
Quasi- camera optical center OcParallel 1 pair to opening up roundlet Sn+And Sn-It projects on plane of delineation Π, wherein with OcIt is established for origin empty
Quasi- camera coordinate system Oc-xcyczc, xc,ycAxis respectively with xw,ywIn parallel, zcAxis and zwIt is overlapped perpendicular to picture plane Π, and intersects
In principal point p.Obtain conic section Cn+And Cn-, wherein claiming Cn-For visible conic section Cn+To opening up ball picture, plane of delineation Π and list
Position view ball centre of sphere OwPlace straight line OcOwVertically.If with OcIt is for the virtual camera Intrinsic Matrix of optical centerWherein fu, fvFor scale factor of the video camera on u axis and v axis direction, video camera principal point homogeneous coordinates
Matrix form p=[u0 v0 1]T, s is the obliquity factor (distortion factor) of u axis and v axis direction.fu,fv,u0,v0, s is calibration process
Middle 5 intrinsic parameters for needing to solve.The mirror surface outline projection marginal point and target extracted using least square method from Edge function
Image border point pixel coordinate fits mirror surface outline projection equation and ball image space journey.If C0For the throwing of the 1st width image mirror surface profile
The coefficient matrix of shadow curve, parameter are expressed as:
Then pass through C0It can get an initial matrix value K of camera intrinsic parameter matrix K0, calculation method is as follows
To obtain absolute conic as ω initial value ω0, by obtained initial value K0, available absolute two
The initial value of the picture of secondary curve
If to ball is opened up as Cn+And Cn-On point be respectivelyWithWherein n=1,2 ... 5, j=1,2 ... N (N >=5)
Indicate N width image, then by initialization intrinsic parameter K0Obtain ω0, on this basis, pass through imaging pointIt calculates to opening up picture pointConstraint equation is as follows:
p0For camera intrinsic parameter K0In corresponding homogeneous matrix principal point coordinate, point set is known by projection mapping associativity
To opening up ball as Cn-On, then point set is fitted by least square methodIt is available to opening up ball as Cn-Equation.For simplification
Expressing identical letter both indicates geometric element, also illustrates that coefficient matrix corresponding to geometric element.
3. determining end point by public self-polar triangle
As shown in Fig. 2, Spatial Sphere Q under unit ball projection model, obtains 1 pair of disjoint conic section on the plane of delineation
C+And C-, wherein C+For visible conic section, C-For invisible conic section.It is defined by public self-polar triangle and knows C+With C-Structure
At 1 public self-polar triangle Δ mAmBmC, wherein mA,mB,mCThree vertex respectively correspondIn feature vector:
X=[x1 x2 x3]T, x1,x2,x3For corresponding 3 feature vectors of 3 characteristic values in matrix operation, pass through SVD points
The method of solution is available.Wherein, 3 vertex x1,x2,x3In 1 be infinite point, 2 by conic section center pole
On line.Then available corresponding end point according to the following formula:
With
There is following formula to set up by (6) and (7):
By (8) as can be seen that end point x1Corresponding value g (x1) it is all larger than 0, remaining point x2,x3Corresponding value g (x2),g
(x3) it is respectively less than 0, it enables
G=Max { g (x1),g(x2),g(x3), (9)
Wherein g indicates g (x1),g(x2),g(x3) in corresponding maximum value, i.e., it is corresponding in public self-polar triangle vertex
End point is x1.Then by the available corresponding 5 public self-polar triangles of 5 width images and corresponding end point, it is denoted as di1(i
=1,2 ..., 5).
4. harmonic conjugates obtain end point
As shown in Figure 1, the roundlet S on unit view ball+On arbitrarily take 1 point M+, by knowing S to opening up property-On there will necessarily be
1 point M-, claim M+And M-For 1 pair of antipodal point.Then M+With M-Ball centre of sphere O is regarded in unitwFor the great circle O in the center of circleIOn, according to projection mapping
Element keeps combining invariance, in the effective subpoint O of virtual cameracUnder, antipodal point M+And M-Projection obtains on plane of delineation Π
1 pair to opening up picture point m+And m-, OwIt is projected as video camera principal point p, m+And m-In unit circle OIPicture OmOn, as shown in Figure 2.Its
In, m+And m-With in the effective subpoint O of virtual cameracThe picture point p obtained under projection is conllinear, by double ratio harmonic conjugates meter
Calculate the end point of corresponding direction:
(m-m+,p0m∞)=- 1, (10)
Wherein m∞For straight line m-m+End point on direction.Then by the available corresponding 5 polar curve directions of 5 width images
End point, be denoted as di2(i=1,2 ..., 5).
5. solving parabolic catadioptric camera intrinsic parameter
According to the constraint relationship between orthogonal end point and absolute conic ω, following equations group is obtained:
ω is obtained by least square method solve system of equation (11), finally according to the relationship of ω and camera intrinsic parameter:
ω=K-TK-1, (12)
Video camera correlation matrix K is obtained to the ω method for carrying out Cholesky decomposition-1, to K-1It inverts to obtain the 5 of video camera
A internal reference numerical value.
Embodiment
The invention proposes a kind of methods for demarcating parabolic catadioptric video camera using Spatial Sphere for target.The present invention uses
Experiment pattern structural schematic diagram it is as shown in Figure 1.Embodiment of the present invention is made with 1 example below and being retouched in more detail
It states.
The experiment pattern that parabolic catadioptric camera calibration based on ball in space uses is 1 ball in space, such as Fig. 1
It is shown, ball Q.The parabolic catadioptric video camera for experiment is demarcated using the method in the present invention, specific steps are such as
Under:
1, mirror surface profile and ball image space journey are fitted
Image size used is 1063 × 1033 in this example.5 width targets are shot by parabolic catadioptric camera chain
Image carries out Canny operator edge detection and binary conversion treatment to target image using MATLAB a2016, passes through least square
Method is fitted the equation of the picture of mirror surface profile equation and Spatial Sphere.Wherein, mirror surface profile is the boundary of image, for initializing camera shooting
Machine intrinsic parameter, the boundary of 1 width image can complete the estimation of camera intrinsic parameter, remember the coefficient matrix of mirror surface outline projection equation
For C0, the coefficient matrix of ball image space journey is Cn+(n=1,2 ... 5), and specific value is as follows:
2. estimation is to opening up ball picture
(13) formula is substituted into (2) and obtains the initialization value K of intrinsic parameter0, parameter matrix value is as follows:
(19) are substituted into the available absolute conic initial value ω of (3) formula0, matrix result is as follows:
In Cn+(n=1,2 ... 5) on take at least five point respectively, substitute into (4) formula respectively and obtain corresponding to picture point is opened up, pass through
Least square method fits corresponding to opening up ball as Cn-(n=1, the coefficient matrix of 2 ... 5) equations are as a result as follows:
3. obtaining end point
(14) formula and (21) formula are substituted into (5) formula, corresponding public self-polar triangle vertex can be calculated by SVD decomposition
Matrix X1:
According to (14) formula, (21) formula, (26) formula as a result, judging the end point in public self-polar triangle by (8) formula
d11, homogeneous coordinates matrix result is as follows:
d11=(1.0e+04) × [4.393790920947279 4.708273333205320
0.000100000000000]T。 (27)
2 intersection points according to public polar curve and ball picture by ball inconocenter are m+,m′+, correspondence is calculated by (4) formula
To opening up picture point m-,m′-, 2 pairs are as follows to picture point homogeneous coordinates matrix result is opened up:
With
By the available video camera principal point initial value p of (19) formula0, homogeneous coordinates matrix result is as follows:
p0=(1.0e+02) × [4.500000000000001 3.500000000000000
0.010000000000000]T。 (30)
(28) formula and (30) formula are substituted into (10) formula and obtain m-m+End point result homogeneous coordinates matrix on direction are as follows:
d12=(1.0e+02) × [- 9.353448071890112 4.486069877156241
0.010000000000000]T。 (31)
(15) formula of utilization and (22) formula, similar method obtain the end point d in public self-polar triangle21And end point
d21End point d on corresponding polar curve direction22, their homogeneous coordinates matrix results are as follows:
(16) formula of utilization and (23) formula, similar method obtain the end point d in public self-polar triangle31And end point
d31End point d on corresponding polar curve direction32, as a result homogeneous coordinates matrix are as follows:
(17) formula of utilization and (24) formula, similar method obtain the end point d in public self-polar triangle41And end point
d41End point d on corresponding polar curve direction42, as a result homogeneous coordinates matrix are as follows:
(18) formula of utilization and (25) formula, similar method obtain the end point d in public self-polar triangle51And end point
d51End point d on corresponding polar curve direction52, as a result homogeneous coordinates matrix are as follows:
4. solving parabolic catadioptric camera intrinsic parameter
By (27) formula and (31) formula, (32) formula, (33) formula, (34) formula substitutes into (11) formula, calculated by least square method
It is as a result as follows to the coefficient matrix of absolute conic ω:
Finally, (36) formula is substituted into (12) formula, ω is decomposed using Cholesky, then invert and obtain camera intrinsic parameter matrix
K, as a result as follows:
By the value of 5 intrinsic parameters of video camera available in (37) formula: for scale of the video camera on u axis and v axis direction
Factor fu=600.2091061072760, fv=550.1916805967444, u axis and v axis direction obliquity factor (distortion because
Son) s=0.800278796555200, video camera principal point u0=449.9999999969917, v=350.0000000011084.
Claims (1)
1. a kind of method using ball and public self-polar triangle calibration parabolic catadioptric video camera, it is characterised in that in space
Single ball is as the calibration target for solving 5 intrinsic parameters of video camera；The described method includes: first, it is extracted from 5 width images respectively
The marginal point and target image marginal point of mirror surface outline projection are fitted using least square method and obtain mirror surface outline projection and ball picture
Projection；Second, according to picture point and its relationship for opening up picture point is obtained to opening up picture point, thus fit ball picture to opening up ball picture；The
Three, public self-polar triangle is obtained according to ball picture and to ball picture is opened up, to obtain public pole and polar curve；According to public pole with
Ball picture and end point and corresponding polar curve are determined to the positional relationship for opening up ball picture, the friendship due to polar curve and ball picture and to ball picture is opened up
Point is to regard ball as the projection put in the great circle in the center of circle, to obtain the end point in public polar curve direction using unit；It is straight according to conjugation
Diameter obtains in the end point in public pole being orthogonal with the end point on public polar curve；Finally by orthogonal end point and take the photograph
The constraint calibrating camera of camera intrinsic parameter；
(1) public self-polar triangle obtains end point
Spatial Sphere Q obtains 2 disjoint 1 couple of conic section C on the plane of delineation under unit ball projection model+And C-, by public affairs
C is known in self-polar triangle definition altogether+With C-Constitute 1 public self-polar triangle Δ mAmBmC, wherein mA,mB,mC3 points respectively correspondIn feature vector；In 3 vertex, 1 is infinite point, and 2 are located across on the polar curve at conic section center, is led to
The method of SVD decomposition is crossed to obtain respective value, and according to the positional relationship of point and conic section to judge the end point in 3 points
With the corresponding polar curve by conic section center；
(2) harmonic conjugates obtain end point
Roundlet S on unit view ball+On arbitrarily take 1 point M+, by knowing S to opening up property-On there will necessarily be 1 point M-, claim M+And M-
For 1 pair of antipodal point；Then M+With M-Ball centre of sphere O is regarded in unitwFor the great circle O in the center of circleIOn, it keeps combining according to projection mapping element
Invariance, in the effective subpoint O of virtual cameracUnder, 1 couple of antipodal point M+And M-Projection obtains 1 pair on plane of delineation Π to opening up
Picture point m+And m-, OwIt is projected as video camera principal point p, m+And m-In great circle OIPicture OmOn；Wherein, m+And m-With in virtual camera
Effective subpoint OcThe picture point p obtained under projection is conllinear；End point (the m of corresponding direction is calculated by double ratio harmonic conjugates-
m+,p0m∞)=- 1, wherein m∞For straight line m-m+End point on direction；
(3) orthogonality of end point
Spatial Sphere Q forms 1 couple of parallel roundlet S on unit view ball+With S-, remember plane ΠSFor parallel S+With S-Plane, then not phase
The parallel roundlet S handed over+With S-Constitute 1 public self-polar triangle Δ A0B0C0, it is assumed here that C0For infinite point；By pole and pole
The definition of line, point C0About roundlet S+With S-Polar curve be respectively lS+With lS-, C is known according to round conjugate value property0With lS+
The infinite point in two directions is orthogonal, same C0With lS-The infinite point in two directions is orthogonal, and because S+With S-In parallel, so lS+With
lS-In parallel；Then parallel lines l in projective geometryS+With lS-Intersect at infinite point x∞, then the judgement vertical with plane according to straight line
Condition knows C0Direction is perpendicular to lS+With lS-Place plane Πl, to obtain C0With x∞For 1 group of orthogonal infinite point；Therefore scheme
As public self-polar triangle Δ m in planeAmBmCMiddle vertex mA,mB,mCThe end point m of corresponding end point and polar curve direction∞It is 1
The orthogonal end point of group, is denoted as d respectivelyi1And di2, wherein i=1,2 ..., 5 indicate the corresponding end point of the i-th width images.
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