CN109325982A - Parabolic catadioptric video camera is demarcated using single ball and parallel circle tangential property - Google Patents

Parabolic catadioptric video camera is demarcated using single ball and parallel circle tangential property Download PDF

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CN109325982A
CN109325982A CN201811214872.2A CN201811214872A CN109325982A CN 109325982 A CN109325982 A CN 109325982A CN 201811214872 A CN201811214872 A CN 201811214872A CN 109325982 A CN109325982 A CN 109325982A
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point
picture
ball
opening
circular
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李远珍
赵越
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Yunnan University YNU
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00—Image analysis
    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The present invention is the method using single ball and parallel circle tangential property calibration parabolic catadioptric video camera, it is characterised in that merely with ball element.Firstly, extracting the marginal point and target image marginal point of mirror surface outline projection from 3 width images respectively, the projection for obtaining mirror surface outline projection and ball picture is fitted using least square method.Secondly, 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.A point is taken on ball picture, and is found out to opening up picture point.By the property to the definition and parallel circle of opening up picture point, above-mentioned one group provides an end point to picture point is opened up.Under parabolic mirror-lens system, ball projects on unit view ball for the first time and forms two parallel roundlets.Two parallel circles of antarafacial have the imaginary intersection point of two pairs of conjugation, wherein the two conjugation imaginary intersection points conllinear with the infinite point of plane where circle are circular point.Finally, using circular point as the constraint solving camera intrinsic parameter to absolute conic picture.

Description

Parabolic catadioptric video camera is demarcated using single ball and parallel circle tangential property
Technical field
The invention belongs to computer vision field, it is related to a kind of asking using the property of a ball and parallel circle tangent line in space The method for solving parabolic catadioptric camera intrinsic parameter.
Background technique
The central task of computer vision is exactly to understand image, and its final goal is to have computer to lead to Cross the ability of two dimensional image cognition three-dimensional environment information.It includes shape, posture, movement that this ability, which will not only cause a machine to perception, The geological information of object in three-dimensional environment Deng including, and they can be described, be stored, identified and understood.Video camera Calibration is exactly to determine that it is many computer vision applications from three-dimensional space point to the mapping relations its two-dimensional image point Essential step.In order to determine this mapping process, need to establish the geometry imaging model of video camera, the ginseng of geometrical model Number is known as camera parameters, and camera parameters can be divided into two class of intrinsic parameter and outer parameter.Intrinsic parameter describes the imaging of imaging system Geometrical property, outer parameter describe direction and position of the imaging system about world coordinate system.Camera calibration can be divided into traditional mark Fixed, self-calibration and the calibration based on geometry entity.No matter which kind of scaling method, be intended to and establish two dimensional image and video camera internal reference The constraint relationship between number, especially linear restriction relationship, this is the target that current camera calibration is pursued, and meter at present One of the hot spot of calculation machine visual field research.
Parabolic catadioptric video camera is made of a parabolic mirror surface and an orthogonal camera, its visual field is big, is One of the hot spot of panoramic vision area research.Document " Catadioptric self-calibration ", (Kang S.B., Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, Vol.1, pp.201-207,2000.) propose a kind of catadioptric camera self-calibration method, the advantages of such methods is to be not required to Calibrating block is used, the disadvantage is that the corresponding points between image must be obtained.And in computer vision, realization one is largely effective The methods of searching corresponding points be highly difficult.Document " Geometric properties of central catadioptric line images and their application in calibration”,(Barreto J.P., Araujo H.,IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol.27, no.8, pp.1327-1333,2005) geometric properties of the picture of straight line under central catadiotric video camera are had studied, and incite somebody to action These properties are applied to the calibration of central catadiotric video camera.Document " A new linear algorithm for calibrating central catadioptric cameras”,(Wu F.,Duan F.,Hu Z.et al.,Pattern Recognition, vol.41, no.10, pp.3166-3172,2008) antipodal point and the definition to picture point is opened up are described, it exports Relationship of the point between the projection and its catadioptric picture point on view ball in space, is established using this relationship The linear restriction of central catadiotric camera intrinsic parameter can be obtained central catadiotric video camera internal reference by this linear restriction Number.Document " Calibration of central catadioptric cameras using a DLT-like approach”,(Puig L.,Bastanlar Y.,Sturm P.,et al.International Journal of Computer Vision, vol.93, no.1, pp.101-114,2011) propose a kind of calibration side based on Three dimensions control point Method extends the coordinate of three-dimensional point and its picture point by using Veronese mapping, on the basis of extending coordinate Based on DLT (direct linear transformation) --- similar method realizes the calibration of central catadiotric video camera, but such methods need The position of known three-dimensional point is wanted, and is easy to extract its picture point from image.
Ball is as a kind of common solid, and most important advantage is to block without itself, in terms of any one direction The occluding contour of an a ball always circle in space, and its contour projection can be extracted all.Due to ball have it is rich Rich visual geometric characteristic, therefore carry out camera calibration using ball and have become a hot spot in recent years.Document " Catadioptric camera calibration using geometric invariants ", (Ying X., Hu Z., IEEE Transactions on Pattern Analysis and Machine Intelligence,vol.26,no.10, Pp.1260-1271,2004 it) has been put forward for the first time and has demarcated central catadiotric video camera using ball.It is catadioptric at center that they demonstrate ball The picture under the unit ball projection model of video camera is penetrated as ellipse, and is mentioned in the projection conic section of the next ball of non degenerate situation For two invariants.In order to reduce the complexity of solution, they propose a kind of substep scaling method, and this method at least needs 4 The projection of a ball could complete the calibration of video camera.But the scaling method that the document proposes is nonlinear, the complexity of calculating Degree is higher, and the scaling method can only demarcate the part intrinsic parameter of parabolic catadioptric video camera.Document " Identical projective geometric properties of central catadioptric line images and Sphere images with applications to calibration ", (Ying X., Zha H., International Journal of Computer Vision, vol.78, no.1, pp.89-105,2008) describe amendment absolute conic Effect of the picture (MIAC) in central catadiotric camera calibration.They are by research ball under central catadiotric video camera As the Analytic Geometry and Algebra relationship with MIAC proposes two kinds of linear calibration's algorithms.The conclusion that they are obtained is also for dual form It sets up.But the theory and scaling method in this article are to degenerate for the case where parabolic catadioptric video camera.Document " A calibration method for paracatadioptric camera from sphere images ", (Duan H., Wu Y., Pattern Recognition Letters, vol.33, no.6, pp.677-684,2012) it is managed based on circular point It is a kind of using to the linear method for opening up ball picture calibration parabolic catadioptric video camera by proposing.But about annulus in this article The selection of the picture of point is more complicated.
Summary of the invention
The present invention provides a kind of production simply, widely applicable, and stability is good to be taken the photograph using target solution parabolic catadioptric The method of camera intrinsic parameter, the target are made of a ball in space.In the process for solving parabolic catadioptric camera intrinsic parameter In, parabolic catadioptric video camera need to be used to solve parabolic catadioptric from 3 width linearities of different position shooting targets and taken the photograph 5 intrinsic parameters of camera.
The present invention adopts the following technical scheme:
The image that 3 width contain a ball is shot from different positions with parabolic catadioptric video camera.The present invention is to utilize sky Between in a ball as target be used for solve parabolic catadioptric camera intrinsic parameter method, it is characterised in that merely with ball member Element.Firstly, extracting the marginal point and target image marginal point of mirror surface outline projection from 3 width images respectively, least square is used Method fitting obtains the projection of mirror surface outline projection and ball picture.Secondly, 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.A point is taken on ball picture, and is found out to opening up picture point.By the definition to picture point is opened up With the property of parallel circle, above-mentioned one group provides an end point to picture point is opened up.Under parabolic mirror-lens system, ball projects for the first time Two parallel roundlets are formed on to unit view ball.Two parallel circles of antarafacial have the imaginary intersection point of two pairs of conjugation, wherein with where circle Two conllinear conjugation imaginary intersection points of the infinite point of plane are circular point.On as plane according to circular point as with end point Synteny, obtains the picture of circular point, and three width images provide the picture of three groups of circular points.Finally, using the picture of circular point to absolute two The constraint solving camera intrinsic parameter of secondary curve picture.Specific step includes: to fit mirror surface outline projection equation and target throwing Shadow equation, estimation ball picture to ball picture is opened up, determine the picture of circular point, solve parabolic catadioptric camera intrinsic parameter.
1. being fitted mirror surface outline projection equation and target projection equation
The picture of mirror surface outline projection marginal point and target image marginal point is extracted using the Edge function in Matlab program Plain coordinate, and the equation for obtaining mirror surface outline projection equation and ball picture is fitted with least square method.
2. estimation ball picture to opening up ball picture
Ball Q in space, the projection under the unit spherical model of parabolic catadioptric video camera are divided into two steps.The first step, will Ball Q is projected as the parallel roundlet S on the view ball of the unit centered on On+And Sn-(n=1,2,3 indicate the n-th width image of shooting), Claim Sn-For Sn+To opening up circle, and Sn-S is symmetrical with depending on ball center O with unitn+, unit regard bulb diameter two endpoints it is right each other It opens up.Second step, with the point O in unit view ball surfacecFor projection centre, O herecThe optical center of a video camera can be regarded as, will be put down Row roundlet Sn+And Sn-The conic section C being projected as on the parabolic catadioptric plane of delineation respectivelyn+,Cn-.Wherein claim visible secondary song Line Cn+For the picture of ball Q, sightless conic section Cn-It is ball as Cn+To opening up ball picture.Corresponding to the S on unit view balln-Referred to as To opening up circle, the parabolic catadioptric plane of delineation and straight line OcO is vertical.Corresponding to an endpoint of unit view bulb diameter, which exists The parabolic catadioptric plane of delineation is invisible to be known as to picture point is opened up, then unit is known as antipodal point depending on this endpoint of bulb diameter.Enable with OcIntrinsic Matrix for the video camera of optical center isWherein rcIt is aspect ratio, fcIt is effective focal length, s It is obliquity factor, [u0 v0 1]TIt is the homogeneous coordinates matrix form of video camera principal point p, rc, fc, s, u0, v0For parabolic catadioptric 5 intrinsic parameters of video camera.The mirror surface outline projection marginal point and 3 width in piece image are extracted using the function in Matlab The pixel coordinate of image target image marginal point is fitted to obtain corresponding quadratic curve equation by least square method.Here it uses C0Indicate the coefficient matrix of piece image mirror surface outline projection curve, Cn+Respectively indicate the coefficient of the ball picture in the n-th width image Matrix.Herein in order to simplify statement, the coefficient matrix of curve and it is indicated with same letter.Pass through C0It can get video camera internal reference Matrix number KcAn initial matrix valueTo obtain absolute conic as ω initial valueHere:Wherein It is the initial value of aspect ratio,It is effective focal length Initial value,It is the initial value of obliquity factor,It is the initial homogeneous coordinates matrix expression of video camera principal point, noteTake Cn+On one group of pointThen one group pair corresponding with it Open up picture pointIt can be by relationshipReally It is fixed,It is indicated with homogeneous coordinates matrix.According to the definition to picture point is opened up, pointIn ball as Cn+To opening up ball as Cn-On, Therefore available least square method is fitted to obtain to opening up ball as Cn-Equation.
3. determining the picture of circular point
In projection roundlet S of the ball Q on unit view ball1+On take a point A1+, use A1-Indicate A1+Ball center is regarded about unit The symmetric points of O, i.e. antipodal point, then point A1-In S1+Symmetrically justify about unit depending on ball center O, i.e., to opening up round S1-On.L1+It indicates A1+About circle S1+Tangent line, L1+Indicate A1-About circle S1-Tangent line.According to the definition of antipodal point and the property of parallel circle, L1+// L1-, then L1+And L1-Infinite point having the same, uses V here1∞Indicate L1+,L1-On infinite point.Roundlet S1+And S1-For Two parallel circles, they intersect at the imaginary intersection point of two pairs of conjugation.Because each circle in plane passes through circular point, circle with The intersection point of line at infinity is two circular points, and circular point is two conjugate imaginary points I (1, i, 0) and J (1 ,-i, 0), i.e. complex point. Because the parallel plane where parallel circle intersects at identical line at infinity, parallel circle all meets at circular point, so Circular point I, J are parallel circle S1+And S1-It is conjugated intersection point.The line at infinity of space circle and its place plane meets at circular point, I.e. circular point and the plane infinite point are conllinear, therefore infinite point V1∞It is conllinear with circular point I, J.On as plane, Use C1+,C1-Respectively indicate S1+,S1-Picture；Use a1+,a1-, respectively indicate A1+,A1-Picture, then a1+,a1-It is a pair to opening up picture point. Record a demerit point a1+About conic section C1+Tangent line be l1+, cross point a1-About conic section C1-Tangent line be l1-.Then according to projection The property of transformation, straight line l1±For straight line L1±Picture, can then pass through straight line l1+,l1-Determine S1+In the plane one disappearance Point v1, i.e. V1∞Picture.Conic section C1+,C1-There are the imaginary intersection point of two groups of conjugation, i.e. S1+And S1-Four imaginary intersection points picture, wherein One group must be the picture m of circular point1I,m1J.Perspective transform keep dotted line associativity, therefore on as plane circular point picture m1I,m1J With end point v1It is also conllinear.According to the judgement of synteny, the picture of circular point can get in four imaginary intersection points.For roundlet S2+,S3+Circular point in the plane picture m2I,m2J},{m3I,m3JCan get.Subscript I, J expression corresponds to circular point I, J.
4. solving parabolic catadioptric camera intrinsic parameter
By the picture m of circular pointnI,mnJ(n=1,2,3) is to absolute conic as the linear restriction of ω obtains ω, it may be assumed thatWherein Re, Im respectively indicate real and imaginary part.Finally, Cholesky decomposition is carried out to ω, Invert available Intrinsic Matrix K againc, that is, obtain the intrinsic parameter of X-ray machine X.
The invention has the advantages that
(1) target production is simple, only needs a ball.
(2) physical size of the target is not required, without knowing coordinate of the centre of sphere under world coordinate system.
(3) sharp point of the target almost can be extracted all, and the accuracy of curve matching can be improved in this way, from And improve stated accuracy.
Detailed description of the invention
Fig. 1 is the schematic diagram for solving the target of parabolic catadioptric camera intrinsic parameter on unit view ball.
Fig. 2 is projection of the target on the parabolic catadioptric plane of delineation.
Specific embodiment
The present invention provides a kind of methods for solving parabolic catadioptric camera intrinsic parameter using target, and target is by space In a ball constitute, such as Fig. 1.It is needed with the solution that this target completes parabolic catadioptric camera intrinsic parameter by following step It is rapid: to extract mirror surface outline projection marginal point and target image marginal point from image, be fitted using least square method and obtain mirror surface The picture of outline projection and ball.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.A point is taken on ball picture, and is acquired to picture point is opened up, and by the definition to picture point is opened up, is opened up picture point for above-mentioned one group and is provided one End point.Ball picture with to the imaginary intersection point opened up ball picture and have two groups of conjugation, wherein one group be circular point picture, according to the picture of circular point with The synteny of end point obtains the picture of circular point.Racket is taken the photograph in the orientation different from three, obtains the picture of three groups of circular points, utilizes Constraint solving camera intrinsic parameter of the picture of circular point to the picture of absolute conic.Using the method in the present invention to for real The parabolic catadioptric video camera tested is demarcated, the specific steps are as follows:
1. being fitted mirror surface outline projection equation and target projection equation
The picture of mirror surface outline projection marginal point and target image marginal point is extracted using the Edge function in Matlab program Plain coordinate, and the equation for obtaining mirror surface outline projection equation and ball picture is fitted with least square method.
2. estimation ball picture to opening up ball picture
Ball Q (such as Fig. 1) in space, the projection under the unit spherical model of parabolic catadioptric video camera are divided into two steps.The One step, parallel roundlet S ball Q being projected as on the unit view ball with the center On+,Sn-, claim Sn-For Sn+To open up circle (n=1,2, 3), (as shown in Figure 1, for n=1).Second step passes through the optical center O of video cameracBy parallel roundlet Sn+,Sn-It is projected as throwing respectively Conic section C on the object catadioptric plane of delineationn+,Cn-, referred to here as visible conic section Cn+For the picture of ball Q, sightless two Secondary curve Cn-It is ball as Cn+To opening up ball picture (as shown in Figure 1, for n=1).It is mentioned respectively using the Edge function in Matlab The pixel coordinate for taking the mirror surface outline projection of the target image marginal point and the 1st width image in 3 width images, passes through least square method Fitting obtains corresponding quadratic curve equation, uses C here0Indicate the coefficient matrix of the 1st width image mirror surface outline projection curve, Cn+ Indicate the coefficient matrix of the ball picture in the n-th width image.Pass through C0It can get camera intrinsic parameter matrix KcAn initial matrix valueSpecifically such as formula (1):
Here, C0(p, q) (p=1,2；Q=1,2,3) representing matrix C0Pth row q column element,φ is to take the photograph The half of camera field angle, ρ are paraboloidal mirror outline projection ellipse C0Major semiaxis it is long.It is obtainingOn the basis of ω can be obtained Initial valueSuch as formula (2):
Take Cn+On one group of pointThen one group corresponding with it to opening up picture pointIt can be determined by relational expression (3):
According to the definition to picture point is opened up, pointIn ball as Cn+To opening up ball as Cn-On, therefore available least square method is quasi- Conjunction is obtained to opening up ball as Cn-Equation.
3. determining the picture of circular point
In the projection roundlet S of ball Q1+On take a point A1+, use A1-Indicate A1+Antipodal point (as shown in Figure 1), then point A1- In S1+To opening up round S1-On.L1+For A1+About circle S1+Tangent line, L1-For A1-About circle S1-Tangent line, according to determining for antipodal point The property of justice and parallel circle, L1+//L1-, then L1+And L1-Infinite point having the same, uses V here1∞Indicate L1+,L1-On Infinite point.Roundlet S1+And S1-For two parallel circles, there is the imaginary intersection point of two pairs of conjugation.Because parallel circle all hands over line at infinity In identical circular point, so circular point I, J are parallel circle S1+And S1-It is conjugated intersection point.Space circle is infinite with plane where it Remote straight line meets at circular point, i.e., circular point and the plane infinite point are conllinear, therefore infinite point V1∞With circular point I, J It is conllinear.As shown in Fig. 2, using C on as plane1+,C1-Respectively indicate S1+,S1-Picture, use a1+,a1-Table A respectively1+,A1- Picture, then a1+,a1-For one group to opening up picture point.Record a demerit point a1+About conic section C1+Tangent line be l1+, cross point a1-About secondary Curve C1-Tangent line be l1-.If a1±Homogeneous coordinates matrix be [ua1± va1± 1]T, straight line l1±Homogeneous line coordinates matrix be [u1± v1± 1]T, then:
λ1+[u1+ v1+ 1]T=C1+[ua1+ va1+ 1]T, (4)
λ1-[u1- v1- 1]T=C1-[ua1- va1- 1]T, (5)
Wherein λ1±Non-zero invariant, subscript ± expression+and-write a Chinese character in simplified form, pair+indicate as it can be seen that-indicates invisible, i.e., Open up meaning.Then according to the property of projective transformation, straight line l1±For straight line L1±Picture, can then pass through straight line { l1+,l1-Determine it is small Circle S1+An end point v in the plane1, pass through simultaneous l1+And l1-Equation can obtain:
Wherein [u v 1]TFor the pixel homogeneous coordinates matrix on the parabolic catadioptric plane of delineation.
If v1Homogeneous coordinates matrix be [uv1 vv1 1]T, then v1=[uv1 vv1 1]TIt is the solution of equation group (6).C1+,C1- There is the imaginary intersection point of two pairs of conjugation, obtain imaginary intersection point with the Solve function in Matlab, wherein one group must be the picture m of circular point1I, m1J.Perspective transform keep dotted line associativity, therefore on as plane circular point picture m1I,m1JWith end point v1It is also conllinear. The necessary and sufficient condition of three point on a straight line is that the homogeneous coordinates composition determinant of a matrix of point is zero.Therefore meet in two groups of conjugation imaginary intersection points The point group of equation (7) is the picture of circular point:
Wherein [xi yi 1]T(i=1,2,3) homogeneous coordinates matrix of representation space point.Respectively two groups of conjugation imaginary intersection points Same v1It substitutes into (7) to test, the point for meeting condition is the picture of circular point.For roundlet S2+,S3+Annulus in the plane The picture m of point2I,m2JAnd m3I,m3JIt is obtained with same method.
4. solving parabolic catadioptric camera intrinsic parameter
Had by the picture of circular point to the linear restriction of the picture of absolute conic:
Wherein Re, Im respectively indicate real and imaginary part.ω can be obtained with least square method Optimization Solution (8), most It is right afterwardsCholesky is carried out to decomposeInvert available Intrinsic Matrix K againc, that is, obtain 5, video camera Intrinsic parameter.
Embodiment
Parabolic catadioptric video camera internal reference is linearly determined using a ball in space as target the invention proposes a kind of Several methods.The experiment pattern that the present invention uses ball as shown in schematic diagram 1.Below with an example to embodiment party of the invention Case makes more detailed description.
The experiment pattern that parabolic catadioptric camera calibration based on ball in space uses is a ball in space, is such as schemed Shown in 1, 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. being fitted image boundary and target curvilinear equation
The image size that the present invention uses is 690 × 1198.With 3 width lab diagrams of parabolic catadioptric video camera shooting target Picture reads in image, extracts the 1st width image mirror surface outline projection marginal point and 3 width image targets using the Edge function in Matlab The pixel coordinate of logo image marginal point, and the equation for obtaining mirror surface outline projection equation and ball picture is fitted with least square method.1st The coefficient matrix of width image mirror surface outline projection equation is C0, the coefficient matrix of the equation of 3 width ball pictures is respectively Cn+(n=1,2, 3), as a result as follows:
2. estimation ball picture to opening up ball picture
(9) substitution (1) and (2) can be obtainedMatrix result is as follows:
First respectively in ball as C1+、C2+And C3+On at least take the point of 5 inequalities, then the point taken and (13) are substituted into respectively (3) to the coordinate for opening up picture point, obtained by least square method fitting to opening up ball as C1-、C2-And C3-Estimation, coefficient matrix knot Fruit is as follows:
3. determining the picture of circular point
In ball as C1+Take up an official post and takes a point a1+, its homogeneous coordinates matrix are as follows:
a1+=[2306.81595265189-1103.75788416464 1]T, (17)
According to the property for opening up picture point, can get and point a1+It is corresponding to opening up picture point a1-, it is as a result as follows:
a1-=[12.170928237332 754.579525040891 1]T, (18)
(17) and (10) substitution (4) can must be crossed into point a1+About conic section C1+Tangent line l1+Homogeneous line coordinates matrix, As a result as follows:
l1+=[- 0.00020846048184 0.00047032056798 1]T, (19)
(18) and (14) substitution (5) can must be crossed into point a1-About conic section C1-Tangent line l1-Homogeneous line coordinates matrix, As a result as follows:
l1-=[- 0.00425493484596-0.00150398356075 1]T； (20)
(19) and (20) substitution (6) can be obtained into end point v1, it is as a result as follows:
v1=[0.85294002718423-1.74816022714045 1]T； (21)
C is solved with Solve function in Matlab1+And C1-Intersection point, imaginary intersection point and (21) generation acquire two pairs conjugation Enter (7) verifying and acquires S1+In the plane circular point picture m1I,m1J, homogeneous coordinates as a result are as follows:
m1I=[- 134.6434007080-638.3999342633i 133.6434007080+638.3999342633i 1]T, (22)
m1J=[- 134.6434007080+638.3999342633i 133.6434007080-638.3999342633i 1]T； (23)
For roundlet S2+Circular point in the plane picture m2I,m2JIt substitutes into (7) verifying with similar approach to obtain, as a result Homogeneous coordinates it is as follows:
m2I=[874.018799097-675.567729827i 1174.610328832+0666.004896463i 1]T, (24)
m2J=[874.018799097+675.567729827i 1174.610328832-0666.004896463i 1]T； (25)
For roundlet S3+Circular point in the plane picture m3I,m3J(7) verifying can be substituted into similar approach to obtain, knot The homogeneous coordinates of fruit are as follows:
m3I=[48.5579120270-358.0765980870i 679.0263343998-528.7511368867i 1]T, (26)
m3J=[48.5579120270+358.0765980870i 679.0263343998+5.7511368867i 1]T。 (27)
4. solving parabolic catadioptric camera intrinsic parameter
(22), (24) and (26) substitution (8) is obtained into the system of linear equations of element in ω, solving using least square method should System of linear equations obtains the coefficient matrix of ω.As a result as follows:
Finally, carrying out Cholesky decomposition, then the available K that inverts to the ω in (28)c, have
Wherein aspect ratio rc=Kc(1,1)/Kc(2,2)(Kc(1,1) representing matrix KcThe 1st row the 1st column element, Kc(2, 2) representing matrix KcThe 2nd row the 2nd column element), therefore 5 intrinsic parameters of parabolic catadioptric video camera are respectively as follows: rc= 1.00455475191844 fc=573.261169054269, s=0.519283357335, u0=343.330665425737, v0=625.176990789005.

Claims (1)

1. a kind of side of the property calibration parabolic catadioptric camera intrinsic parameter using the ball and parallel circle tangent line in space Method, it is characterised in that by a ball in space as target；Under parabolic mirror-lens system, the ball in space regards ball in unit On projection roundlet and its be parallel circle to circle is opened up, there are four intersection point；It is special using imaging of the ball under parabolic catadioptric video camera Sign and circular point and the synteny of infinite point solve parabolic catadioptric camera intrinsic parameter；The method specific steps include: Firstly, shooting the image that 3 width contain ball from different positions with parabolic catadioptric video camera, the edge of mirror surface outline projection is extracted Point and target image marginal point are fitted the image for obtaining mirror surface outline projection and ball using least square method；Secondly, according to ball Picture point and its relationship for opening up picture point is obtained to opening up picture point, thus estimate ball picture to opening up ball picture；Take up an official post in ball picture and take a point, And acquire to picture point is opened up, by the definition to picture point is opened up, point on ball picture is about the tangent line of ball picture and to opening up picture point about to opening up ball The tangent line of picture meets at end point；As solve in plane ball picture with to two groups of conjugation imaginary intersection points for opening up ball picture, further according to circular point Picture the picture of circular point is linearly obtained with the synteny of end point；Finally, using circular point as to absolute conic picture Constraint solving camera intrinsic parameter；
(1) picture of circular point is determined
In projection roundlet S of the ball Q on unit view ball1+Take up an official post and takes a point A1+, use A1-Indicate A1+About unit view ball centre of sphere O's Symmetric points, i.e. antipodal point, then point A1-In S1+About the symmetrical circle of unit view ball centre of sphere O, i.e., to opening up round S1-On；L1+For point A1+It closes In circle S1+Tangent line, L1-For point A1-About circle S1-Tangent line, according to the definition of antipodal point and the property of parallel circle, L1+//L1-, Then L1+And L1-Infinite point having the same, uses V here1∞Indicate L1+,L1-On infinite point；Roundlet S1+And S1-It is two A parallel circle has the imaginary intersection point of two groups of conjugation；Known parallel circle all meets at circular point, so circular point I, J are parallel circle S1+ And S1-One group of conjugation imaginary intersection point；Space circle and the line at infinity of plane where it meet at circular point, i.e. circular point is flat with this Face infinite point is conllinear, therefore infinite point V1∞It is conllinear with circular point I, J；On as plane, C is used1+,C1-Table respectively Show S1+,S1-Picture, use a1+,a1-Respectively indicate A1+,A1-Picture, then a1+,a1-It is a pair to opening up picture point；Record a demerit point a1+About two Secondary curve C1+Tangent line be l1+, cross point a1-About conic section C1-Tangent line be l1-, then according to the property of projective transformation, straight line l1±For straight line L1±Picture, then pass through straight line l1+,l1-Determine S1+An end point v in the plane1, it is V1∞Picture； C1+,C1-There is the imaginary intersection point of two groups of conjugation, wherein one group must be the picture m of circular point1I,m1J；The combination of perspective transform holding dotted line Property, thus on as plane circular point picture m1I,m1JWith end point v1It is also conllinear；It is total at two groups according to the judgement of synteny It can determine whether the picture of circular point in yoke imaginary intersection point.
CN201811214872.2A 2018-10-18 2018-10-18 Parabolic catadioptric video camera is demarcated using single ball and parallel circle tangential property Pending CN109325982A (en)

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