CN109544646A - Utilize the method for ball and three orthogonal end point calibration parabolic catadioptric video cameras - Google Patents
Utilize the method for ball and three orthogonal end point calibration parabolic catadioptric video cameras Download PDFInfo
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- G—PHYSICS
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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Abstract
The present invention relates to a kind of methods using ball and three orthogonal end point calibration parabolic catadioptric video cameras.According to the property of antipodal point, to opening up on roundlet there are two antipodal points, making the two points about to the tangent line for opening up roundlet, it may be determined that two infinite points can be obtained in two groups of parallel lines, and connecting two infinite points can be obtained line at infinity.According to the property of round conjugate value, infinite point about the infinite point on round polar curve direction be with the infinite point it is orthogonal, that is, can determine the infinite point on one group of orthogonal direction.Again according to two parallel roundlet centers of circle infinite point in the straight direction roundlet place plane parallel with two be orthogonal, therefore can determine the infinite point on one group of three orthogonal direction.According to affine-invariant features, one group of three orthogonal end point can be obtained, to solve parabolic catadioptric camera intrinsic parameter matrix.
Description
Technical field
The invention belongs to computer vision field, it is related to a kind of solving and throwing using a ball in space and three orthogonal end points
The method of object catadioptric camera intrinsic parameter.
Background technique
Computation vision is to replace human eye to be identified, tracked and measured to target by computer and relevant device, then
After carrying out image procossing, instrument detection or eye-observation are sent to.The main task that computer is felt is exactly by the figure to acquisition
As being handled to obtain the three-dimensional information of corresponding scene, and camera calibration is an important step for realizing image procossing.
Camera calibration is a mapping process in computer field between three-dimensional scaling object and its two dimensional image.It is also by two dimension
Image restores to obtain back projection's process of corresponding three-dimensional information.
With extensive application of the computer vision technique in every field, the visual range of traditional cameras is small, meets
The not requirement of computation vision technology, to there is the birth of catadioptric video camera.Document " Atheory of single-
viewpoint catadioptric image formation”(Baker S.,Nayar S.K.,International
Journal of Computer Vision, 1999,35 (2): 175-196.) whether there is fixed list according to catadioptric video camera
Catadioptric video camera is divided into two classes: central catadiotric video camera and non-central catadioptric video camera by viewpoint.Document " Stereo
With mirrors " (Sameer A., Nene and Shree K., Computer Vision1998.) takes the photograph central catadiotric
The mirror surface of camera is divided into four classes: paraboloidal mirror, plane mirror, hyperbolic mirror and off-axis paraboloids and ellipsoids mirrors.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, 27 (8), 2005,1327-1333.) have studied straight line under central catadiotric video camera
The geometric properties of picture, and the calibration by these properties applied to central catadiotric video camera.
Herein, ball is demarcated into parabolic catadioptric video camera as calibration object, its advantage is that ball itself is unobstructed.?
That is from a ball, its an occluding contour always circle, and its projected outline in space in terms of any one orientation
Line can be extracted all.For demarcating object compared to other, ball makes the accuracy of camera calibration higher as calibration object.Document
“Catadioptric Camera Calibration Using Geometric Invariants”(Ying X.,Hu Z.,
IEEE Transactions on Pattern Analysis and Machine Intelligence,2004,26(10):
It 1260-1271.) analyzes under central catadiotric video camera, relationship of the ball as profile and camera intrinsic parameter, it was demonstrated that space
Ball is projected as a conic section under central catadiotric video camera, and also demonstrating can mention in the next ball picture of nonsingular situation
It is constrained for two, i.e. three achievable calibration of ball.But this method be it is nonlinear, to intrinsic parameter initial value in calibration process
Precise requirements are very high.Document " Intrinsic parameter determination of a para-catadioptric
camera by the intersection of two sphere projections”(Zhao Y.,Wang Y.,Journal
2015,32 (11): of the Optical Society of America A 2201-2209.) is intersected using two for the first time
Calibration object of the ball as parabolic catadioptric video camera, two balls intersect at four intersection points.According to the property for opening up picture point, by this four
A intersection point, which forms a rectangle, can obtain one group of orthogonal end point according to affine-invariant features, thus linear calibration's video camera internal reference
Number.But the part of the two balls intersection is blocked, therefore ball cannot be extracted completely and influence the accuracy of calibration algorithm.Text
Offer " Calibration of a paracatadioptric camera by projection imaging of a single
Sphere " (Li Y, Zhao Y., Applied Optics, 2017,56 (8): 2230.) using single Spatial Sphere as calibration object,
Under parabolic catadioptric video camera, Spatial Sphere forms the parallel roundlet of two antarafacials on unit view ball, according to opening up property, circle
The property of conjugate value obtains orthogonal end point, circular point, parallel circle, thus linear calibration's camera intrinsic parameter.
Summary of the invention
It is widely applicable the present invention provides a kind of production is simple, robustness it is good to solve parabolic using Spatial Sphere catadioptric
The method for penetrating camera intrinsic parameter.During solving parabolic catadioptric camera intrinsic parameter, parabolic catadioptric need to be used to take the photograph
The two images linear solution of camera shooting Spatial Sphere goes out five intrinsic parameters of parabolic catadioptric video camera.
The present invention adopts the following technical scheme:
Two images are shot from different orientation by parabolic catadioptric video camera.The present invention considers that Spatial Sphere is regarded in unit
Projection model on ball forms two parallel roundlets (also referred to as a pair to open up roundlet) depending on projection on ball in unit, takes on roundlet
The point of two groups of inequalities, makees the tangent line about roundlet respectively.According to the property of antipodal point, to opening up on roundlet, there are two to opening up
Point makees the two points about to the tangent line for opening up roundlet, it may be determined that two infinite points, connection two can be obtained in two groups of parallel lines
Line at infinity can be obtained in a infinite point.According to the property of round conjugate value, infinite point is about on round polar curve direction
Infinite point with the infinite point be it is orthogonal, that is, can determine the infinite point on one group of orthogonal direction.It is again flat according to two
The row roundlet center of circle plane where infinite point in the straight direction roundlet parallel with two be orthogonal, therefore can determine one group
Infinite point on three orthogonal directions.According to affine-invariant features, one group of three orthogonal end point can be obtained, to solve parabolic catadioptric
Camera intrinsic parameter matrix.
1. being fitted mirror surface outline projection equation and ball image space journey
The ball of mirror surface outline projection marginal point and shooting is extracted as image edge point using the function in Matlab program
Pixel coordinate, and the equation for obtaining mirror surface outline projection equation and ball picture is fitted with least square method.
2. calculate ball picture to opening up ball image space journey
For Spatial Sphere Q under parabolic catadioptric video camera, the projection process of ball is divided into two steps: the first step, in unit view ball
Heart O is that projection centre establishes world coordinate system O-xwywzw, Spatial Sphere Q projection two parallel antarafacials of formation on unit view ball
Roundlet Sn+And Sn-(n=1,2 indicate the image of shooting), wherein roundlet Sn+And Sn-It is referred to as a pair of to opening up roundlet；Second step, with list
That in the ball surface of position is a little camera optical center OcEstablish camera coordinate system Oc-xcyczc, wherein xc,ycAxis and xw,ywAxis is flat
Row, zcAxis and zwOverlapping of axles, i.e. imaging plane and optical axis OOcVertically meet at principal point p.Two parallel roundlet Sn+And Sn-To throw
Shadow center OcTwo conic section C are projected as on as plane πn+And Cn-, wherein Cn+It is Spatial Sphere Q for visible conic section
Picture；Invisible conic section Cn-It is ball as Cn+To opening up ball picture.It enables with OcIntrinsic Matrix for the video camera of optical center isWherein r is aspect ratio, and f is effective focal length, and s is obliquity factor, [u0 v0 1]TIt is video camera principal point p
Homogeneous coordinates matrix form.The mirror surface outline projection marginal point and 2 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 piece image mirror surface profile in the coefficient matrix as the drop shadow curve in plane, Cn+Respectively indicate ball in 2 width images
The coefficient matrix of picture.Herein in order to simplify statement, ball image space journey and corresponding coefficient matrix are indicated with identical letter.Pass through C0
It can get an initial matrix value of camera intrinsic parameter matrix KTo obtain absolute conic as ω initial valueHere: ω=K-TK-1,Wherein It is the initial value of aspect ratio,It is effective coke
Away from initial value,It is the initial value of obliquity factor,It is the initial homogeneous coordinates matrix form of video camera principal point, note
Take Cn+On one group of pointAccording to a pair to the relationship for opening up picture point satisfaction
Formula
It can determine to opening up ball as Cn-On one group to opening up picture pointThen to opening up ball as Cn-
Equation can be fitted to obtain with least square method.
3. the acquisition of vanishing line
In the projection roundlet S of Spatial Sphere Q1+On take two mutual dissimilarity A1+And B1+, use A1-And B1-It respectively indicates to opening up roundlet
S1-Present on antipodal point.In point A1+And B1+Make roundlet S in place1+Tangent line be respectively L1+And L2+, in point A1-And B1-Place, which opposes, to open up
Roundlet S1-Tangent line be denoted as L respectively1-And L2-.Because of roundlet S1+And S1-It is a pair to roundlet is opened up, so S1+//S1-, OO+=OO-
(O is that unit regards the ball centre of sphere, O+And O-Respectively roundlet S1+And S1-The center of circle).A1+And A1-It is a pair of of antipodal point, so OA1+=
OA1-.That is quadrangle A1+O+A1-O-It is parallelogram, so A1+O+//A1-O-.Again because of L1+It is roundlet S1+In point A1+Place is cut
Line, L1-It is roundlet S1-In point A1-The tangent line at place, so L1+⊥A1+O+, L1-⊥A1-O-, i.e. L1+//L1-, L1+And L1-Intersect at nothing
Poor far point D1∞.It can similarly obtain, L2+//L2-, L2+And L2-Intersect at infinite point D2∞。
On as plane, a1+And a1-Respectively indicate A1+And A1-Picture, b1+And b1-Respectively indicate B1+And B1-Picture, C1+With
C1-Respectively indicate roundlet S1+And S1-Picture, then point a1+About ball as C1+Tangent line be l1+, point a1-About to opening up ball as C1-Cut
Line is l1-, point b1+About ball as C1+Tangent line be l2+, point b1-About to opening up ball as C1-Tangent line be l2-, i.e. l1+、l1-、l2+With
l2-Respectively L1+、L1-、L2+And L2-Picture.According to affine-invariant features, tangent line l1+And l1-Intersection point be end point d1(D1∞'s
Picture).It can similarly obtain, tangent line l2+And l2-Intersection point be end point d2(D2∞Picture).Connect end point d1And d2Disappearance can be obtained
Line l (two parallel roundlet S1+And S1-The line at infinity L of place plane∞Picture).
4. the acquisition of the picture in the roundlet center of circle
Infinite point D1∞About roundlet S1+Polar curve be denoted as H1, infinite point D2∞About roundlet S1+Polar curve be denoted as H2, root
According to the definition (diameter that infinite point is known as about the finite polar curve of conic section conic section) of the diameter of conic section, then pole
Line H1With polar curve H2It is all roundlet S1+Diameter, i.e. roundlet S1+Center of circle O+For polar curve H1And H2Intersection point.Roundlet S can similarly be obtained1-
Center of circle O_。
On as plane, end point d1About ball as C1+Polar curve be denoted as h1(H1Picture), end point d2About ball as C1+'s
Polar curve is denoted as h2(H2Picture).According to affine-invariant features, roundlet center of circle O+Picture be polar curve h1And h2Intersection point, be denoted as o+.Similarly
Can to opening up roundlet center of circle O_Picture, be denoted as o_。
5. the acquisition of one group of three orthogonal end point
In the projection roundlet S of Spatial Sphere Q1+Diametrically take two terminal As1+With A '1+, in point A1+With A '1+Place make about
Roundlet S1+Tangent line be denoted as L respectively1+And L3+.According to round property and match Principle for Extreme Nodes and Lines, L can be obtained1+//L3+, intersect at infinite point
D3∞.According to the definition of the diameter of conic section, infinite point D3∞It is straight line A about round polar curve1+A′1+.According to the property of tangent line
Matter, it is known that L1+⊥A1+A′1+, L3+⊥A1+A′1+, so infinite point D3∞Perpendicular to A1+A′1+, i.e. infinite point D3∞With polar curve A1+
A′1+Infinite point D on direction4∞It is orthogonal.It can similarly obtain, infinite point D1∞With polar curve H1Infinite point V on direction1∞It is
Orthogonal；Again because of S1+//S1-, and straight line O+O-Perpendicular to plane where two parallel roundlets, so straight line O+O-It is also perpendicularly to two
The line at infinity L of plane where parallel roundlet∞.That is straight line O+O-Infinite point V on direction2∞With line at infinity L∞It is also
Vertical.Therefore, infinite point D1∞, V1∞And V2∞For the infinite point on one group of three orthogonal direction.
On as plane, according to affine-invariant features, d1, v1And v2For one group of three orthogonal end point, wherein d1, v1And v2Respectively
Indicate infinite point D1∞, V1∞And V2∞As the picture in plane.For roundlet S2+And S2-Three orthogonal end points in the plane
d′1,v′1,v′2, can be obtained with similar method.
6. solving parabolic catadioptric camera intrinsic parameter
Two group of three orthogonal end point { d1,v1,v2}、{d′1,v′1,v′2Six can be provided about absolute conic ω
Linear Constraints, it may be assumed thatThen to ω=K-TK-1It carries out Cholesky decomposition to invert again, so that it may obtain
Intrinsic Matrix K, i.e. acquisition parabolic catadioptric camera intrinsic parameter.
Detailed description of the invention
Fig. 1 is projection model of the Spatial Sphere on unit view ball.
Fig. 2 is one group of three orthogonal end point.
Specific embodiment
The method that a ball solves parabolic catadioptric camera intrinsic parameter in space is utilized the present invention provides a kind of.Space
Ball, depending on forming two parallel roundlets (also referred to as a pair of to open up roundlet) on ball, the point of two groups of inequalities is taken on roundlet, is distinguished in unit
Make the tangent line about roundlet.According to the property of antipodal point, closed to opening up on roundlet there are two antipodal points, making the two points respectively
In to the tangent line for opening up roundlet, it may be determined that two infinite points can be obtained in two groups of parallel lines, and it is available to connect two infinite points
Line at infinity.According to the property of round conjugate value, infinite point is about the infinite point and the nothing on round polar curve direction
Far point is orthogonal thoroughly, that is, can determine the infinite point on one group of orthogonal direction.Again according to straight where two parallel roundlet centers of circle
Plane where infinite point roundlet parallel with two on line direction is orthogonal, therefore can determine the nothing on one group of three orthogonal direction
Poor far point.According to affine-invariant features, one group of three orthogonal end point can be obtained, to solve parabolic catadioptric camera intrinsic parameter square
Battle array.Specific step is as follows:
1. being fitted mirror surface outline projection equation and ball image space journey
The ball of mirror surface outline projection marginal point and shooting is extracted as image edge point using the function in Matlab program
Pixel coordinate, and the equation for obtaining mirror surface outline projection equation and ball picture is fitted with least square method.
2. calculate ball picture to opening up ball image space journey
For Spatial Sphere Q under parabolic catadioptric video camera, the projection process of ball is divided into two steps: the first step, in unit view ball
Heart O is that projection centre establishes world coordinate system O-xwywzw, Spatial Sphere Q projection two parallel antarafacials of formation on unit view ball
Roundlet Sn+And Sn-(n=1,2 indicate the image of shooting), wherein roundlet Sn+And Sn-It is referred to as a pair of to opening up roundlet；Second step, with list
That in the ball surface of position is a little camera optical center OcEstablish camera coordinate system Oc-xcyczc, wherein xc,ycAxis and xw,ywAxis is flat
Row, zcAxis and zwOverlapping of axles, i.e. imaging plane and optical axis OOcVertically meet at principal point p.Two parallel roundlet Sn+And Sn-To throw
Shadow center OcTwo conic section C are projected as on as plane πn+And Cn-, wherein Cn+It is Spatial Sphere Q for visible conic section
Picture；Invisible conic section Cn-It is ball as Cn+To ball picture is opened up, as shown in Figure 1.
Target image marginal point in 2 width images and the 1st width image are extracted respectively using the Edge function in Matlab
The pixel coordinate of mirror surface outline projection is fitted to obtain corresponding quadratic curve equation by least square method, uses C here0It indicates
The coefficient matrix of 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 C0
It can get an initial matrix value of camera intrinsic parameter matrix KSpecifically 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.
Obtaining initial matrix valueOn the basis of can be obtained absolute conic as ω initial value
Take C+On one group of pointThen one group corresponding with it to opening up picture pointIt can be by
Relational expression (3) determines:
According to the definition to picture point is opened up, pointIn ball as C+To opening up ball as C-On, therefore available least square method fitting
It obtains to opening up ball as C-Equation.
3. the acquisition of vanishing line
In the projection roundlet S of Spatial Sphere Q1+On take two mutual dissimilarity A1+And B1+, use A1-And B1-It respectively indicates to opening up roundlet
S1-Present on antipodal point, only show A in Fig. 11+, A1-.In point A1+And B1+Make roundlet S in place1+Tangent line be respectively L1+And L2+,
In point A1-And B1-Place, which opposes, opens up roundlet S1-Tangent line be denoted as L respectively1-And L2-.Because of roundlet S1+And S1-It is a pair of to opening up roundlet,
So S1+//S1-, OO+=OO_(O is that unit regards the ball centre of sphere, O+And O_Respectively roundlet S1+And S1-The center of circle).A1+And A1-It is one
To antipodal point, so OA1+=OA1-.That is quadrangle A1+O+A1-O_It is parallelogram, so A1+O+//A1-O-.Again because of L1+It is
Roundlet S1+In point A1+The tangent line at place, L1-It is roundlet S1-In point A1-The tangent line at place, so L1+⊥A1+O+, L1-⊥A1-O-, i.e. L1+//
L1-, L1+And L1-Intersect at infinite point D1∞.It can similarly obtain, L2+//L2-, L2+And L2-Intersect at infinite point D2∞。
As shown in Figure 2 on as plane, a1+And a1-Respectively indicate A1+And A1-Picture, C1+And C1-Respectively indicate roundlet S1+With
S1-Picture, then point a1+About ball as C1+Tangent line be l1+, point a1-About to opening up ball as C1-Tangent line be l1-(l1+、l1-Respectively
L1+、L1-Picture):
Wherein " " indicates dot product.According to affine-invariant features, tangent line l1+And l1-Intersection point be end point d1(D1∞Picture):
d1=l1+×l1-, (5)
Wherein "×" indicates cross product.B can similarly be obtained1+And B1-Picture b1+And b1-Tangent line l2+And l2-Intersection point be end point
d2, wherein l2+、l2-Respectively L2+、L2-Picture, d2Indicate D2∞Picture.Connect end point d1And d2Vanishing line l (two can be obtained
Parallel roundlet S1+And S1-The line at infinity L of place plane∞Picture):
L=d1×d2。 (6)
Wherein "×" indicates cross product.
4. the acquisition of the picture in the roundlet center of circle
Infinite point D1∞About roundlet S1+Polar curve be denoted as H1, infinite point D2∞About roundlet S1+Polar curve be denoted as H2, root
According to the definition (diameter that infinite point is known as about the finite polar curve of conic section conic section) of the diameter of conic section, then pole
Line H1With polar curve H2It is all roundlet S1+Diameter, i.e. roundlet S1+Center of circle O+For polar curve H1And H2Intersection point.Roundlet S can similarly be obtained1-
Center of circle O-。
As shown in Fig. 2, on as plane, end point d1About ball as C1+Polar curve be denoted as h1(H1Picture), end point d2It closes
In ball as C1+Polar curve be denoted as h2(H2Picture):
Wherein " " indicates dot product.According to affine-invariant features, polar curve h1And h2Intersection point be roundlet center of circle O+Picture, be denoted as
o+:
o+=h1×h2。 (8)
Wherein "×" indicates cross product.Similarly can to opening up roundlet S1-Center of circle O-Picture, be denoted as o-。
5. the acquisition of one group of three orthogonal end point
In the projection roundlet S of Spatial Sphere Q1+Diametrically take two terminal As1+With A '1+, in point A1+With A '1+Place make about
Roundlet S1+Tangent line be denoted as L respectively1+And L3+.According to round property and match Principle for Extreme Nodes and Lines, L can be obtained1+//L3+, intersect at infinite point
D3∞.According to the definition of the diameter of conic section, infinite point D3∞It is straight line A about round polar curve1+A′1+.According to the property of tangent line
Matter, it is known that L1+⊥A1+A′1+, L3+⊥A1+A′1+, so infinite point D3∞Perpendicular to A1+A′1+, i.e. infinite point D3∞With polar curve A1+
A′1+Infinite point D on direction4∞It is orthogonal.It can similarly obtain, infinite point D1∞With polar curve H1Infinite point V on direction1∞It is
Orthogonal；Again because of S1+//S1-, and straight line O+O-Perpendicular to plane where two parallel roundlets, so straight line O+O-It is also perpendicularly to two
The line at infinity L of plane where parallel roundlet∞.That is straight line O+O-Infinite point V on direction2∞With line at infinity L∞It is also
Vertical.Therefore, infinite point D1∞, V1∞And V2∞For the infinite point on one group of three orthogonal direction.
As shown in Fig. 2, on as plane, according to affine-invariant features, d1, v1And v2For one group of three orthogonal end point, d1, v1With
v2Respectively indicate infinite point D1∞, V1∞And V2∞As the picture in plane.Polar curve h1End point v on direction1It is polar curve h1With disappear
Lose the intersection point of line l:
v1=h1× l, (9)
Wherein "×" indicates cross product.Straight line o+o-End point v on direction2With o+、o-Meet in projective geometry with principal point p and adjusts
And conjugate relation, there is following double ratio relationship:
(o-,p；o+,v2)=- 1. (10)
For roundlet S2+And S2-One group of three orthogonal end point d ' in the plane1,v′1,v′2, can be obtained with similar approach
?.
6. solving parabolic catadioptric camera intrinsic parameter
Two group of three orthogonal end point { d1,v1,v2, { d '1,v′1,v′2Six can be provided about absolute conic ω
Linear Constraints:
Then to ω=K-TK-1It carries out Cholesky decomposition to invert again, so that it may obtain Intrinsic Matrix K, that is, be thrown
Object catadioptric camera intrinsic parameter.
Embodiment
Parabolic catadioptric video camera internal reference is demarcated with a ball in space and three orthogonal end points the invention proposes a kind of
Several methods.The experiment pattern structural schematic diagram that the present invention uses is as shown in Figure 1.In true experiment, experiment that we use
Equipment is parabolic catadioptric video camera, and the angle of visibility of the equipment is 180 °.Specific step is as follows:
1. being fitted mirror surface outline projection equation and ball image space journey
The image size that the present invention uses is 2510 × 2400.It is calibration object with a Spatial Sphere, according to the different positions of ball
It sets, shoots three width images with above-mentioned parabolic catadioptric video camera.The three width images that shooting is handled with Canny boundary operator, are used in combination
Least square method fitting obtains the equation of mirror surface outline projection equation and ball picture.Piece image mirror surface outline projection equation is
Matrix number is C0, the coefficient matrix of two width ball image space journeys is respectively Cn+(n=1,2), as a result as follows:
2. estimation ball picture to opening up ball image space journey
(12) are brought into (1) and can be obtainedAs a result as follows:
(15) formula, which is brought into (2) formula, to be obtainedAs a result as follows:
In ball as C1+, C2+On respectively take the points of at least five inequalities, the point taken and (16) formula are brought into respectively in (3) formula
It can obtain corresponding to opening up picture point, C can be obtained with least square method fitting1+, C2+To the coefficient matrix C for opening up ball picturen-(n=1,
2), as a result as follows:
3. the acquisition of vanishing line
In ball as C1+Take up an official post and takes the point a of two inequalities1+And b1+, their homogeneous coordinates matrix are respectively as follows:
a1+=[998.8710467984296-946.6700647869636 1]T, (19)
b1+=[0.997782953925435-1.091627950312619 1]T, (20)
According to the property for opening up picture point, can get and point a1+,b1+It is corresponding to opening up picture point a1-,b1-, their homogeneous coordinates
Matrix is respectively as follows:
a1-=[- 163.5353896437098 568.7548971309556 1]T, (21)
b1-=[- 119.4688215387295 557.8786824951096 1]T, (22)
It can invocation point a by (4) formula is brought into respectively with (19) formula, (17) formula and (21) formula when (13)1+About ball as C1+Tangent line
For l1+, point a1-About to opening up ball as C1-Tangent line be l1-, homogeneous line coordinates matrix result is as follows:
l1+=[- 0.000962353292067 0.000175432043196 1]T, (23)
l1-=[- 0.000073289435987-0.001846375319155 1]T, (24)
End point d can be obtained by bringing (23) formula and (24) formula into (5) formula1, homogeneous coordinates matrix result is as follows:
d1=[1199.576920616086 537.5795013591563 1]T, (25)
Bringing (14) formula and (20) formula, (18) formula and (22) formula into (4) formula respectively can invocation point b1+About ball as C1+Tangent line
For l2+, point b1-About to opening up ball as C1-Tangent line be l2-, homogeneous line coordinates matrix result is as follows:
l2+=[- 0.001275964396256-0.000159356325108 1]T, (26)
l2-=[- 0.001062578329575-0.002685190515835 1]T, (27)
End point d can be obtained by bringing (26) formula and (27) formula into (5) formula2, homogeneous coordinates matrix result is as follows:
d2=[858.8969426785198 78.26787918510665 1]T, (28)
It brings (25) formula and (28) formula into (6) formula, vanishing line l can be obtained, homogeneous line coordinates matrix result is as follows:
L=[- 0.001264796093046 0.000957453649382 1]T。 (29)
4. the acquisition of the picture in the roundlet center of circle
(25) formula and (28) formula are brought into (7) formula, end point d can be obtained1About ball as C1+Polar curve h1, end point d2It closes
In ball as C1+Polar curve h2, homogeneous line coordinates matrix result is as follows:
h1=[- 0.000262189412484 0.000987427197424 1]T, (30)
h2=[- 0.000278932590352 0.000362872514437 1]T, (31)
It is brought into (8) formula according to the definition of conic section diameter, and by (30) formula and (31) formula, the picture in the roundlet center of circle can be obtained
o+, homogeneous coordinates matrix result is as follows:
o+=[170.1734828741245-114.3278283251432 1]T, (32)
It can similarly obtain to the picture o for opening up the roundlet center of circle-, homogeneous coordinates matrix result is as follows:
o-=[24.14245217424343-68.26381452847146 1]T。 (33)
5. the acquisition of one group of three orthogonal end point
It brings (29) formula and (30) formula into (9) formula, end point d can be obtained1About conic section C1+Polar curve h1On direction
End point v1, homogeneous coordinates matrix result is as follows:
v1=[- 67.62729515039456-1170.852849214321 1]T, (34)
It brings (32) formula and (33) formula into (10) formula, the picture place straight line o in the roundlet center of circle can be obtained+o-End point on direction
v2, homogeneous coordinates matrix result is as follows:
v2=[- 736.3467825382454 1387.724823158795 1]T。 (35)
For roundlet S2+And S2-One group of three orthogonal end point d ' in the plane1,v′1,v′2It can be obtained with similar approach
, homogeneous coordinates matrix result is as follows:
d′1=[983.3519263285633 821.1174532955389 1]T, (36)
v′1=[147.7147252957865-1013.976894628712 1]T, (37)
v′2=[- 1314.089361626585 1302.382563287511 1]T。 (38)
(25) formula, (34) to (38) formula are brought into (11) formula 6. solving parabolic catadioptric camera intrinsic parameter, are obtained in ω
The system of linear equations of element solves the system of linear equations using SVD decomposition and obtains the coefficient matrix of ω, as a result as follows:
Finally, to ω=K in (39) formula-TK-1It carries out Cholesky decomposition to invert to obtain Intrinsic Matrix K again, that is, obtains
Parabolic catadioptric camera intrinsic parameter matrix is obtained, as a result as follows:
Therefore 5 intrinsic parameters of parabolic catadioptric video camera are respectively as follows: r=0.907808547, f=
879.1643673866085 s=0.199145753757383, u0=150.3162865365889, v0=
159.3241461751960。
Claims (1)
1. a kind of method using ball and three orthogonal end point calibration parabolic catadioptric video cameras, it is characterised in that by space
Single ball is as target；The specific steps of the method include: that least square method fitting first obtains mirror surface outline projection equation
With the equation of ball picture；The point that two groups of inequalities are taken on roundlet, makees the tangent line about roundlet respectively；According to the property of antipodal point,
To opening up on roundlet there are two antipodal points, make the two points about to the tangent line for opening up roundlet, determining two groups of parallel lines to get to two
A infinite point connects two infinite points and obtains line at infinity；According to the property of round conjugate value, infinite point about
Infinite point on round polar curve direction is orthogonal, i.e., on determining one group of orthogonal direction infinite point with the infinite point；
Again according to two parallel roundlet centers of circle infinite point in the straight direction roundlet place plane parallel with two be it is orthogonal, because
This determines the infinite point on one group of three orthogonal direction；According to affine-invariant features, one group of three orthogonal end point is obtained, to solve throwing
Object catadioptric camera intrinsic parameter matrix；
(1) acquisition of vanishing line
In the projection roundlet S of Spatial Sphere Q1+On take two mutual dissimilarity A1+And B1+, use A1-And B1-It respectively indicates to opening up roundlet S1-On
Existing antipodal point；In point A1+And B1+Make roundlet S in place1+Tangent line be respectively L1+And L2+, in point A1-And B1-Place, which opposes, opens up roundlet
S1-Tangent line be denoted as L respectively1-And L2-；Because of roundlet S1+And S1-It is a pair to roundlet is opened up, so S1+//S1-, OO+=OO-,
Middle O is that unit regards the ball centre of sphere, O+And O-Respectively roundlet S1+And S1-The center of circle；A1+And A1-It is a pair of of antipodal point, so OA1+=
OA1-；That is quadrangle A1+O+A1-O-It is parallelogram, so A1+O+//A1-O-；Again because of L1+It is roundlet S1+In point A1+Place is cut
Line, L1-It is roundlet S1-In point A1-The tangent line at place, so L1+⊥A1+O+, L1-⊥A1-O_, i.e. L1+//L1-, L1+And L1-Intersect at nothing
Poor far point D1∞；Similarly, L2+//L2-, L2+And L2-Intersect at infinite point D2∞；
On as plane, a1+And a1-Respectively indicate A1+And A1-Picture, b1+And b1-Respectively indicate B1+And B1-Picture, C1+And C1-Point
It Biao Shi not roundlet S1+And S1-Picture, then point a1+About ball as C1+Tangent line be l1+, point a1-About to opening up ball as C1-Tangent line be
l1-, point b1+About ball as C1+Tangent line be l2+, point b1-About to opening up ball as C1-Tangent line be l2-；According to affine-invariant features, cut
Line l1+And l1-Intersection point be end point d1, i.e. D1∞Picture；Similarly, tangent line l2+And l2-Intersection point be end point d2, i.e. D2∞'s
Picture；Connect end point d1And d2Obtain vanishing line l, i.e., two parallel roundlet S1+And S1-The line at infinity L of place plane∞'s
Picture；
(2) acquisition of the picture in the roundlet center of circle
Infinite point D1∞About roundlet S1+Polar curve be denoted as H1, infinite point D2∞About roundlet S1+Polar curve be denoted as H2, according to two
The definition of the diameter of secondary curve: infinite point is known as the diameter of conic section about the finite polar curve of conic section, then polar curve H1
With polar curve H2It is all roundlet S1+Diameter, i.e. roundlet S1+Center of circle O+For polar curve H1And H2Intersection point；Similarly obtain roundlet S1-Circle
Heart O-；
On as plane, end point d1About ball as C1+Polar curve be denoted as h1, i.e. H1Picture, end point d2About ball as C1+Pole
Line is denoted as h2, i.e. H2Picture；According to affine-invariant features, roundlet center of circle O+Picture be polar curve h1And h2Intersection point, be denoted as o+；Similarly
To opening up roundlet center of circle O-Picture, be denoted as o-；
The acquisition of (3) one group of three orthogonal end point
In the projection roundlet S of Spatial Sphere Q1+Diametrically take two terminal As1+With A '1+, in point A1+With A '1+Make about roundlet at place
S1+Tangent line be denoted as L respectively1+And L3+；According to round property and match Principle for Extreme Nodes and Lines, L is obtained1+//L3+, intersect at infinite point D3∞；Root
According to the definition of the diameter of conic section, infinite point D3∞It is straight line A about round polar curve1+A′1+；According to the property of tangent line, know
L1+⊥A1+A′1+, L3+⊥A1+A′1+, so infinite point D3∞Perpendicular to A1+A′1+, i.e. infinite point D3∞With polar curve A1+A′1+Side
Upward infinite point D4∞It is orthogonal；Similarly, infinite point D1∞With polar curve H1Infinite point V on direction1∞It is orthogonal；
Again because of S1+//S1-, and straight line O+O-Perpendicular to plane where two parallel roundlets, so straight line O+O-It is also perpendicularly to two parallel roundlets
The line at infinity L of place plane∞；That is straight line O+O-Infinite point V on direction2∞With line at infinity L∞It is also vertical；
Therefore, infinite point D1∞, V1∞And V2∞For the infinite point on one group of three orthogonal direction；
On as plane, according to affine-invariant features, d1, v1And v2For one group of three orthogonal end point, wherein d1, v1And v2It respectively indicates
Infinite point D1∞, V1∞And V2∞As the picture in plane；It obtains for roundlet S2+And S2-Three orthogonal end points in the plane
d′1,v′1,v′2；
(4) parabolic catadioptric camera intrinsic parameter is solved
Two group of three orthogonal end point { d1,v1,v2}、{d′1,v′1,v′2To provide six about the linear of absolute conic ω
Constraint condition, it may be assumed thatThen to ω=K-TK-1It carries out Cholesky decomposition to invert again, just to obtain intrinsic parameter square
Battle array K, i.e. acquisition parabolic catadioptric camera intrinsic parameter.
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