CN106327504A - Method of calibrating paracatadioptric camera using image of single sphere and circular points - Google Patents
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Abstract
The present invention relates to a method for calibrating a paracatadioptric camera using the images of a single sphere and circular points. According to the method, two different points are selected from the image of the sphere, so that two vanishing points are obtained; a straight line where the two vanishing points are located is a vanishing line, the images of the vanishing line and the image of the sphere intersect with the images of the circular points, and three images can provide the images of three circular points; and the inner parameters of the camera are solved through using the constraint of the images of the circular points for an absolute conic curve image. The method specifically includes the following steps of: fitting a mirror surface contour projection equation and a target projection equation; estimating an antipodal sphere image; determining the images of the circular points; and solving the inner parameters of the paracatadioptric camera. In a process of solving the inner parameters of the paracatadioptric camera, five inner parameters of the paracatadioptric camera are solved by using three images of a target shoot by the paracatadioptric camera.
Description
Technical field
The invention belongs to computer vision field, relate to a kind of utilize in space a ball and circular point as solving parabolic
The method of catadioptric camera intrinsic parameter.
Background technology
Image is understood by the central task of computer vision exactly, and its final goal is that to make computer have logical
Cross the ability of two dimensional image cognition three-dimensional environment information.This ability will not only cause a machine to perception and include shape, attitude, motion
Deng the geological information of object in interior three-dimensional environment, and they can be described, store, identify and understand.Video camera
Demarcating and just determine that the mapping relations from three dimensions point to its X-Y scheme picture point, it is many computer vision application
Requisite step.In order to determine this mapping process, need to set up the geometry imaging model of video camera, the ginseng of geometric model
Number is referred to as camera parameters, and camera parameters can be divided into intrinsic parameter and outer parameter two class.Intrinsic parameter describes the imaging of imaging system
Geometrical property, outer parameter describes imaging system about the direction of world coordinate system and position.Camera calibration can be divided into tradition mark
Calmly, self-calibration and demarcation based on geometry entity.No matter which kind of scaling method, is intended to set up two dimensional image and video camera internal reference
Restriction relation between number, particularly linear restriction relation, this is the target that current camera calibration is pursued, and is also to count at present
One of focus of calculation machine visual field research.
Parabolic catadioptric video camera is made up of a parabolic mirror surface and an orthogonal camera, and its visual field is big, is
One of focus 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 advantage of this kind of method is
Need not use calibrating block, shortcoming is to obtain the corresponding point between image.And in computer vision, it is achieved one is very
The effective method finding corresponding point is 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) have studied straight line under central catadiotric video camera
The geometric properties of picture, and these character are applied to the demarcation 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) describe right
Opening up a little with to opening up picture point, the point being derived in space is in the projection on ball and the pass between its catadioptric picture point
System, is used this relation to establish the linear restriction of central catadiotric camera intrinsic parameter, can be obtained by this linear restriction
Central catadiotric camera intrinsic parameter.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 based on
The scaling method of Three dimensions control point, by using the coordinate of Veronese mapping pair three-dimensional point and its picture point to be extended,
Achieve the mark of central catadiotric video camera based on DLT (direct linear transformation) similarity method on the basis of extension coordinate
Fixed, but this kind of method needs the position of known three-dimensional point, and easily from image, extract its picture point.
Ball is as a kind of common solid, and its most important advantage is to block without self, in terms of any one direction
The occluding contour of an a ball always circle in space, and its contour projection can all extract.Owing to ball has rich
Rich visual geometric characteristic, carries out camera calibration hence with ball and has become a focus 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) propose first utilize ball demarcate central catadiotric video camera.They demonstrate ball
Picture under the unit ball projection model of central catadiotric video camera is oval, and in the projection of non degenerate situation next one ball
Conic section provides two invariants.In order to reduce the complexity solved, they propose a kind of substep scaling method, the method
The projection at least needing 4 balls just can complete the demarcation of video camera.But the scaling method that the document proposes is nonlinear, meter
The complexity calculated is higher, and this 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) introduce
Revise the effect in central catadiotric camera calibration of the picture (MIAC) of absolute conic.They by research ball in
The picture being filled with admiration under reflection video camera proposes two kinds of linear calibration's algorithms with the Analytic Geometry and Algebra relation of MIAC.The knot that they draw
Opinion is also to set up for dual form.But the theory in this article and scaling method are for parabolic catadioptric video camera
Situation is to degenerate.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) propose a kind of utilization based on circular point theory and determine parabolic catadioptric video camera to opening up ball image scale
Linear method.But in this article about circular point picture choose more complicated.
Summary of the invention
The invention provides a kind of make simple, widely applicable, good stability utilize target to solve parabolic catadioptric to take the photograph
The method of camera intrinsic parameter, this target is made up of in space ball.In the process solving parabolic catadioptric camera intrinsic parameter
In, 3 width linearity of parabolic catadioptric video camera shooting target need to be used to solve 5 internal references of parabolic catadioptric video camera
Number.
The present invention adopts the following technical scheme that
Shoot 3 width with parabolic catadioptric video camera from different positions and contain the image of a ball.The present invention is to utilize in space
The method that one ball is used for solving parabolic catadioptric camera intrinsic parameter as target, it is characterised in that merely with ball element.First
First, from 3 width images, the marginal point of target image marginal point and the wherein minute surface outline projection of piece image, use are extracted respectively
Least square fitting obtains minute surface outline projection and the projection of ball picture.Secondly, the relation opening up picture point is obtained with it according to picture point
Must to opening up picture point, thus simulate ball picture to opening up ball picture.Ball picture takes two points of inequality, and obtain two points to opening up
Picture point.By to opening up the definition of picture point and round character, above-mentioned two groups provide a shadow to disappear a little to opening up picture point.Ball picture takes two groups
Two points of inequality, obtain two shadows and disappear a little.The disappear straight line at a place of two shadows is that shadow disappears line, shadow disappear line and ball as meeting at circle
The picture of circling point, three width images provide the picture of three groups of circular point.Finally, utilize circular point as constraint to absolute conic picture
Solve camera intrinsic parameter.Concrete step includes: simulate minute surface outline projection equation and target projection equation, estimates ball picture
To opening up ball picture, determine the picture of circular point, solve parabolic catadioptric camera intrinsic parameter.
1. matching minute surface outline projection equation and target projection equation
The pixel utilizing the Edge function in Matlab program to extract minute surface outline projection marginal point and target image marginal point is sat
Mark, and obtain minute surface outline projection equation and the equation of ball picture with least square fitting.
2. estimate ball picture to opening up ball picture
Ball in space, the projection under the unit ball model of thing catadioptric video camera is divided into two steps.The first step, ballThrow
Shadow be withCentered by unit regard the parallel roundlet on ballWith(Represent three width images of shooting), claim
ForTo opening up circle, andBall center is regarded with unitIt is symmetrical in, unit depending on two end points of bulb diameter each other to opening up.
Second step, regards a bit on ball surface with unitFor projection centre, hereThe photocentre of a video camera can be regarded as, by parallel
RoundletWithIt is projected as the conic section on the parabolic catadioptric plane of delineation respectively, wherein claim visible secondary bent
LineFor ballPicture, sightless conic sectionFor ball pictureTo opening up ball picture.Regard on ball corresponding to unitClaim
For to opening up circle, the parabolic catadioptric plane of delineation and straight lineVertically.An end points of bulb diameter, this end points is regarded corresponding to unit
Invisible referred to as to opening up picture point at the parabolic catadioptric plane of delineation, then unit is referred to as antipodal point depending on this end points of bulb diameter.Order
WithIntrinsic Matrix for the video camera of photocentre is, whereinIt is aspect ratio,It is effective Jiao
Away from,It is obliquity factor,It it is video camera principal pointHomogeneous coordinates matrix form,,,,,Catadioptric for parabolic
Penetrate 5 intrinsic parameters of video camera.The function in Matlab is utilized to extract the minute surface outline projection marginal point and 3 in piece image
The pixel coordinate of width image target image marginal point, obtains corresponding quadratic curve equation by least square fitting.Here
WithRepresent the coefficient matrix of the 1st width image minute surface outline projection curve,Represent respectivelynBall picture in width image be
Matrix number.Herein in order to simplify statement, represent curve and its coefficient matrix by same letter.Pass throughCan obtain in video camera
Parameter matrixAn initial matrix value, thus obtain the picture of absolute conicInitial value, here:,, wherein,It is the initial value of aspect ratio,It it is effective focal length
Initial value,It is the initial value of obliquity factor,It is that the initial homogeneous coordinates matrix of video camera principal point represents, note.TakeOn one group of point, then corresponding with it one group pair
Open up picture pointCan be by relation
Determine,Represent with homogeneous coordinates matrix.According to opening up the definition of picture point, pointAt ball pictureTo opening up ball pictureOn, therefore can obtain opening up ball picture with least square fittingEquation.
3. determine the picture of circular point
At ballProjection roundletOn take two points of two groups of inequalitiesWith, wherein subscript, useWith
Represent respectivelyWithThe center of ball is regarded about unitSymmetrical point, i.e. antipodal point, then pointWithIt isAbout
Unit regards the ball centre of sphereSymmetrical circle, i.e. to opening up circleOn.ForThe straight line at 2 places,For
The straight line at 2 places, according to the definition of antipodal point,, thenWithThere is identical infinite point, here
WithRepresentOn infinite point.Pass throughMay determine that roundletTwo infinitys in the plane
Point, then can determine that the line at infinity in this plane, uses hereRepresent the line at infinity of this plane.Because in plane
Each circle through circular point, so the intersection point of circle and line at infinity is two circular point, circular point is conjugate complex
PointWith。With roundletMeet at this flat circle circling point.WithRepresent respectivelyPicture, thenIt is two to opening up picture point.Record a demeritThe straight line of 2 is, mistakeThe straight line of 2 is, then according to the character of projective transformation, straight lineFor straight linePicture, then may be used
Pass through straight lineDetermine roundletTwo shadows in the plane disappear a little(Picture),
Thus can determine that the shadow of this plane disappears line(Picture).Finally, straight line is soughtWith ball pictureIntersection point obtain a pair conjugate radical
Point, for roundletThe picture of circular point in the plane.For roundletCircular point in the plane
PictureAvailable similar method can obtain.SubscriptRepresent corresponding to circular point。
4. solve parabolic catadioptric camera intrinsic parameter
By the picture of circular point() picture to absolute conicLinear restriction obtain, it may be assumed that.WhereinRepresent real and imaginary part respectively.Finally, rightCarry out Cholesky decomposition
Invert again and obtain intrinsic parameter square, i.e. obtain 5 intrinsic parameters of video camera.
The invention have the advantages that
(1) this target makes simple, only need to be fixed on a support by a ball.
(2) the physical size not requirement to this target, it is not necessary to know centre of sphere coordinate under world coordinate system.
(3) sharp point of this target almost can all extract, and so can improve the degree of accuracy of curve matching, from
And improve stated accuracy.
Accompanying drawing explanation
Fig. 1 is for solving the schematic diagram that the target of parabolic catadioptric camera intrinsic parameter regards on ball in unit.
Fig. 2 is target projection on the parabolic catadioptric plane of delineation.
Detailed description of the invention
The invention provides a kind of method utilizing target to solve parabolic catadioptric camera intrinsic parameter, target is by space
In ball constitute, such as Fig. 1.Complete solving of parabolic catadioptric camera intrinsic parameter with this target to need through following step
Rapid: from catadioptric image, to extract minute surface outline projection marginal point and target image marginal point, use least square fitting to obtain
Obtain minute surface outline projection and the picture of ball.With it, relation opening up picture point is obtained opening up picture point according to picture point, thus simulate ball picture
To opening up ball picture.Ball picture takes four points of inequality, and tries to achieve opening up picture point, by opening up the definition of picture point, above-mentioned four groups pairs
Open up picture point and the picture of a pair circular point is provided.From three different orientation, racket is taken the photograph picture, obtain the picture of three groups of circular point.Utilize
The picture of the circular point constraint solving camera intrinsic parameter to absolute conic picture.Utilize the method in the present invention to for testing
Thing catadioptric video camera demarcate, specifically comprise the following steps that
1. matching minute surface outline projection equation and target projection equation
The pixel utilizing the Edge function in Matlab program to extract minute surface outline projection marginal point and target image marginal point is sat
Mark, and obtain minute surface outline projection equation and the equation of ball picture with least square fitting.
2. estimate ball picture to opening up ball picture
Ball in space(such as Fig. 1), the projection under the unit ball model of thing catadioptric video camera is divided into two steps.First
Step, by ballBe projected as withThe unit at center regards the parallel roundlet on ball, claimForTo opening up circle, this process as shown in Figure 1 (As a example by).Second step, by the photocentre of video cameraBy parallel roundletIt is not projected as the conic section on the parabolic catadioptric plane of delineation, referred to here as visible conic section
For ballPicture, sightless conic sectionFor ball pictureTo opening up ball picture, as shown in Figure 1.Utilize in Matlab
Edge function extracts the pixel coordinate of the minute surface outline projection of the target image marginal point in 3 width images and the 1st width image respectively,
Obtain corresponding quadratic curve equation by least square fitting, use hereRepresent that piece image minute surface outline projection is bent
The coefficient matrix of line,Represent theThe coefficient matrix of the ball picture in width image.Pass throughCamera intrinsic parameter matrix can be obtainedAn initial matrix value, concrete such as formula (1):
, (1)
Here,Representing matrix?RowColumn element,,For shooting
The half of the machine angle of visual field,Oval for paraboloidal mirror outline projectionMajor semiaxis long.ObtainingOn the basis of available
Initial value, such as formula (2):
.(2)
TakeOn one group of point, then corresponding with it one group to opening up picture pointCan be determined by relational expression (3):
.(3)
According to opening up the definition of picture point, pointAt ball pictureTo opening up ball pictureOn, therefore can use least square fitting
Obtain opening up ball pictureEquation.
3. determine the picture of circular point
At ballProjection roundletUpper take the two of two groups of inequalities respectively to pointWith, wherein subscript, use
WithRepresent respectivelyWithAntipodal point, as it is shown in figure 1, in order to simplify expression, scheme upper second subscripti=1, represent
Two pairs of pointsWithIn any pair.Then pointWith?To opening up circleOn.For2 institutes
Straight line,ForThe straight line at 2 places.According to the definition of antipodal point,, thenWithTool
There is identical infinite point, use hereRepresentOn infinite point；Pass throughMay determine that roundletInstitute
Two infinite points in the plane, then can determine that the line at infinity in this plane, use hereRepresent the nothing of this plane
Poor remote straight line.Circle intersects two circular point with line at infinity,With roundletMeet at this flat circle circling point.Such as Fig. 2 institute
Show, useRepresent respectivelyPicture, thenBe two groups to opening up
Picture point, wherein.Record a demeritThe straight line of 2 is, mistakeThe straight line of 2 isIf,'s
Homogeneous coordinates matrix is respectively,Homogeneous line coordinates matrix is
,In+represent visible ,-represent invisible, subscriptPicture point corresponding to projectionThen:
, (4)
；(5)
, (6)
, (7)
WhereinIt it is non-zero scale factor.Then according to the character of projective transformation, straight lineFor straight linePicture, in
It is to pass through straight lineDetermine roundletTwo shadows in the plane disappear a little.Pass through simultaneousWithEquation can obtain:
, (8)
WhereinFor the pixel homogeneous coordinates matrix on the parabolic catadioptric plane of delineation.In like manner, simultaneous is passed throughWith
Equation can obtain:
.(9)
IfWithHomogeneous coordinates matrix be respectivelyWith, then
It is the solution of equation group (8),It is the solution of equation group (9), subscriptWithCorresponding.Pass through
RoundletTwo shadows in the plane disappear a littleWithCan determine that the shadow of this plane disappears line.IfHomogeneous line coordinates square
Battle array is, then
, (10)
WhereinIt it is non-zero invariant.Finally, simultaneous is passed throughWithEquation can obtain
, (11)
The solution of equation group (11) is roundletThe picture of circular point in the plane.For roundletPlace
The picture of the circular point in planeWithAvailable similar method obtains.
4. solve parabolic catadioptric camera intrinsic parameter
By the picture of circular point, the linear restriction of the picture of absolute conic is had:
, (12)
WhereinRepresent real and imaginary part respectively.Available method of least square Optimization Solution (12) obtains, finally
RightCarry out Cholesky to decomposeInvert again and just obtain Intrinsic Matrix, i.e. obtain 5 intrinsic parameters of video camera.
Embodiment
The present invention proposes a kind of ball utilizing space and linearly determines parabolic catadioptric video camera internal reference as target
The method of number.The experiment pattern structural representation that the present invention uses is as shown in Figure 1.Below with the example embodiment party to the present invention
Case makes more detailed description.
The experiment pattern used based on the parabolic catadioptric camera calibration of ball in space is a ball in space, such as figure
Shown in 1, ball is.Utilize the method in the present invention that the parabolic catadioptric video camera for experiment is demarcated, concrete steps
As follows:
1. matching image boundary and target curvilinear equation
The image size that the present invention uses is.3 width experimental image of target are shot with parabolic catadioptric video camera,
Read in image, utilize the Edge function in Matlab to extract the 1st width image minute surface outline projection marginal point and 3 width image target figures
As the pixel coordinate of marginal point, and obtain minute surface outline projection equation and the equation of ball picture with least square fitting.1st width figure
As the coefficient matrix of minute surface outline projection equation is, the coefficient matrix of the equation of 3 width ball pictures is respectively, knot
Fruit is as follows:
, (13)
, (14)
, (15)
.(16)
2. estimate double ball picture to opening up ball picture
(13) substitution (1) and (2) can be obtained, result is as follows:
.(17)
The most respectively at ball picture、WithOn take the point of at least 5 inequalities, then bring the point taken and (17) into (3) respectively
Must be obtained opening up ball picture by least square fitting opening up the coordinate of point on ball picture、WithEstimation, result is such as
Under:
, (18)
, (19)
.(20)
3. determine the picture of circular point
At ball pictureTake up an official post and take the point of two groups of two inequalities, be designated as, their homogeneous coordinates matrix
It is respectively as follows:
, (21)
；(22)
, (23)
.(24)
According to opening up the character of picture point, can obtain and pointCorresponding to opening up picture point,
Result is as follows:
, (25)
；(26)
, (27)
.(28)
(21) and (22) are brought into (4) can cross a littleStraight lineHomogeneous line coordinates matrix, result is as follows:
, (29)
(25) and (26) are brought into (5) can cross a littleStraight lineHomogeneous line coordinates matrix, result is as follows:
；(30)
(23) and (24) are brought into (6) can cross a littleStraight lineHomogeneous line coordinates matrix, result is as follows:
, (31)
(27) and (28) are brought into (7) can cross a littleStraight lineHomogeneous line coordinates matrix, result is as follows:
.(32)
(29) and (30) substitution (8) can be obtained shadow disappear a little, result is as follows:
；(33)
(31) and (32) substitution (9) can be obtained shadow disappear a little, result is as follows:
.(34)
(33) and (34) are brought into (10) and can determine that roundletShadow in the plane disappear line, its homogeneous line coordinates is:
.(35)
(35) and (14) are brought into (11) roundlet can be obtainedThe picture of circular point in the plane, result is as follows:
, (36)
；(37)
For roundletThe picture of circular point in the planeAvailable similar approach obtains, and result is as follows:
, (38)
；(39)
For roundletThe picture of circular point in the planeAvailable similar approach obtains, and result is as follows:
, (40)
.(41)
4. solve parabolic catadioptric camera intrinsic parameter
Bring (36) (38) and (40) into (12) to obtainThe system of linear equations of middle element, uses method of least square to solve this linear
Equation group obtainsCoefficient matrix.Result is as follows:
.(42)
Finally, in (42)Carry out Cholesky to decompose and invert again and just can obtain, result is as follows:
, (43)
Wherein aspect ratio(Representing matrixThe 1st row the 1st row element,Represent
MatrixThe element of the 2nd row the 2nd row), therefore 5 intrinsic parameters of parabolic catadioptric video camera are respectively as follows:,,,,。
Claims (1)
1. utilizing the method that the image scale of in space ball and circular point determines parabolic catadioptric camera intrinsic parameter, it is special
Levy and be by a ball in space as target；The concrete steps of described method include: first, with parabolic catadioptric video camera
Shoot the image that 3 width contain ball from different positions, extract marginal point and the target image marginal point of minute surface outline projection, use
Least square fitting obtains minute surface outline projection and the image of ball；Secondly, according to picture point and its relation to opening up picture point of ball
Obtain to opening up picture point, thus estimate ball picture to opening up ball picture；Ball picture takes two points of inequality, and tries to achieve opening up picture point, by
To opening up the definition of picture point, the straight line at two some places on ball picture with the straight line opening up picture point place met at shadow disappear a little；At ball picture
On take two points of two groups of inequalities, it is thus achieved that two shadows disappear a little, and two shadows disappear and a little determine that a shadow disappears line；Shadow disappears the friendship of line and ball picture
Point is the picture of circular point, and three width images provide the picture of three groups of circular point；Finally, utilize the picture of circular point to absolute conic picture
Constraint solving camera intrinsic parameter；
(1) picture of circular point is determined
At ballThe projection roundlet on ball is regarded in unitUpper two points taking two groups of inequalities respectivelyWith, wherein subscript, useWithRepresent respectivelyWithThe ball centre of sphere is regarded about unitPoint of symmetry, i.e. antipodal point, then point
With?The ball centre of sphere is regarded about unitSymmetrical circle, i.e. to opening up circleOn；For2 places straight
Line,ForThe straight line at 2 places, according to the definition of antipodal point,, thenWithHave identical
Infinite point, use hereRepresentOn infinite point；Pass throughWithDetermine roundletInstitute
Two infinite points in the plane, it is thus determined that the line at infinity in this plane, use hereRepresent the infinite of this plane
Remote straight line；According to the definition of circular point,With roundletMeet at this flat circle circling point；WithRespectively
RepresentPicture, thenWithIt is two to opening up picture point；Record a demeritThe straight line of 2
For, mistakeThe straight line of 2 is, then according to the character of projective transformation, straight lineFor straight linePicture, then lead to
Cross two groups of straight linesWithDetermine roundletTwo shadows of place plane disappear a little, correspondence i.e. respectivelyPicture, the line so that it is determined that the shadow of this plane disappears, i.e.Picture；Finally, straight line is soughtWith ball pictureIntersection point obtain
A pair conjugate imaginary points, for roundletThe picture of circular point in the plane。
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| CN110148183B (en) * | 2019-05-08 | 2022-09-06 | 云南大学 | Method, storage medium, and system for calibrating a camera using sphere and pole lines |
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