CN110148182A - A kind of method of calibrating camera, storage medium, arithmetic unit and system - Google Patents
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Abstract
The invention discloses a kind of method of calibrating camera, storage medium, arithmetic unit and system, method flow includes the steps that obtaining scene image, feature point extraction is carried out to scene image and the step of conic fitting, calculate it is orthogonal it is hidden disappear set of coordinates the step of and the step of calculate camera intrinsic parameter.Storage medium is stored with the program of the execution above method after operation.Arithmetic unit includes a processor and above-mentioned storage medium.System includes a plane catadioptric video camera and above-mentioned arithmetic unit.The test scene construction of the present invention program is simple, low to scene required precision, and convenient for operation, operand is small, and operational precision is high.
Description
Technical field
The present invention relates to computer vision field, especially a kind of symmetry and pole using reflection point in bimirror
The property of point polar curve and conjugate value solves method, storage medium, arithmetic unit and the system of 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.
Document " A theory of single-viewpoint catadioptric image formation " (Baker
S., 1999,35 (2): Nayar S.International Journal of Computer Vision 175-196) proposes folding
Reflecting system is made of the mirror surface of a traditional video camera and front.And be classified as two major classes: center is catadioptric
Penetrate system and non-central mirror-lens system.Wherein, the difference for the reflecting mirror that central catadiotric system is put according to camera front
Be divided into again: parabolic catadioptric (parabolic mirror surface of a rotation is placed before orthogonal camera), hyperbolic catadioptric are (in perspective camera
Before place the hyperboloidal mirror of a rotation), oval catadioptric (oval shape mirror of a rotation is placed before perspective camera
Face), plane catadioptric (perspective video camera before place a plane).
The central catadiotric video camera imaging visual field is big, has single effective viewpoint constraint, and the process of imaging easily establishes number
Model is learned, it has a wide range of applications in robot navigation, virtual monitor with fields such as three-dimensional modelings, since plane mirror makes
Simply and there is good imaging property so the research to central catadiotric video camera especially grinds plane mirror-lens system
Study carefully with very big meaning.
Document " Shape-from-Silhouette with two mirrors and an uncalibrated
camera”(Forbes K.,Nicolls F.,Jager G.D.,et al.European Conference on Computer
Vision.2006 the plane mirror-lens system using two plane mirrors and video camera composition) is proposed, first comprising more
In the image of a view extract object silhouettes, recycle the common tangent of these profiles estimate video camera intrinsic parameter,
The normal vector of plane mirror and the position of pinhole camera.
Document " 3-D reconstruction using mirror images based on a plane symmetry
recovering method”(Mitsumoto H.,Tamura S.,Okazaki K.,et al.IEEE Transactions
On Pattern Analysis&Machine Intelligence, 1992,14 (9): 941-946) for the first time to bimirror
The geometric properties and three-dimensional reconstruction of imaging are studied, document " Geometric properties of multiple
reflections in catadioptric camera with two planar mirrors”(Ying X.,Peng K.,
Ren R.,et al.2010IEEE International Conference on Vision and Pattern
Recognition.2010:1126-1132 on) pointing out that space three-dimensional point and its reflection picture point are round at one, all these circles
All it is coaxial parallel circle, utilizes circle, document " Camera calibration from relatively more to the method for camera calibration
the quasi-affine invariance of two parallel circles”(Wu Y.,Zhu H.,Hu Z.,et
) and " Coplanar circles, quasi-affine invariance and al.2004,3021:190-202
calibration”(Wu Y.,Li X.,Wu F.and et al.Image&Vision Computing,2002,24(4):
The method of the camera calibration based on two parallel circles and coplanar circle is proposed in 319-326), but is not provided outside video camera
The method for solving of parameter.Document " Self-calibration of catadioptric camera with two planar
mirrors from silhouettes”(Ying X.,Peng K.,Hou Y.,et al.IEEE Transactions on
Pattern Analysis&Machine Intelligence, 2013,35 (5): 1206-1220) in propose with two planes
Pole geometrical relationship in plane mirror-lens system composed by mirror and a pinhole camera in five view outlines and to exhausted
Constraint to the picture of conic section solves the intrinsic parameter of video camera, but this method calculation amount is larger, needs to obtain hidden
The accurate coordinate to disappear a little.Document " Calibration of a paracatadioptric camera by projection
(2017,56 (8): Li Y., Zhao Y.Applied Optics 2230) is proposed imaging of a single sphere "
In plane mirror-lens system based on the orthogonal hidden method for disappearing camera self-calibration a little, but this method calculation amount is inclined
Greatly.
Summary of the invention
Goal of the invention of the invention is: in view of the above problems, it is simple, widely applicable, steady to provide a kind of production
The method and system of qualitative calibrating camera good, calculation amount is small.The present invention program is flat using two angled rectangles
Face mirror, and plane mirror is vertical with the plane where the bottom edge of two plane mirrors, the angle of two plane mirrors is between 60 ° to 80 °.This
When plane mirror between there are an internal reflection, object forms four virtual images in bimirror device.Using in bimirror
The property of the symmetry and pole polar curve of reflection point and conjugate value solves six groups and orthogonal hidden disappears a little.It is imaged in solution procedure
Machine shoots the multiple image including four virtual images in object and plane mirror from different directions.Six groups are established orthogonal hidden to disappear a little about exhausted
To several constraint equations of conic section picture, linear solution camera intrinsic parameter.
The technical solution adopted by the invention is as follows:
A method of utilizing the symmetry calibrating camera at bimirror midpoint comprising following steps:
A. scene image of at least 3 width under different perspectives is obtained, the corresponding test scene of the scene image are as follows: pressing from both sides
Two articles point is placed at angle between two plane mirrors of predetermined angular, is formed test scene and is obtained two groups of quantity under the test scene
Be 5 point hytes: object point and its 4 catadioptric exit points in two plane mirrors, 5 points of each hyte must
So on same circle；
B. it is directed to each width scene image, executes following B1-B2:
B1: extracting the characteristic point coordinate of scene image, according to the characteristic point coordinate of extracted scene image, calculates pair
The quadratic curve equation answered；
B2: it obtains in each point hyte respectively, the picture of wantonly two groups of adjacent points, the two groups of consecutive points taken in hyte on one point
Position is corresponding with the two groups of adjacent points taken in another point hyte respectively；According to the two groups of adjacent points taken in two o'clock hyte
Picture, be based on pole polar curve relationship, calculate corresponding two pairs of orthogonal hidden coordinates that disappear；It is so-called in two o'clock hyte, taken
Consecutive points hyte it is corresponding, refer in two o'clock hyte, the attribute of each group of adjacent point taken is identical, is such as object
Point and picture point of the object point in same plane mirror；
C. according to the coordinate of the orthogonal hidden group that disappears of all scene images, based on it is orthogonal it is hidden disappear a little with absolute conic
The linear restriction relationship of picture, calculates the intrinsic parameter of video camera.
Further, in above-mentioned steps B1, the characteristic point coordinate according to extracted scene image is calculated corresponding
Quadratic curve equation specifically: according to the characteristic point coordinate of extracted scene image, be fitted, obtained using least square method
To corresponding quadratic curve equation.
Further, in above-mentioned steps B2, the picture according to the two groups of adjacent points taken in two o'clock hyte is based on pole
Polar curve relationship calculates corresponding two pairs of orthogonal hidden coordinates that disappear specifically:
Two corresponding phases are calculated according to photography invariance according to the picture of the one group of adjacent point taken in two o'clock hyte
Adjoint point hyte as place straight line intersection point, obtain the hidden coordinate that disappears, then according to pole polar curve relationship, hidden disappeared by described
The coordinate of point, calculates orthogonal another hidden coordinate to disappear a little, obtains the hidden coordinate to disappear a little of a pair of orthogonal, by same
Mode calculates the orthogonal hidden coordinate to disappear a little of another pair according to the picture of another group of adjacent point taken in two o'clock hyte.
Further, in the test scene, the angle of two plane mirrors is 60-80 degree.
Further, the step C specifically: according to each to the orthogonal hidden coordinate to disappear a little, orthogonal hidden disappeared using SVD to all
The linear restriction relationship of point and the picture of absolute conic carries out preliminary exposition, then carries out Cholesky points to preliminary exposition result
Xie Hou inverts to obtain camera intrinsic parameter matrix, and the corresponding parameter extracted in the Intrinsic Matrix obtains required intrinsic parameter.
A kind of storage medium, be stored with program, run the program can be performed it is above-mentioned using bimirror midpoint
The method of symmetry calibrating camera.
A kind of arithmetic unit a comprising processor and above-mentioned storage medium, the processor is for running the storage
The program stored in medium, and export operation result.
A kind of system of the symmetry calibrating camera using bimirror midpoint comprising a plane catadioptric video camera
With above-mentioned arithmetic unit, the scene image of acquisition is sent to by the plane catadioptric video camera for acquiring scene image
The arithmetic unit, the arithmetic unit are used to carry out operation to received scene image.
In conclusion by adopting the above-described technical solution, the beneficial effects of the present invention are:
1, the test scene construction in the present invention is simple, not high for test scene required precision.To the physics ruler of target
Degree does not require, without knowing coordinate of the center of circle of circle composed by reflection point group under world coordinate system.
2, in the present invention, in each width scene image, there is no overlappings between object point and picture point, so that final stated accuracy
It is high.
3, calculating process of the invention belongs to linear calculating, and 3 times or more more traditional polynomial solutions can be substantially
Reduce operand.
Detailed description of the invention
Examples of the present invention will be described by way of reference to the accompanying drawings, in which:
Fig. 1 is the schematic diagram that two real points are imaged under bimirror device in space.
Fig. 2 is that infinite point and the infinite point of its polar curve direction are illustrated for the infinite point of one group of orthogonal direction
Figure.
Fig. 3 is the hidden schematic diagram that disappears of a pair of orthogonal.
Specific embodiment
All features disclosed in this specification or disclosed all methods or in the process the step of, in addition to mutually exclusive
Feature and/or step other than, can combine in any way.
Any feature disclosed in this specification (including any accessory claim, abstract), unless specifically stated,
It is replaced by other equivalent or with similar purpose alternative features.That is, unless specifically stated, each feature is a series of
An example in equivalent or similar characteristics.
Embodiment one
Present embodiment discloses a kind of methods of symmetry calibrating camera using bimirror midpoint, including following step
It is rapid:
1, the characteristic point in image, and fit equation are extracted
From several scene images that plane catadioptric video camera acquires, the scene image under 3 width different perspectivess is obtained, is adopted
With the coordinate for extracting scene image characteristic point in Matlab software using Harris corner detection approach, and utilize least square method
The equation of conic section (picture of the circle i.e. where 5 points) where fit characteristic point.
The acquisition of scene image is divided into following two step:
The first step tests building for scene, as shown in Figure 1, two rectangle reality plane mirrors are denoted as M1 and M2, M1, M2 respectively
Between angle be between 60 to 80 degree, two real plane mirror M1 and M2 can have an internal reflection, picture note of the M2 in M1
It is empty plane mirror for M3, M3, picture of the M1 in M2 is denoted as M4, and M4 is empty plane mirror.Point A0, B0 are two of inequality in space
Real point, point A1, B1 are the virtual image of point A0, the B0 in plane mirror M1 respectively, and point A2, B2 are point A0, B0 respectively in plane mirror M2
The virtual image, the virtual image that point A3, B3 are point A1, B1 respectively in empty plane mirror M3, point A4, B4 are point A2, B2 respectively empty
The virtual image in plane mirror M4, by plane mirror imaging principle: wait it is big, equidistant, as vertical with mirror surface with the line of object, it is known that point
The line of A0, A1 are perpendicular to plane mirror M1, and for the line of point A0, A2 perpendicular to plane mirror M2, the line of point A1, A3 are flat perpendicular to void
The line of face mirror M3, point A2, A4 are perpendicular to empty plane mirror M4.It is flat to know that point A0, A1, A2, A3, A4 are located at by plane geometry knowledge
Justify C in faceAOn.Similarly, B0, B1, B2, B3, B4 are in flat circle CBOn.Because of CA、CBPlace plane and two real plane mirror M1, M2
Intersection it is vertical, so CAAnd CBIn parallel.Second step acquires the scene under several different perspectivess using plane catadioptric video camera
Image includes that there is no block between 5 views and each view in every width scene image.
2, determine that the orthogonal of every width scene image hidden disappears a little
For straight line where point A0, A1 with straight line parallel where point B0, B1 and perpendicular to plane mirror M1, intersection point is parallel circle
CA、CBInfinite point P in the plane1∞.By pole polar curve relationship: giving a conic section C for any point in plane
Straight line determined by P, L=CP is known as polar curve of the point P about C, and point P is known as pole of the straight line L about C, it is known that P1∞About circle CA
Polar curve be circle CAA diameter LA1, LA1And CAE and F two o'clock is met at, E and F is crossed and makees CATangent line REAnd RF, and RE∥RF.In
It is REAnd RFInfinite point P having the same1∞, L is known by the property of tangent lineA1⊥RE, LA1⊥RF。P1∞About circle CBPolar curve be circle
CBA diameter LB1, LB1And CBG and H two o'clock is intersected at, G and H is crossed and makees CBTangent line RGAnd RHAnd RG∥RH, then RGAnd RH's
Infinite point P having the same1∞.L is known by the property of tangent lineB1⊥RG, LB1⊥RH, and polar curve LA1∥LB1。
Polar curve LA1And LB1Meet at parallel circle CA、CBInstitute infinite point P ' in the plane1∞, by match Principle for Extreme Nodes and Lines: as fruit dot A is closed
Point B is crossed in a conic section polar curve, then point B also crosses point A about the polar curve of this conic section, it is known that P '1∞About CAPole
Line LC1Cross OA (CAThe center of circle) and infinite point P1∞, P '1∞' about CBPolar curve LD1 cross OB (CBThe center of circle) and infinite point
P1∞, and LC1∥LD1.Again because of LC1∥RE, LD1∥RGAnd RG∥RETherefore LC1⊥LA1, LD1⊥LB1, therefore LC1、LA1It is total for one group
Yoke diameter (LD1、LB1For one group of conjugate value).Therefore infinite point P1∞With infinite point P '1∞For the infinite of one group of orthogonal direction
Far point.Wherein P1∞It is polar curve LC1And LD1The infinite point of direction, P '1∞It is polar curve LA1、LB1, the infinity of direction
Point.
Similarly, for straight line where point A0, A2 with straight line parallel where point B0, B2 and perpendicular to plane mirror M2, intersection point is flat
Row circle CA、CBInfinite point P in the plane2∞。P′2∞About CAPolar curve be LA2, P '2∞About CBPolar curve be LB2, and
LA2∥LB2, LA2、LB2Intersect at parallel circle CA、CBInstitute infinite point P ' in the plane2∞, wherein P2∞With P '2∞For one group of orthogonal side
To infinite point.
On as plane, point a0, a1, a2, a3, a4 are respectively the picture of A0, A1, A2, A3, A4, point b0, b1, b2, b3, b4
The respectively picture of B0, B1, B2, B3, B4, the conic section where point a0, a1, a2, a3, a4 are ca, point b0, b1, b2, b3, b4
The conic section at place is cb.By projective invariance, as tie point a0, a1 and point b0, b1 in plane, the place point a0, a1 is straight
The intersection point of line and the place point b0, b1 straight line is the hidden point v1 that disappears.V1 is infinite point P1∞Picture, v1 is about conic section caPolar curve
It is denoted as la1, wherein caFor CAPicture, la1For LA1Picture.V1 is about conic section cbPolar curve be denoted as lb1, wherein cbFor CBPicture,
lb1For straight line LB1Picture.Polar curve la1And lb1Intersection point be the hidden point v1' that disappears, v1' be infinite point P '1∞Picture.It is constant by projection
Property know v1 and v1' be one group of the hidden of orthogonal direction disappear a little.
Similarly, according to projective invariance, tie point a0, a2 and point b0, b2, straight line where point a0, a2 and the place point b0, b2
The intersection point of straight line is the hidden point v2 that disappears.V2 is infinite point P2∞Picture, v2 is about conic section caPolar curve be denoted as la2, wherein caIt is
CAPicture, la2For LA2Picture.V2 is about conic section cbPolar curve be denoted as lb2, wherein cbFor CBPicture, lb2For LB2Picture.Polar curve
la2And lb2Intersection point be the hidden point v2' that disappears, v2' be infinite point P '2∞Picture.Know that v2 and v2' is one group orthogonal by projective invariance
The hidden of direction disappears a little.
Note v1, v1'} and v2, v2'} be piece image on two groups it is orthogonal it is hidden disappear a little, similarly on the second width image
Solving two groups of orthogonal hidden disappear a little is respectively { v3, v3'} and { v4, v4'} solve two groups on third width image and orthogonal hidden disappear
Point is respectively { v5, v5'} and { v6, v6'}.
3, the intrinsic parameter of plane catadioptric video camera is solved
By orthogonal end point, { vi, vi'} (i=1,2 ... 6) are to absolute conic as the linear restriction relationship of w
vi TwviSeek w in '=0.V is solved with SVD DECOMPOSED OPTIMIZATIONi Twvi'=0.Finally, to w=K-TK-1Cholesky decomposition is carried out to ask again
It is inverse just to obtain intrinsic parameter square K, correspond to matrixIn each parameter definition: fuFor as plane u axis
Effective focal length, fvFor in the effective focal length as plane v axis, (u0 v0)TReferred to as principal point coordinate, s are obliquity factor, be can be obtained
The intrinsic parameter of video camera.
Embodiment two
Present embodiment discloses a kind of methods of symmetry calibrating camera using bimirror midpoint, based on building
Test scene: the plane mirror to be formed an angle by two and two objects are constituted, and bottom of two plane mirrors with two plane mirrors
Plane where side is vertical.The angle for adjusting two plane mirrors is between 60 to 80 degree, and object is placed on two planes
Between mirror, the angle for adjusting plane mirror object occur four in plane mirror not to be overlapped the virtual image, take the photograph using plane catadioptric
Camera acquires at least 3 width scene images, and therefrom chooses the scene image under 3 width different perspectivess.The method packet of calibrating camera
Include following steps:
A. it is directed to each width scene image, executes following steps:
1, the characteristic point in scene image, and fit equation are extracted
The coordinate of the characteristic point of each scene image is extracted using Harris corner detection approach in Matlab software, is utilized
The equation of conic section where least square method fit characteristic point.
2, orthogonal hidden disappear a little is determined
As shown in Figure 1, two rectangle reality plane mirrors are denoted as M1 and M2 respectively, the angle between M1, M2 is 60 to 80 degree
Between, two real plane mirror M1 and M2 can have an internal reflection, and picture of the M2 in M1 is denoted as M3, and M3 is empty plane mirror, M1
Picture in M2 is denoted as M4, and M4 is empty plane mirror.Point A0, B0 are two real points of inequality in space, and point A1, B1 are a little respectively
The virtual image of A0, B0 in plane mirror M1, point A2, B2 are the virtual image of point A0, the B0 in plane mirror M2 respectively, and point A3, B3 are respectively
The virtual image of point A1, the B1 in empty plane mirror M3, point A4, B4 are the virtual image of point A2, the B2 in empty plane mirror M4 respectively, by putting down
Face mirror image-forming principle: wait it is big, equidistant, as vertical with mirror surface with the line of object, it is known that the line of point A0, A1 are perpendicular to plane mirror
The line of M1, point A0, A2 are perpendicular to plane mirror M2, and perpendicular to imaginary plane mirror M3, the line of point A2, A4 hang down the line of point A1, A3
Directly in empty plane mirror M4.Know that point A0, A1, A2, A3, A4 are located at flat circle C by plane geometry knowledgeAOn.Similarly, B0, B1,
B2, B3, B4 are in flat circle CBOn.Because of CA、CBThe intersection of place plane and two real plane mirror M1, M2 are vertical so CAAnd CBIt is flat
Row.Second step acquires the scene image under several different perspectivess using plane catadioptric video camera, includes in every width scene image
Have to be not present between 5 views and each view and block.
As shown in Fig. 2, straight line where point A0, A1 is with straight line parallel where point B0, B1 and perpendicular to plane mirror M1, intersection point
For parallel circle CA、CBInfinite point P in the plane1∞.By pole polar curve relationship: giving a conic section C for plane
Straight line determined by upper any point P, L=CP is known as polar curve of the point P about C, and point P is known as pole of the straight line L about C, it is known that P1∞
About circle CAPolar curve be circle CAA diameter LA1, LA1And CAE and F two o'clock is met at, E and F is crossed and makees CATangent line REAnd RF, and
RE//RF.Then REAnd RFInfinite point P having the same1∞, L is known by the property of tangent lineA1⊥RE, LA1⊥RF。P1∞About circle CB
Polar curve be circle CBA diameter LB1, LB1And CBG and H two o'clock is intersected at, G and H is crossed and makees CBTangent line RGAnd RHAnd RG//RH, in
It is RGAnd RHInfinite point P having the same1∞.L is known by the property of tangent lineB1⊥RG, LB1⊥RH, and polar curve LA1//LB1。
Polar curve LA1And LB1Meet at parallel circle CA、CBInstitute infinite point P ' in the plane1∞, by match Principle for Extreme Nodes and Lines: as fruit dot A is closed
Point B is crossed in a conic section polar curve, then point B also crosses point A about the polar curve of this conic section, it is known that P '1∞About CAPole
Line LC1Cross OA (CAThe center of circle) and infinite point P1∞, P '1∞' about CBPolar curve LD1 cross OB (CBThe center of circle) and infinite point
P1∞, and LC1//LD1.Again because of LC1//RE, LD1//RGAnd RG//RETherefore LC1⊥LA1, LD1⊥LB1, therefore LC1、LA1It is total for one group
Yoke diameter (LD1、LB1For one group of conjugate value).Therefore infinite point P1∞With infinite point P '1∞For the infinite of one group of orthogonal direction
Far point.Wherein P1∞It is polar curve LC1And LD1The infinite point of direction, P '1∞It is polar curve LA1、LB1, the infinity of direction
Point.
Similarly, for straight line where point A0, A2 with straight line parallel where point B0, B2 and perpendicular to plane mirror M2, intersection point is flat
Row circle CA、CBInfinite point P in the plane2∞。P′2∞About CAPolar curve be LA2, P '2∞About CBPolar curve be LB2, and
LA2//LB2, LA2、LB2Intersect at parallel circle CA、CBInstitute infinite point P ' in the plane2∞, wherein P2∞With P '2∞For one group of orthogonal side
To infinite point.
As shown in figure 3, be respectively the picture of A0, A1, A2, A3, A4 as Plane-point a0, a1, a2, a3, a4, point b0, b1,
B2, b3, b4 are respectively the picture of B0, B1, B2, B3, B4, and the conic section where point a0, a1, a2, a3, a4 is ca, point b0, b1,
Conic section where b2, b3, b4 is cb.By projective invariance as tie point a0, a1 and point b0, b1, point a0, a1 in plane
The intersection point of place straight line and the place point b0, b1 straight line is the hidden point v1 that disappears.V1 is infinite point P1∞Picture, v1 is about conic section ca
Polar curve be denoted as 1a1, wherein caFor CAPicture, la1For LA1Picture.V1 is about conic section cbPolar curve be denoted as lb1, wherein cbFor
CBPicture, lb1For straight line LB1Picture.Polar curve la1And lb1Intersection point be the hidden point v1 ' that disappears, v1 ' be infinite point P '1∞Picture.By penetrating
Shadow invariance knows that v1 and v1 ' is that one group of the hidden of orthogonal direction disappears a little.
Set up an office a0, a1, a2 homogeneous coordinates matrix be respectively [ua0 va0 1]T、[ua1 va1 1]T、[ua2 va2 1]T, point
The matrix of the homogeneous coordinates of b0, b1, b2 is respectively [ub0 vb0 1]T、[ub1 vb1 1]T、[ub2 vb2 1]T.Set up an office the place a0, a1
Straight line is l11, l11Homogeneous line coordinates matrix be [u11 v11 1]T, straight line where point b0, b1 is l12, l12Homogeneous line coordinates
Matrix is [u12 v12 1]T, straight line where point a0, a3 is l13, l13Homogeneous line coordinates matrix be [u13 v13 1]T, point b0, b2
Place straight line is l14, l14Homogeneous line coordinates matrix be [u14 v14 1]T。
Straight line l11、l12、l13、l14Homogeneous line coordinates matrix acquired by following equations:
[u11 v11 1]T=[ua0 va0 1]T×[ua1 va1 1]T, (1)
[u12 v12 1]T=[ub0 vb0 1]T×[ub1 vb1 1]T, (2)
[u13 v13 1]T=[ua0 va0 1]T×[ua2 va2 1]T, (3)
[u14 v14 1]T=[ub0 vb0 1]T×[ub2 vb2 1]T。 (4)
If the homogeneous coordinates matrix of v1, v2 are respectively [uv1 vv1 1]T, [uv2 vv2 1]T, v1 pass through simultaneous l11、l12It asks
, v2 passes through simultaneous l13、l14It acquires, meets following equations:
[uv1 vv1 1]T=[u11 v11 1]T×[u12 v12 1]T, (5)
[uv2 vv2 1]T=[u13 v13 1]T×[u14 v14 1]T。 (6)
The hidden point v1 that disappears is about conic section ca、cbPolar curve be respectively la1、lb1.If la1、lb1Homogeneous line coordinates matrix point
It Wei not [ula1 vla1 1]T、[ulb1 vlb1 1]T, v2 is about ca、cbPolar curve be respectively la2、lb2.If la2、lb2Homogeneous line sit
Marking matrix is respectively [ula2 vla2 1]T、[ulb2 vlb2 1]T.Meet following equation:
la1=cav1, (7)
lb1=cbv1, (8)
la2=cav2, (9)
lb2=cbv2。 (10)
If the homogeneous coordinates matrix of v1 ', v2 ' are respectively [uv1, vv1, 1]T、[uv2, vv2, 1]T, v1 ' is (corresponding to v1 just
Hand over hidden disappear a little) it is polar curve la1、lb1Intersection point, v2 ' (corresponding to v1 orthogonal hidden disappear a little) is polar curve la2、lb2Intersection point, joint type
(7) (8) obtain the homogeneous coordinates matrix of v1 ', joint type (9) (810 obtain the homogeneous coordinates matrix of v2 ':
[uv1′ vv1′ 1]T=[ula1 vla1 1]T×[ulb1 vlb1 1]T, (11)
[uv2′ vv2′ 1]T=[ula2 vla2 1]T×[ulb2 vlb2 1]T。 (12)
Therefore available two groups of orthogonal hidden disappear a little are respectively { v1, v1 ' } and { v2, v2 ' } on piece image.
By the same method, obtaining orthogonal hidden disappear of two groups of the second width figure is a little respectively { v3, v3 ' } and { v4, v4 ' },
It is a little respectively { v5, v5 ' } and { v6, v6 ' } that two groups of orthogonal hidden disappear are solved on third width image.
B. the intrinsic parameter of plane catadioptric video camera is solved
A little the linear restriction relationship of the picture of absolute conic is obtained by orthogonal hidden disappear:
Formula (13) are solved with SVD DECOMPOSED OPTIMIZATION and obtain w, finally to w=K-TK-1Progress Cholesky decomposition is inverted again just to be obtained
To intrinsic parameter square K, matrix is corresponded toIn each parameter definition: fuFor effective as plane u axis
Focal length, fvFor in the effective focal length as plane v axis, (u0 v0)TReferred to as principal point coordinate, s are obliquity factor, and video camera can be obtained
Intrinsic parameter.
Embodiment three
Based on embodiment two, present embodiment discloses a kind of sides of symmetry calibrating camera using bimirror midpoint
Method.In the present embodiment, the size of the 3 width scene images acquired by pinhole cameras is 800*600 pixel.Scaling method
The following steps are included:
1, the characteristic point on image is extracted, and fits quadratic curve equation
3 width images are read in Matlab respectively, the coordinate of image characteristic point is extracted using Harris corner detection approach:
The characteristic point homogeneous coordinates matrix extracted on piece image are as follows, point a0, a1, a2, a3, a4 be respectively A0, A1,
The picture of A2, A3, A4, point b0, b1, b2, b3, b4 are respectively the picture of B0, B1, B2, B3, B4.
a0=[152.406635338115 1795.231490479015 1]T, (14)
a1=[- 1011.872795754164 659.378290768644 1]T, (15)
a2=[174.8987773437959 61.7546429628980 1]T, (16)
a3=[1856.467976790139 696.723300919440 1]T, (17)
a4=[584.4534447124727 443.6296146571376 1]T； (18)
b0=[184.214527356971 2723.357192032778 1]T, (19)
b1=[- 1190.000748241581 964.071379840200 1]T, (20)
b2=[165.6455502635185-29.5339399566531 1]T, (21)
b3=[1652.852391974504 487.424003557335 1]T, (22)
b4=[558.8379111534696 366.6517609636513 1]T。 (23)
The homogeneous coordinates matrix for the characteristic point extracted on second width figure image are as follows, a20, a21, a22, a23, a24 difference
For the picture of A20, A21, A22, A23, A24, point b20, b21, b22, b23, b24 are respectively the picture of B20, B21, B22, B23, B24
a20=[2674.253564341555 3638.473413770824 1]T, (24)
a21=[821.3321704241428-419.1402580777827 1]T, (25)
a22=[- 1865.256112512369 1539.246610008860 1]T, (26)
a23=[697.7121926335417 292.5528677225135 1]T, (27)
a24=[400.0536878784562 677.5452474984588 1]T； (28)
b20=[6430.469880791326 6825.161999744550 1]T, (29)
b21=[623.3518866087570-438.1365396174539 1]T, (30)
b22=[- 1984.235947314589 1100.407980466520 1]T, (31)
b23=[605.2863969666524 262.6538345948490 1]T, (32)
b24=[294.4648619781759 625.7564729006444 1]T。 (33)
The homogeneous coordinates matrix for the characteristic point extracted on third width image are as follows, point a30, a31, a32, a33, a34 difference
For the picture of A30, A31, A32, A33, A34, point b30, b31, b32, b33, b34 are respectively the picture of B30, B31, B32, B33, B34.
a30=[- 4506.600323281641-990.191128085771 1]T, (34)
a31=[484.3723087549791 27.0466316664101 1]T, (35)
a32=[2745.655459664655-2300.772163915937 1]T, (36)
a33=[770.3212422459758 541.9004639853862 1]T, (37)
a34=[625.772168593614 1884.031587701811 1]T； (38)
b30=[- 1841.223678285884-368.229782142383 1]T, (39)
b31=[386.2858814938033 25.0881187344616 1]T, (40)
b32=[15260.78795116761-12111.00405620616 1]T, (41)
b33=[656.0665780392803 480.0605238559518 1]T, (42)
b34=[420.315724500052 1422.151624886802 1]T。 (43)
The coefficient matrix of quadratic curve equation corresponding to each width image characteristic point is fitted using least square method.First width
The coefficient matrix of the corresponding quadratic curve equation of characteristic point on image is respectively ca、cb:
The coefficient matrix of the corresponding quadratic curve equation of characteristic point on second width image is respectively c2a、c2b:
The coefficient matrix of the corresponding quadratic curve equation of characteristic point on third width image is respectively c3a、c3b:
2, orthogonal hidden disappear a little is solved
(14) (15) are updated to (1) formula and solve straight line l11Homogeneous line coordinates matrix, (19) (20) are updated to (2)
Formula solves straight line l12Homogeneous line coordinates matrix, (14) (16) are updated to the homogeneous line coordinates that (3) formula solves straight line 113
(19) (21) are updated to (4) formula and solve straight line l by matrix14Homogeneous line coordinates matrix.Again the neat of 111 solved
Secondary line coordinates matrix and l12Homogeneous line coordinates matrix substitute into (5) formula, l13Homogeneous line coordinates matrix and l14Homogeneous line sit
Mark matrix be updated to (6) formula, obtain two hidden point v1v2 that disappear on piece image, homogeneous coordinates matrix, it is as a result as follows:
v1=[- 2760.684735753406-1046.735881390429 1]T, (50)
v2=[1264.889932108702 1078.078895954805 1]T。 (51)
Similarly, the homogeneous coordinates matrix of two on the second width image hidden point v3, v4 that disappear are solved, on third width image
The homogeneous coordinates matrix of two hidden point v5, v6 that disappear are as a result as follows:
v3=[1064.790644771093 113.996461742303 1]T, (52)
v4=[828.7971162625690 514.4555030660497 1]T。 (53)
v5=[1048.228004272335 141.969182202923 1]T, (54)
v6=[1237.012497793531 677.398735058523 1]T。 (55)
(44) (50) formula is substituted into (7) formula and obtains v1 about caPolar curve la1Homogeneous line coordinates matrix, (45) (50)
Formula substitutes into (8) formula and obtains v1 about cbPolar curve lb1Homogeneous line coordinates matrix, (44) (51) formula substitute into (9) formula obtain v2 close
In caPolar curve la2Homogeneous line coordinates matrix, (45) (51) formula substitute into (10) formula obtain v2 about cbPolar curve lb2It is homogeneous
Line coordinates matrix, as a result as follows:
la1=[- 0.000721536113005-0.001303555295146 1]T, (56)
lb1=[- 0.001059179486060-0.001113018924009 1]T； (57)
la2=[- 0.000622910123176-0.002472489359547 1]T, (58)
lb2=[- 0.001171120681320-0.002482839483783 1]T。 (59)
Similarly, v3 is acquired about c on the second width image2aPolar curve l2a1Homogeneous line coordinates matrix, v3 is about c2b's
Polar curve l2b1Homogeneous line coordinates matrix, v4 is about c2aPolar curve l2a2Homogeneous line coordinates matrix, v4 is about c2bPolar curve l2b2
Homogeneous line coordinates matrix；Ask v5 about c on third width image3aPolar curve l3a1Homogeneous line coordinates matrix, v5 is about c3b
Polar curve l3b1Homogeneous line coordinates matrix, v6 is about c3aPolar curve l3a2Homogeneous line coordinates matrix, v6 is about c3bPolar curve
l3b2Homogeneous line coordinates matrix, it is as a result as follows:
l2a1=[- 0.002304424407224-0.000115278673625 1]T, (60)
l2b1=[- 0.004453941914762 0.000497844456558 1]T； (61)
l2a2=[- 0.001758364506834-0.001059791628778 1]T, (62)
l2b2=[- 0.002800543151769-0.001702035301223 1]T。 (63)
l3a1=[- 0.022223114858196 0.006850525682248 1]T, (64)
l3b1=[0.070592012778784-0.021566570299754 1]T； (65)
l3a1=[- 0.002033115490537-0.000562552707890 1]T, (66)
l3b2=[- 0.002523914228431-0.000998383646100 1]T。 (67)
(56) (57) are substituted into (11) formula, (58) (59) are substituted into (12) formula, it is corresponding just to obtain v1 on piece image
The homogeneous coordinates matrix of the hidden point v1 ' that disappears are handed over, the homogeneous coordinates matrix of the corresponding orthogonal hidden point v2 ' that disappears of v2 are as a result as follows:
v′1=[329.8670342957368 584.5467584713720 1]T, (68)
v′2=[- 7.6724557779073 406.3836499413423 1]T。 (69)
Similarly, the homogeneous coordinates matrix of the corresponding orthogonal hidden point v3 ' that disappears of v3 are found out on the second width image, v4 is corresponding just
Hand over the homogeneous coordinates matrix of the hidden point v4 ' that disappears；The homogeneous coordinates square of the corresponding orthogonal hidden point v5 ' that disappears of v5 is found out on third width image
Battle array, the homogeneous coordinates matrix of the corresponding orthogonal hidden point v6 ' that disappears of v6 are as a result as follows:
v′3=[369.197947544039 1294.352492875096 1]T, (70)
v′4=[2589.037162318578-4201.270261238919 1]T。 (71)
v′5=[- 6584.085736413682-21504.75750178990 1]T, (72)
v′6=[714.4834219270807-804.5953854692119 1]T。 (73)
(50)-(55) formula and (68)-(73) formula are updated to (13) formula, obtain the system of linear equations of element in w, is used
SVD decomposition solves the system of linear equations and obtains the coefficient matrix of w.As a result as follows:
K can be obtained finally, carrying out Cholesky decomposition to the w in (74) and inverting again, as a result as follows:
Therefore 5 intrinsic parameters of plane catadioptric video camera are respectively as follows: fu=499.9999999997993, fv=
449.9999999998695, u0=399.9999999999496, v0=299.9999999998277, s=
0.8000000001911。
Example IV
Present embodiment discloses a kind of storage medium, which is stored with program, run the program can be performed it is above-mentioned
Described in embodiment using bimirror midpoint symmetry calibrating camera method.
Embodiment five
Present embodiment discloses a kind of system of symmetry calibrating camera using bimirror midpoint, the system packets one
Arithmetic unit, storage medium of the arithmetic unit equipped with above-described embodiment four.
Embodiment six
Present embodiment discloses the system of another symmetry calibrating camera using bimirror midpoint, the system packets
Include the arithmetic unit in a pinhole camera and an embodiment five, pinhole cameras is for acquiring scene image, and by scene image
It is sent to arithmetic unit, arithmetic unit executes operation movement, and exports operation result.
The invention is not limited to specific embodiments above-mentioned.The present invention, which expands to, any in the present specification to be disclosed
New feature or any new combination, and disclose any new method or process the step of or any new combination.
Claims (8)
1. a kind of method of the symmetry calibrating camera using bimirror midpoint, which comprises the following steps:
A. scene image of at least 3 width under different perspectives is obtained, the corresponding test scene of the scene image are as follows: be in angle
Two articles point is placed between two plane mirrors of predetermined angular, forms test scene, under the test scene, obtaining two groups of quantity is
5 point hytes: 5 points of object point and its 4 catadioptric exit points in two plane mirrors, each hyte necessarily exist
On same circle；
B. it is directed to each width scene image, executes following B1-B2:
B1: extracting the characteristic point coordinate of scene image, according to the characteristic point coordinate of extracted scene image, calculates corresponding
Quadratic curve equation；
B2: obtaining in each point hyte, the picture of wantonly two groups of adjacent points respectively, the two groups of adjacent points taken in hyte on one point point
It is not corresponding with the two groups of adjacent points taken in another point hyte；According to the two groups of adjacent points taken in two o'clock hyte
Picture is based on pole polar curve relationship, calculates corresponding two pairs of orthogonal hidden coordinates that disappear；
C. according to the coordinate of the orthogonal hidden group that disappears of all scene images, based on it is orthogonal it is hidden disappear a little with absolute conic as
Linear restriction relationship calculates the intrinsic parameter of video camera.
2. utilizing the method for the symmetry calibrating camera at bimirror midpoint as described in claim 1, which is characterized in that step
In rapid B1, the characteristic point coordinate according to extracted scene image calculates corresponding quadratic curve equation specifically: according to
It according to the characteristic point coordinate of extracted scene image, is fitted using least square method, obtains corresponding quadratic curve equation.
3. the method for utilizing the symmetry calibrating camera at bimirror midpoint as claimed in claim 1 or 2, feature exist
In in step B2, the picture according to the two groups of adjacent points taken in two o'clock hyte is based on pole polar curve relationship, calculates
Corresponding two pairs of orthogonal hidden coordinates that disappear specifically:
Two corresponding consecutive points are calculated according to photography invariance according to the picture of the one group of adjacent point taken in two o'clock hyte
Hyte as place straight line intersection point, obtain the hidden coordinate that disappears, then according to pole polar curve relationship, hidden disappeared a little by described
Coordinate calculates orthogonal another hidden coordinate to disappear a little, obtains the hidden coordinate to disappear a little of a pair of orthogonal, passes through same side
Formula calculates the orthogonal hidden coordinate to disappear a little of another pair according to the picture of another group of adjacent point taken in two o'clock hyte.
4. utilizing the method for the symmetry calibrating camera at bimirror midpoint as described in claim 1, which is characterized in that institute
It states in test scene, the angle of two plane mirrors is 60-80 degree.
5. utilizing the method for the symmetry calibrating camera at bimirror midpoint as described in claim 1, which is characterized in that institute
State step C specifically: according to each to the orthogonal hidden coordinate to disappear a little, orthogonal hidden disappear a little and absolute conic using SVD to all
Picture linear restriction relationship carry out preliminary exposition, then to preliminary exposition result carry out Cholesky decomposition after, invert and taken the photograph
Camera Intrinsic Matrix, the corresponding parameter extracted in the Intrinsic Matrix obtain required intrinsic parameter.
6. a kind of storage medium, which is characterized in that be stored with program, run the program it is executable as claim 1-5 it
Described in one using bimirror midpoint symmetry calibrating camera method.
7. a kind of arithmetic unit, which is characterized in that it includes a processor and storage medium as claimed in claim 6, the place
Reason device exports operation result for running the program stored in the storage medium.
8. a kind of system of the symmetry calibrating camera using bimirror midpoint, which is characterized in that it includes plane folding
Video camera and arithmetic unit as claimed in claim 7 are reflected, the plane catadioptric video camera is used to acquire scene image, and will
The scene image of acquisition is sent to the arithmetic unit, and the arithmetic unit is used to carry out operation to received scene image.
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