CN107146254A - The Camera extrinsic number scaling method of multicamera system - Google Patents
The Camera extrinsic number scaling method of multicamera system Download PDFInfo
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- CN107146254A CN107146254A CN201710216290.7A CN201710216290A CN107146254A CN 107146254 A CN107146254 A CN 107146254A CN 201710216290 A CN201710216290 A CN 201710216290A CN 107146254 A CN107146254 A CN 107146254A
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- G06T7/85—Stereo camera calibration
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Abstract
The invention discloses a kind of Camera extrinsic number scaling method of multicamera system, solving present in existing method three-dimensional Accurate Calibration thing, to make difficult, polyphaser external parameters calibration process efficiency low and the problem of have accumulated error.Its realization includes：Fitting obtains the conic section matrix that each camera shoots ball projection；Solve inhomogeneous coordinate of three centre ofs sphere in camera coordinates system；Three coplanar world coordinate systems of the centre of sphere are set up with plane and sphere center position where three centre ofs sphere；Outer parameter of multiple cameras in three coplanar world coordinate systems of the centre of sphere is solved, two coordinate systems are overlapped, and complete the external parameters calibration of each camera in multicamera system.The present invention is quick, easy, accurately calculate outer parameter of multiple cameras under same world coordinate system.More conversions are not needed, without accumulated error, Camera extrinsic number stated accuracy is high.For in the fields such as image measurement, three-dimensional reconstruction, Navigation of Pilotless Aircraft.
Description
Technical field
The invention belongs to technical field of computer vision, space target positioning is related generally to and photogrammetric, specifically one
Plant the Camera extrinsic number scaling method of multicamera system.Applied to fields such as image measurement, Navigation of Pilotless Aircraft, three-dimensional reconstructions.
Background technology
Camera calibration is the basic step for recovering object dimensional geometry information from two dimensional image.At present, carried
A variety of camera calibration methods are gone out.Camera calibration is divided into calibration of camera internal parameters and demarcated with Camera extrinsic number, and camera intrinsic parameter is retouched
What is stated is camera internal geometrical construction parameter, and Camera extrinsic number describe camera coordinates system with set up world coordinate system it
Between rotation, translation relation.At present, camera calibration method mainly has：
One class is Camera Self-Calibration method.This method does not use demarcation thing to be demarcated, and only passes through pair between image
Restriction relation is answered, the demarcation of camera is completed.Such a method demarcating steps are simple, and automaticity is higher.But be currently not
Very ripe, subject matter is that the precision of camera calibration is relatively low.
Also it is the demarcation based on demarcation thing.This method is typically demarcated using the demarcation thing of known geological information,
The camera calibration method of early stage uses more accurate three-dimensional scaling object, and such method calibration result accuracy is high, but three
The manufacturing process of dimension demarcation object is relatively difficult.Subsequent someone proposes the classical scaling method based on two dimensional surface scaling board again,
This method calibration result accuracy is high and demarcation thing manufacturing process is simpler.But answering with increasing multicamera system
With simultaneously because plane reference plate can not be simultaneously visible to the camera of different azimuth, neighbouring camera can be seen same flat
Face scaling board, can calibrate outer parameter of the camera relative to the plane reference plate, come the world for describing camera coordinates system and setting up
Rotation, translation relation between coordinate system；And the larger camera of adjacent spacing cannot visual one block of plane reference plate simultaneously, no
The outer parameter relative to same scaling board can be calibrated, it is necessary to be obtained by the position transformational relation between adjacent cameras in system
Outer parameter under one world coordinate system.So in the Camera extrinsic number demarcation of multicamera system, plane reference method, calibration process
Cumbersome, demarcation speed is relatively slow, stated accuracy with computing accumulated error influence Camera extrinsic number.
The problem of being demarcated for polyphaser, although also there is some camera calibration methods that thing is demarcated based on ball at present.But
Mainly by studying the relation between geometric properties such as ball projection and absolute conic projection that ball is projected, ball
Relation between the antithesis of projection and the antithesis of absolute conic etc., sets up constraint equation, completes the intrinsic parameter demarcation of camera,
Or the camera calibration method based on ball obtained according to forefathers, build experimental situation and camera is demarcated, then analyze
Ball is used for the actual restricted problem of the presence of camera calibration, provides some significant conclusions.But it is above-mentioned based on ball
Camera calibration method and research, what is mainly studied is calibration of camera internal parameters method, is seldom related to outside the camera of multicamera system
Parameter calibration method.The Camera extrinsic number scaling method research to multicamera system focuses primarily upon the mark of intrinsic parameter both at home and abroad
Fixed, the Camera extrinsic number demarcation of multicamera system is the previous practical problem for being badly in need of solving of mesh.
To sum up, in the existing external parameters calibration method on multicamera system, the method that thing is demarcated using accurate three-dimensional is deposited
The problem of more difficult, Feature Points Matching is difficult is made demarcating thing；The method of thing is demarcated, it is necessary to polyphaser using two dimensional surface
The Camera extrinsic number in the relatively different world coordinate systems of each camera in system, is converted into the camera of relatively same world coordinate system
Parameter, can cause the Camera extrinsic number calibration process of multicamera system it is cumbersome, demarcate less efficient, computing accumulated error it is direct
Influence the stated accuracy of Camera extrinsic number.The demarcation of the current outer parameter on multicamera system, still without a kind of calibration process
Efficiency high, calculating process be easy, while the higher method of stated accuracy.
The content of the invention
It is an object of the invention to provide a kind of scaling method of the Camera extrinsic number of multicamera system, it is intended to solves existing
There is calibration process complexity, the problem of there is accumulated error in polyphaser external parameters calibration method.
The present invention is a kind of Camera extrinsic number scaling method of multicamera system, it is characterised in that the multicamera system
Camera extrinsic number scaling method includes having the following steps:
(1) fitting obtains the conic section matrix that each camera shoots ball projection：Multiple cameras are constituted known to intrinsic parameter
Multicamera system, polyphaser, to being shot in ball known to three different spatial radiuses, passes through from respective visual angle
Sub-pixel Edge Detection obtains the marginal point of ball projection, and fitting obtains the shooting ball of the camera of each in multicamera system
The conic section matrix of projection；
(2) inhomogeneous coordinate of three centre ofs sphere in camera coordinates system is solved：According to the perspective geometry relation for shooting ball,
Using known camera intrinsic parameter, crown radius and obtained shooting ball projection conic section matrix are shot, three shootings are solved
Inhomogeneous coordinate of the ball centre of sphere in multicamera system in the camera coordinates system of each camera；
(3) three coplanar world coordinate systems of the centre of sphere are set up：One shot using three in ball centre of sphere Special composition
Individual plane, using this plane as the xoy planes in three-dimensional coordinate system, using resolution of vectors, sets up three centre ofs sphere same
The world coordinate system of plane, the coordinate system is using one of centre of sphere as origin, and this is used as the centre of sphere and another ball of origin
The line of the heart is x-axis, and plane where three centre ofs sphere is xoy planes；
(4) the outer parameter of each camera in demarcation multicamera system：The ball centre of sphere is shot each using three obtained
Inhomogeneous coordinate under individual camera coordinates system, sets up world coordinates of the plane as xoy planes where shooting the ball centre of sphere using three
System, each camera coordinates system is overlapped by rotation, translation with the coplanar world coordinate system of three centre ofs sphere set up, polyphaser is obtained
The outer parameter matrix of each camera in system, completes the external parameters calibration of each camera in multicamera system.
The present invention is used as demarcation thing, ball demarcation thing system in the Camera extrinsic number demarcation of multicamera system using ball
Make simple, facility requirements are demarcated to Camera extrinsic number simply, the relatively same world coordinate system of each Camera extrinsic number is directly obtained
Under outer parameter, demarcation efficiency high, without accumulated error, Camera extrinsic number stated accuracy is high.Compared with prior art, it is of the invention
Technical advantage：
First, the present invention is used for multiphase using ball known to ball known to three radiuses or a radius as demarcation thing
Camera extrinsic number demarcation in machine system.The ball demarcation thing that the present invention is used does not need special facture, as that can use commonly
Table tennis influences whether that the demarcation of the Camera extrinsic number of multicamera system is smart as demarcation thing, but the precision of used ball
Degree.
2nd, the present invention is directed to the calibration process of Camera extrinsic number in multicamera system, and camera intrinsic parameter therein is known
, each camera is only needed while shooting ball known to ball image known to three radiuses or a radius in space
Three width images of three diverse locations, it becomes possible to complete the external parameters calibration of multiple cameras.Polyphaser external parameters calibration process is grasped
Make easy.
3rd, the present invention is when the Camera extrinsic number to multicamera system is demarcated, and the outer parameter of each obtained camera is phase
For the coplanar world coordinate system of same three centre ofs sphere.Such as three-dimensional reconstruction in the Camera extrinsic number application of multicamera system,
Usually need first to obtain the outer parameter of the relatively different world coordinate systems of each camera, then by the outer ginseng of relatively different world coordinate systems
Number is converted into the outer parameter of relatively same world coordinate system, and the present invention need not be the relatively different world coordinate systems of each camera
Outer parameter is converted into the process of the Camera extrinsic number of same world coordinate system, that is, the present invention directly turns the outer parameter of camera
It is changed to the outer parameter of relatively same world coordinate system.So accumulated error is not present in the present invention, calculating process is easy, polyphaser
Camera extrinsic number stated accuracy is high, and demarcation speed is fast.
Brief description of the drawings
Fig. 1 is the flow chart of the Camera extrinsic number scaling method of multicamera system of the present invention；
Fig. 2 is the orientation schematic diagram shot using polyphaser to three balls of the present invention；
Fig. 3 is the projection relation schematic diagram of the space ball of the present invention on the image plane；
Fig. 4 is the coplanar world coordinate system schematic diagram of three centre ofs sphere of the present invention；
Fig. 5 is transforming relationship schematic diagram between two coordinate systems of the invention.
Embodiment
In order to make the purpose , technical scheme and advantage of the present invention be clearer, it is detailed to the present invention below in conjunction with the accompanying drawings
Describe in detail bright
Embodiment 1
In the Camera extrinsic number scaling method of multicamera system, in method of the existing use ball as demarcation thing,
Seldom it is related to the demarcation to parameter outside polyphaser, and the method for early stage needs to use accurate three-dimensional scaling thing, this method lacks
Point is needed using accurate demarcation thing, and calibration cost is higher；Plane is used to demarcate in the scaling method of thing, due to plane
Can not be simultaneously visible for the polyphaser of all directions, so needing first to obtain the outer ginseng of the relatively different world coordinate systems of each camera
The outer parameter of relatively different world coordinate systems, is then converted into the outer parameter of relatively same world coordinate system, calculating process by number
It is numerous and diverse, and with accumulated error.
Propose that a kind of demarcation thing is simple for this present invention, efficiency high is demarcated, without the high multiphase of accumulated error, stated accuracy
The Camera extrinsic number scaling method of machine system, referring to Fig. 1, multicamera system Camera extrinsic number scaling method of the present invention include just like
Lower step:
(1) fitting obtains the conic section matrix of each camera shooting ball projection of multicamera system：Known to intrinsic parameter
Multiple cameras, need to constitute multicamera system according to application, polyphaser from respective visual angle, in three different spatials and
Ball known to radius is shot or shot using ball known to a radius, shoots the ball three, space not
With the image of position, Fig. 2 is seen, it is understood that enter to be placed with three an equal amount of balls on the diverse location of three, space
Row is shot.It is shown in Fig. 2 and shoots ball between two parties, polyphaser is in periphery, is not limited in practice in this situation, the present invention
Only need that there is common viewing angle between each camera.
The ball used in the present invention does not need special facture, such as can be met using common table tennis yet, to camera outside
The stated accuracy of parameter has certain requirements occasion, but uses the precision of ball, can influence the Camera extrinsic of multicamera system
Several stated accuracy, so the ball for participating in shooting should also be the higher ball of the smooth of the edge, precision.Pass through sub-pixel edge
Detection algorithm obtains shooting the marginal point of ball projection, and fitting obtains the shooting ball projection of the camera of each in multicamera system
Conic section matrix.The intrinsic parameter of each camera in the present invention in multicamera system, it is necessary to be demarcated, so as to obtain in advance
The measure intrinsic parameter of each camera.Because, it is necessary to using in each camera during the Camera extrinsic number of multicamera system is calculated
Parameter, so each camera intrinsic parameter measure is more accurate, is more favorably improved the external parameters calibration precision of each camera.
(2) inhomogeneous coordinate of three centre ofs sphere in the camera coordinates system of each camera is solved：According to the throwing for shooting ball
Shadow geometrical relationship, is shown in Fig. 3, although described in figure is space circle spheric projection geometrical relationship, but shoots the projection relation of ball
It is consistent with space circle spheric projection geometrical relationship.Using the camera Intrinsic Matrix of each camera in known multicamera system,
The shooting ball projection conic section matrix for shooting the radius of ball and obtaining, solves three and shoots the ball centre of sphere in polyphaser system
Inhomogeneous coordinate in the camera coordinates system of the camera of each in system.Three shooting ball centre ofs sphere that the present invention is solved are sat in each camera
Inhomogeneous coordinate in mark system, is the camera for calculating each camera coplanar world coordinate system of same three centre ofs sphere relatively
The outer necessary process of parameter one.
(3) three coplanar world coordinate systems of the centre of sphere are set up：Three diverse locations place a circle respectively in space
Ball is three shooting balls, and same ball is taken on the diverse location of three, space in other words, obtains three shooting balls
A plane in inhomogeneous coordinate of the centre of sphere under camera coordinates system, the space that this three shooting ball centre ofs sphere are constituted, by this
Individual plane shoots non homogeneity of the ball centre of sphere under camera coordinates system as the xoy planes in three-dimensional coordinate system using three
Secondary coordinate vector is decomposed, and is set up a coplanar world coordinate system of three centre ofs sphere, is seen Fig. 4, the coordinate system is with one of ball
The heart is origin, and this is x-axis as the centre of sphere of origin and the line of another centre of sphere, and plane is flat for xoy where three centre ofs sphere
The world coordinate system in face.The present invention establishes a coplanar world coordinate system of three centre ofs sphere, then can directly obtain polyphaser
The Camera extrinsic number of the relative same world coordinate system set up of each camera in system.Avoid the relatively different worlds of each camera
The Camera extrinsic number of coordinate system, is converted into the Camera extrinsic number of relatively same world coordinate system.
(4) the outer parameter matrix under the coplanar world coordinate system of relative three centre ofs sphere is solved, demarcation polyphaser system is completed
The outer parameter of each camera in system：For each camera in multicamera system, shoot the ball centre of sphere using three obtained and exist
Inhomogeneous coordinate under each camera coordinates system, sets up plane where shooting the ball centre of sphere using three and is sat as the world of xoy planes
Mark system, then by the camera coordinates system of each camera by the coplanar world coordinate system weight of three centre ofs sphere for rotating, translating with set up
Close, obtain the outer parameter matrix of each camera in multicamera system, complete the outer parameter of each camera in multicamera system
Demarcation.
The coplanar world coordinate system of three centre ofs sphere：Referring to Fig. 4, with it in the coplanar world coordinate system of three centre ofs sphere
In centre of sphere be origin, and the centre of sphere and the line of another centre of sphere as origin are x-axis, pass through resolution of vectors, set up
Three coplanar world coordinate systems of the centre of sphere；The coincidence of camera coordinates system and world coordinate system in the present invention, space any point
Inhomogeneous coordinate under camera coordinates system is directly obtained in the coplanar world coordinate system of three centre ofs sphere by rotation, translation
Under inhomogeneous coordinate.
The coincidence process of two coordinate systems in the present invention：It is photocentre first the origin of camera coordinates system, moves to three
The coplanar world coordinates origin of the centre of sphere is overlapped, and then rotates the camera coordinates system translated so that camera coordinates system x, y, z
Three reference axis and three overlapping of axles of the coplanar world coordinate system of three centre ofs sphere.
The present invention is directed to each Camera extrinsic number problem of calibrating of multicamera system, and demarcation thing, profit are used as using three balls
Being capable of simultaneously visible geometrical property, solution multicamera system for each camera of the different azimuth in multicamera system with ball
External parameters calibration in need demarcate the simultaneously visible problem of thing.With three shooting ball centre ofs sphere, three centre ofs sphere are set up coplanar
World coordinate system, directly calculate each camera relative to the outer parameter under the world coordinate system, make the outer ginseng of multiple cameras
Number is built under same world coordinate system.
Embodiment 2
The Camera extrinsic number scaling method be the same as Example 1 of multicamera system, wherein, fitting obtains polyphaser in step (1)
Each camera in system shoots the conic section matrix of ball projection, includes：
If there is each camera in M camera, multicamera system in multicamera system, three are shot from respective different visual angles
Ball image known to different spatial and radius, referring to Fig. 2, wherein on the corresponding plane of delineation of i-th of camera, obtaining three
Individual shooting ball projecting edge, extracts these three marginal points for shooting ball projection using sub-pixel edge extraction algorithm, passes through
Conic fitting algorithm, obtains the conic section matrix for three balls projection that i-th of camera is shot, is designated as successivelyFor other cameras in multicamera system, also the secondary of three balls projections of shooting is solved according to i-th of camera
Curve method, solves the conic section matrix that respective camera shoots ball projection, finally gives each camera in multicamera system
For three conic section matrixes for shooting ball projection.
Polyphaser is shot from respective visual angle to ball known to three different spatials and radius, and this is one
The description of the scheme of kind, can also allow the ball to be respectively at space diverse location, shoot in practical operation by shooting a ball
Its three width images, then obtain ball projecting edge point by rim detection, and fitting obtains ball projection conic section.
The camera calibration thing very simple that the present invention is used, only need to be respectively placed in difference using ball known to three radiuses
Position, or ball known to a radius are successively placed in three diverse locations；Shooting process is simple, and each camera only needs to shoot
Ball image known to one three radius shoots three width figures of the ball in three different spatials known to a radius
Picture, is then synthesized in piece image；The ball in image is generally photographed in image domains to be also referred to as shooting ball projection, is adopted
Three are extracted with sub-pixel edge algorithm and shoots the edge that ball is projected, it is possible to increase the extraction accuracy of ball projecting edge, are entered
And it is favorably improved Camera extrinsic number stated accuracy.
Using common table tennis as demarcation thing in this example, table tennis is using extensive, and the smooth of the edge, make precision compared with
It is high.The image of table tennis is shot, the projecting edge of table tennis is extracted using sub-pixel edge extraction algorithm, fitting obtains table tennis
The conic section matrix of projection.Using obtained table tennis spheric projection quadratic matrix, each Camera extrinsic number in multicamera system
Stated accuracy is higher.
Embodiment 3
The Camera extrinsic number scaling method be the same as Example 1-2 of multicamera system, three shooting ball balls described in step (2)
The specific steps of inhomogeneous coordinate of the heart in multicamera system in the camera coordinates system of each camera include：
2.1 clear and definite space circle spheric projections and the relation of camera intrinsic parameter：Referring to Fig. 3, using plane shock wave relation, clapped
Take the photograph the relation of the relation of ball projection conic section and camera intrinsic parameter, camera coordinates system and world coordinate system, camera coordinates system
Origin be camera photocentre OcIf the origin of world coordinate system is Ow, the world coordinate system is with Ow-XwYwZwRepresent, wherein OwZw
Axle, by forming the centre of sphere for the space projection ball that camera image plane is projected, the ball centre of sphere is designated as O, straight line OcO sits for the world
Mark the Z axis of system；Space circle spheric projection relation, the space projection ball is projected as c in camera image plane, and projection c is simultaneously
It is also with camera photocentre OcThe projection of tangent normal cone for summit and with space projection ball, therefore, projection c are being considered as this just
The projection of circular cone bottom surface；The circle for remembering normal cone bottom surface is C, and its center of circle is designated as O1, its radius is designated as rc, plane where it is designated as
II2, the center of circle O that space projection ball centre of sphere O and normal cone bottom surface are justified1And camera photocentre OcOn same straight line, and OcO1
The circle C of vertical normal cone bottom surface, remembers OcO1Distance be h.Referred to herein as world coordinate system with Ow-XwYwZwThe world of expression is sat
Mark system, is the coordinate system in order to illustrate the relation of space projection ball and camera intrinsic parameter and set up, and is built in non-invention
The coplanar world coordinate system of three centre ofs sphere.
Justify C equation and plane II according to ball projection relation, normal cone bottom surface2It should be related to the list of the plane of delineation,
The relation for obtaining space circle spheric projection conic section c and camera intrinsic parameter K is：
Wherein camera intrinsic parameterfx、fyRespectively represent camera image plane both horizontally and vertically on
Scale factor, (u0,v0) image coordinate of principal point for camera is represented, s represents the obliquity factor of camera；R is represented by world coordinate system
To the spin matrix of camera coordinates system；Namely obtain the relation of space circle spheric projection and camera intrinsic parameter.
2.2 obtain the distance between the space projection ball centre of sphere and camera photocentre：According to ball perspective geometry relation, including
Triangular form relation, obtains space projection ball centre of sphere O and camera photocentre OcThe distance between d.
Referring to Fig. 3, if camera photocentre Oc, space projection ball centre of sphere O, camera photocentre OcWith the formation of space projection ball
The bottom surface C of normal cone, its center of circle is designated as O1, OcO1The circle C of vertical normal cone bottom surface.The geometrical relationship projected according to ball, if circle
There is a point P on C, because circle C is by camera photocentre OcWith the tangent formation of space projection ball surface point, then ray OcP and space
Projection circle is tangential on point P, triangle OcOP is right angled triangle；Because OcO1The circle C of vertical normal cone bottom surface, then line segment PO1Hang down
Directly in OcO1, then triangle OcO1P is also right angled triangle；It is readily obtained triangle OcOP and OcO1P is similar vertical triangle,
Space projection ball centre of sphere O and camera photocentre O then can be obtained by the similitude of trianglecThe distance between d be：
Wherein d is camera photocentre OcTo space projection ball centre of sphere O distance, rsFor the radius of space projection ball, rcFor
Camera photocentre OcJustify C radius with the bottom surface of the normal cone of space projection ball formation, its center of circle is designated as O1, h is OcO1Away from
From；
Inhomogeneous coordinate of the 2.3 solution room projection sphere centre ofs sphere under camera coordinates system：
The relation with camera intrinsic parameter is projected using ball, if matrix A is
Set again matrix M as
Wherein R is spin matrix, and is unit orthogonal matrix then RRT=E, rcFor camera photocentre OcWith space projection ball
C radius is justified in the bottom surface of the normal cone of formation, and h is OcTo the distance in the C centers of circle, according to matrix theory, it is known that M is real symmetrical square
Battle array, then by matrix Orthogonal Decomposition can obtain R andBecause the space projection ball centre of sphere is in the Z axis of the world coordinate system of foundation
On, and the centre of sphere to camera photocentre distance be d, so inhomogeneous coordinate of the centre of sphere under world coordinate system for (0,0, d)T, R is
Spin matrix and overlapped because setting up world coordinate system with camera coordinates system origin, translation vector be (0,0,0)T,
Then the space projection ball centre of sphere, using rotation, translation relation under two coordinate systems, can obtain in world coordinate system inhomogeneous coordinate
Inhomogeneous coordinate of the space projection ball centre of sphere under camera coordinates system be
The method that the present invention calculates inhomogeneous coordinate of the space projection ball centre of sphere under camera coordinates system, available for calculating
Three shoot inhomogeneous coordinate of the ball centre of sphere in the camera coordinates system of each camera.
2.4, which obtain three, shoots inhomogeneous coordinate of the ball centre of sphere under camera coordinates：Three captured by i-th of camera
The shooting ball of position projects conic section matrixUsing in known camera intrinsic parameter, ball projection and camera
The relation of parameter, obtaining inhomogeneous coordinate of three shooting ball centre ofs sphere under the camera coordinates system of i-th of camera is respectively
Wherein,The nonhomogeneous seat of the centre of sphere of the ball centre of sphere under i-th of camera coordinates system is shot for three
Mark,It is the rotation that origin is tied to camera coordinates system in photocentre and Z axis for the world coordinates of the centre of sphere to photocentre line
Matrix,It is distance of three centre ofs sphere to camera photocentre, solving three according to i-th of camera shoots the ball centre of sphere
The method of inhomogeneous coordinate in camera coordinates system, can obtain three and shoot each camera of the ball centre of sphere in multicamera system
Camera coordinates system under inhomogeneous coordinate.
The present invention is projected according to ball need to only utilize the projection of ball in the relation with camera intrinsic parameter, actual calibration process
Conic section and known camera intrinsic parameter, it becomes possible to obtain three shoot the ball centre ofs sphere it is non-under each camera coordinates system
Homogeneous coordinates, the calculating process is easy.
Embodiment 4
The Camera extrinsic number scaling method be the same as Example 1-3 of multicamera system, referring to Fig. 4, three are set up described in step (3)
The individual centre of sphere coplanar world coordinate system is concretely comprised the following steps：
3.1 place the known ball that shoots of three radiuses in space diverse location, and three shoot the ball centre of sphere and are designated as O1、O2、
O3。
3.2 due to space any 3 points may be constructed a plane, with three shootings one of ball centre of sphere Special composition
Plane.
3.3 utilize resolution of vectors, set up the coplanar world coordinate system of three centre ofs sphere.If one of shoot ball centre of sphere O1
For the world coordinate system origin, centre of sphere O1With another centre of sphere O2Line is the X-axis of world coordinate system, sets up vector O1O2With
O1O3, two vector multiplication cross obtain the Z axis of the world coordinate system.
3.4 carry out multiplication cross by X-axis and two reference axis of Z axis, obtain the Y of three coplanar world coordinate systems of the centre of sphere
Axle, so as to set up three coplanar world coordinate systems of the centre of sphere；Three reference axis of the world coordinate system are obtained simultaneously to sit in camera
Unit direction vector a, b, c under mark system, also obtain three and shoot the ball centre of sphere in the coplanar world coordinates of three centre ofs sphere
Inhomogeneous coordinate under system is respectively Ow1、Ow2、Ow3。
The present invention shoots inhomogeneous coordinate of the ball centre of sphere under camera coordinates system using three, according to resolution of vectors, builds
The world coordinate system using the plane where three shooting ball centre ofs sphere as xoy planes is found.
Embodiment 5
The Camera extrinsic number scaling method be the same as Example 1-4 of multicamera system, solves multiple cameras described in step (4)
Outer parameter matrix specific steps under the coplanar world coordinate system of relatively same three centre ofs sphere include：
4.1 rotations set up between two coordinate systems, translation relation：If the point X of space one is in the coplanar generation of three centre ofs sphere
Inhomogeneous coordinate under boundary's coordinate system is designated asInhomogeneous coordinate in i-th of camera coordinates system is designated asBetween them
Translation, rotation relationship be
Wherein RcFor the spin matrix referred to, tcFor the translation vector referred to.
4.2 obtain the outer parameter of i-th of camera:Referring to Fig. 5, using three shoot ball projections, known camera intrinsic parameter,
The radius of known three shootings ball and the projection relation for shooting ball and camera intrinsic parameter, obtain three shooting ball centre ofs sphere
Inhomogeneous coordinate under i-th of camera coordinates systemThen using these three shooting ball centre ofs sphere at i-th
Inhomogeneous coordinate under camera coordinates systemSet up three coplanar world coordinate systems of the centre of sphere, the wherein coordinate
Direction unit vector of three reference axis under camera coordinates system in system is a, b, c, and three shoot the ball centre of sphere in foundation
Inhomogeneous coordinate under spatial world coordinate system is Ow1、Ow2、Ow3, the spatial world coordinate system coplanar by three centre ofs sphere are set up,
Three reference axis unit vectors synthesize a R1Matrix is：
R1=[a, b, c]T
Because the coordinate of arbitrfary point in three-dimensional system of coordinate, can represent the vector of the point, the projection under three reference axis,
It is then vectorialRepresent under camera system, pointArriveVector, shouldIt is multiplied, obtains respectively with vectorial a, b, c
In the projection of three reference axis of world coordinate system, i.e. point X under the coplanar world coordinate system of three centre ofs sphere inhomogeneous coordinate, thenWith the inhomogeneous coordinate in i-th of camera coordinates systemTransforming relationship is：
If RiIt is spin matrix, the t of the coplanar world coordinate system of with respect to three centre ofs sphere of i-th of cameraiIt is i-th of camera
The coplanar world coordinate system translation vector of with respect to three centre ofs sphere, wherein：
Ri=R1
Calculating obtains i-th of camera, the Camera extrinsic number square of the coplanar world coordinate system of relative three centre ofs sphere set up
Battle array.
4.3 obtain each Camera extrinsic number in multicamera system：The side of Camera extrinsic number is obtained according to i-th of camera
Method, obtains the coplanar world coordinate system spin matrix of relatively same three centre ofs sphere of each camera of multicamera system, translation and closes
System, that is, complete each Camera extrinsic number demarcation of polyphaser.
The present invention is using three shooting ball centre ofs sphere, and the inhomogeneous coordinate in the camera coordinates system of multiple cameras is set up
With three coplanar world coordinate systems of the centre of sphere, utilization space is a little in the inhomogeneous coordinate of each camera coordinates system, Yi Ji
The inhomogeneous coordinate for the coplanar world coordinate system of three centre ofs sphere set up, by geometrical inversion relation, is obtained in multicamera system
Each camera coplanar world coordinate system of same three centre ofs sphere relatively position relationship, i.e. the present invention directly obtains relatively same
The outer parameter of the camera of one world coordinate system.Accumulated error is not present in the present invention, and calculating process is easy, the Camera extrinsic of polyphaser
Number stated accuracy is higher.
A more detailed example is given below, and the present invention is further described
Embodiment 6
The Camera extrinsic number scaling method be the same as Example 1-5 of multicamera system, the Camera extrinsic of multicamera system of the present invention
The specific steps of number scaling method are described as follows：
Step 1: the Intrinsic Matrix of calibration for cameras：If needing multiple cameras in the multicamera system demarcated to remember successively
For CA,CB,CC,….Zhang Zhengyou plane reference methods are utilized in this example, shooting several two dimensional surfaces respectively by multiple cameras demarcates
The image of version, obtains the Intrinsic Matrix of multiple cameras, K is designated as successivelyA,KB,KC,….The Zhang Zhengyou plane marks that the present invention is used
Determine method, be the camera calibration method generally used at present.Each camera intrinsic parameter precision in multicamera system is higher, and calculating is obtained
The Camera extrinsic number precision of multicamera system is higher.
Step 2: shooting ball image, extract and shoot ball profile：Referring to Fig. 2, multiple cameras shoot and are placed on sky simultaneously
Between three balls known to three diverse locations and radius piece image or clapped using ball known to a radius
Take the photograph, shoot image three width image of the ball in three diverse locations in space, and ball projective renderings are shot to same by three
In width image；Obtain three and shoot projection of the ball in camera image plane, three shooting balls are designated as Q1,Q2,Q3, accordingly
The centre of sphere be designated as O1,O2,O3.In multicamera system, wherein three shooting ball projections that i-th of camera is shot, utilize sub- picture
Plain Boundary extracting algorithm, extracts the marginal point of three shooting balls, and is fitted the secondary songs for obtaining three shooting ball projections
Wire matrix, is designated as successivelyOther cameras in multicamera system, obtain three according to i-th of camera and shoot ball throwing
The method of the conic section matrix at shadow edge, obtains the secondary song in three shooting ball projecting edges of each camera image plane
Wire matrix.During each Camera extrinsic number of the present invention in demarcation multicamera system, each camera need to only shoot width shooting
Ball image or three width shoot ball image, and required demarcation thing is simple, and calibration process is easy to operate.
Step 3: space projection ball perspective geometry relation：Referring to Fig. 3, if camera coordinates system and the original of world coordinate system
Point is camera photocentre, and sets photocentre OcDistance to space projection ball centre of sphere O is d, and line OcO is the z of world coordinate system
Axle.According to the perspective geometry characteristic of space projection ball, the projection of space projection ball can be considered as a normal cone, the positive round
The summit of cone is camera photocentre, and the circle that bottom circle is constituted for space projection ball projected outline is designated as C, center of circle note O1.Wherein O
And O1And photocentre OcOn same straight line, projection of the space projection ball centre of sphere on image is designated as o', and OcO1Vertical C.
Remember OcO1Distance be h, OcO distances are d, rsFor the radius of space projection ball, rcC radius is justified in bottom surface, and the plane where C is
π, point homogeneous coordinates thereon areThen according to camera projection matrix P, corresponding image picture point can be obtained and be designated as
Wherein K is camera intrinsic parameter, and R is Camera extrinsic number.
Obtaining the list where justifying C between plane and the plane of delineation should be related to：
Wherein H is homography matrixs of the place plane π to the plane of delineation, and the homogeneous coordinates of Plane-point are (x, y, 1).Note
C radius of circle is rc, then can obtain space projection circle matrix be expressed as：
The projection c equations for deriving C are:
The present invention specify that the perspective geometry relation of space projection ball, and utilization space ball perspective geometry relation can
Camera photocentre is calculated to the distance of the space projection ball centre of sphere.
Step 4: calculating camera photocentre to the centre of sphere apart from d：According to space circle spheric projection relation, Fig. 3 is seen.If having one on C
Point P, because circle C is by camera photocentre OcWith the tangent formation of space projection ball surface point, then ray OcP justifies with space projection
It is tangential on point P, triangle OcOP is right angled triangle；Because OcO1The circle C of vertical normal cone bottom surface, then line segment PO1Perpendicular to
OcO1, then triangle OcO1P is also right angled triangle；It is readily obtained triangle OcOP and OcO1P is similar vertical triangle, then by
The similitude of triangle can obtain space projection ball centre of sphere O and camera photocentre OcThe distance between d be：
Wherein, rsFor the radius of space projection ball, rcJustify C radius in bottom surface.
Step 5: calculating coordinate of the centre of sphere under camera coordinates system：Known to the intrinsic parameter K of camera, thrown according to space ball
Shadow geometrical relationship, is shown in Fig. 3.
If matrix A is
Wherein it is R units orthogonal matrix then RRT=E.
Set again matrix M as：
Wherein M is real symmetric matrix, by SVD Orthogonal Decompositions, be can obtain：
M=[S V D]
Understand S=R-T, D=R-1, V is diagonal matrix, can obtain R andBecause the space projection ball centre of sphere is being set up
World coordinate system Z axis on, and the centre of sphere to camera photocentre distance be d, so the centre of sphere is nonhomogeneous under world coordinate system
Coordinate for (0,0, d)T, R is spin matrix.Because setting up world coordinate system to overlap with camera coordinates system origin, put down
It is (0,0,0) to move vectorT, then the space projection ball centre of sphere utilize two coordinate system backspins in world coordinate system inhomogeneous coordinate
Turn, translation relation, can obtain inhomogeneous coordinate of the space projection ball centre of sphere under camera coordinates system is：
The geometrical relationship that the present invention is justified by space projection has obtained the space projection ball centre of sphere, under camera coordinates system
Inhomogeneous coordinate.Because shooting ball perspective geometry relation is similar with the perspective geometry relation of space projection ball,
According to the inhomogeneous coordinate method under camera coordinates system for calculating the space projection ball centre of sphere, three shooting balls can be calculated
Inhomogeneous coordinate of the centre of sphere under each camera coordinates system.
Step 6: setting up three coplanar world coordinate systems of the centre of sphere：Shooting is placed on three, space diverse location, radius
Known ball is shot using ball known to a radius, shoots figure of the ball in three diverse locations in space
As three width images.The shooting ball centre of sphere of three balls is designated as O successively1,O2,O3.Because any 3 points may be constructed one in space
Space plane, if one of shoot ball centre of sphere O1For world coordinate system origin, centre of sphere O1With another centre of sphere O2Line is generation
The X-axis of boundary's coordinate system, sets up vector O1O2With O1Ο3, two vector multiplication cross obtain the Z axis of world coordinate system；By X-axis and Z
Two reference axis of axle carry out multiplication cross, the Y-axis of three coplanar world coordinate systems of the centre of sphere are obtained, so that it is same to set up three centre ofs sphere
The world coordinate system of plane.
Step 7: setting up the rotation between two coordinate systems, translation relation：If the point X of space one is coplanar in three centre ofs sphere
World coordinate system under inhomogeneous coordinate be designated asInhomogeneous coordinate in i-th of camera coordinates system is designated asThey
Between translation, rotation relationship be
Wherein RcFor the spin matrix referred to, tcFor the translation vector referred to；
Step 8: obtaining each Camera extrinsic number in multicamera system：Ball projection, known camera are shot using three
Intrinsic parameter, the radius of known three shootings ball and the projection relation for shooting ball and camera intrinsic parameter, obtain three shootings
Inhomogeneous coordinate of the ball centre of sphere under i-th of camera coordinates systemThen these three shooting ball centre ofs sphere are utilized
Inhomogeneous coordinate under i-th of camera coordinates systemThree coplanar world coordinate systems of the centre of sphere are set up, wherein
Direction unit vector of three reference axis under camera coordinates system in the coordinate system is a, b, c, and three shoot the ball centre of sphere and exist
Inhomogeneous coordinate under the spatial world coordinate system of foundation is Ow1、Ow2、Ow3, three coplanar spatial worlds of the centre of sphere will be set up
Coordinate system, three reference axis unit vectors synthesize a R1Matrix is：
R1=[a, b, c]T
Because the coordinate of arbitrfary point in three-dimensional system of coordinate, can represent the vector of the point, the projection under three reference axis,
It is then vectorialRepresent under camera system, pointArriveVector, the vectorEnter row vector phase respectively with vectorial a, b, c
Multiply, obtainProjection under three centre ofs sphere, three reference axis of coplanar world coordinate system, i.e. point X is same in three centre ofs sphere
Inhomogeneous coordinate under the world coordinate system of plane, thenWith the inhomogeneous coordinate in i-th of camera coordinates systemTransforming relationship
For：
Wherein RiIt is spin matrix, the t of the coplanar world coordinate system of with respect to three centre ofs sphere of i-th of cameraiIt is i-th of phase
The coplanar world coordinate system translation vector of with respect to three centre ofs sphere of machine；Wherein：
Ri=R1
Calculating obtains i-th of camera, the Camera extrinsic number square of the coplanar world coordinate system of relative three centre ofs sphere set up
Battle array.The method that Camera extrinsic number is obtained according to i-th of camera, obtains relatively same three centre ofs sphere of each camera of multicamera system
Coplanar world coordinate system spin matrix, translation relation, that is, complete each Camera extrinsic number demarcation of polyphaser.It is of the invention straight
It is the coplanar world coordinate system of same three centre ofs sphere relatively to connect and obtain the outer parameter of the camera of each in multicamera system, is not required to
The Camera extrinsic number of the relatively different world coordinate systems of each camera is converted under the relatively same world coordinate system of each camera
Outer parameter, so accumulated error is not present in the present invention, calculating process is easy, and the Camera extrinsic number stated accuracy of multicamera system
It is higher.
In the prior art, the external parameters calibration of camera is in the application of multicamera system, in such as three-dimensional reconstruction, in system
The outer parameter of each camera needs to carry out twice or multiple conversions process, and to directly obtain each camera relatively same by the present invention
The outer parameter of the coplanar world coordinate system of individual three centre ofs sphere, it is not necessary to change, without accumulated error, Camera extrinsic number demarcation essence
Degree is high.
Experimental result is explained again to the technique effect of the present invention below in conjunction with the accompanying drawings and specifically.
Embodiment 7
In the Camera extrinsic number scaling method be the same as Example 1-6 of multicamera system, this example, a phase in multicamera system
Machine, camera model is BaslarA640, using Zhang Zhengyou plane reference algorithms, is calculated and is shot in camera using scaling board image
Parameter, and it is used as ideal value.Because Camera extrinsic number true value is unknown in experiment, it is impossible to directly verify required Camera extrinsic number
Correctness, therefore use the method for indirect verification.
Three tablees tennis are fixed on plane reference plate, the table tennis radius of a ball is 20mm, mobile camera, shooting image.With
One angle point of plane reference plate crosses two straight lines of angle point respectively as x-axis and y-axis as origin, after x-axis and y-axis multiplication cross
Z-axis is obtained, scaling board coordinate system is opened into.Following rotation and translation relation is met between scaling board coordinate system and camera coordinates system
XC=Rb·Xb+tb
Wherein RbAnd tbObtained by plane homography and known camera intrinsic parameter.
Using the inventive method, obtain shooting the outer ginseng of with respect to the three coplanar world coordinate systems of the table tennis centre of sphere of camera
Number is formula
XC=RS·XS+tS
Wherein RSAnd tSIt can also solve and, but RSAnd tSTrue value it is unknown, it is impossible to compare.To solve the problem, we
Derive that the relation between three coplanar world coordinate systems of the table tennis centre of sphere and scaling board coordinate system is met from above-mentioned two formula
When camera motion, relative motion is not present in change in Camera extrinsic number between ball and scaling board.If clapping
The outer parametric solution of camera is accurate, i.e., ideally, from each width image, the spin matrix R tried to achieverAnd translation vector
trValue should be definite value, but be due to that the outer parametric solution precision for shooting camera is influenceed by factors such as noises, from each width image
Middle calculated RrValue and trValue is different, there is fluctuation.But fluctuation is smaller, illustrates that outer parametric solution is more accurate.
With 10 width shooting images, respectively obtain three and shoot between table tennis centre of sphere world coordinate system and scaling board coordinate system
Spin matrix RrWith translation vector tr.Use Eulerian angles αx、αyAnd αz, represent RrIn three anglecs of rotation；Coordinate components are used again
tx, tyAnd tzRepresent scaling board coordinate system and three translation vector t shot between table tennis centre of sphere world coordinate systemr.Experiment knot
Really show, RrIn three Eulerian angles αx、αyAnd αz, variance is respectively 2.25 × 10-5、3.23×10-5With 4.20 × 10-5, it is single
Position is radian；Translation vector trIn three coordinate components tx, tyAnd tz, variance is respectively 1.1319,0.1219 and 0.0401,
Unit is mm2.Referring to Tables 1 and 2, table 1 is the spin matrix experimental result between two coordinate systems, and table 2 is two coordinate systems
Between translation vector experimental result.
Spin matrix experimental result between 1 two coordinate systems of table
Translation vector experimental result between 2 two coordinate systems of table
Test result indicates that the present invention solves Camera extrinsic number by the use of ball as demarcation thing, it can obtain ideal
Stated accuracy.In the Camera extrinsic number calibration experiment of multicamera system, the camera of multiple different visual angles can shoot ball simultaneously, mark
Determine process efficiency high, using table tennis or other types of ball as demarcation thing, demarcation thing is simple.
In brief, a kind of Camera extrinsic number scaling method of multicamera system disclosed by the invention, solves existing side
It is relative to same that camera calibration thing present in method, which makes difficult, needs the outer Parameter Switch of relatively different world coordinate systems,
The Camera extrinsic number of individual world coordinate system, the problem of causing polyphaser external parameters calibration process efficiency low and there is accumulated error.
Its realization includes：Fitting obtains the conic section matrix that each camera shoots ball projection, from each to visuality, polyphaser of ball
Each camera in system can be shot to same ball, shot the image that the ball is in three diverse locations in space, carried
Take ball projecting edge, fitting circle spheric projection conic section；Solve inhomogeneous coordinate of three centre ofs sphere in camera coordinates system；With
Plane and sphere center position set up three coplanar world coordinate systems of the centre of sphere where three centre ofs sphere；Multiple cameras are solved in three balls
Outer parameter matrix in the coplanar world coordinate system of the heart, two coordinate systems are overlapped, and complete each camera in multicamera system
External parameters calibration.The present invention is quick, easy, accurately calculate outer parameter matrix of multiple cameras under same world coordinate system,
More conversions are not needed, without accumulated error, Camera extrinsic number stated accuracy is high.With image measurement, Navigation of Pilotless Aircraft, Three-dimensional Gravity
Build.
Claims (5)
1. a kind of Camera extrinsic number scaling method of multicamera system, it is characterised in that the multicamera system Camera extrinsic number
Scaling method includes having the following steps:
(1) fitting obtains the conic section matrix that each camera shoots ball projection：Multiple cameras constitute multiphase known to intrinsic parameter
Machine system, polyphaser, to being shot in ball known to three different spatial radiuses, passes through sub- picture from respective visual angle
Plain edge detection algorithm obtains the marginal point of ball projection, and fitting obtains the shooting ball projection of the camera of each in multicamera system
Conic section matrix；
(2) inhomogeneous coordinate of three centre ofs sphere in camera coordinates system is solved：According to the perspective geometry relation for shooting ball, utilize
Known camera intrinsic parameter, shooting crown radius and obtained shooting ball projection conic section matrix, solve three shooting balls
Inhomogeneous coordinate of the centre of sphere in multicamera system in the camera coordinates system of each camera；
(3) three coplanar world coordinate systems of the centre of sphere are set up：Put down using three one shot in ball centre of sphere Special composition
Face, using this plane as the xoy planes in three-dimensional coordinate system, using resolution of vectors, sets up three centre ofs sphere coplanar
World coordinate system, the coordinate system is using one of centre of sphere as origin, and this is used as the centre of sphere and another centre of sphere of origin
Line is x-axis, and plane where three centre ofs sphere is xoy planes；
(4) the outer parameter of each camera in demarcation multicamera system：The ball centre of sphere is shot in each phase using three obtained
Inhomogeneous coordinate under machine coordinate system, sets up world coordinate system of the plane where shooting the ball centre of sphere using three as xoy planes, will
Each camera coordinates system is overlapped by rotation, the translation world coordinate system coplanar with three centre ofs sphere set up, and obtains multicamera system
In each camera outer parameter matrix, complete multicamera system in each camera external parameters calibration.
2. the Camera extrinsic number scaling method of multicamera system as claimed in claim 1, it is characterised in that：Intend in step (1)
Close and obtain the conic section matrix that each camera shoots ball projection, include：
Each camera in multicamera system, ball known to three different spatials and radius is shot from respective different visual angles
Image, wherein on the corresponding plane of delineation of i-th of camera, obtaining three shooting ball projecting edges, being carried using sub-pixel edge
Take algorithm to extract these three marginal points for shooting ball projection, by conic fitting algorithm, obtain what i-th of camera was shot
The conic section matrix of three ball projections, is designated as successivelyOther cameras, also solve according to i-th of camera and shoot
The conic section method of three ball projections, solves the conic section matrix that respective camera shoots ball projection, finally gives
Each camera is for three conic section matrixes for shooting ball projection in multicamera system.
3. the Camera extrinsic number scaling method of multicamera system as claimed in claim 1, it is characterised in that：Step (2) is described
The specific steps of inhomogeneous coordinate of the solution centre of sphere include：
2.1 clear and definite space circle spheric projections and the relation of camera intrinsic parameter：The relation of camera coordinates system and world coordinate system, camera is sat
The origin of mark system is camera photocentre OcIf the origin of world coordinate system is Ow, the world coordinate system is with Ow-XwYwZwRepresent, its
Middle OwZwAxle is by forming the centre of sphere of the space projection ball that camera image plane is projected, and the ball centre of sphere is designated as O, straight line OcO is generation
The Z axis of boundary's coordinate system；Space circle spheric projection relation, the space projection ball is projected as c in camera image plane, projection c
It is also simultaneously with camera photocentre OcThe projection of tangent normal cone for summit and with space projection ball, projection c is considered as the positive round
Bore the projection of bottom surface；The circle for remembering normal cone bottom surface is C, and its center of circle is designated as O1, its radius is designated as rc, plane where it is designated as II2,
Space projection ball centre of sphere O and normal cone bottom surface circle center of circle O1And camera photocentre OcOn same straight line, and OcO1Vertically
The circle C of normal cone bottom surface, remembers OcO1Distance be h；
Justify C equation and plane II according to ball projection relation, normal cone bottom surface2It should be related to the list of the plane of delineation, obtain sky
Between ball projection conic section c and camera intrinsic parameter K relation be：
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Spend the factor, (u0,v0) image coordinate of principal point for camera is represented, s represents the obliquity factor of camera；R represents to be tied to phase by world coordinates
The spin matrix of machine coordinate system；
2.2 obtain the distance between the space projection ball centre of sphere and camera photocentre：The geometrical relationship projected according to ball, including three
Angular similarity relation, obtains space projection ball centre of sphere O and camera photocentre OcThe distance between d, obtained by the similitude of triangle
To space projection ball centre of sphere O and camera photocentre OcThe distance between d be：
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Wherein d is camera photocentre OcTo space projection ball centre of sphere O distance, rsFor the radius of space projection ball, rcFor camera
Photocentre OcJustify C radius with the bottom surface of the normal cone of space projection ball formation, its center of circle is designated as O1, h is OcO1Distance；
Inhomogeneous coordinate of the 2.3 solution room projection sphere centre ofs sphere under camera coordinates system：
The relation with camera intrinsic parameter is projected using ball, if matrix A is
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Wherein R is spin matrix, and is unit orthogonal matrix, RRT=E, according to matrix theory, it is known that M is real symmetric matrix, then
By matrix Orthogonal Decomposition can obtain R andBecause on the Z axis of space projection ball centre of sphere world coordinate system, and the centre of sphere is to phase
The distance of machine photocentre be d, so inhomogeneous coordinate of the centre of sphere under world coordinate system for (0,0, d)T, R is spin matrix.Because
World coordinate system is overlapped with camera coordinates system origin, so translation vector is (0,0,0)T, from the space projection ball centre of sphere
In world coordinate system inhomogeneous coordinate, using rotation, translation relation under two coordinate systems, it can obtain non-under camera coordinates system
Homogeneous coordinates are
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2.4, which obtain three, shoots inhomogeneous coordinate of the ball centre of sphere under camera coordinates：Three according to captured by i-th of camera
The shooting ball of position projects conic sectionUtilize known camera intrinsic parameter, ball projection and camera internal reference
Several relations, obtaining inhomogeneous coordinate of three centre ofs sphere under the camera coordinates system of i-th of camera is respectively
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</mrow>
WhereinFor centre of sphere inhomogeneous coordinate of three centre ofs sphere under i-th of camera coordinates system, It is
Origin is tied to the spin matrix of camera coordinates system in photocentre and Z axis for the world coordinates of the centre of sphere to photocentre line,
It is distance of three centre ofs sphere to camera photocentre, according to i-th of camera solution, three shooting ball centre ofs sphere in camera coordinates system
Inhomogeneous coordinate method, three can be obtained and shoot inhomogeneous coordinate of the ball centre ofs sphere under the camera coordinates system of each camera.
4. the Camera extrinsic number scaling method of multicamera system as claimed in claim 1, it is characterised in that step (3) is described
Set up three centre ofs sphere where planes concretely comprising the following steps for the world coordinate system of xoy planes：
3.1 place the known ball that shoots of three radiuses in space diverse location, and three shoot the ball centre of sphere and are designated as O1、O2、O3；
3.2 think the XOY plane of three shooting ball centre of sphere Special compositions；
3.3 set one of shooting ball centre of sphere O1For world coordinate system origin, centre of sphere O1With another centre of sphere O2Line is the world
The X-axis of coordinate system, sets up vector O1O2With O1O3, two vector multiplication cross obtain the Z axis of world coordinate system；
3.4 carry out multiplication cross by X-axis and two reference axis of Z axis, obtain the Y-axis of three coplanar world coordinate systems of the centre of sphere, from
And set up three coplanar world coordinate systems of the centre of sphere；Three reference axis of the world coordinate system are obtained under camera coordinates system simultaneously
Unit direction vector a, b, c, also obtain three shoot the ball centre ofs sphere under the world coordinate system inhomogeneous coordinate difference
For Ow1、Ow2、Ow3。
5. the Camera extrinsic number scaling method of multicamera system as claimed in claim 1, it is characterised in that step (4) is described
Demarcation multicamera system in the outer parameter specific steps of each camera include：
4.1 rotations set up between two coordinate systems, translation relation：If the point X of space one is sat in the coplanar world of three centre ofs sphere
Inhomogeneous coordinate under mark system is designated asInhomogeneous coordinate in i-th of camera coordinates system is designated asIt is flat between them
Move, rotation relationship is
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>w</mi>
</msub>
<mo>=</mo>
<msub>
<mi>R</mi>
<mi>c</mi>
</msub>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>c</mi>
</msub>
<mo>+</mo>
<msub>
<mi>t</mi>
<mi>c</mi>
</msub>
</mrow>
Wherein RcFor the spin matrix referred to, tcFor the translation vector referred to；
4.2 obtain the outer parameter of i-th of camera:Ball projection, known camera intrinsic parameter, known three shootings are shot using three
The radius of ball and the projection relation for shooting ball and camera intrinsic parameter, obtain three and shoot the ball centre of sphere in i-th of camera
Inhomogeneous coordinate under coordinate systemThen using these three shooting ball centre ofs sphere under i-th of camera coordinates system
Inhomogeneous coordinateThree coplanar world coordinate systems of the centre of sphere are set up, three seats wherein in the coordinate system
Direction unit vector of the parameter under camera coordinates system is a, b, c, and three shoot spatial world coordinate of the ball centre of sphere in foundation
Inhomogeneous coordinate under system is Ow1、Ow2、Ow3, the spatial world coordinate system coplanar by three centre ofs sphere are set up, three reference axis lists
Bit vector synthesizes a R1Matrix is
R1=[a, b, c]T
The coordinate of arbitrfary point in three-dimensional system of coordinate, can represent projection of the vector under three reference axis of the arbitrfary point, then to
AmountRepresent under camera system, pointArriveVector, shouldIt is multiplied, obtains respectively with vectorial a, b, cIt is alive
The projection of three reference axis of boundary's coordinate system, i.e. point the X inhomogeneous coordinate under the coplanar world coordinate system of three centre ofs sphere, then
With the inhomogeneous coordinate in i-th of camera coordinates systemTransformational relation is：
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>w</mi>
</msub>
<mo>=</mo>
<msub>
<mi>R</mi>
<mn>1</mn>
</msub>
<mrow>
<mo>(</mo>
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>c</mi>
</msub>
<mo>-</mo>
<msubsup>
<mover>
<mi>O</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
<mn>1</mn>
</msubsup>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>R</mi>
<mn>1</mn>
</msub>
<msub>
<mover>
<mi>X</mi>
<mo>&OverBar;</mo>
</mover>
<mi>c</mi>
</msub>
<mo>-</mo>
<msub>
<mi>R</mi>
<mn>1</mn>
</msub>
<msubsup>
<mover>
<mi>O</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
<mn>1</mn>
</msubsup>
</mrow>
Wherein RiIt is spin matrix, the t of the coplanar world coordinate system of with respect to three centre ofs sphere of i-th of cameraiIt is i-th of camera phase
The world coordinate system translation vector coplanar to three centre ofs sphere；Wherein：
Ri=R1
<mrow>
<msub>
<mi>t</mi>
<mi>i</mi>
</msub>
<mo>=</mo>
<mo>-</mo>
<msub>
<mi>R</mi>
<mn>1</mn>
</msub>
<msubsup>
<mover>
<mi>O</mi>
<mo>&OverBar;</mo>
</mover>
<mi>i</mi>
<mn>1</mn>
</msubsup>
</mrow>
Calculate the Camera extrinsic matrix number for obtaining the coplanar world coordinate system of relative three centre ofs sphere set up of i-th of camera.
4.3 obtain each Camera extrinsic number in multicamera system：The method that Camera extrinsic number is obtained according to i-th of camera, is obtained
To the coplanar world coordinate system spin matrix of relatively same three centre ofs sphere of each camera of multicamera system, translation relation, i.e.,
Complete the demarcation of each Camera extrinsic number of polyphaser.
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