CN108444449B - Method for measuring target space attitude with parallel line characteristics - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
- G01C11/02—Picture taking arrangements specially adapted for photogrammetry or photographic surveying, e.g. controlling overlapping of pictures
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract
The invention relates to a method for measuring the attitude of a target space with parallel line characteristics, which solves the problems that the existing measuring method has to set cooperative mark points on a straight line, the measuring steps are complicated, the measuring instrument is complex and the equipment is expensive. The method comprises the following steps: 1) establishing a measuring system; 2) calibrating a line laser plane equation; 3) solving the space direction vector of a straight line of the surface of the measured target irradiated by the linear laser; 4) solving the expression of the target space direction of the parallel line characteristic in a camera coordinate system; 5) and solving the attitude angle and the azimuth angle through the rotation transformation of the coordinate system. The invention can directly utilize the parallel straight line characteristics of the surface of the measured target object without setting a cooperative mark point on the target, can obtain the three-dimensional attitude information of the measured target object in the space without an expensive three-dimensional coordinate measuring instrument, and has the advantages of convenient erection of a measuring system, low cost and simple measuring steps.
Description
Technical field
The present invention relates to field of optical measuring technologies, and in particular to a kind of to the object space posture with parallel lines feature
Measurement method.
Background technique
In accurate measurement, intelligent automation assembly, attitude angle measurement field, measuring targets space is frequently referred to
The measurement of posture, as the assembly of strip structure part misses in the installation direction error measure of girder steel in architectural engineering, precision instrument assembly
Difference detection (such as motion guide rail), cube pedestal attitude measurement.To the appearance of this kind of object space with parallel lines feature
State detection, is usually respectively set two index points in two parallel lines, using space coordinate measuring instrument, is as binocular measures
System, three-coordinates measuring machine, laser tracker, a kind of total station (invention: position and orientation mark of the extraterrestrial target based on total station
Determine method, 105424024 A of application publication number CN), two transits multi-theodolite intersection system etc., four the three-dimensional of index points are sat
Mark measures, then is converted into the posture information of parallel lines place plane.
In the above measurement method, binocular measuring system need to set up two Image-forming instruments on straight line mark point carry out at
Picture, and pixel coordinate is extracted, the three dimensional space coordinate of mark point is obtained by intersection measurement；Three-coordinates measuring machine detection range
Small, measured target must be limited within measurement arm scope of activities, and need contact measurement；Laser tracker utilizes interfeerometry ranging
Principle realize target three-dimensional coordinate measurement, it is necessary on index point set up reflecting target mark, laser tracker issue laser must
Reflecting target must be emitted to put on, and be reflected back laser tracker, target is moved in the process of index point from laser tracker,
The auto-collimation state that must assure that target can malfunction if reflection target deviates from laser beam axis, and the light that cannot break renews,
It must begin the beguine, the step of during this, reflecting target frame set, pH effect is complicated, and measurement process is slow；Total station is to straight line
Orientation, pitch angle and the distance value of upper two index points measure, to obtain the three-dimensional coordinate of index point；Two transits
Multi-theodolite intersection system is according to separate unit theodolite to the position between the orientation, pitch angle angle value and two transits of index point, appearance
State relationship calculates the three-dimensional coordinate of index point by triangle intersection principle, must be carried out before two transits position and
The calibration of posture；Cooperation index point must be all arranged in the above measurement method on straight line, and measuring process is complicated, and measuring instrument is multiple
Miscellaneous, equipment is expensive.
Summary of the invention
Present invention aim to address existing measurement method, that cooperation index point, measuring process must all be arranged on straight line is numerous
Multiple, measuring instrument complexity, the problem of equipment valuableness, provide a kind of to the object space attitude measurement side with parallel lines feature
Method.
The technical scheme is that
It is a kind of to the object space attitude measurement method with parallel lines feature, comprising the following steps:
1) measuring system is established；
Camera and single line laser device are set up, the measured target with parallel lines feature is placed into camera imaging region,
The line laser that single line laser device issues projects on measured target, and line laser is not parallel with parallel lines feature, and camera is to projection
Line laser and target to measured target surface are imaged；
2) calibration of line laser plane equation；
2.1) coordinate system is established；
Camera coordinates system Oc-XcYcZc is established, is Zc along imaging lens optical axis direction using camera photocentre as coordinate origin Oc
Axis, is Xc axis along imaging detector horizontal edge, and vertical edge is Yc axis；
The plane of delineation is set away from the place f ' in front of coordinate origin on optical axis, f ' is lens focus, the plane of delineation and detector
Plane is parallel, and two dimensional image coordinate oxy is established on the plane of delineation, and x is parallel to Xc axis, and y is parallel to Yc axis, and o point is optical axis and figure
As the intersection point of plane, object point, picture point and optical center meet collinear relationship；
2.2) intersection k1Canonical form equation seek；
In front of the measuring system that camera and single line laser device form, the intersection of imaging region and the line laser projection of camera
4 plane target drones are placed in region, and the cooperative target punctuate of four known coordinates is set on plane target drone, by photogrammetric
P4P algorithm obtains target co-ordinates system O1-X1Y1Z1Rotation translation relation between camera coordinates system Oc-XcYcZc, i.e. spin moment
Battle array R and translation vector T, is expressed as follows:
Transformational relation between target co-ordinates system and camera coordinates system are as follows:
Target plane equation is expressed as Z in target co-ordinates system1=0, then target plane equation is in camera coordinates system
Statement are as follows: Z1=r16Xc+r17Yc+r18Zc+t1z=0, which is denoted as π1；
On the image plane, by lines detection Processing Algorithm, the linear equation of line laser on the image plane is extracted:
A1x+B1y+C1=0, obtain A1、B1、C1；
Then linear equation of the line laser under camera coordinates system are as follows:
The plane that straight line and optical center determine is solved, Planes Equation is established, there is A1X+B1Y+C1+ L (Z-f')=0 substitutes into light
Heart coordinate (0,0,0), solvesThe then plane equation are as follows:The plane is denoted as π2；
According to space geometry theorem, the direction vector of two plane intersection lines is equal to the cross product of two plane law vectors, then line laser
Target plane intersection line k under plane and the state1Direction vector are as follows:
Wherein, r16、r17、r18It is obtained by P4P algorithm, f ' is lens focus, calculates to obtain l11、m11、n11Numerical value；
Seek a bit under line laser plane and the state on target plane intersection line, simultaneous π1、π2:
Take x1=0, it obtainsWherein, t1zIt is resolved by P4P algorithm
It obtains；
By rectilinear direction vector obtained aboveWith coordinate (x some on straight line1,y1,z1) bring straight line side into
The canonical form of journey to get arrive intersection k1Canonical form equation be
2.3) intersection k2Canonical form equation seek；
2.2) line laser of the posture of any transformation target, 4 points of target and projection repeats in camera imaging region
Calculating process obtains intersection k2Equation are as follows:
Calculate to obtain l12、m12、n12Numerical value；
2.4) association type (1) and formula (2), obtain the law vector of line laser plane are as follows:
The l that will be obtained11、m11、n11And l12、m12、n12Substitution formula (3) obtains l, the numerical value of m, n；
2.5) by calculating above, pass through a bit (x in plane1,y1,z1) with the law vector of plane
Obtain optic plane equations of the line laser under camera coordinates system:
lX+m(Y-y1)+n(Z-z1)=0 (4)
3) the direction in space vector that line laser is irradiated to the straight line on measured target surface is sought；
Formula (4) is arranged as general expression, A is obtained0X+B0Y+C0Z+D0=0, wherein A0=l, B0=m, C0=n, D0=-m ×
y1-n×z1；By image processing algorithm, side of the line laser in camera image plane projected in measured target plane is extracted
Journey are as follows: A0'x+B0'y+D0'=0, repetition seek the solution process of π 2, obtain the straight line that line laser is irradiated to measured target surface,
Plane equation of the camera photocentre plane under camera coordinates system beObtain A0'、B0'、D0'；
The direction vector of two plane intersection lines is equal to the cross product of two plane normal vectors, then line laser is irradiated to measured target table
The direction in space vector of the straight line in face are as follows:
By A0'、B0'、D0' and A0、B0、C0Substitution formula (5), obtains l1,m1,n1；
4) statement of the direction vector of parallel lines feature in camera coordinates system is sought；
Image procossing and object edge contours extract, measured target length side are carried out to the parallel lines feature on measured target
L is set to edge contour1And L2, L1And L2In parallel, world coordinate system O is established on measured target surfacew-XwYwZw, YwAxis with
Straight line L1And L2In parallel, ZwPerpendicular to L1And L2Identified plane, XwAxis direction meets the right-hand rule；In the plane of delineation, object
Space line L1And L2Institute is straight line L at image1' and L2', in image coordinate system oxy, L1' and L2' plane equation expression formula
It is respectively as follows:
A3x+B3y+D3=0 (6)
A2x+B2y+D2=0 (7)
In image coordinate system oxy, on the image plane, by lines detection Processing Algorithm, A is obtained3、B3、D3、A2、B2、
D2；It will obtain A3、B3、D3、A2、B2、D2And lens focus value f ' substitution formula (13), the direction vector for obtaining parallel lines feature exist
Statement in camera coordinates system:
5) attitude angle and azimuth are solved by the rotation transformation of coordinate system；
Parallel lines L1、L2With line laser in world coordinate system ZwIn=0 plane, therefore ZwSide of the axis in camera coordinates system
To vector are as follows:L, m, n are substituted into formula (15), formula (16) and formula (20), obtain target
Being directed toward 3 d pose value, θ in camera coordinates system is pitch angle, and γ is angle of heel,For azimuth；
Advantages of the present invention are as follows:
1. the present invention, can be directly using possessed by measured target body surface without the setting cooperation index point in target
The three-dimensional appearance of measured target object in space can be obtained without expensive three-dimensional coordinate measuring instrument device in parallel lines feature
State information, measuring system erection is convenient, at low cost, measuring process is simple.
2. the method for the present invention need to only set up monocular camera and single line laser device before target, it is equipped with common computer,
Measuring device is simple, at low cost, and measuring device sets up convenient；In measurement process, target image acquisition and target image are carried out
Measurement can be completed in edge extracting, graph line equation solver, parameter substitution, and measuring process is convenient；Method calculating process is to add
Subtract multiplication and division arithmetic, extracting operation and trigonometric function operation, calculates simple.
3. having the line laser light based on intersection of the propositions such as Bi Dexue about existing line laser plane equation scaling method
Plane equation calibration algorithm, Bai Ruilin (invention: the welding robot system calibration side based on line structured light vision sensor guidance
Method) (application number: the scaling method of propositions such as 201210318783.9) is both needed to repeatedly (at least three times) conversion line laser and is demarcating
It is transmitted on target plate, only needs twice the arbitrarily posture of transformation target plate in the present invention, line laser can be calibrated in monocular camera
Optic plane equations under coordinate, operation is simpler, calculation amount is smaller.
Detailed description of the invention
Fig. 1 is coordinate system of the present invention definition and object-image relation figure；
Fig. 2 is double parallel line imaging schematic diagram of the present invention；
Fig. 3 is the definition schematic diagram of camera coordinates system of the present invention and world coordinate system；
Fig. 4 is parallel lines object of the present invention, as, optical center geometrical relationship figure；
Fig. 5 is measuring system figure of the present invention；
Fig. 6 is measured target pictorial diagram of the present invention.
Appended drawing reference: 1- camera, 2- single line laser device, 3- measured target.
Specific embodiment
Technical solution of the present invention is clearly and completely described with reference to the accompanying drawings of the specification.
The method of the present invention is a kind of 3 d pose measurement method of universality, is related to the target empty with parallel lines feature
Between 3 d pose (pitch angle, angle of heel and azimuth) measurement, such as with the girder steel of parallel edge, sleeper, assembly parts, cube
Body structural member, or the measurement etc. for the object space posture that parallel lines identify can be portrayed on surface.
The step of present invention is to the object space attitude measurement method with parallel lines feature is as follows:
As shown in figure 5, camera 1 and single line laser device 2 are installed in the method for the present invention, when being applied to different scenes,
According to the distance of 3 object of measured target, can adjust baseline length between the two, and guarantee line laser project camera at
As the near center location in region, the distortion of this area camera imaging is minimum, it is ensured that the extraction accuracy of line laser throw light.
In measuring system (the referred to as three appearance measuring systems) front being made of camera and single line laser device, the imaging area of camera
The intersecting area in domain and line laser projection, places 4 plane target drones, calibrates optical plane of the line laser under camera coordinates system
Equation: A0x+B0y+C0z+D0=0；
Target with double flat line feature is placed under 3 d pose measuring system measured zone, camera is to projecting
The line laser and target of target surface are imaged, and in a computer, carry out figure to the parallel lines feature on line laser and target
As extracting, the direction vector of line laser and double flat line under camera coordinates system, i.e. formula (5) and formula (13) is obtained by calculation；
Previous step is resolvedWithSubstitution formula (15), formula (16) and formula (20), can be obtained mesh
Mark is directed toward the 3 d pose value in camera coordinates system.
The present invention meets to the measurement rapidity of object space posture, convenience requirement in a variety of application demands, for tool
There are parallel line profile, boundary characteristic or the targets of parallel lines can be portrayed in table plane, a kind of object space attitude measurement is provided
Method utilizes camera and single line laser, wherein plane equation of the single line laser under camera coordinates system is demarcated in advance to be provided, line
On laser projection to parallel lines feature, camera takes pictures to parallel lines and line laser, to object edge profile or markings into
Mathematical description of the object space posture in camera three-dimensional system of coordinate can be realized by algorithm in row image zooming-out.
The technical solution adopted in the present invention specifically:
One, the calibration of line laser optic plane equations
Camera imaging model uses national forest park in Xiaokeng, the inner parameter of camera: equivalent focal length (Fx,Fy), optical axis and imaging
Intersection point pixel coordinate (the C of sensor arrayx,Cy) and characterization imaging sensor array tilt degree physical quantity, by
Positive friend's calibration algorithm provides.Next the optic plane equations of line laser are demarcated；
Step 1: as shown in Figure 1, establish camera coordinates system Oc-XcYcZc, using camera photocentre as coordinate origin Oc, along at
Picture camera lens optical axis direction is Zc axis, is Xc axis along imaging detector horizontal edge, and vertical edge is Yc axis, and Oc-XcYcZc meets right-handed scale (R.H.scale)
System；Locate on optical axis away from coordinate origin Oc rear f ' as detector position (f ' is lens focus), object is being detected by camera lens
At inverted image on device, but when usual camera electronics processing, to guarantee that observed image meets human eye habit, by the image on detector
It being overturn, therefore the plane of delineation is set away from the place f ' in front of coordinate origin Oc on optical axis, the plane of delineation is parallel with detector plane,
To meet the overturning relationship of detector plane and the plane of delineation, two dimensional image coordinate oxy, x are established on the plane of delineation and is parallel to Xc
Axis, y are parallel to Yc axis, and o point is the intersection point of optical axis and the plane of delineation；Under the definition of the above coordinate system, object point, picture point and optical center are full
Foot collinear relationship as shown in Figure 1.
In front of the measuring system being made of camera and single line laser device, the phase of imaging region and the line laser projection of camera
Region is handed over, 4 plane target drones are placed, the cooperative target punctuate of four known coordinates is set on plane target drone, by photogrammetric
P4P algorithm can obtain target co-ordinates system O1-X1Y1Z1Rotation translation relation between camera coordinates system Oc-XcYcZc, that is, revolve
Torque battle array R and translation vector T, is expressed as follows:
Transformational relation between target co-ordinates system and camera coordinates system are as follows:
Target plane equation is expressed as Z in target co-ordinates system1=0, then target plane equation is in camera coordinates system
Statement are as follows: Z1=r16Xc+r17Yc+r18Zc+t1z=0, which is denoted as π1；
On the image plane, by lines detection Processing Algorithm, the linear equation of line laser on the image plane is extracted:
A1x+B1y+C1=0, obtain A1、B1、C1；
Then linear equation of the line laser under camera coordinates system is (space equation):
The plane that straight line and optical center determine is solved, Planes Equation is established, there is A1X+B1Y+C1+ L (Z-f')=0 substitutes into light
Heart coordinate (0,0,0), solvesThe then plane equation are as follows:
The plane is denoted as π2；According to space geometry theorem, the direction vector of two plane intersection lines is equal to two plane law vectors
Cross product, then target plane intersection line k under line laser plane and the state1Direction vector are as follows:
Wherein, r16、r17、r18It is obtained by P4P algorithm, f ' is lens focus, then can calculate to obtain l11、m11、n11Numerical value；
A bit under line laser plane and the state on target plane intersection line, simultaneous π are sought below1、π2:
Desirable x1=0, it can be obtained
Wherein, t1zIt resolves to obtain by P4P algorithm；
By rectilinear direction vector obtained aboveWith coordinate (x some on straight line1,y1,z1) bring straight line side into
Intersection k can be obtained in the canonical form of journey1Canonical form equation be
Step 2: the line laser of the posture of arbitrarily transformation target, 4 points of target of guarantee and projection is all in camera imaging region
Interior, the calculating process for repeating the first step obtains intersection k2Equation are as follows:
Equally, l is calculated to obtain12、m12、n12Numerical value；
Association type (1) and formula (2), then can obtain the law vector of line laser plane:
The l that will be obtained11、m11、n11And l12、m12、n12L, the numerical value of m, n, by calculating above can be obtained in substitution formula (3)
Process, a bit (x in obtained plane1,y1,z1) with the law vector of planeThen available line laser is sat in camera
Optic plane equations under mark system:
lX+m(Y-y1)+n(Z-z1)=0 (4)
Two, the object space 3 d pose with parallel lines feature is solved；
Measured target object with parallel lines feature is placed into monocular camera imaging region, decorating position guarantees phase
Machine can be to target at a certain size clear image, and to the decorating position of camera without particular/special requirement, line laser projects tested
On target object, and line laser is not parallel with parallel lines feature, below the three-dimensional to measured target object under camera coordinates system
Posture is solved；
Step 1: solving direction vector of the line laser under camera coordinates system projected in measured target plane；
By back line laser camera coordinates system plane equation lX+m (Y-y obtained by calibrating1)+n(Z-z1)=0 arranges
General type, it may be assumed that A0X+B0Y+C0Z+D0=0, wherein A0=l, B0=m, C0=n, D0=-m × y1-n×z1；At image
Adjustment method extracts equation of the line laser in camera image plane projected in measured target plane are as follows: A0'x+B0'y+D0'
=0, plane equation π is sought in repetition2Solution process, available line laser is irradiated to the straight line on measured target surface, camera
Plane equation of the optical center plane under camera coordinates system beExtraction obtains A0'、B0'、D0'；
It it is easy to show that, the direction vector of two plane intersection lines is equal to the cross product of two plane normal vectors, then line laser is irradiated to
The direction in space vector of the straight line on measured target surface are as follows:
By A0'、B0'、D0' and A0、B0、C0Substitution formula (5), obtains l1,m1,n1。
Second step solves direction vector of the parallel bilinear of measured target under camera coordinates system；
L is set in measured target lengthwise edge profile1And L2, L1And L2In parallel, camera is computed at image
After machine processing, parallel lines can be obtained and be directed toward the statement in camera coordinates system；The world is established on measured target body surface
Coordinate system Ow-XwYwZw, YwAxis and straight line L1And L2In parallel, ZwPerpendicular to L1And L2Identified plane, XwAxis direction meets the right hand
Rule, as shown in Figure 3.
To the two or more pieces parallel lines of object space, this sentences two parallel lines and is illustrated, a plurality of collimation principle class
Seemingly, each line of object space institute is object space straight line at image, and the intersection of optical center O formed plane and the plane of delineation is as shown in Fig. 2, object is empty
Between straight line L1And L2Institute is L at image1' and L2', L1、L1', O it is coplanar, L2、L2', O it is coplanar；Image geometrical relationship is summarized are as follows: plane
L1O and plane L2O intersection, O point is on intersection, L1' in plane L1On O, L2' in plane L2On O.
In Fig. 4, object space parallel lines L is described1With optical center formed plane and L2Intersection, object with optical center formed plane
Straight line, as the geometrical relationship between straight line；Be easy to show that on two intersecting planes, if it exists two straight line parallels, then this two
Straight line must be parallel to the intersection of two planes.Due to L1And L2For the parallel lines of object space, direction vector is identical, is set asL1O and L2The intersection direction vector of O plane is alsoPlane L1O and plane L1' O is same plane,
Plane L2O and plane L2' O is same plane, therefore passes through picture straight line L in image1' and L2' and optical center O, intersection can be acquired, i.e.,
Parallel lines L can be acquired1And L2Direction vectorSpecific derivation is as follows:
By image procossing and object edge contours extract, in image coordinate system oxy, L1' and L2' plane equation table
It is respectively as follows: up to formula
A3x+B3y+D3=0 (6)
A2x+B2y+D2=0 (7)
In image coordinate system oxy, on the image plane, by lines detection Processing Algorithm, A is obtained3、B3、D3、A2、B2、
D2；
Then its space line equation under camera coordinates system is respectively as follows:
Solve straight line L1The plane determined with optical center, establishes Planes Equation, there is A3X+B3Y+D3+ L (Z-f')=0 is substituted into
Optical center coordinate (0,0,0), solvesThe then plane equation are as follows:
Similarly, straight line L2The plane equation determined with optical center are as follows:
Then plane intersection line equation are as follows:
According to space geometry theorem, the direction vector of two plane intersection lines is equal to the cross product of two plane law vectors, according to formula
(12), intersection direction vector is acquired are as follows:
This is also L1And L2The expression formula of rectilinear direction vector, the A that will be acquired3、B3、D3、A2、B2、D2Substitution formula (13), obtains
To direction vector of the parallel bilinear under camera coordinates system；
Third step solves attitude angle and azimuth by the rotation transformation of coordinate system；
Parallel lines L1、L2With structure light in world coordinate system ZWIn=0 plane, therefore ZWSide of the axis in camera coordinates system
To vector are as follows:
Transformational relation between camera coordinates system and world coordinate system are as follows:
Wherein, θ is pitch angle, and γ is angle of heel；
It substitutes into: (Xc,Yc,Zc)T=(l, m, n)T, (XW,YW,ZW)T=(0,0,1)T, then can solve θ and γ is respectively as follows:
Consider further around world coordinate system ZwAzimuth, then have:
Due to double flat line and YWAxis direction is parallel, therefore under world coordinate system, the direction vector of double flat line can indicate
For (0,1,0)T, substitute into (Xc,Yc,Zc)T=(l2,m2,n2)T, (XW,YW,ZW)T=(0,1,0)T, note:
Then:
Azimuth can be solved
By solving above, so that it may the object that there is parallel lines feature or surface can portray parallel lines mark is obtained,
3 d pose information under camera coordinates.
To verify feasibility of the invention, Proof-Of Principle platform is built, measured target platform is designed and machined, target is flat
Platform is packed on 3 d pose turntable, to adjust the 3 d pose of transformation Target Station, and by the posture of 3 d pose turntable
Value is used as true value, detects the 3 d pose measurement accuracy of measuring system, measured target object upper surface is as shown in fig. 6, with error
The correctness of measurement method of the present invention is verified, illustrates that measurement method of the present invention is effective；Under the present embodiment, pitching of the invention
Angle θ and roll angle γ measurement error are within 0.03 °, azimuthMeasurement error is within 0.02, no gross error.
Claims (1)
1. a kind of to the object space attitude measurement method with parallel lines feature, which comprises the following steps:
1) measuring system is established；
Camera and single line laser device are set up, the measured target with parallel lines feature is placed into camera imaging region, single line
The line laser that laser issues projects on measured target, and line laser is not parallel with parallel lines feature, camera to project by
The line laser and target for surveying target surface are imaged；
2) calibration of line laser plane equation；
2.1) coordinate system is established；
Camera coordinates system Oc-XcYcZc is established, is Zc axis along imaging lens optical axis direction using camera photocentre as coordinate origin Oc,
It is Xc axis along imaging detector horizontal edge, vertical edge is Yc axis；
The plane of delineation is set away from the place f ' in front of coordinate origin on optical axis, f ' is lens focus, the plane of delineation and detector plane
In parallel, two dimensional image coordinate oxy is established on the plane of delineation, x is parallel to Xc axis, and y is parallel to Yc axis, and o point is that optical axis and image are flat
The intersection point in face, object point, picture point and optical center meet collinear relationship；
2.2) intersection k1Canonical form equation seek；
In front of the measuring system that camera and single line laser device form, the intersecting area of imaging region and the line laser projection of camera
The cooperative target punctuate of four known coordinates is arranged on plane target drone, is calculated by photogrammetric P4P for 4 plane target drones of interior placement
Method obtains target co-ordinates system O1-X1Y1Z1Rotation translation relation between camera coordinates system Oc-XcYcZc, i.e. spin matrix R and
Translation vector T, is expressed as follows:
Transformational relation between target co-ordinates system and camera coordinates system are as follows:
Target plane equation is expressed as Z in target co-ordinates system1=0, then statement of the target plane equation in camera coordinates system
Are as follows: Z1=r16Xc+r17Yc+r18Zc+t1z=0, which is denoted as π1；
On the image plane, by lines detection Processing Algorithm, the linear equation of line laser on the image plane: A is extracted1x+B1y
+C1=0, obtain A1、B1、C1；
Then linear equation of the line laser under camera coordinates system are as follows:
The plane that straight line and optical center determine is solved, Planes Equation is established, there is A1X+B1Y+C1+ L (Z-f')=0 substitutes into optical center and sits
It marks (0,0,0), solvesThe then plane equation are as follows:The plane is denoted as π2；
According to space geometry theorem, the direction vector of two plane intersection lines is equal to the cross product of two plane law vectors, then line laser plane
With target plane intersection line k1Direction vector are as follows:
Wherein, r16、r17、r18It is obtained by P4P algorithm, f ' is lens focus, calculates to obtain l11、m11、n11Numerical value；
Seek a bit in line laser plane and target plane intersection line, simultaneous π1、π2:
Take x1=0, it obtainsWherein, t1zIt is resolved by P4P algorithm
It arrives；
By rectilinear direction vector obtained aboveWith coordinate (x some on straight line1,y1,z1) bring linear equation into
Canonical form to get arrive intersection k1Canonical form equation be
2.3) intersection k2Canonical form equation seek；
The line laser of the posture of any transformation target, 4 points of target and projection repeats calculating 2.2) in camera imaging region
Process obtains intersection k2Equation are as follows:
Calculate to obtain l12、m12、n12Numerical value；
2.4) association type (1) and formula (2), obtain the law vector of line laser plane are as follows:
The l that will be obtained11、m11、n11And l12、m12、n12Substitution formula (3) obtains l, the numerical value of m, n；
2.5) by calculating above, pass through a bit (x in plane1,y1,z1) with the law vector of planeLine laser is obtained to exist
Optic plane equations under camera coordinates system:
lX+m(Y-y1)+n(Z-z1)=0 (4)
3) the direction in space vector that line laser is irradiated to the straight line on measured target surface is sought；
Formula (4) is arranged as general expression, A is obtained0X+B0Y+C0Z+D0=0, wherein A0=l, B0=m, C0=n, D0=-m × y1-n
×z1；By image processing algorithm, equation of the line laser in camera image plane projected in measured target plane is extracted
Are as follows: A0'x+B0'y+D0'=0, repetition seek the solution process of π 2, obtain the straight line that line laser is irradiated to measured target surface, phase
Machine optical center plane camera coordinates system under plane equation beObtain A0'、B0'、D0'；
The direction vector of two plane intersection lines is equal to the cross product of two plane normal vectors, then line laser is irradiated to measured target surface
The direction in space vector of straight line are as follows:
By A0'、B0'、D0' and A0、B0、C0Substitution formula (5), obtains l1,m1,n1；
4) statement of the direction vector of parallel lines feature in camera coordinates system is sought；
Image procossing and object edge contours extract, measured target length direction side are carried out to the parallel lines feature on measured target
Edge profile is set to L1And L2, L1And L2In parallel, world coordinate system O is established on measured target surfacew-XwYwZw, YwAxis and straight line
L1And L2In parallel, ZwPerpendicular to L1And L2Identified plane, XwAxis direction meets the right-hand rule；In the plane of delineation, object space
Straight line L1And L2Institute is straight line L at image1' and L2', in image coordinate system oxy, L1' and L2' plane equation expression formula difference
Are as follows:
A3x+B3y+D3=0 (6)
A2x+B2y+D2=0 (7)
In image coordinate system oxy, on the image plane, by lines detection Processing Algorithm, A is obtained3、B3、D3、A2、B2、D2；It will
Obtain A3、B3、D3、A2、B2、D2And lens focus value f ' substitution formula (13), the direction vector of parallel lines feature is obtained in camera
Statement in coordinate system:
5) attitude angle and azimuth are solved by the rotation transformation of coordinate system；
Parallel lines L1、L2With line laser in world coordinate system ZwIn=0 plane, therefore ZwDirection vector of the axis in camera coordinates system
Are as follows:L, m, n are substituted into formula (15), formula (16) and formula (20), target is obtained and is directed toward
3 d pose value in camera coordinates system, θ are pitch angle, and γ is angle of heel,For azimuth；
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