CN111174726A - Shaft end grounding binocular reconstruction system and method for concentric quadratic curve polar line geometry - Google Patents

Shaft end grounding binocular reconstruction system and method for concentric quadratic curve polar line geometry Download PDF

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CN111174726A
CN111174726A CN201911426735.XA CN201911426735A CN111174726A CN 111174726 A CN111174726 A CN 111174726A CN 201911426735 A CN201911426735 A CN 201911426735A CN 111174726 A CN111174726 A CN 111174726A
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coordinate system
camera
laser
concentric
image
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徐观
朱尧平
陈熔
苏建
张立斌
刘玉梅
戴建国
单红梅
林慧英
李晓韬
陈芳
沈慧
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Jilin University
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Jilin University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
    • G01B11/00—Measuring arrangements characterised by the use of optical techniques
    • G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures

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Abstract

The invention discloses a system and a method for reconstructing a shaft end grounding binocular of a concentric quadratic curve polar line geometry, and aims to solve the problem of shaft end grounding binocular detection of the concentric quadratic curve polar line geometry. The shaft end grounding binocular reconstruction system of the concentric secondary curve polar line geometry mainly comprises a base (1), a support rod (2), a laser connecting rod (3), a left video camera (4), a laser (5), a right video camera (6), a camera connecting block (7), a target plate (8), a linear sliding table (9), a connecting rod (11), a support rod fixing block (12), a connecting rod fixing block (13) and a laser fixing block (14). The target plate (8) is a flat plate with a concentric quadratic curve pasted on the surface, the supporting rod fixing block (12) is a cuboid iron block with two circular through holes with mutually vertical axes processed on the surface and two threaded holes processed at two ends respectively, and the shaft end grounding binocular reconstruction system and the shaft end grounding binocular reconstruction method of the concentric quadratic curve polar line geometry are simple in structure and reliable in performance.

Description

Shaft end grounding binocular reconstruction system and method for concentric quadratic curve polar line geometry
Technical Field
The invention relates to measuring equipment and a measuring method in the field of railway vehicles, in particular to a shaft end grounding binocular reconstruction system and a shaft end grounding binocular reconstruction method of concentric quadratic curve polar line geometry.
Background
With the continuous improvement of the speed of the high-speed motor train, the performance requirements on each component of the high-speed motor train unit are higher and higher. The increase of the speed of a motor vehicle increases the abrasion between the contact disc and the carbon brush of the axle end grounding device of the bogie, which brings serious threat to the running safety of the railway vehicle. The contact pad measurement systems that are commonly used are mainly contact measurement systems. However, in the contact measurement system, the measurement instrument needs to be in contact with the surface of the measured object, the measured object is easily scratched, the measurement speed is slow, and some complicated areas are difficult to measure. How to realize non-contact measurement and recover the three-dimensional information of the measured object with high precision and high efficiency is very important. In order to realize three-dimensional reconstruction of the shaft end grounding contact disc and detect abrasion of the shaft end grounding contact disc, a shaft end grounding binocular reconstruction system and method of concentric quadratic curve polar line geometry are designed.
Disclosure of Invention
The invention aims at solving the problems that the traditional contact detection equipment has low precision and efficiency and some complex areas are difficult to measure in the process of measuring the appearance of the contact disc, designs a method and a system with reliable non-contact performance, simple structure and simple and convenient operation, realizes the three-dimensional free reconstruction of the appearance characteristic points of the contact disc, and lays a foundation for further perfecting the detection technology of part abrasion and improving the driving safety of high-speed motor cars. The method mainly comprises two industrial cameras, a line laser, a stepping motor and a sliding table, wherein the cameras and a light plane are calibrated through a concentric quadratic curve polar line geometric relation, and the system global reconstruction is carried out by adopting the steps of bundling adjustment optimization and the like.
The invention is realized by adopting the following technical scheme by combining the attached drawings of the specification:
the shaft end grounding binocular reconstruction system of the concentric secondary curve polar line geometry comprises a base, a supporting rod, a laser connecting rod, a left camera, a laser, a right camera, a camera connecting block, a target plate, a linear sliding table, a connecting rod, a supporting rod fixing block, a connecting rod fixing block and a laser fixing block;
the base is placed on a flat ground, the bottoms of four support rods are placed on the base, a bolt penetrates through holes at the bottoms of the four support rods from top to bottom and is fixedly connected with a thread through hole on the upper surface of the base, the linear sliding table is placed in the middle of the base and is fixedly connected with the bolt of the base, a target plate is placed on a workbench of the linear sliding table during calibration, a contact disc is placed on the workbench of the linear sliding table during reconstruction, the through holes at one ends of the four support rod fixing blocks are respectively sleeved at the thread holes of the support rods along the axial diameter direction of the four support rods, the bolt penetrates through a circular through hole at the end part of the support rod fixing block and is fixedly connected with the thread of the support rods, one ends of the two connecting rods respectively penetrate through the other through holes of the two support rod fixing blocks at the same side, the through holes at one end of the two connecting rod fixing blocks are respectively sleeved with the two connecting rods and then moved back to the threaded holes of the connecting rods, the bolt passes through the circular through hole at the bottom end of the connecting rod fixing block and is fixedly connected with the connecting rod threads, the two connecting rods penetrate through the through holes at the other end of the two supporting rod fixing blocks, the bolt passes through the circular through hole at one end of the two supporting rod fixing blocks and is fixedly connected with the connecting rod threads, one end of the laser connecting rod passes through the through hole at one end of the connecting rod fixing block, the through hole at one end of the laser fixing block penetrates along the laser connecting rod, the end of the laser connecting rod is sleeved with the laser connecting rod, the bolt passes through the circular through hole at the bottom end of the laser fixing block and is fixedly connected with the laser connecting rod threads, the front ends of, the bolt penetrates through a threaded hole at one end of the laser fixing block and is fixedly connected with the laser through threads.
The base in the technical scheme is a rectangular steel plate with a threaded hole on the surface.
The supporting rod in the technical scheme is formed by vertically welding a cylindrical long rod with a threaded hole formed in the upper end and a circular iron sheet with six circular through holes uniformly formed in the upper end.
The laser connecting rod in the technical scheme is a cylindrical long rod with a threaded hole.
In the technical scheme, the left video camera is a wide-angle industrial camera provided with a narrow-band filter.
The laser in the technical scheme is a cylindrical part capable of emitting a laser plane.
In the technical scheme, the right video camera is a wide-angle industrial camera provided with a narrow-band filter.
The camera connecting block in the technical scheme is formed by welding an iron ring with a threaded hole and a rectangular iron block with two circular through holes with mutually vertical axes.
The target plate in the technical scheme is a flat plate with a surface adhered with a concentric quadratic curve.
The linear sliding table in the technical scheme is driven by a stepping motor and can make an object do reciprocating linear motion.
The connecting rod in the technical scheme is a cylindrical long rod with a threaded hole processed on the surface.
In the technical scheme, the supporting rod fixing block is a cuboid iron block with two circular through holes with mutually vertical axes processed on the surface and two circular through holes processed at two ends respectively.
In the technical scheme, the connecting rod fixing block is a rectangular iron block which is provided with two circular through holes with mutually vertical axes and two ends of which are respectively provided with a circular through hole.
The laser fixing block in the technical scheme is a square iron block with two circular through holes with mutually vertical axes processed on the surface and two threaded holes and one circular through hole processed at two ends respectively.
The method for reconstructing the axle end grounding binocular of the concentric quadratic curve polar line geometry comprises the following specific steps:
the first step is as follows: acquiring images of a concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
placing a shaft end grounding binocular reconstruction system of concentric secondary curve polar geometry on a horizontal ground, placing a two-dimensional target plate below a left camera, a right camera and a laser, starting the laser, and simultaneously collecting a plurality of images including the target plate, laser planes emitted by the laser and laser lines intersected with the target plate and a plurality of images including laser lines intersected with a contact disc when a workbench moves;
the second step is that: solving internal and external parameters of a left camera and a right camera of the concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
establishing an image coordinate system according to the image collected by the left camera, wherein the origin of the target board coordinate system is positioned at the center of the secondary curve pattern of the target board, and the conversion relation of the secondary curve from the target board coordinate system to the image coordinate system is
Figure BSA0000199864170000031
Wherein
Figure BSA0000199864170000032
The image coordinates of the jth quadratic curve in the ith image,
Figure BSA0000199864170000033
the coordinates of the target plate coordinate system which is a quadratic curve,
Figure BSA0000199864170000034
is a homography from the target plate coordinate system to the image coordinate system;
according to the conversion relation of the quadratic curve from the target board coordinate system to the image coordinate system
Figure BSA0000199864170000035
Will be provided with
Figure BSA0000199864170000036
And
Figure BSA0000199864170000037
substituted into the above formula to obtain
Figure BSA0000199864170000038
Three or more than three of the above relations can be obtained by three or more than three quadratic curves, and the relation can be obtained
Figure BSA0000199864170000039
Respectively decomposing by singular value decomposition
Figure BSA00001998641700000310
Figure BSA00001998641700000311
Can be sequentially obtained
Figure BSA00001998641700000312
Thereby obtaining a homography matrix
Figure BSA00001998641700000313
According to Zhangyingyou scaling, it is possible to use homography matrix
Figure BSA00001998641700000314
Obtaining internal parameter K of left cameraLAnd extrinsic parameters
Figure BSA00001998641700000315
Meanwhile, an image coordinate system is established according to the image collected by the right camera, and a conversion relation of a quadratic curve from a target plate coordinate system to the image coordinate system can be obtained
Figure BSA00001998641700000316
Wherein
Figure BSA00001998641700000317
The image coordinates of the jth quadratic curve in the ith image,
Figure BSA00001998641700000318
the coordinates of the target plate coordinate system which is a quadratic curve,
Figure BSA00001998641700000319
is a homography from the target plate coordinate system to the image coordinate system;
according to the conversion relation of the quadratic curve from the target board coordinate system to the image coordinate system
Figure BSA0000199864170000041
Will be provided with
Figure BSA0000199864170000042
And
Figure BSA0000199864170000043
substituted into the above formula to obtain
Figure BSA0000199864170000044
Three or more than three of the above relations can be obtained through three or more than three quadratic curves to obtain
Figure BSA0000199864170000045
Respectively decomposing by singular value decomposition
Figure BSA0000199864170000046
Figure BSA0000199864170000047
Can be sequentially obtained
Figure BSA0000199864170000048
Thereby obtaining a homography matrix
Figure BSA0000199864170000049
According to the method of expanding friends, the homography matrix can be used
Figure BSA00001998641700000410
Determining the internal parameter K of the left camera 4RAnd extrinsic parameters
Figure BSA00001998641700000411
The third step: solving the optical plane coordinates of the left camera coordinate system of the concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
establishing an image coordinate system according to the image collected by the left camera, wherein the relationship among the pole of the secondary curve, the polar line and the secondary curve in the image coordinate system is known as
Figure BSA00001998641700000412
Wherein
Figure BSA00001998641700000413
The pole of the quadratic curve is the pole of the quadratic curve,
Figure BSA00001998641700000414
polar line coordinates and conic coordinates in the image coordinate system can be extracted by Hough transformation to obtain polar line of conic curve
Figure BSA00001998641700000415
The intersection point of the polar line and the secondary curve is set as
Figure BSA00001998641700000416
The relationship between the tangent line of the intersection point and the line of polar line is
Figure BSA00001998641700000417
Wherein
Figure BSA00001998641700000418
Is a tangent line passing through the intersection point, and the relationship among the intersection point, the tangent line passing through the intersection point and the pole is
Figure BSA00001998641700000419
The two simultaneous methods can obtain the intersection point of polar line and secondary curve
Figure BSA00001998641700000420
Coordinates of intersection points on image coordinate system
Figure BSA00001998641700000421
Coordinates to the target plate coordinate system
Figure BSA00001998641700000422
Has a conversion relation of
Figure BSA00001998641700000423
Coordinates of the target plate coordinate system
Figure BSA00001998641700000424
To the left camera 4 coordinate system
Figure BSA00001998641700000425
Has a conversion relation of
Figure BSA00001998641700000426
Then in the left camera coordinate system the intersection point
Figure BSA00001998641700000427
In relation to the laser plane
Figure BSA0000199864170000051
The laser plane Pi in the coordinate system of the left camera can be obtained by a singular value decomposition methodCL；
Establishing an image coordinate system according to the image acquired by the right camera, wherein the relationship among the pole of the secondary curve, the polar line and the secondary curve in the image coordinate system is known as
Figure BSA0000199864170000052
Wherein
Figure BSA0000199864170000053
The pole of the quadratic curve is the pole of the quadratic curve,
Figure BSA0000199864170000054
polar line coordinates and conic coordinates in the image coordinate system can be extracted by Hough transformation to obtain polar line of conic curve
Figure BSA0000199864170000055
The intersection point of the polar line and the secondary curve is set as
Figure BSA0000199864170000056
The relationship between the tangent line of the intersection point and the crossing point and the polar line is known as
Figure BSA0000199864170000057
Wherein
Figure BSA0000199864170000058
Is a tangent of the crossing point, and the relation among the crossing point, the tangent of the crossing point and the pole is known as
Figure BSA0000199864170000059
The two simultaneous methods can obtain the intersection point of polar line and secondary curve
Figure BSA00001998641700000510
Coordinates of intersection points on image coordinate system
Figure BSA00001998641700000511
Coordinates to the target plate coordinate system
Figure BSA00001998641700000512
Has a conversion relation of
Figure BSA00001998641700000513
Coordinates of the target plate coordinate system
Figure BSA00001998641700000514
To the right camera 6 coordinate system
Figure BSA00001998641700000515
Has a conversion relation of
Figure BSA00001998641700000516
Then in the right camera coordinate system, the intersection point
Figure BSA00001998641700000517
And laser plane piCRIn a relationship of
Figure BSA00001998641700000518
Obtaining laser plane pi in left camera coordinate system by singular value decomposition methodCR；
The fourth step: left camera, right camera internal and external parameters and left camera light plane coordinate pi of shaft end grounding binocular reconstruction method of concentric quadratic curve polar line geometryCLOptimizing:
homography matrix from right camera coordinate system to left camera coordinate system is
Figure BSA00001998641700000519
Obtaining the light plane coordinate pi of the coordinate system of the right cameraCRTo the left camera coordinate system light plane coordinate piCLHas a conversion relation of
πCL＝Hi，qπCR
Establishing an objective optimization function
Figure BSA00001998641700000520
Solving each optimized parameter pi by adopting a bundle set adjusting method and an LM methodCL、
Figure BSA00001998641700000521
The fifth step: rebuilding the contact disc characteristic points of the concentric quadratic curve polar line geometric shaft end grounding binocular rebuilding method under the left camera coordinate system:
feature point W in the left camera coordinate systemCLAnd the plane of light piCLIn a relationship of
(WCL)TπCL＝0
Feature point W in the left camera coordinate systemCLAnd feature point image coordinates wCLIn a relationship of
WCL＝(KL)-1wCL
Feature point W in the left camera coordinate systemCLIs smooth and flatPlane piCLAnd a feature point W in the left camera coordinate systemCLAnd feature point image coordinates wCLBy simultaneous correlation of (A) and (B), W can be obtainedCL；
Feature point W in the right camera coordinate systemCRAnd the plane of light piCRIn a relationship of
(WCR)TπCR＝0
Feature point W in the right camera coordinate systemCRAnd feature point image coordinates wCRIn a relationship of
WCR＝(KL)-1wCR
Feature point W in the right camera coordinate systemCRAnd the plane of light piCRAnd a feature point W in the left camera coordinate systemCRAnd feature point image coordinates wCRBy simultaneous correlation of (A) and (B), W can be obtainedCR；
Homography matrix from right camera coordinate system to left camera coordinate system
Figure BSA0000199864170000061
Knowing the feature point W in the right camera coordinate systemCRWith a feature point W in the left camera coordinate systemCLIn a relationship of
WCL＝Hi，qWCR
The characteristic point coordinate W in the coordinate system of the right camera can be obtained by the above formulaCRAnd uniformly converting into a left camera coordinate system.
The invention has the beneficial effects that:
1. the invention adopts a shaft end grounding binocular reconstruction method of concentric quadratic curve polar line geometry. Firstly, calibrating internal and external parameters of a camera by using a concentric quadric curve of a two-dimensional target, calibrating a light projection plane of a laser according to the pole line relation of the two-dimensional target, and finally realizing three-dimensional reconstruction of the surface of a contact disc by driving a stepping motor to move the contact disc.
2. The invention adopts two cameras for detection, the measured result has higher precision than that of a single camera, a system parameter optimization model is established, and meanwhile, the LM method is utilized to optimize the reconstruction result so as to obtain the optimal internal and external parameters of the cameras, thereby realizing the high-precision reconstruction of the target object.
3. The measuring system solves the problems of low measuring efficiency, poor convenience and the like of the contact type measuring system, and can drive the contact discs to move after driving the stepping motor, shoot images of the contact discs with laser lines on the surfaces and realize the reconstruction of the surfaces of the friction discs.
4. Compared with the traditional contact measurement method, the method has the advantages that the non-contact measurement is adopted, the abrasion to the surface of the measured piece during measurement can be greatly reduced, the measured piece is protected, and the surface of the measured piece is prevented from being damaged.
Drawings
FIG. 1 is a calibration state axonometric view of an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 2 is an isometric view of reconstruction states of an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 3 is an isometric view of the base 1 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 4 is an isometric view of the support rod 2 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 5 is an isometric view of the laser connecting rod 3 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 6 is an isometric view of the left camera 4 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 7 is an isometric view of a laser 5 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 8 is an isometric view of the right camera 6 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
fig. 9 is an isometric view of a camera connection block 7 in an axial-end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 10 is an isometric view of a target plate 8 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
FIG. 11 is an isometric view of a linear sliding table 9 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
fig. 12 is an isometric view of the contact disk 10 in an axial end grounded binocular reconstruction system of concentric conic polar geometry;
fig. 13 is an isometric view of the connecting rod 11 in an axial-end grounded binocular reconstruction system of concentric conic polar geometry;
fig. 14 is an isometric view of the support rod fixation block 12 in an axial end grounded binocular reconstruction system of concentric quadratic curvilinear polar geometry;
FIG. 15 is a flowchart for solving internal and external parameters of the left camera 4 and the right camera 6 in the axial end grounding binocular reconstruction method of concentric quadratic curve epipolar geometry;
FIG. 16 is a flow chart for solving the coordinates of the light plane under the coordinates of the left camera 4 in the axial end grounding binocular reconstruction method of the concentric quadratic curve epipolar geometry;
FIG. 17 is a flow chart for solving the coordinates of the light plane under the coordinates of the right camera 6 in the axial end grounding binocular reconstruction method of the concentric quadratic curve epipolar geometry;
FIG. 18 shows the conversion of the optical plane coordinates of the right camera 6 to the optical plane coordinates of the left camera 4 in the axial end grounding binocular reconstruction method of concentric quadratic curvilinear polar geometryCLA flow chart of (1);
FIG. 19 is a flow chart of optimizing the inside and outside parameters and the optical plane of the left camera 4 and the right camera 6 in the axial end grounded binocular reconstruction method of concentric conic polar geometry;
FIG. 20 is a flowchart of reconstructing laser feature points of the left camera 4 and the right camera 6 in an axial end grounding binocular reconstruction method of concentric quadratic curve epipolar geometry;
in the figure: 1. the laser positioning device comprises a base, a supporting rod 2, a laser connecting rod 3, a left camera 4, a laser 5, a right camera 6, a camera connecting block 7, a target board 8, a linear sliding table 9, a contact disc 10, a connecting rod 11, a supporting rod fixing block 12, a connecting rod fixing block 13 and a laser fixing block 14.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
referring to fig. 1 to 14, the shaft end grounding binocular reconstruction system of the concentric secondary curve polar geometry includes a base 1, a support rod 2, a laser connecting rod 3, a left camera 4, a laser 5, a right camera 6, a camera connecting block 7, a target plate 8, a linear sliding table 9, a connecting rod 11, a support rod fixing block 12, a connecting rod fixing block 13 and a laser fixing block 14;
the base 1 is a rectangular steel plate with a threaded hole processed on the surface, the base 1 is placed on a flat ground, the support rods 2 are formed by vertically welding a cylindrical long rod with a threaded hole processed at the upper end and a circular iron sheet with six circular through holes uniformly processed, the bottoms of the four support rods 2 are placed on the base 1, bolts penetrate through the through holes at the bottoms of the four support rods 2 from top to bottom and are fixedly connected with the threads of the threaded through holes on the upper surface of the base 1, the linear sliding table 9 is a sliding table driven by a stepping motor and can enable an object to do reciprocating linear motion, the linear sliding table 9 is placed in the middle of the base 1 and is fixedly connected with the bolts of the base 1, the target plate 8 is a flat plate with concentric secondary curves pasted on the surface, the target plate 8 during calibration is placed on a workbench of the linear sliding table 9, the contact disc 10 is a cylindrical part with a through hole, and, the supporting rod fixing block 12 is a cuboid iron block with two circular through holes with mutually vertical axes processed on the surface and two circular through holes processed on two ends, the through holes at one end of the four supporting rod fixing blocks 12 are respectively sleeved into the threaded holes of the supporting rod 2 along the axial diameter direction of the four supporting rods 2, a bolt passes through the circular through holes at the end parts of the supporting rod fixing blocks 12 and is fixedly connected with the threads of the supporting rods 2, the connecting rod 11 is a cylindrical long rod with threaded holes processed on the surface, one end of the two connecting rods 11 respectively passes through the other through hole of the two supporting rod fixing blocks 12 on the same side, the camera connecting block 7 is formed by welding an iron ring with threaded holes processed and a rectangular iron block with two circular through holes with mutually vertical axes processed, the through holes of the two camera connecting blocks 7 are respectively sleeved into the connecting rods 11 and then move to the threaded holes in, the connecting rod fixing block 13 is a rectangular iron block which is provided with two circular through holes with mutually vertical axes and two ends of which are respectively provided with a circular through hole, the through holes at one end of the two connecting rod fixing blocks 13 are respectively sleeved in the two connecting rods 11 and then move to the threaded holes of the connecting rods 11, a bolt passes through the circular through hole at the bottom end of the connecting rod fixing block 13 and is fixedly connected with the threads of the connecting rods 11, the two connecting rods 11 pass through the through holes of the two supporting rod fixing blocks 12 at the other end, the bolt passes through the circular through hole at one end of the two supporting rod fixing blocks 12 and is fixedly connected with the threads of the connecting rods 11, the laser connecting rod 3 is a cylindrical long rod which is provided with a threaded hole, one end of the laser connecting rod 3 passes through the through hole of one connecting rod fixing block, the through-hole of 14 one ends of laser fixed block penetrates the end cover along laser connecting rod 3 and goes into laser connecting rod 3, the bolt passes the circular through-hole in 14 bottoms of laser fixed block and laser connecting rod 3 screw thread fixed connection, left camera 4 and right camera 6 are the wide angle industrial camera who is equipped with the narrowband optical filter, left camera 4 embolias the 7 front end rings of camera connecting block respectively with right camera 6 front end top-down, the three screw hole that the bolt passed 7 rings of camera connecting block and left camera 4 and right camera 6 fixed connection, laser 5 is the planar cylindrical part of laser that can emit, laser 5 penetrates the round hole of 14 front ends of laser fixed block from bottom to top, the bolt passes 14 one end screw holes of laser fixed block and laser 5 screw thread fixed connection.
Referring to fig. 15 to 20, the method for reconstructing the concentric conic polar geometry of the binocular ground at the axis end can be divided into the following five steps:
the first step is as follows: acquiring images of a concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
placing a shaft end grounding binocular reconstruction system of concentric secondary curve polar geometry on the horizontal ground, placing a two-dimensional target plate below a left camera 4, a right camera 6 and a laser 5, turning on the laser 5, and simultaneously collecting a plurality of images including the target plate 8, laser planes emitted by the laser 5 and laser lines intersected with the target plate 8 and a plurality of images including laser lines intersected with a contact disc 10 and laser planes emitted by the laser 5 and the contact disc 10 when a workbench moves by the left camera 4 and the right camera 6;
the second step is that: solving internal and external parameters of a left camera 4 and a right camera 6 of the concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
establishing an image coordinate system according to the image collected by the left camera 4, wherein the origin of the coordinate system of the target plate 8 is positioned at the center of the secondary curve pattern of the target plate 8, and the conversion relation of the secondary curve from the coordinate system of the target plate 8 to the image coordinate system is
Figure BSA0000199864170000091
Wherein
Figure BSA0000199864170000092
The image coordinates of the jth quadratic curve in the ith image,
Figure BSA0000199864170000093
the coordinates of the target plate 8 coordinate system being a quadratic curve,
Figure BSA0000199864170000094
is a homography from the target plate 8 coordinate system to the image coordinate system;
according to the conversion relation of the quadratic curve from the coordinate system of the target plate 8 to the image coordinate system
Figure BSA0000199864170000095
Will be provided with
Figure BSA0000199864170000096
And
Figure BSA0000199864170000097
substituted into the above formula to obtain
Figure BSA0000199864170000098
Three or more than three of the above relations can be obtained by three or more than three quadratic curves, and the relation can be obtained
Figure BSA0000199864170000099
Respectively decomposing by singular value decomposition
Figure BSA00001998641700000910
Figure BSA00001998641700000911
Can be sequentially obtained
Figure BSA00001998641700000912
Thereby obtaining a homography matrix
Figure BSA00001998641700000913
According to Zhangyingyou scaling, it is possible to use homography matrix
Figure BSA0000199864170000101
Determining the internal parameter K of the left camera 4LAnd extrinsic parameters
Figure BSA0000199864170000102
Meanwhile, an image coordinate system is established according to the image acquired by the right camera 6, and a conversion relation of a quadratic curve from the target plate 8 coordinate system to the image coordinate system can be obtained
Figure BSA0000199864170000103
Wherein
Figure BSA0000199864170000104
The image coordinates of the jth quadratic curve in the ith image,
Figure BSA0000199864170000105
the coordinates of the target plate 8 coordinate system being a quadratic curve,
Figure BSA0000199864170000106
is a homography from the target plate 8 coordinate system to the image coordinate system;
according to the conversion relation of the quadratic curve from the coordinate system of the target plate 8 to the image coordinate system
Figure BSA0000199864170000107
Will be provided with
Figure BSA0000199864170000108
And
Figure BSA0000199864170000109
substituted into the above formula to obtain
Figure BSA00001998641700001010
Three or more than three of the above relations can be obtained through three or more than three quadratic curves to obtain
Figure BSA00001998641700001011
Respectively decomposing by singular value decomposition
Figure BSA00001998641700001012
Figure BSA00001998641700001013
Can be sequentially obtained
Figure BSA00001998641700001014
Thereby obtaining a homography matrix
Figure BSA00001998641700001015
According to the method of expanding friends, the homography matrix can be used
Figure BSA00001998641700001016
Determining the internal parameter K of the left camera 4RAnd extrinsic parameters
Figure BSA00001998641700001017
The third step: solving the optical plane coordinates of the left camera 4 coordinate system of the concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
an image coordinate system is established according to the image collected by the left camera 4, and the relationship among the pole of the secondary curve, the polar line and the secondary curve in the image coordinate system is known as
Figure BSA00001998641700001018
Wherein
Figure BSA00001998641700001019
The pole of the quadratic curve is the pole of the quadratic curve,
Figure BSA00001998641700001020
polar line coordinates and conic coordinates in the image coordinate system can be extracted by Hough transformation to obtain polar line of conic curve
Figure BSA00001998641700001021
The intersection point of the polar line and the secondary curve is set as
Figure BSA00001998641700001022
The relationship between the tangent line of the intersection point and the line of polar line is
Figure BSA0000199864170000111
Wherein
Figure BSA0000199864170000112
Is a tangent line passing through the intersection point, and the relationship among the intersection point, the tangent line passing through the intersection point and the pole is
Figure BSA0000199864170000113
Two-way typeThe intersection point of polar line and secondary curve can be obtained simultaneously
Figure BSA0000199864170000114
Coordinates of intersection points on image coordinate system
Figure BSA0000199864170000115
Coordinates to the target plate 8 coordinate system
Figure BSA0000199864170000116
Has a conversion relation of
Figure BSA0000199864170000117
Coordinates of the target board 8 coordinate system
Figure BSA0000199864170000118
To the left camera 4 coordinate system
Figure BSA0000199864170000119
Has a conversion relation of
Figure BSA00001998641700001110
The intersection point is then in the left camera 4 coordinate system
Figure BSA00001998641700001111
In relation to the laser plane
Figure BSA00001998641700001112
The laser plane pi in the coordinate system of the left camera 4 can be obtained by a singular value decomposition methodCL；
An image coordinate system is established according to the image collected by the right camera 6, and the relationship among the pole of the secondary curve, the polar line and the secondary curve in the image coordinate system is known as
Figure BSA00001998641700001113
Wherein
Figure BSA00001998641700001114
The pole of the quadratic curve is the pole of the quadratic curve,
Figure BSA00001998641700001115
polar line coordinates and conic coordinates in the image coordinate system can be extracted by Hough transformation to obtain polar line of conic curve
Figure BSA00001998641700001116
The intersection point of the polar line and the secondary curve is set as
Figure BSA00001998641700001117
The relationship between the tangent line of the intersection point and the crossing point and the polar line is known as
Figure BSA00001998641700001118
Wherein
Figure BSA00001998641700001119
Is a tangent of the crossing point, and the relation among the crossing point, the tangent of the crossing point and the pole is known as
Figure BSA00001998641700001120
The two simultaneous methods can obtain the intersection point of polar line and secondary curve
Figure BSA00001998641700001121
Coordinates of intersection points on image coordinate system
Figure BSA00001998641700001122
Coordinates to the target plate 8 coordinate system
Figure BSA00001998641700001123
Has a conversion relation of
Figure BSA00001998641700001124
Coordinates of the target board 8 coordinate system
Figure BSA00001998641700001125
To the right camera 6 coordinate system
Figure BSA00001998641700001126
Has a conversion relation of
Figure BSA00001998641700001127
The intersection point is then in the right camera 6 coordinate system
Figure BSA00001998641700001128
And laser plane piCRIn a relationship of
Figure BSA00001998641700001129
Obtaining laser plane pi in left camera 4 coordinate system by singular value decomposition methodCR；
The fourth step: left camera 4, right camera 6 internal and external parameters and left camera 4 light plane coordinate pi of shaft end grounding binocular reconstruction method of concentric quadratic curve polar line geometryCLOptimizing:
homography matrix from right camera 6 coordinate system to left camera 4 coordinate system is
Figure BSA0000199864170000121
Obtaining the light plane coordinate pi of the 6 coordinate system of the right cameraCRTo the left camera 4 coordinate system light plane coordinate piCLHas a conversion relation of
πCL＝Hi，qπCR
Establishing an objective optimization function
Figure BSA0000199864170000122
Solving each optimized parameter pi by adopting a bundle set adjusting method and an LM methodCL、
Figure BSA0000199864170000123
The fifth step: rebuilding the contact disc characteristic points of the concentric quadratic curve polar line geometric shaft end grounding binocular rebuilding method under the left camera 4 coordinate system:
feature point W in the left camera 4 coordinate systemCLAnd the plane of light piCLIn a relationship of
(WCL)TπCL＝0
Feature point W in the left camera 4 coordinate systemCLAnd feature point image coordinates wCLIn a relationship of
WCL＝(KL)-1wCL
The characteristic point W in the coordinate system of the left camera 4 is calculatedCLAnd the plane of light piCLAnd the feature point W in the left camera 4 coordinate systemCLAnd feature point image coordinates wCLBy simultaneous correlation of (A) and (B), W can be obtainedCL；
Feature point W in the coordinate system of the right camera 6CRAnd the plane of light piCRIn a relationship of
(WCR)TπCR＝0
Feature point W in the coordinate system of the right camera 6CRAnd feature point image coordinates wCRIn a relationship of
WCR＝(KL)-1wCR
Feature point W in the coordinate system of the right camera 6CRAnd the plane of light piCRAnd the feature point W in the left camera 4 coordinate systemCRAnd feature point image coordinates wCRBy simultaneous correlation of (A) and (B), W can be obtainedCR；
From the right camera 6 coordinate system to the left camera 4Homography matrix of mark system
Figure BSA0000199864170000124
The feature point W in the coordinate system of the right camera 6 can be knownCRWith the feature point W in the left camera 4 coordinate systemCLIn a relationship of
WCL＝Hi，qWCR
The characteristic point coordinate W of the coordinate system of the right camera 6 can be obtained by the above formulaCRAnd uniformly converting into a coordinate system of the left camera 4.

Claims (10)

1. The shaft end grounding binocular reconstruction system of the concentric secondary curve polar line geometry is characterized by comprising a base (1), a support rod (2), a laser connecting rod (3), a left camera (4), a laser (5), a right camera (6), a camera connecting block (7), a target plate (8), a linear sliding table (9), a connecting rod (11), a support rod fixing block (12), a connecting rod fixing block (13) and a laser fixing block (14);
the base (1) is placed on a flat ground, the bottoms of four supporting rods (2) are placed on the base (1), a bolt penetrates through holes at the bottoms of the four supporting rods (2) from top to bottom and is fixedly connected with a thread through hole on the upper surface of the base (1) in a threaded manner, a straight sliding table (9) is placed in the middle of the base (1) and is fixedly connected with the bolt of the base (1), a target board (8) during calibration is placed on a workbench of the straight sliding table (9), a contact disc (10) is placed on the workbench of the straight sliding table (9) during reconstruction, the through holes at one ends of four supporting rod fixing blocks (12) are respectively sleeved in the thread holes of the supporting rods (2) along the axial diameter direction of the four supporting rods (2), the bolt penetrates through a circular through hole at the end of the supporting rod fixing block (12) and is fixedly connected with the thread of the supporting rods (2), one ends of two connecting, the through holes of the two camera connecting blocks (7) are respectively sleeved in the connecting rod (11) and then moved to the middle threaded hole part of the connecting rod (11), a bolt passes through the circular through hole of the camera connecting block (7) and is fixedly connected with the connecting rod (11) by threads, the through holes at one ends of the two connecting rod fixing blocks (13) are respectively sleeved in the two connecting rods (11) and then are moved to the threaded hole parts of the connecting rod (11), the bolt passes through the circular through hole at the bottom end of the connecting rod fixing block (13) and is fixedly connected with the connecting rod (11) by threads, the two connecting rods (11) penetrate through the through holes at the other ends of the two supporting rod fixing blocks (12), the bolt passes through the circular through hole at one end of the two supporting rod fixing blocks (12) and is fixedly connected with the connecting rod (11) by threads, one end of the laser connecting rod (3) penetrates through, the bolt passes the circular through-hole in laser fixed block (14) bottom and laser connecting rod (3) screw thread fixed connection, camera connecting block (7) front end ring is emboliaed respectively to left side camera (4) and right camera (6) front end top-down, the three screw hole and left camera (4) and right camera (6) fixed connection that the bolt passed camera connecting block (7) ring, laser instrument (5) penetrate the round hole of laser fixed block (14) front end from bottom to top, the bolt passes laser fixed block (14) one end screw hole and laser instrument (5) screw thread fixed connection.
2. The axial-end grounded binocular reconstruction system of the concentric quadric curvilinear polar geometry as claimed in claim 1, wherein the support rod (2) is vertically welded by a cylindrical long rod with a threaded hole formed at the upper end and a circular iron sheet with six circular through holes uniformly formed at the upper end.
3. The axial end grounding binocular reconstruction system of concentric conic epipolar geometry of claim 1, wherein said laser connecting rod (3) is a cylindrical long rod with a threaded bore.
4. The axial-grounded binocular reconstruction system of concentric conic epipolar geometry of claim 1, wherein said left video camera (4) is a wide-angle industrial camera fitted with a narrow-band filter.
5. The axial-end grounded binocular reconstruction system of concentric conic epipolar geometry of claim 1, wherein said laser (5) is a cylindrical part emitting a laser plane.
6. The axial-end grounded binocular reconstruction system of concentric conic polar geometry of claim 1, wherein the camera attachment block (7) is welded by an iron ring having a threaded hole and a rectangular iron block having two circular through holes with axes perpendicular to each other.
7. The axial-end grounded binocular reconstruction system of the concentric conic epipolar geometry of claim 1, wherein the target board (8) is a flat board with a surface to which the concentric conic is affixed.
8. The axial-end grounding binocular reconstruction system of the concentric quadratic curvilinear polar geometry according to claim 1, wherein the support rod fixing block (12) is a rectangular parallelepiped iron block with two circular through holes with mutually perpendicular axes machined on the surface and a circular through hole machined at each of two ends.
9. The axial-end grounded binocular reconstruction system of the concentric conic polar geometry of claim 1, wherein the connecting rod fixing block (13) is a rectangular iron block having two circular through holes with axes perpendicular to each other and having a circular through hole at each of both ends.
10. The reconstruction method of the axial-end grounded binocular reconstruction system of the concentric conic epipolar geometry according to claims 1 to 9, comprising the specific steps of:
the first step is as follows: and (3) acquiring images of shaft end grounding binocular reconstruction of concentric quadratic curve polar line geometry:
the first step is as follows: acquiring images of a concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
the method comprises the steps that a shaft end grounding binocular reconstruction system of concentric secondary curve polar line geometry is placed on the horizontal ground, a two-dimensional target plate is placed below a left camera (4), a right camera (6) and a laser (5), the laser (5) is turned on, and the left camera (4) and the right camera (6) simultaneously acquire images of a plurality of laser lines which comprise the target plate (8) and are formed by intersecting a laser plane sent by the laser (5) and the target plate (8) and images of laser lines which are formed by intersecting a contact disc (10) and a laser plane sent by the laser (5) and the contact disc (10) when a plurality of workbenches move;
the second step is that: solving internal and external parameters of a left camera (4) and a right camera (6) of the concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
an image coordinate system is established according to the image collected by the left camera (4), the origin of the coordinate system of the target plate (8) is positioned at the center of the secondary curve pattern of the target plate (8), and the conversion relation of the secondary curve from the coordinate system of the target plate (8) to the image coordinate system is
Figure FSA0000199864160000021
Wherein
Figure FSA0000199864160000022
The image coordinates of the jth quadratic curve in the ith image,
Figure FSA0000199864160000023
is the coordinates of the coordinate system of the target plate (8) of the quadratic curve,
Figure FSA0000199864160000024
is a homography from the target plate (8) coordinate system to the image coordinate system;
according to the conversion relation of the quadratic curve from the coordinate system of the target plate (8) to the image coordinate system
Figure FSA0000199864160000031
Will be provided with
Figure FSA0000199864160000032
And
Figure FSA0000199864160000033
substituted into the above formula to obtain
Figure FSA0000199864160000034
Three or more than three of the above relations can be obtained by three or more than three quadratic curves, and the relation can be obtained
Figure FSA0000199864160000035
Respectively decomposing by singular value decomposition
Figure FSA0000199864160000036
Figure FSA0000199864160000037
Can be sequentially obtained
Figure FSA0000199864160000038
Thereby obtaining a homography matrix
Figure FSA0000199864160000039
According to Zhangyingyou scaling, it is possible to use homography matrix
Figure FSA00001998641600000319
Determining the internal parameters K of the left camera (4)LAnd extrinsic parameters
Figure FSA00001998641600000310
Meanwhile, an image coordinate system is established according to the image acquired by the right camera (6), and a conversion relation of a quadratic curve from the coordinate system of the target plate (8) to the image coordinate system can be obtained
Figure FSA00001998641600000311
Wherein
Figure FSA00001998641600000312
The image coordinates of the jth quadratic curve in the ith image,
Figure FSA00001998641600000313
is the coordinates of the coordinate system of the target plate (8) of the quadratic curve,
Figure FSA00001998641600000314
is a homography from the target plate (8) coordinate system to the image coordinate system;
according to the conversion relation of the quadratic curve from the coordinate system of the target plate (8) to the image coordinate system
Figure FSA00001998641600000315
Will be provided with
Figure FSA00001998641600000316
And
Figure FSA00001998641600000317
substituted into the above formula to obtain
Figure FSA00001998641600000318
Three or more than three of the above relations can be obtained through three or more than three quadratic curves to obtain
Figure FSA0000199864160000041
Respectively decomposing by singular value decomposition
Figure FSA0000199864160000042
Figure FSA0000199864160000043
Can be sequentially obtained
Figure FSA0000199864160000044
Thereby obtaining a homography matrix
Figure FSA0000199864160000045
According to the method of expanding friends, the homography matrix can be used
Figure FSA0000199864160000046
Determining the internal parameters K of the left camera (4)RAnd extrinsic parameters
Figure FSA0000199864160000047
The third step: solving the optical plane coordinates of the left camera (4) coordinate system of the concentric quadratic curve polar line geometric shaft end grounding binocular reconstruction method:
an image coordinate system is established according to the image collected by the left camera (4), and the relationship among the pole of the secondary curve, the polar line and the secondary curve in the image coordinate system is known as
Figure FSA0000199864160000048
Wherein
Figure FSA0000199864160000049
The pole of the quadratic curve is the pole of the quadratic curve,
Figure FSA00001998641600000410
polar line coordinates and conic coordinates in the image coordinate system can be extracted by Hough transformation to obtain polar line of conic curve
Figure FSA00001998641600000411
The intersection point of the polar line and the secondary curve is set as
Figure FSA00001998641600000412
The relationship between the tangent line of the intersection point and the line of polar line is
Figure FSA00001998641600000413
Wherein
Figure FSA00001998641600000414
Is a tangent line passing through the intersection point, and the relationship among the intersection point, the tangent line passing through the intersection point and the pole is
Figure FSA00001998641600000415
The two simultaneous methods can obtain the intersection point of polar line and secondary curve
Figure FSA00001998641600000416
Coordinates of intersection points on image coordinate system
Figure FSA00001998641600000417
To the coordinates of the target plate (8) coordinate system
Figure FSA00001998641600000418
Has a conversion relation of
Figure FSA00001998641600000419
Coordinates of the coordinate system of the target plate (8)
Figure FSA00001998641600000420
To the left camera (4) coordinate system
Figure FSA00001998641600000421
Has a conversion relation of
Figure FSA00001998641600000422
Then take a picture on the leftIntersection point in machine (4) coordinate system
Figure FSA00001998641600000423
In relation to the laser plane
Figure FSA00001998641600000424
The laser plane pi in the coordinate system of the left camera (4) can be obtained by a singular value decomposition methodCL；
An image coordinate system is established according to the image collected by the right camera (6), and the relationship among the pole of the secondary curve, the polar line and the secondary curve in the image coordinate system is known as
Figure FSA00001998641600000425
Wherein
Figure FSA00001998641600000426
The pole of the quadratic curve is the pole of the quadratic curve,
Figure FSA00001998641600000427
polar line coordinates and conic coordinates in the image coordinate system can be extracted by Hough transformation to obtain polar line of conic curve
Figure FSA00001998641600000428
The intersection point of the polar line and the secondary curve is set as
Figure FSA00001998641600000429
The relationship between the tangent line of the intersection point and the crossing point and the polar line is known as
Figure FSA00001998641600000430
Wherein
Figure FSA0000199864160000051
Is a tangent of the crossing point, and the relation among the crossing point, the tangent of the crossing point and the pole is known as
Figure FSA0000199864160000052
The two simultaneous methods can obtain the intersection point of polar line and secondary curve
Figure FSA0000199864160000053
Coordinates of intersection points on image coordinate system
Figure FSA0000199864160000054
To the coordinates of the target plate (8) coordinate system
Figure FSA0000199864160000055
Has a conversion relation of
Figure FSA0000199864160000056
Coordinates of the coordinate system of the target plate (8)
Figure FSA0000199864160000057
To the right camera (6) coordinate system
Figure FSA0000199864160000058
Has a conversion relation of
Figure FSA0000199864160000059
Then in the right camera (6) coordinate system, the intersection point
Figure FSA00001998641600000510
And laser plane piCRIn a relationship of
Figure FSA00001998641600000511
The laser plane pi in the coordinate system of the left camera (4) is obtained by a singular value decomposition methodCR；
The fourth step: left camera (4), right camera (6) internal and external parameters and left camera (4) light plane coordinate pi of shaft end grounding binocular reconstruction method of concentric quadratic curve polar line geometryCLOptimizing:
the homography matrix from the coordinate system of the right camera (6) to the coordinate system of the left camera (4) is
Figure FSA00001998641600000512
The light plane coordinate pi of the coordinate system of the right camera (6) can be obtainedCRTo the left camera (4) coordinate system light plane coordinate piCLHas a conversion relation of
πCL＝Hi，qπCR
Establishing an objective optimization function
Figure FSA00001998641600000513
Calculating each optimized parameter by bundle set adjustment method and LM method
Figure FSA00001998641600000514
The fifth step: rebuilding the contact disc characteristic points of the concentric quadratic curve polar line geometric shaft end grounding binocular rebuilding method under the coordinate system of the left camera (4):
characteristic point W in the coordinate system of the left camera (4)CLAnd the plane of light piCLIn a relationship of
(WCL)TπCL＝0
Characteristic point W in the coordinate system of the left camera (4)CLAnd feature point image coordinates wCLIn a relationship of
WCL＝(KL)-1wCL
The characteristic point W in the coordinate system of the left camera (4) is calculatedCLAnd the plane of light piCLAnd a feature point W in the left camera (4) coordinate systemCLAnd feature point image coordinates wCLBy simultaneous correlation of (A) and (B), W can be obtainedCL；
Characteristic point W in the coordinate system of the right camera (6)CRAnd the plane of light piCRIn a relationship of
(WCR)TπCR＝0
Characteristic point W in the coordinate system of the right camera (6)CRAnd feature point image coordinates wCRIn a relationship of
WCR＝(KL)-1wCR
Characteristic point W in the coordinate system of the right camera (6)CRAnd the plane of light piCRAnd a feature point W in the left camera (4) coordinate systemCRAnd feature point image coordinates wCRBy simultaneous correlation of (A) and (B), W can be obtainedCR；
Homography matrix from right camera (6) coordinate system to left camera (4) coordinate system
Figure FSA0000199864160000061
The feature point W in the coordinate system of the right camera (6) can be knownCRWith the feature point W in the coordinate system of the left camera (4)CLIn a relationship of
WCL＝Hi，qWCR
The characteristic point coordinate W in the coordinate system of the right camera (6) can be obtained by the above formulaCRAnd uniformly converting the coordinate system into a coordinate system of the left camera (4).
CN201911426735.XA 2019-12-31 2019-12-31 Shaft end grounding binocular reconstruction system and method for concentric quadratic curve polar line geometry Pending CN111174726A (en)

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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114152202A (en) * 2021-11-26 2022-03-08 东风设备制造有限公司 Device for optically detecting undercut groove and undercut groove optical detection system

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114152202A (en) * 2021-11-26 2022-03-08 东风设备制造有限公司 Device for optically detecting undercut groove and undercut groove optical detection system

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