CN109900205B - High-precision single-line laser and optical camera rapid calibration method - Google Patents
High-precision single-line laser and optical camera rapid calibration method Download PDFInfo
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Abstract
The invention provides a high-precision fast calibration method of a single-line laser and an optical camera, which comprises the steps of firstly installing the laser and the camera, fixing the camera and the single-line laser on the same measurement device, then laying a photogrammetry control field in a room to obtain accurate coordinate values of a control point, then placing the measurement device in the photogrammetry control field to collect a group of effective data comprising camera image data and laser distance data, then calibrating the position and the posture of the camera according to the camera image data, then calibrating the position and the posture of the laser according to the laser distance data, and finally obtaining external parameters of the single-line laser and the camera by taking a control field coordinate system as an intermediary. Compared with the traditional calibration method, the method not only can simplify the calibration process and obviously reduce the observation times, but also can obtain high enough precision and stability.
Description
Technical Field
The invention relates to the technical field of computer vision and mobile measurement, in particular to a calibration system and a calibration method between a single-line laser and an optical camera.
Background
In the fields of surveying and mapping, motion measurement and instant positioning and mapping, two sensors, a high-resolution camera and a single-line laser, are often used in combination. The camera can provide color and texture information of the surrounding scene, but the imaging process of the camera cannot obtain accurate object distance information. Compared with a camera, the single-line laser can obtain high-precision object distance information in the field of view of the camera, but the resolution is low, and texture information is missing or not abundant. In order to fully utilize the advantages of the two sensors and simultaneously obtain the three-dimensional geometric and color texture information of the scene, the data of the two sensors needs to be fused. Because of the difference of the installation position, the acquisition mode and the expression of the reference coordinate, the data of the two sensors are required to be in one-to-one correspondence, and the first problem is to calibrate rigid body transformation parameters between the laser and the optical camera, namely external parameters such as a rotation matrix, a translation vector and the like between a laser coordinate system and a camera coordinate system.
The existing calibration method generally has the following two problems that firstly, at least a plurality of groups of observation data under different postures need to be collected to solve an equation theoretically, and in practice, in order to obtain higher precision, even more than 20 groups of observation need to be carried out, and the calibration process is complicated and time-consuming. Secondly, optimizing the initial value of the external parameter by using an LM optimization method in the calibration process, wherein if the initial value is inaccurate, the final solution may fall into a local minimum value, and a stable external parameter solution cannot be obtained.
The invention provides a method for quickly calibrating a single-line laser and an optical camera based on a photogrammetric control field, which not only can simplify a calibration process and obviously reduce observation times, but also can obtain high enough precision and stability.
Disclosure of Invention
The invention provides a single-line laser and camera external reference calibration method based on a control field. The position relation of the camera and the laser relative to the control field reference coordinate system is solved by using a Direct Linear Transformation (DLT) method and a three-point perspective (P3P) method respectively by taking a high-precision control field as a common reference standard.
The technical scheme adopted by the invention is as follows: a high-precision single-line laser and optical camera rapid calibration method comprises the following steps: firstly, a laser and a camera are installed, the camera and the single-line laser are fixed on the same measuring device, then a photogrammetry control field is arranged in a room to obtain accurate coordinate values of control points, then the measuring device is placed in the photogrammetry control field to collect a group of effective data including camera image data and laser distance data, then the position and the posture of the camera are calibrated according to the camera image data, then the position and the posture of the laser are calibrated according to the laser distance data, and finally the control field coordinate system is used as an intermediary to obtain external parameters of the single-line laser and the camera.
The method specifically comprises the following steps:
(1) and installing a laser and a camera, fixing the camera and the single-line laser on the same measuring device, ensuring that the positions between the camera and the single-line laser are not changed, and defining a laser coordinate system and a camera coordinate system. According to the working principle of a line laser, a laser coordinate system is set, wherein a laser scanning center is used as an original point, and a scanning plane is used as an x-o-z plane to establish a right-hand system. The camera coordinate system is established according to the pinhole imaging model, an x-o-y plane is established by taking the optical center of the camera as an origin and being parallel to an imaging plane, and a right-hand system is established by taking the front of the optical center as a z-axis.
(2) A photogrammetry control field is arranged in a room, a large number of targets and markers are placed in a three-dimensional space, and a total station is used for measuring the accurate coordinates of a control point in a control field coordinate system. The control field coordinate system is a right-hand system which is established by taking the vertex of a wall corner of the control field as an origin and dividing three edges of the wall corner into an x axis, a y axis and a z axis.
(3) The measuring device is placed in a photogrammetry control field, the laser acquisition equipment and the camera equipment are opened, and the position of the equipment is adjusted, so that the laser can be ensured to be simultaneously emitted to three surfaces of a corner of the control field, and meanwhile, the camera can shoot enough target points. And after the equipment works stably, acquiring a group of observation data including camera image data and laser distance data.
(4) And calibrating the position and the posture of the camera according to the camera image data. The pixel coordinates of the control points are selected from the image, and a collinear condition equation can be established according to the condition that the optical center of the camera, the image points of the control points and the control points in the three-dimensional space are collinear. And (3) linearizing the internal reference and external reference elements of the camera in the collinear equation to obtain a linearized form of the collinear equation, and solving the linearized form to finally obtain the position and the posture of the camera in a control field coordinate system.
(5) And calibrating the position and the posture of the laser according to the laser distance data. Laser points hitting three planes of the wall corner are selected from the laser distance data, the laser points are fitted respectively to obtain three laser line equations, intersection points between every two of the three lines are solved, and coordinates of the three intersection points in a laser coordinate system are obtained. And calculating the distance between every two three intersection points, wherein the three laser intersection points and the vertex of the corner form a vertical triangular pyramid, and the distance from the laser point to the vertex of the corner can be obtained by utilizing the pythagorean theorem, namely the coordinates of the three intersection points under the control field coordinate system are obtained. And finally, solving the position and the posture of the laser in the control field coordinate system by using different coordinate values of the three points in the two coordinate systems.
(6) The method comprises the following steps of jointly calibrating a laser and a camera, establishing a relation between a camera coordinate system and a laser coordinate system relative to a control field coordinate system through the steps, and obtaining a conversion relation between the laser coordinate system and the camera coordinate system through coordinate transformation by using the control field coordinate system as a medium, namely the external reference between a laser and the camera which are required to be calibrated.
Further, the specific implementation manner of the step (4) is as follows,
let the camera internal parameter be (x)0，y0，f)，(x0，y0) Representing the coordinates of the image principal point, and f represents the focal length of the camera, and the value of the focal length can be obtained through camera internal reference calibration. Two external parameters of the camera in the control field are (R)CW，TCW)，RCWRepresenting a 3 x 3 rotation matrix formed by rotation about 3 coordinate axes, TCWA translation vector representing 3 × 1 of the origin of the camera coordinate system relative to the origin of the control field coordinate system;
TCW＝(XsYsZs)T
camera origin S ═ XsYsZs)TControl point A ═ X Y Z)TAnd the corresponding image point a ═ x, y on the photo is collinear, and the collinear condition equation can be expressed as:
using the unknown parameter in the above formula as l1-l11And expressing to obtain an equation form only related to the coordinates of the image point and the coordinates of the control point, wherein the equation form is as follows:
further simplification of the above equation yields a linearized form of the collinearity equation:
when there are n control points in the control field, 2n equations can be listed, written in matrix form as follows:
recording a left coefficient matrix of the equation as A, recording an unknown number as X, and recording a value on the right of the equation as L; according to the least square method, the solution of the unknowns can be found as:
X＝(ATA)-1ATL
solving the above equation yields the coefficient l1-l11The translation vector of the camera external parameter satisfies the following relationship:
solving three unknowns of the translation vector by a simultaneous equation, and determining the position of the camera in a control field coordinate system;
in the same way, coefficient liThe relationship between (i ═ 1, 2 … 11) and the three rotation angles that make up the rotation matrix is as follows:
three angles forming a rotation matrix can be obtained by the formula, and the posture of the camera in a control field coordinate system is determined;
through the process, the external parameter (R) of the camera in the control field coordinate system is finally obtainedCW，TCW)。
Further, the specific implementation manner of the step (5) is as follows,
three planes with corners are denoted respectively as pi1、Π2And pi3The scanning surface of the single-line laser and three edges of the wall corner are respectively intersected at P1、P2And P3Three points, wherein P1And P2Dividing the laser point into three sections, respectively marked as L1、L2And L3；
Fitting the laser points on the three planes to obtain a linear equation L of three laser line segments1、L2And L3And performing cross multiplication on every two points to calculate the intersection point of the straight lines, and obtaining the coordinates of the three intersection points under the laser coordinate system as follows:
the three intersection points and the origin O of the control field coordinate system form a vertical triangular pyramid, and the lengths of three base sides of the triangular pyramid are recorded as d1，d2，d3The calculation formula is as follows:
setting OP1、OP2And OP3Length is respectively lambda1、λ2And λ3And because the three edges are vertical to each other, the following results are obtained according to the pythagorean theorem:
there are eight possible sets of solutions to the above equation, but the lengths of the three edges in the control field are all greater than zero, and the only real solution for this equation is derived:
in the control field coordinate system, three intersection points are located on three coordinate axes, and the lengths of the three edges are known, so the coordinates of the three intersection points in the control field coordinate system can be expressed as:
(P1，P2，P3) And (Q)1，Q2，Q3) The coordinates of the three intersection points in the laser coordinate system and in the control field coordinate system, respectively, so that the rotation matrix R between the two coordinate systems is solvedLWAnd translation vector TLWA three-point correspondence problem is formed, which is solved as follows:
1) setting P1As an origin, the x-axis is set to P2P1Unit vector of (d):
2) the y-axis is set as a unit vector perpendicular to the x-axis on a plane formed by three points:
3) the z-axis is set perpendicular to both the unit vectors which are the x-axis and the y-axis:
4) the rotation matrix in the laser coordinate system is thus represented as:
R1＝[vxvyvz]
5) to Q1、Q2、Q3The same process is repeated to calculate a rotation matrix R under a control field coordinate system2；
6) Therefore, the rotation matrix between two coordinate axes can be expressed as:
RLW＝R1R2 -1
7) the translation vector between the two coordinate systems can be expressed as:
thus, the external parameter (R) of the laser coordinate system under the control field coordinate system is obtainedLW，TLW)。
Further, the specific implementation manner of the step (6) is as follows,
for any point P in space, the coordinate in the control field coordinate system is Pw＝(Xw，Yw，Zw)TThe coordinate in the camera coordinate system is Pc＝(Xc，Yc，Zc)TThe coordinate in the laser coordinate system is Pl＝(Xl，Yl，Zl)TThen the three satisfy the following relationship:
Pc＝RCWPw+TCW
Pl＝RLWPw+TLW
combining two formulas, external reference (R) from laser coordinate system to camera coordinate systemCL，TCL) Can be expressed as:
compared with the prior art, the method can quickly finish the calibration of the single-line laser and the camera, can ensure higher precision, and has higher practicability in engineering practice.
Drawings
FIG. 1 is a schematic view of a measuring device according to the present invention;
FIG. 2 is a flow chart of the method of the present invention;
FIG. 3 is a schematic diagram of the apparatus coordinate system of the present invention;
FIG. 4 is a diagram of a photogrammetric control field layout of the present invention;
FIG. 5 is a schematic diagram of the optical camera calibration process of the present invention;
FIG. 6 is a schematic diagram of the single line laser calibration process of the present invention.
Detailed Description
The invention will now be described in further detail with reference to the figures and specific embodiments.
FIG. 1 is a calibrated apparatus of the present invention, which contains a panoramic camera and 3 single line lasers. The invention relates to a method for calibrating external parameters of a single-line laser and a camera, which comprises the steps of firstly installing the laser and the camera, fixing the camera and the single-line laser on the same measuring device, then laying a photogrammetry control field in a room to obtain accurate coordinate values of a control point, then placing the measuring device in the photogrammetry control field to collect a group of effective data, then calibrating the position and the posture of the camera according to camera image data, then calibrating the position and the posture of the laser according to laser distance data, and finally using a control field coordinate system as an intermediary to obtain the external parameters of the single-line laser and the camera. The general flow of the laser and camera calibration method is shown in fig. 2. Next, embodiments of each part will be specifically described.
The method comprises the following steps: and a laser and a camera are arranged, the camera and the single-line laser are fixed on the same measuring device, and the position between the camera and the single-line laser is ensured not to change. The laser coordinate system and the camera coordinate system are defined next as shown in fig. 3. Setting a laser coordinate system O according to the working principle of line laserL-XLYLZLA right-handed system is established by taking a laser scanning center as an origin and a scanning plane as an x-o-z plane. Camera coordinate system Oc-XcYcZcAnd establishing an x-o-y plane parallel to an imaging plane by taking the optical center of the camera as an origin according to the pinhole imaging model, and establishing a right-hand system by taking the front of the optical center as a z-axis.
Step two: as shown in fig. 4, a photogrammetric control field is laid out in a room, a large number of targets and markers are placed in a three-dimensional space, and the precise coordinates of a control point in the control field coordinate system are measured with a total station. Wherein the control field coordinate system Ow-XwYwZwUsing the vertex of the wall corner of the control field as the origin, and three edges of the wall corner are respectivelyA right hand system is established for the x, y and z axes.
Step three: the measuring device is placed in a photogrammetry control field, the laser acquisition equipment and the camera equipment are opened, and the position of the equipment is adjusted, so that the laser can be ensured to be simultaneously emitted to three surfaces of a corner of the control field, and meanwhile, the camera can shoot enough target points. And after the equipment works stably, acquiring a group of observation data including camera image data and laser distance data.
Step four: let the camera internal parameter be (x)0，y0，f)，(x0，y0) Representing the coordinates of the principal point of the image, f representing the focal length of the camera, and the internal reference value can be obtained through calibration of the internal reference of the camera. Two external parameters of the camera in the control field are (R)CW，TCW)，，RCWRepresenting a 3 x 3 rotation matrix formed by rotation about 3 coordinate axes, TCWA translation vector representing the 3 x 1 of the origin of the camera coordinate system relative to the origin of the control field coordinate system.
TCW＝(XsYsZs)T
As shown in fig. 5, in the control field coordinate system, the origin coordinate of the camera is represented by S ═ X (X)sYsZs)TThe coordinate of the control point is A ═ X Y Z)TThe corresponding image point on the photo is (x, y). Three-point collinearity is satisfied in the imaging process, and a collinearity condition equation can be expressed as follows:
using the unknown parameter in the above formula as l1-l11And expressing to obtain an equation form only related to the coordinates of the image point and the coordinates of the control point, wherein the equation form is as follows:
further simplification of the above equation yields a linearized form of the collinearity equation:
when there are n control points in the control field, 2n equations can be listed, written in matrix form as follows:
let the left coefficient matrix of the equation be A, the unknowns be X, and the right value of the equation be L. According to the least square method, the solution of the unknowns can be found as:
X＝(ATA)-1ATL
solving the above equation yields the coefficient l1-l11The translation vector of the camera external parameter satisfies the following relationship:
the simultaneous equations solve for the three unknowns of the translation vector, determining the position of the camera in the control field coordinate system.
In the same way, coefficient liThe relationship between (i ═ 1, 2 … 11) and the three rotation angles that make up the rotation matrix is as follows:
the three angles that make up the rotation matrix are found from the above equation, determining the pose of the camera in the control field coordinate system.
Through the process, the external parameter (R) of the camera in the control field coordinate system is finally obtainedCW，TCW)。
Step five: as shown in FIG. 6, three planes of the corner are denoted as |, respectively1、∏2And II3. Three edges of scanning surface and wall corner of single-line laserRespectively intersect at P1、P2And P3Three points, wherein P1And P2Dividing the laser point into three sections, respectively marked as L1、L2And L3。
Fitting the laser points on the three planes to obtain a linear equation L of three laser line segments1、L2And L3. And performing cross multiplication on every two points to calculate the intersection point of the straight lines, and obtaining the coordinates of the three intersection points under a laser coordinate system as follows:
the three intersection points and the origin O of the control field coordinate system form a vertical triangular pyramid, and the lengths of three base sides of the triangular pyramid are recorded as d1，d2，d3The calculation formula is as follows:
setting OP1、OP2And OP3Length is respectively lambda1、λ2And λ3. Because two of three edges are perpendicular, can obtain according to the pythagorean theorem:
there are eight possible sets of solutions to the above equation, but the lengths of the three edges in the control field are all greater than zero, and the only real solution for this equation can be derived:
in the control field coordinate system, three intersection points are located on three coordinate axes, and the lengths of the three edges are known, so the coordinates of the three intersection points in the control field coordinate system can be expressed as:
(P1，P2，P3) And (Q)1，Q2，Q3) The coordinates of the three intersection points in the laser coordinate system and in the control field coordinate system, respectively, so that the rotation matrix R between the two coordinate systems is solvedLWAnd translation vector TLWA three-point correspondence problem is formed, which is solved as follows:
1) setting P1As an origin, the x-axis is set to P2P1Unit vector of (d):
2) the y-axis is set as a unit vector perpendicular to the x-axis on a plane formed by three points:
3) the z-axis is set perpendicular to both the unit vectors which are the x-axis and the y-axis:
4) the rotation matrix in the laser coordinate system is thus represented as:
R1＝[vxvyvz]
5) to Q1、Q2、Q3The same process is repeated to calculate a rotation matrix R under a control field coordinate system2。
6) Therefore, the rotation matrix between two coordinate axes can be expressed as:
RLW＝R1R2 -1
7) the translation vector between the two coordinate systems can be expressed as:
to this end, we obtain an external reference (R) of the laser coordinate system under the control field coordinate systemLW，TLW)。
Step six: establishing the relation between the camera coordinate system and the laser coordinate system relative to the control field coordinate system through the fourth step and the fifth step, and then obtaining the conversion relation between the laser coordinate system and the camera coordinate system through coordinate transformation by using the control field coordinate system as a medium. For any point P in space, the coordinate in the control field coordinate system is Pw＝(Xw，Yw，Zw)TThe coordinate in the camera coordinate system is Pc＝(Xc，Yc，Zc)TThe coordinate in the laser coordinate system is Pl＝(Xl，Yl，Zl)T. The three satisfy the following relationship:
Pc＝RCWPw+TCW
Pl＝RLWPw+TLW
combining two formulas, external reference (R) from laser coordinate system to camera coordinate systemCL，TCL) Can be expressed as:
by means of the control field coordinate system, the relation between the laser and the camera can be conveniently established. After the conversion from the camera coordinate system and the laser coordinate system to the control field coordinate system is determined, the external parameters between the laser and the camera can be calculated according to the formula.
The present invention is not limited to the above exemplary embodiments, and therefore, any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (3)
1. A high-precision single-line laser and optical area-array camera rapid calibration method is characterized by comprising the following steps: firstly, installing a laser and a camera, fixing the camera and the single-line laser on the same measuring device, then laying a photogrammetry control field in a room to obtain accurate coordinate values of control points, then placing the measuring device in the photogrammetry control field to collect a group of effective data comprising camera image data and laser distance data, then calibrating the position and the posture of the camera according to the camera image data, then calibrating the position and the posture of the laser according to the laser distance data, and finally obtaining external parameters of the single-line laser and the camera by taking a control field coordinate system as an intermediary; the method specifically comprises the following steps:
step (1), installing a laser and a camera, fixing the camera and the single-line laser on the same measuring device, ensuring that the position between the camera and the single-line laser is not changed, and defining a laser coordinate system and a camera coordinate system; according to the working principle of line laser, a laser coordinate system is set, wherein a laser scanning center is used as an original point, and a scanning plane is used as an x-o-z plane to establish a right-hand system; establishing a camera coordinate system according to a pinhole imaging model, establishing an x-o-y plane parallel to an imaging plane by taking a camera optical center as an origin, and establishing a right-hand system by taking the optical center in front of the optical center as a z axis;
step (2), a photogrammetry control field is arranged in a room, a large number of targets are arranged in a three-dimensional space, and a total station is used for measuring the accurate coordinates of a control point in a control field coordinate system; the control field coordinate system is a right-hand system which is established by taking the vertex of a wall corner of the photogrammetric control field as an origin and dividing three edges of the wall corner into an x axis, a y axis and a z axis;
step (3), placing the measuring device in a photogrammetry control field, opening laser acquisition equipment and camera equipment, adjusting the positions of the equipment, enabling laser to be simultaneously emitted to three surfaces of a corner of the photogrammetry control field, and enabling the camera to shoot enough target points; after the equipment works stably, acquiring a group of observation data comprising camera image data and laser distance data;
step (4), calibrating the position and the posture of the camera according to the camera image data; selecting pixel coordinates of control points from the image, establishing a collinear condition equation according to the condition that the optical center of the camera, the image points of the control points and the control points in the three-dimensional space are collinear, linearizing internal reference elements and external reference elements of the camera in the collinear equation to obtain a linearization form of the collinear equation, and solving the collinear equation in the linearization form to finally obtain the position and the posture of the camera in a control field coordinate system;
step (5), calibrating the position and the posture of the laser according to the laser distance data; selecting laser points hitting three planes of a wall corner from the laser distance data, respectively fitting the laser points to obtain three laser line equations, solving intersection points of the three laser lines in pairs to obtain coordinates of the three intersection points in a laser coordinate system, calculating the distance between the three intersection points in pairs to obtain the distance from the laser points to the top point of the wall corner, and obtaining the coordinates of the three intersection points in a control field coordinate system; finally, solving the position and the posture of the laser in the control field coordinate system by using different coordinate values of the three intersection points under the laser coordinate system and the control field coordinate system;
the specific implementation manner of the step (5) is as follows,
three planes with corners are denoted respectively as pi1、Π2And pi3The scanning surface of the single-line laser and three edges of the wall corner are respectively intersected at P1、P2And P3Three points, wherein P1And P2Dividing the laser point into three sections, respectively marked as L1、L2And L3；
Fitting the laser points on the three planes to obtain a linear equation L of three laser line segments1、L2And L3And performing cross multiplication on every two points to calculate the intersection point of the straight lines, and obtaining the coordinates of the three intersection points under the laser coordinate system as follows:
the three intersection points and the origin O of the control field coordinate system form a vertical triangular pyramid, and the lengths of three base sides of the triangular pyramid are recorded as d1，d2，d3The calculation formula is as follows:
setting OP1、OP2And OP3Length is respectively lambda1、λ2And λ3And because the three edges are vertical to each other, the following results are obtained according to the pythagorean theorem:
there are eight possible sets of solutions to the above equation, but the lengths of the three edges in the control field are all greater than zero, and the only real solution for this equation is derived:
in the control field coordinate system, three intersection points are located on three coordinate axes, and the lengths of the three edges are known, so that the coordinates of the three intersection points in the control field coordinate system are represented as follows:
(P1，P2，P3) And (Q)1，Q2，Q3) The coordinates of the three intersection points in the laser coordinate system and in the control field coordinate system, respectively, so that the rotation matrix R between the two coordinate systems is solvedLWAnd translation vector TLWA three-point correspondence problem is formed, which is solved as follows:
1) setting P1As an origin, the x-axis is set to P2P1Unit vector of (d):
2) the y-axis is set as a unit vector perpendicular to the x-axis on a plane formed by three points:
3) the z-axis is set perpendicular to both the unit vectors which are the x-axis and the y-axis:
4) the rotation matrix in the laser coordinate system is thus represented as:
R1＝[vxvyvz]
5) to Q1、Q2、Q3The same process is repeated to calculate a rotation matrix R under a control field coordinate system2；
6) Therefore, the rotation matrix between two coordinate axes can be expressed as:
RLW＝R1R2 -1
7) the translation vector between the two coordinate systems is represented as:
thus, the external parameter (R) of the laser coordinate system under the control field coordinate system is obtainedLW，TLW)；
Step (6), jointly calibrating a laser and a camera; and (3) obtaining a conversion relation between a laser coordinate system and a camera coordinate system through coordinate transformation by using a control field coordinate system as a medium, namely, external parameters between the calibrated laser and the camera.
2. The method for rapidly calibrating a single-line laser and an optical area-array camera according to claim 1, wherein: the specific implementation manner of the step (4) is as follows,
let the camera internal parameter be (x)0，y0，f)，(x0，y0) Representing the coordinates of the principal point of the image, wherein f represents the focal length of the camera, and the value of f is obtained by calibrating internal parameters of the camera; two external parameters of the camera in the control field are (R)CW，TCW)，RCWRepresenting a 3 x 3 rotation matrix formed by rotation about 3 coordinate axes, TCWA translation vector representing 3 × 1 of the origin of the camera coordinate system relative to the origin of the control field coordinate system;
TCW＝(XsYsZs)T
camera origin S ═ XsYsZs)TControl point A ═ X Y Z)TAnd the corresponding image point a ═ x, y on the photo is collinear, and the collinear condition equation is expressed as:
using the unknown parameter in the above formula as l1-l11And expressing to obtain an equation form only related to the coordinates of the image point and the coordinates of the control point, wherein the equation form is as follows:
further simplification of the above equation yields a linearized form of the collinearity equation:
when there are n control points in the control field, i.e. 2n equations are listed, the writing into a matrix is as follows:
recording a left coefficient matrix of the equation as A, recording an unknown number as X, and recording a value on the right of the equation as L; according to the least square method, the solution of the unknowns can be found as:
X＝(ATA)-1ATL
solving the above equation yields the coefficient l1-l11The translation vector of the camera external parameter satisfies the following relationship:
solving three unknowns of the translation vector by a simultaneous equation, and determining the position of the camera in a control field coordinate system;
in the same way, coefficient liThe relationship between (i ═ 1, 2 … 11) and the three rotation angles that make up the rotation matrix is as follows:
three angles forming a rotation matrix are obtained by the formula, and the posture of the camera in a control field coordinate system is determined;
finally obtaining an external parameter (R) of the camera in a control field coordinate systemCW，TCW)。
3. The method for rapidly calibrating a single-line laser and an optical area-array camera according to claim 2, wherein: the specific implementation manner of the step (6) is as follows,
for any point P in space, the coordinate in the control field coordinate system is Pw＝(Xw，Yw，Zw)TThe coordinate in the camera coordinate system is Pc＝(Xc，Yc，Zc)TThe coordinate in the laser coordinate system is Pl＝(Xl，Yl，Zl)TThen the three satisfy the following relationship:
Pc＝RCWPw+TCW
Pl＝RLWPw+TLW
combining two formulas, external reference (R) from laser coordinate system to camera coordinate systemCL，TCL) Can be expressed as:
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| CN110827359A (en) * | 2019-10-29 | 2020-02-21 | 武汉大学 | Checkerboard trihedron-based camera and laser external reference checking and correcting method and device |
| CN111765902A (en) * | 2020-06-18 | 2020-10-13 | 山东科技大学 | Laser point cloud precision evaluation method based on polygonal pyramid target |
| CN111830049B (en) * | 2020-07-24 | 2023-09-22 | 深圳市道通科技股份有限公司 | Brake disc wear area identification method and wear identification system |
| CN113409396B (en) * | 2021-05-11 | 2024-03-29 | 广州敏视数码科技有限公司 | Calibrating method of ADAS monocular camera |
| CN117705004B (en) * | 2023-12-27 | 2024-05-28 | 福建省高速公路科技创新研究院有限公司 | High-precision measurement and calibration method for compaction of filled soil layer |
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