CN113610928B - Camera external parameter calibration method based on camera position and two mark points - Google Patents
Camera external parameter calibration method based on camera position and two mark points Download PDFInfo
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Abstract
The invention belongs to the technical field of camera parameter calibration, and relates to a camera external parameter calibration method based on a camera position and two mark points. The invention is suitable for application scenes capable of acquiring the position of a camera in advance, such as a fixed monitoring camera, a staring camera for measuring the attitude of an aircraft in an outfield, or a camera with a positioning device and the like.
Description
The technical field is as follows:
the invention belongs to the technical field of camera parameter calibration, and particularly relates to a camera external parameter calibration method.
Background
The P3P (periodic-3-point) problem is to use three known mark points in the field of view and their imaging positions in the camera to solve the rotational translation relationship between the camera coordinate system and the world coordinate system, i.e. the camera external parameters. At present, a plurality of P3P algorithms exist, the algorithms can obtain at most 4 groups of external parameter solutions by utilizing cameras with known internal parameters, and the problem of multiple solutions can be eliminated through the 4 th mark point and the imaging position thereof to obtain a unique solution. In the existing algorithm, when solving external parameters, if a unique solution needs to be obtained, at least 4 mark points are needed, and a large amount of manpower and material resources are needed for obtaining and maintaining the accurate mark points, for example, when measuring the attitude of an aircraft in a field strong wind environment, a plurality of mark points need to be set for calibrating a camera in advance, and the establishment of the field strong wind environment mark points brings severe challenges. And the calibration of the camera external parameters carried out by reducing to 3 mark points has the problem of multiple solutions.
Disclosure of Invention
The invention aims to provide a camera extrinsic parameter calibration method based on a camera position and two mark points, which realizes extrinsic parameter calibration of a camera according to known 2 mark points and camera positions and solves the technical problems that extrinsic parameter calibration of the camera in the prior art needs at least 3 mark points and multiple solutions exist.
In order to achieve the purpose, the technical scheme of the invention comprises the following steps:
initial coordinate system C-X of camera c Y c Z c Expressed in relation to the world coordinate system O-XYZ, X C The axis being parallel and co-directional with the X axis, Y C Parallel and opposite to the Z axis, Z C The axis is parallel to and in the same direction as the Y axis; p 1 、P 2 Is a mark point, p 1 、p 2 Is a mark point P 1 、P 2 Imaging position in camera, camera position C (x) 0 y 0 z 0 ) Known, two marker points P 1 (x 1 y 1 z 1 )、P 2 (x 2 y 2 z 2 ) If known, the corresponding relationship between the mark point and the camera imaging position is as follows:
According to the initial camera pose, firstly, translating T, T = [ x ] to the world coordinate system 0 y 0 z 0 ] T The world coordinate system and the camera coordinate system can then be brought into coincidence by rotation through 90 ° about the X axis, so that P 1 The coordinates in the camera coordinate system are
P 1-c ＝R ox ·[P 1 -T] (2)
Wherein:
according to the imaging relationship, obtainTo p 1 The coordinates of the point in the camera coordinate system are
Wherein (u) 0 v 0 ) Is a camera principal point; d is the pixel size; f is the focal length of the lens; at external calibration, the internal parameters are assumed to be known, and therefore, the parameters are also known quantities;
first time camera winds around Y C The shaft rotates according to the following angles:
after rotating, make
And
two vectors in plane Y c Projection collinearity of =0 and obtaining a new camera coordinate system C-X c1 Y c1 Z c1 Lower P 1 Point coordinates of
Wherein
New camera coordinate system C-X c1 Y c1 Z c1 Lower p 1 Point coordinate p 1_c1 ＝p 1_c ；
Second time the camera winds X c1 The rotation is carried out according to the following angles:
after rotating, make
And
two vectors are collinear to complete P 1 -p 1 -C three points are collinear;
step 2, P 2 -p 2 Implementation of-C three-point collinearity
After the camera completes the rotation transformation in the step 1, a new camera coordinate system C-X is obtained c2 Y c2 Z c2 ，p 2 The coordinates of the point under a world coordinate system O-XYZ are
Wherein
Establishing a new world coordinate system O 1 -X 1 Y 1 Z 1 Wherein the origin of the coordinate system is O 1 Coincident with point C, new world coordinate system O 1 -X 1 Y 1 Z 1 The unit directional vectors for each axis are as follows:
then P is 2 Point and p 2 Point in new world coordinate system O 1 -X 1 Y 1 Z 1 The lower three-dimensional coordinates are respectively
P 2-O1 ＝R O1 (P 2 -C)
p 2-O1 ＝R O1 (p 2-o -C) (13)
Wherein,
at this time, the fixed camera position is fixed, and the world coordinate system O is adopted 1 -X 1 Y 1 Z 1 Around X 1 The axes rotate and the coordinate systems O-XYZ and P 1 、P 2 The point follows the rotation, at this time, O 1 -X 1 Y 1 Z 1 O-XYZ and P 1 、P 2 The relative pose relationship of the points does not change, and only the relative pose of the points and the camera changes; assuming that the rotation angle is α, α ∈ (0 360)]World coordinate system O after rotation 1 -X 1 Y 1 Z 1 Redefined as O 2 -X 2 Y 2 Z 2 The coordinate system O-XYZ is redefined as O '-X' Y 'Z', when p 2 Point is at O 2 -X 2 Y 2 Z 2 The coordinates of
p 2-O2 ＝R O2 ·p 2-O1 (15)
Wherein,
to make P after rotation 2 Completion with p 2 The rotation angle satisfies the following conditions:
thus to realize P 2 -p 2 Co-linear of the three points C.
Step 3, obtaining external parameters of the camera
After the two-point mapping is completed according to the steps 1 and 2, the camera coordinate system C-X c2 Y c2 Z c2 And (3) determining the rotation and translation relation with the world coordinate system O '-X' Y 'Z', and obtaining the coordinates of the world coordinate system O '-X' Y 'Z' in each coordinate system according to the conversion relation, thereby obtaining the algebraic expression of the camera external parameters as follows:
and finishing the calibration of the camera external parameters.
Effective gain of the invention
1. The method is characterized in that the relation between a camera coordinate system and a world coordinate system is known in an initial state, the corresponding relation between two points is obtained through geometric constraint and rotation of the camera coordinate system and the world coordinate system, and finally, the calibration of the camera external parameters is completed according to the rotation translation of the camera coordinate system and the world coordinate system at the initial moment and the rotation angle in the rotation process.
2. The invention provides a camera external parameter calibration method based on a camera position and two mark points, which only needs to arrange the two mark points, measure the camera position and the two mark point positions, shoot the mark point images, obtain the imaging corresponding relation between the camera and the mark points, and obtain the camera external parameters through coordinate system transformation.
3. The invention is suitable for application scenes capable of acquiring the position of a camera in advance, such as a fixed monitoring camera, a staring camera for measuring the attitude of an aircraft in an outfield, or a camera with a positioning device and the like.
Drawings
FIG. 1 is a schematic diagram of a camera coordinate system and a world coordinate system after calibration of extrinsic parameters is completed;
FIG. 2 is a schematic diagram of a coordinate system of a camera and a coordinate system of a world in an initial state according to the present invention;
FIG. 3 is a schematic diagram of a landmark in a camera coordinate system after one rotation according to the present invention;
FIG. 4 shows the present invention P 1 -p 1 -C three points collinear diagram;
FIG. 5 is a world coordinate system O of the present invention 1 -X 1 Y 1 Z 1
FIG. 6 shows the present invention P 2 -p 2 -C three points collinear diagram;
FIG. 7 is a general diagram illustrating the rotation and translation process between coordinate systems according to the present invention.
Detailed Description
The following detailed description and the accompanying drawings illustrate the implementation of the present invention.
The general idea of the invention is expressed as follows, the invention can solve and obtain the camera extrinsic parameters by geometric constraint and geometric rotation by utilizing 2 mark points and the known camera position, and ensures that the camera extrinsic parameters have unique solutions.
When the camera is at position C (x) 0 y 0 z 0 ) Known, two marker points P 1 (x 1 y 1 z 1 )、P 2 (x 2 y 2 z 2 ) If known, the corresponding relation between the mark point and the camera imaging position is determined as follows:
after the external parameters are calibrated, the 2-point correspondence between the camera coordinate system and the world coordinate system is shown in fig. 1, wherein p is 1 、p 2 Is P 1 、P 2 An imaging position in the camera. The invention utilizes the known conditions to find the camera coordinate system C-X in the final state in a rotating and translating manner c2 Y c2 Z c2 And (4) relation with a world coordinate system O '-X' Y 'Z', so as to obtain an external parameter matrix of the camera.
Initial coordinate system C-X of camera c Y c Z c And the world coordinate system O-XYZ are shown in fig. 2.
Wherein, X C The axis being parallel and co-directional with the X axis, Y C Parallel and opposite to the Z axis, Z C The axis is parallel to and in the same direction as the Y axis; p is 1 、P 2 Is a mark point, p 1 、p 2 Is a mark point P 1 、P 2 Imaging position in the camera by aligning the initial camera coordinate system C-X c Y c Z c Rotate and rotationally translate the initial world coordinate system O-XYZ so that point P 1 -p 1 Co-linear of three points-C, P 2 -p 2 And C three points are collinear, so that the solution of the camera external parameters is completed. The following is a detailed explanation and description of the implementation steps of the present invention:
The purpose of this step is to rotate the camera twice, by rotating the geometric transformation, so that p 1 Corresponds to P 1 Due to points C and P 1 Known in the world coordinate system, the rotation angle can be obtained through solving.
Camera winding Y C The axes are rotated so that, in the camera coordinate system,
and
two vectors in the plane Y c Projection of =0 is collinear:
according to the initial camera pose, firstly translating T, T = [ x ] to the world coordinate system 0 y 0 z 0 ] T The world coordinate system and the camera coordinate system can then be brought into coincidence by rotation through 90 ° about the X axis, so that P 1 The coordinates in the camera coordinate system are
P 1-c ＝R ox ·[P 1 -T] (2)
Wherein:
according to the imaging relationship, obtainingp 1 The coordinates of the point in the camera coordinate system are
Wherein (u) 0 v 0 ) Is a camera principal point; d is the pixel size; f is the focal length of the lens; when external standard, the internal parameters are assumed to be known, therefore, the parameters are also known quantities;
first time the camera winds around Y C The shaft rotates in order to
And
two vectors in the plane Y c Projection of =0 is collinear, camera is around Y C The angle of rotation of the shaft is
After rotation, a new camera coordinate system C-X is obtained c1 Y c1 Z c1 Lower P 1 Point coordinates of
Wherein
Point p 1 Follows the coordinate system clockwise rotation, so the new camera coordinate system C-X c1 Y c1 Z c1 Lower p 1 Point coordinate p 1_c1 ＝p 1_c After one rotation, the corresponding relationship is shown in fig. 3.
In FIG. 3, point p after rotation 1 、P 1 In the camera coordinate system C-X c1 Y c1 Z c1 Lower Y C1 =0 projection point on plane and point C collinear with straight line l 2 。
Second time the camera winds around X c1 The axes rotate to obtain a new camera coordinate system C-X c2 Y c2 Z c2 So that, under the coordinate system,
and
the two vectors are collinear, and the rotation angle of the camera is as follows:
the correspondence after rotation is shown in fig. 4, up to this point, point P 1 And p 1 Is completed, i.e. P 1 -p 1 The three points-C are collinear.
Step 2, P 2 -p 2 Implementation of-C three-point collinearity
After the camera completes the rotation transformation in the step 1, a new camera coordinate system C-X is obtained c2 Y c2 Z c2 Lower p 2 The coordinates of the point under the world coordinate system O-XYZ are
Wherein
To ensure P 1 The mapping relation of the point is unchanged in the rotating process, and the CP is wound around the world coordinate system 1 Rotate due toIn this way, a new world coordinate system O is established 1 -X 1 Y 1 Z 1 Wherein the origin of the coordinate system is O 1 Coincident with point C, as shown in FIG. 5, the new world coordinate system O 1 -X 1 Y 1 Z 1 The unit directional vectors for each axis are as follows:
then P is 2 Point and p 2 Point in new world coordinate system O 1 -X 1 Y 1 Z 1 The lower three-dimensional coordinates are respectively
P 2-O1 ＝R O1 (P 2 -C)
p 2-O1 ＝R O1 (p 2-o -C)
Wherein,
at this time, the camera position is fixed, and the world coordinate system O is fixed 1 -X 1 Y 1 Z 1 Around X 1 The axes rotate and the coordinate systems O-XYZ and P 1 、P 2 The point follows the rotation, at this time, O 1 -X 1 Y 1 Z 1 O-XYZ and P 1 、P 2 The relative position and pose relationship of the points does not change, and only the relative position and pose of the points and the camera change. Assuming that the rotation angle is α, α ∈ (0 360)]World coordinate system O after rotation 1 -X 1 Y 1 Z 1 Redefined as O 2 -X 2 Y 2 Z 2 At this time p 2 Point is at O 2 -X 2 Y 2 Z 2 The coordinates of
p 2-O2 ＝R O2 ·p 2-O1
Wherein,
to make P after rotation 2 Completion with p 2 The rotation angle satisfies the following conditions:
at this time, the process of the present invention,
and
and (4) collinear, obtaining a rotation angle alpha, and completing the whole mapping of two points, as shown in fig. 6.
And the world coordinate system O-XYZ rotates to O '-X' Y 'Z' after following the rotation, and has a rotation relation of a rotation angle alpha with the original world coordinate system.
Step 3, obtaining external parameters of the camera
Completing two-point mapping according to the steps 1 and 2, and obtaining a camera coordinate system C-X c2 Y c2 Z c2 The whole process of rotation and translation with the world coordinate system O '-X' Y 'Z' is shown in fig. 7. And determining the rotational-translational relationship between every two coordinate systems, and obtaining the coordinates of the coordinate systems under the coordinate systems according to the conversion relationship, thereby obtaining the algebraic expression of the camera external parameters as follows:
and finishing the calibration of the camera external parameters.
Example 1
Given two landmark coordinates P1 (20, -20, 1.5), P2 (20, 1.5), camera position C (353, 100, -10), the imaging relationship of the camera to the landmark is known, and the pixel coordinates of the landmark are (247.2541, 231.4668), (829.7369, 560.4963), respectively. The camera intrinsic parameters are known, the resolution is 1280 multiplied by 800, the focal length is 85mm, and the pixel size is 14 mu m. Substituting the known conditions into the calculation process to obtain the following relevant parameters:
according to the setting of simulation parameters, the theoretical camera external parameters are
T＝[-2.4979 4.3265 366.9932]
For better error comparison, the rotation matrix is converted into a rotation angle description
Angle measurement value = [ 35.0192.3276-59.6105 ]
Theoretical value of angle = [ 35.0364.3276-59.6277 ]
It can be seen that the values of the rotation angle matrix and the transfer matrix are very small in relative error or absolute error, the absolute error is 0.0172 degrees at most, and the relative error is 0.19 percent at most.
And establishing a landmark reprojection error for evaluating the external parameter error of the rotation and translation matrix, and analyzing the landmark reprojection error. And carrying out reprojection on the two mark points by adopting the external parameters obtained by calculation, comparing the reprojection with the actual imaging position to obtain reprojection errors which are lower than 0.5 pixel, and judging that the external parameter calibration result is good.
Claims (1)
1. A camera external parameter calibration method based on camera position and two mark points is characterized in that,
initial coordinate system C-X of camera c Y c Z c Expressed in relation to the world coordinate system O-XYZ, X C The axis being parallel and co-directional with the X axis, Y C Parallel and opposite to the Z axis, Z C The axis is parallel to and in the same direction as the Y axis; p 1 、P 2 Is a mark point, p 1 、p 2 Is a mark point P 1 、P 2 Imaging position in camera, camera position C (x) 0 y 0 z 0 ) Known, two marker points P 1 (x 1 y 1 z 1 )、P 2 (x 2 y 2 z 2 ) If known, the corresponding relationship between the mark point and the camera imaging position is as follows:
step 1, P 1 -p 1 Implementation of-C three-point collinearity
According to the initial camera pose, firstly, translating T, T = [ x ] to the world coordinate system 0 y 0 z 0 ] T The world coordinate system and the camera coordinate system can then be brought into coincidence by rotation through 90 ° about the X axis, so that P 1 The coordinates in the camera coordinate system are
P 1-c ＝R ox ·[P 1 -T] (2)
Wherein:
obtaining p according to the imaging relation 1 The coordinates of the point in the camera coordinate system are
Wherein (u) 0 v 0 ) Is a camera principal point; d is the pixel size; f is the focal length of the lens; at external calibration, the internal parameters are assumed to be known, and therefore, the parameters are also known quantities;
first time camera winds around Y C The shaft rotates according to the following angles:
after rotating, make
And
two vectors in the plane Y c Projection collinearity of =0 and obtaining a new camera coordinate system C-X c1 Y c1 Z c1 Lower P 1 Point coordinates of
Wherein
New camera coordinate system C-X c1 Y c1 Z c1 Lower p 1 Point coordinate is p 1_c1 ＝p 1_c ；
Second time the camera winds X c1 The shaft rotates according to the following angles:
after rotating make
And
two vectors are collinear to complete P 1 -p 1 -C three points are collinear;
step 2, P 2 -p 2 Implementation of-C three-point collinearity
After the camera completes the rotation transformation in the step 1, a new camera coordinate system C-X is obtained c2 Y c2 Z c2 ，p 2 The coordinates of the point under a world coordinate system O-XYZ are
Wherein
Establishing a new world coordinate system O 1 -X 1 Y 1 Z 1 Wherein the origin of the coordinate system is O 1 Coincident with point C, new world coordinate system O 1 -X 1 Y 1 Z 1 The unit directional vectors of each axis are as follows:
then P is 2 Point and p 2 Point in new world coordinate system O 1 -X 1 Y 1 Z 1 The lower three-dimensional coordinates are respectively
P 2-O1 ＝R O1 (P 2 -C)
p 2-O1 ＝R O1 (p 2-o -C) (13)
Wherein,
at this time, the fixed camera position is fixed, and the world coordinate system O is adopted 1 -X 1 Y 1 Z 1 Around X 1 The axes rotate and the coordinate systems O-XYZ and P 1 、P 2 The point follows the rotation, at this time, O 1 -X 1 Y 1 Z 1 O-XYZ and P 1 、P 2 The relative pose relationship of the points does not change, and only the relative pose of the points and the camera changes; assumed angle of rotationIs alpha, alpha epsilon (0 360)]World coordinate system O after rotation 1 -X 1 Y 1 Z 1 Redefined as O 2 -X 2 Y 2 Z 2 The coordinate system O-XYZ is redefined as O '-X' Y 'Z', when p 2 Point is at O 2 -X 2 Y 2 Z 2 The coordinates of
p 2-O2 ＝R O2 ·p 2-O1 (15)
Wherein,
to make P after rotation 2 Completion with p 2 The rotation angle satisfies the following conditions:
thus, P is realized 2 -p 2 -co-linearity of the C three points;
step 3, obtaining external parameters of the camera
After the two-point mapping is completed according to the steps 1 and 2, the camera coordinate system C-X c2 Y c2 Z c2 And (3) determining the rotation and translation relation with the world coordinate system O '-X' Y 'Z', and obtaining the coordinates of the world coordinate system O '-X' Y 'Z' in each coordinate system according to the conversion relation, thereby obtaining the algebraic expression of the camera external parameters as follows:
and finishing the calibration of the camera external parameters.
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| CN107146254A (en) * | 2017-04-05 | 2017-09-08 | 西安电子科技大学 | The Camera extrinsic number scaling method of multicamera system |
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