CN114820810A - Analysis method based on Tsai camera plane calibration algorithm - Google Patents
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Abstract
The invention relates to the technical field of camera calibration, in particular to an analysis method based on a Tsai camera plane calibration algorithm, which comprises the steps of obtaining a picture of a target; extracting a two-dimensional image coordinate value at the center of the original point of the photo, and obtaining a distortion coefficient of the two-dimensional image coordinate value; solving a distortion coefficient matrix; and (5) evaluating the result. According to the method, on the premise that the center point of the image is overlapped with the center of the CCD or CMOS sensor, the internal and external parameters of the camera are separated from the distortion parameters of the camera model, so that the camera calibration can be further performed linearly. The method avoids errors caused by nonlinear optimization, reduces algorithm complexity, can properly improve calibration precision and save calculation time, and compared with the Tsai method, the method saves about 35% of calibration time and at least 15% of calibration precision, the calibration process is simple and easy to operate, and possible instability in other nonlinear optimization methods can be avoided.
Description
Technical Field
The invention relates to the technical field of camera calibration, in particular to an analysis method based on a Tsai camera plane calibration algorithm.
Background
When the camera is used for three-dimensional reconstruction of images, the relation between the positions of points on the images and the geometric positions of corresponding points on the surfaces of space objects needs to be determined in advance. The process of imaging a geometric model by a camera and determining the parameters of the geometric model by means of the correlation between the world coordinate system of a certain point on the surface of a spatial object and its corresponding point in the image is called camera calibration. Camera calibration is an essential step in computer vision work, and the accuracy of camera calibration results and the difficulty of operation in the calibration process respectively influence the accuracy and convenience of camera production results. Since 1971, various camera calibration methods have been developed. The improvement from the earliest Horaud calibration method to Zhuang and other distortion increasing improvements, static and dynamic scanning imaging calibration methods, a classical self-calibration method of Kruppa equation, Zhang Zheng and Tsai calibration algorithms. Tsai provides a two-step calibration method for calibrating a planar target based on radial constraint, and the method has the advantage of high precision, but has the disadvantages of complex optimization program, low speed and result precision depending on the initial value of the image center. The method for improving the Tsai camera plane calibration algorithm is provided by introducing a camera linear pinhole model and a distortion model and using the Tsai camera plane calibration algorithm for reference.
Disclosure of Invention
The invention aims to provide an analysis method based on a Tsai camera plane calibration algorithm, so as to solve the problems in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme:
an analysis method based on a Tsai camera plane calibration algorithm comprises the following steps:
acquiring a picture of a target;
extracting a two-dimensional image coordinate value of the center of the original point of the photo to obtain a distortion coefficient of the two-dimensional image coordinate value;
solving a distortion coefficient matrix;
and (5) evaluating the result.
Further, obtaining a photograph of the target includes:
setting a camera linear pinhole model and a camera distortion model;
the extracting of the two-dimensional image coordinate value of the center of the origin of the photograph includes:
converting the internal parameter relationship of the camera;
the method for obtaining the distortion coefficient of the coordinate value of the two-dimensional image comprises the following steps:
a comprehensive model according to known points;
setting a calibration plate;
and calibrating the distortion coefficient.
Further, setting the camera linear pinhole model includes:
the transformation coordinates of the imaging process of the pinhole camera comprise a world coordinate system O w X w Y w Z w Camera coordinate system O c X c Y c Z c Ideal imaging physical coordinate system O ud X u Y u Actual imaging physical coordinate system O ud X d Y d And the actual image pixel coordinate system O I UV；
Setting a camera coordinate system by a right-hand coordinate system;
the coordinate values of the points in the world coordinate system in the camera coordinate system may be:
to obtain
Setting a lens distortion model includes:
suppose D x And D y Respectively representing the amount of distortion in the x and y directions, k 1 ,k 2 Referred to as 1 st order and 2 nd order radial distortion coefficients, respectively
radial distortion satisfies
The expressed constraints;
the camera internal parameter relationship specifically includes:
P u and P d Are abstract concepts in the camera imaging model,and P is d Satisfies the actual image pixel coordinate (u, v, f)
dx, dy denote the physical dimensions of the individual pixels in the X (U) and Y (inverse of V) directions, C x And C y Respectively represent a coordinate system O I UV and O ud X d Y d The offset in units of pixels between them yields:
the comprehensive model of the known points specifically includes:
setting a set of known points P in a world coordinate system wi ＝(x wi ,y wi ,z wi 1) which can be represented as P in the camera coordinate system ci ＝(x ci ,y ci ,z ci ) The coordinate position of the corresponding pixel after projection imaging is measurable (u) i ,v i ) All of the above can be combined to obtain
Thereby obtaining
The setting of the calibration plate specifically includes:
adopting a dot arrangement mode to design a plane calibration pattern;
the distortion coefficient calibration specifically comprises:
the distortion coefficient k can be obtained from 4 collinear control points 1 ；
According to P w0 ,P w1 ,P w2 ,P w3 Cross ratio of each other
According to the cross ratio invariance of perspective projection and the corresponding cross ratio of ideal image point
Thereby obtaining
In order to solve k 1 More accurate, adopting residual minimum constraint to solve;
each straight line can be obtained as two 1 The left squares of 2n equations obtained from n straight lines are summed:
convert into to solve f (k) 1 ) Minimum value of (d);
solving for k by Taylor method 1 A value of (d);
wherein; rij: i is 1,2, 3; j is 1,2, and 3 each denote 9 elements in a 3 × 3 rotation matrix, i denotes a row number, and j denotes a column number.
Further, the matrix solving specifically includes:
let the image center point (C) x ,C y ) Setting a reasonable estimation, and taking a corresponding value at the central point of the image;
can be obtained according to the comprehensive model
Wherein
Using a distortion model and a comprehensive model
The influence of distortion on the equation can be naturally eliminated;
when setting up
And using a rotation-translation matrix R t After the component of (a) is spread out
Wherein
When the calibration target is planar, the matrix R t The components of (c) can be expressed as:
is a linear homogeneous equation;
compare | u 0 -C x I and | v 0 -C y The magnitude of the value of the | is,
when u 0 -C x |>|v 0 -C y When, both sides of the equation are divided by sy simultaneously t Derived from
Obtained by least square solution
A value of (d);
will be provided with
By the orthogonality of the rotation matrix
Thereby obtaining s and z t A value of (d);
binding to y t ,s,z t ,
Can find r 1i ,r 2i ,r 3i ,x t ,
A value of (d);
similarly, when | u 0 -C x |≤|v 0 -C y When, both sides of the equation are divided by x simultaneously t Solving for s, z t A corresponding value;
where zt represents the amount of translation in the z direction.
Further, evaluating the results includes: selecting two different cameras for calibration and comparison, wherein parameters of each camera are known; the evaluation is compared with the aspects of reprojection errors and image center errors, distance errors and running time.
Furthermore, 20 calibration point circles are arranged on the target surface of the target for the plane calibration pattern, and the calculated internal reference and external reference are brought into
Calculating a new group of pixel point data and recording as (u ', v') and calculating the square error sum of the root of the data of the true pixel point (u, v) obtained from the image, averaging and recording as
Known image center sum of the calculated internal and external parameters
Calculated distortion center, marked as C' x ,C′ y The error between;
set distortion center C x ,C y And calculating C' x ,C′ y Is recorded as
Bringing the calculated internal and external parameters of the camera into
Calculating a point P in the world coordinate system wi Point P in the camera coordinate system ci Moving the calibration plate by a certain distance through the control shaft, and calculating the point P in the world coordinate system after moving again wi The set of points in the camera coordinate system is: p' ci The error at this time is denoted as E 3 ＝|D′-D|。
In order to achieve the above purpose, the invention also provides the following technical scheme:
an analytic device based on Tsai camera plane calibration algorithm comprises:
the acquisition module is used for acquiring a picture of the target;
the processing module is used for extracting the coordinate value of the two-dimensional image at the center of the original point of the photo and solving the distortion coefficient of the coordinate value of the two-dimensional image;
the solving module is used for solving the distortion coefficient matrix;
and the output module is used for evaluating the result.
In order to achieve the above purpose, the invention also provides the following technical scheme:
a computer device comprising a memory storing a computer program and a processor implementing the steps of the method as claimed in any one of the above when the computer program is executed.
In order to achieve the above purpose, the invention also provides the following technical scheme:
a computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the steps of the method according to any one of the preceding claims.
Compared with the prior art, the invention has the beneficial effects that:
compared with the Tsai camera calibration algorithm, the method needs few known conditions, is simple to calculate, and is completely non-iterative in the calculation process. Therefore, the method reduces the calculation complexity, improves the calibration speed and the calibration precision, has simple and easy operation in the calibration process, and can avoid instability possibly encountered in other nonlinear optimization methods. Compared with a Zhangyingyou camera calibration algorithm, the method can finish camera calibration by only one image, and has a certain reference value for the high-precision real-time measurement method of the dynamic target pose. Similar calibration results to other camera calibration algorithms depend on the selection of the coordinate values of the image center. The method saves about 35% of calibration time, improves at least 15% of precision, is simple and easy to operate in the calibration process, and can avoid instability possibly encountered in other nonlinear optimization methods.
Drawings
Fig. 1 is a schematic flow chart of an analysis method based on a Tsai camera plane calibration algorithm provided by the present invention.
Fig. 2 is a camera imaging model provided by the present invention.
FIG. 3 shows a pattern on a calibration target according to the present invention.
Fig. 4 is a block diagram of an analysis device based on the Tsai camera plane calibration algorithm.
Fig. 5 is an internal structural view of the computer device of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-5, the present invention provides a technical solution:
an analysis method based on a Tsai camera plane calibration algorithm comprises the following steps:
s101, extracting a target and photographing;
s102, extracting a coordinate value of the two-dimensional image at the center of the origin, and substituting the coordinate value into a formula to obtain a distortion coefficient;
s103, matrix solving;
and S104, comparing the algorithm with the Tsai method.
The target extraction photographing specifically comprises:
setting the transformation coordinates of the pinhole camera imaging process as shown in fig. 2, the following properties of the rotation matrix were found:
r 31 ＝r 12 r 23 -r 13 r 22
r 32 ＝r 13 r 21 -r 11 r 23
r 33 ＝r 11 r 22 -r 12 r 23
r 13 ＝r 21 r 32 -r 31 r 22
r 23 ＝r 31 r 12 -r 11 r 32
where rij (i ═ 1,2, 3; j ═ 1,2,3) denotes 9 elements in the 3 × 3 rotation matrix, respectively (i denotes a row number and j denotes a column number).
The extracting of the two-dimensional image coordinate value of the origin center specifically includes:
suppose D x And D y Respectively representing the amount of distortion in the x and y directions, k 1 ,k 2 Referred to as 1 st order and 2 nd order radial distortion coefficients, respectively
radial distortion satisfies
The expressed constraints;
obtaining a distortion coefficient by applying the cross ratio invariant property in perspective projection and a Taylor method;
according to the derivation method in the operation step 4, the internal parameters and the external parameters of the camera can be rapidly, accurately and robustly solved.
1) According to the formula
Can be solved by the equation by using the least square method
The value of (c).
Wherein x is t ，y t And s represents the amount of translation in the x direction, the amount of translation in the y direction, and the aspect ratio of the imaged pixel after signal disturbance, respectively.
2) Will be provided with
By the orthogonality of the rotation matrix
Thereby obtaining s and z t The value of (c).
Wherein z is t Indicating the amount of translation in the z-direction, and the remaining symbols have the same meaning as described above.
The algorithm is compared with the Tsai method.
Selecting two different cameras for calibration and comparison, wherein parameters of each camera are known; the evaluation is compared with the aspects of reprojection errors and image center errors, distance errors and running time.
The following is further illustrated in connection with the examples and figures:
the improvement method comprises the following steps:
setting a camera linear pinhole model;
setting a camera distortion model;
camera internal parameter relationships;
a comprehensive model of known points;
setting a calibration plate;
calibrating a distortion coefficient;
solving a matrix;
the algorithm is compared with the Tsai method.
Further, the linear pinhole model specifically includes:
the transformation coordinates of the imaging process of the pinhole camera are set as shown in figure 2;
comprising a world coordinate system O w X w Y w Z w Camera coordinate system O c X c Y c Z c Ideal imaging physical coordinate system O ud X u Y u Actual imaging physical coordinate system O ud X d Y d And the actual image pixel coordinate system O I UV；
In order to ensure that the measured depth values are positive values, a camera coordinate system is set as a right-hand coordinate system;
the coordinate values of the points in the world coordinate system in the camera coordinate system may be:
to obtain
Further, the setting of the lens distortion model specifically includes:
suppose D x And D y Respectively representing the amount of distortion in the x and y directions, k 1 ,k 2 Referred to as 1 st order and 2 nd order radial distortion coefficients, respectively
radial distortion satisfies
The expressed constraints;
further, the camera internal parameter relationship specifically includes:
P u and P d Are all abstractions in the camera imaging model, and P d Satisfies the actual image pixel coordinate (u, v, f)
dx, dy denote the physical dimensions of the individual pixels in the x (u) and Y (inverse of V) directions, respectively. C x And C y Respectively represent a coordinate system O I UV and O ud X d Y d The offset in units of pixels between them yields:
further, the comprehensive model of the known point specifically includes:
setting a set of known points P in a world coordinate system wi ＝(x wi ,y wi ,z wi 1) which can be represented as P in the camera coordinate system ci ＝(x ci ,y ci ,z ci ) The coordinate position of the corresponding pixel after projection imaging is measurable (u) i ,v i ) All of the above can be combined to obtain
Thereby obtaining
Further, the setting calibration board specifically includes:
the dot arrangement is used to design a planar calibration pattern, as shown in fig. 3.
Further, the distortion coefficient calibration specifically includes:
the method of reference handshakes only needs to know 4 collinear control pointsThe distortion coefficient k can be obtained 1 ；
According to P in FIG. 3 w0 ,P w1 ,P w2 ,P w3 Cross ratio of each other
According to the cross ratio invariance of perspective projection and the corresponding cross ratio of ideal image points
Thereby obtaining
In order to solve k 1 More accurate, adopting residual minimum constraint to solve;
each straight line can be obtained as two 1 The left squares of 2n equations obtained by n straight lines are summed:
convert into to solve f (k) 1 ) Minimum value of (d);
solving for k by Taylor method 1 The value of (c).
Further, the matrix solving specifically includes:
let the image center point (C) x ,C y ) Setting a reasonable estimation, and taking a corresponding value at the central point of the image;
can be obtained from the comprehensive model
Wherein
Using a distortion model and a comprehensive model
The influence of distortion on the equation can be naturally eliminated;
when setting up
And using a rotation-translation matrix R t After the component of (a) is spread out
Wherein
When the calibration target is planar, the matrix R t The components of (c) can be expressed as:
is a linear homogeneous equation;
comparison | u 0 -C x I and | v 0 -C y The magnitude of the value of the | is,
when u 0 -C x |>|v 0 -C y When, both sides of the equation are divided by sy simultaneously t Derived from
Obtained by least square solution
A value of (d);
will be provided with
By the orthogonality of the rotation matrix
Thereby obtaining s and z t The value of (c).
Binding to y t ,s,z t ,
Can find r 1i ,r 2i ,r 3i ,x t ,
A value of (d);
similarly, when | u 0 -C x |≤|v 0 -C y When, both sides of the equation are divided by x simultaneously t Solving for s, z t The corresponding value.
Further, the comparison between the algorithm and the Tsai method specifically includes:
selecting two different cameras for calibration and comparison, wherein the parameters of each camera are known;
the target is shown in figure 3, and the target surface has 20 calibration point circles;
estimating from the aspects of reprojection errors and image center errors, distance errors and running time;
the calculated internal parameters and external parameters are substituted into
Calculating a new group of pixel point data and recording as (u ', v') and calculating the square error sum of the root of the data of the true pixel point (u, v) obtained from the image, averaging and recording as
Known image center sum of the calculated internal and external parameters
In the calculated distortionHeart, recorded as C' x ,C′ y The error between;
set distortion center C x ,C y And calculating C' x ,C′ y Is recorded as
Bringing the calculated internal and external parameters of the camera into
Calculating a point P in the world coordinate system wi Point P in the camera coordinate system ci Moving the calibration plate by a certain distance through the control shaft, and calculating the point P in the world coordinate system after moving again wi The set of points in the camera coordinate system is: p' ci At this time, the error is denoted as E 3 ＝|D′-D|。
The analysis method comprises the following steps:
s101, shooting a target to obtain a picture of the target;
s102, extracting a two-dimensional image coordinate value of an origin center;
s103, substituting the formula to obtain a distortion coefficient;
s104, solving a matrix;
and S105, evaluating the result.
Specifically, the method is an improvement on a Tsai camera plane calibration algorithm. The algorithm is divided into five parts, wherein the first part is used for shooting a target, the second part is used for extracting a two-dimensional image coordinate value of the center of an origin, the third part is used for solving a distortion coefficient by being brought into a formula, the fourth part is used for solving a matrix, and the fifth part is used for comparing the experimental result of the algorithm with the Tsai algorithm.
The overall flow of the algorithm is improved.
First, photograph the target pattern of fig. 3;
secondly, acquiring a coordinate value of the two-dimensional image of the center of the origin;
thirdly, substituting the distortion coefficient into a formula to obtain a distortion coefficient;
fourthly, solving a matrix;
when the program starts, a picture is taken of the target pattern, the coordinate value of the two-dimensional image of the center of the origin is obtained through analysis, and the distortion coefficient is obtained by utilizing an intersection invariance formula in perspective projection; the following properties of the rotation matrix are utilized, the decoupling of the nonlinear problem into the linear problem is realized, meanwhile, an analytic solution can be directly obtained, and the precision and the efficiency are improved.
r 31 ＝r 12 r 23 -r 13 r 22
r 32 ＝r 13 r 21 -r 11 r 23
r 33 ＝r 11 r 22 -r 12 r 23
r 13 ＝r 21 r 32 -r 31 r 22
r 23 ＝r 31 r 12 -r 11 r 32
And fifthly, evaluating results, and comparing the algorithm with the Tsai method.
And evaluating the reprojection error, the image center error, the distance error and the running time according to the acquired internal and external parameters of the camera.
In the present invention, a computer device may include a memory, a storage controller, one or more processors (only one shown in the figure), and the like, and the elements are electrically connected directly or indirectly to realize the transmission or interaction of data. For example, electrical connections between these components may be made through one or more communication or signal buses. The resolution method based on the Tsai's camera plane calibration algorithm includes at least one software functional module that can be stored in a memory in the form of software or firmware (firmware), for example, the resolution device based on the Tsai's camera plane calibration algorithm includes a software functional module or a computer program. The memory may store various software programs and modules, such as program instructions/modules corresponding to the resolution method and apparatus based on the Tsai camera plane calibration algorithm provided in the embodiments of the present application. The processor executes various functional applications and data processing by running software programs and modules stored in the memory, that is, implements the parsing method in the embodiments of the present application.
The hardware environment for the system operation of the invention is CPU: intel (R) core (TM) i3-6300 CPU @3.80GHz, memory: 4GB, hard disk: 240GB (solid state disk); the system environment in which the system operates is windows10 professional edition; the software environment in which the system runs is Visual Studio 2017.
The method mainly has the following functions:
(1) finding the properties of a rotation matrix
r 31 ＝r 12 r 23 -r 13 r 22
r 32 ＝r 13 r 21 -r 11 r 23
r 33 ＝r 11 r 22 -r 12 r 23
r 13 ＝r 21 r 32 -r 31 r 22
r 23 ＝r 31 r 12 -r 11 r 32 ；
(2) By utilizing the property of (1) and combining orthogonality, the coupling relation among all parameters can be effectively eliminated, and the nonlinear solving problem is converted into a linear solving problem;
(3) and solving the matrix according to the operation step 4, and quickly, accurately and robustly calculating the internal parameters and the external parameters of the computer camera.
The invention relates to a simple and quick camera calibration method. The method separates the internal and external parameters of the camera and the distortion parameters of the camera model on the premise of assuming that the center point of the image is coincident with the center of the CCD or CMOS sensor, so that the calibration of the camera can be further carried out linearly.
Firstly, a linear pinhole model and a distortion model of a camera are set, a distortion coefficient of a lens is calibrated according to an intersection ratio invariance principle of perspective projection, then, according to a rotation transformation relation and a translation transformation relation, radial distortion constraint, orthogonality of rotation transformation and characteristic property constraint linearity of a rotation matrix are fully utilized to solve internal parameters and external parameters of the camera, and comparison is carried out with a Tsai algorithm through the algorithm.
The invention avoids the error caused by nonlinear optimization, reduces the algorithm complexity, can properly improve the calibration precision and saves the calculation time. Finally, compared with the Tsai method, the method saves about 35% of the calibration time and improves the precision by at least 15%.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (9)
1. An analysis method based on a Tsai camera plane calibration algorithm is characterized by comprising the following steps:
acquiring a picture of a target;
extracting a two-dimensional image coordinate value of the center of the original point of the photo to obtain a distortion coefficient of the two-dimensional image coordinate value;
solving a distortion coefficient matrix;
and (5) evaluating the result.
2. The analysis method according to claim 1,
acquiring a photograph of a target includes:
setting a camera linear pinhole model and a camera distortion model;
the extracting of the two-dimensional image coordinate value of the center of the origin of the photograph includes:
converting the relation of the internal parameters of the camera;
the method for obtaining the distortion coefficient of the coordinate value of the two-dimensional image comprises the following steps:
a comprehensive model according to known points;
setting a calibration plate;
and calibrating the distortion coefficient.
3. The parsing method according to claim 2,
setting a camera linear pinhole model includes:
the transformation coordinates of the imaging process of the pinhole camera comprise a world coordinate system O w X w Y w Z w Camera coordinate system O c X c Y c Z c Ideal imaged physical coordinate system O ud X u Y u Actual imaging physical coordinate system O ud X d Y d And an actual image pixel coordinate system O I UV；
Setting a camera coordinate system by a right-hand coordinate system;
the coordinate values of the points in the world coordinate system in the camera coordinate system may be:
to obtain
Setting a lens distortion model includes:
suppose D x And D y Respectively representing the amount of distortion in the x and y directions, k 1 ,k 2 Are called radial distortion coefficients of 1 st order and 2 nd order, respectively
radial distortion satisfies
The expressed constraints;
the camera internal parameter relationship specifically includes:
P u and P d Are all abstractions in the camera imaging model, and P d Satisfies the actual image pixel coordinate (u, v, f)
dx,d y Respectively, the physical dimensions of the individual pixels in the X (U) and Y (V, the inverse) directions, C x And C y Respectively represent a coordinate system O I UV and O ud X d Y d The offset in units of pixels between them yields:
the comprehensive model of the known points specifically includes:
setting a set of known points P in a world coordinate system wi ＝(x wi ,y wi ,z wi 1) which can be represented as P in the camera coordinate system ci ＝(x ci ,y ci ,z ci ) The coordinate position of the corresponding pixel after projection imaging is measurable (u) i ,v i ) All of the above can be combined to obtain
Thereby obtaining
The setting of the calibration plate specifically includes:
adopting a dot arrangement mode to design a plane calibration pattern;
the distortion coefficient calibration specifically comprises:
the distortion coefficient k can be obtained from 4 collinear control points 1 ；
According to P w0 ,P w1 ,P w2 ,P w3 Cross ratio of each other
According to the cross ratio invariance of perspective projection and the corresponding cross ratio of ideal image point
Thereby obtaining
In order to solve k 1 More accurate, adopting residual minimum constraint to solve;
each straight line can be obtained as two 1 The left squares of 2n equations obtained by n straight lines are summed:
convert into to solve f (k) 1 ) Minimum value of (d);
solving for k by Taylor method 1 A value of (d);
wherein; rij: i is 1,2, 3; j is 1,2, and 3 each denote 9 elements in a 3 × 3 rotation matrix, i denotes a row number, and j denotes a column number.
4. The parsing method according to claim 3,
the matrix solving specifically comprises:
let the image center point (C) x ,C y ) Setting a reasonable estimation, and taking a corresponding value at the central point of the image;
can be obtained from the comprehensive model
Wherein
Using a distortion model and a comprehensive model
The influence of distortion on the equation can be naturally eliminated;
when setting up
And using a rotation-translation matrix R t After the component of (a) is spread out
Wherein
When the calibration target is planar, the matrix R t The components of (c) can be expressed as:
is a linear homogeneous equation;
compare | u 0 -C x I and | v 0 -C y The magnitude of the value of the | is,
when u 0 -C x |>|v 0 -C y When, both sides of the equation are divided by sy simultaneously t Derived from
Solved by least square method
A value of (d);
will be provided with
By the orthogonality of the rotation matrix
Thereby obtaining s and z t A value of (d);
binding to y t ,s,z t ,
Can find r 1i ,r 2i ,r 3i ,x t ,
A value of (d);
similarly, when | u 0 -C x |≤|v 0 -C y When, both sides of the equation are divided by x simultaneously t Solving for s, z t A corresponding value;
where zt represents the amount of translation in the z direction.
5. The parsing method according to claim 3,
the evaluation of the results included: selecting two different cameras for calibration and comparison, wherein parameters of each camera are known; the evaluation is compared with the aspects of reprojection errors and image center errors, distance errors and running time.
6. The parsing method according to claim 5,
the target surface of the target for the plane calibration pattern has 20 calibration point circles, and the calculated internal reference and external reference are introduced into the target surface
Calculating a new group of pixel point data and recording as (u ', v') and calculating the square error sum of the root of the data of the true pixel point (u, v) obtained from the image, averaging and recording as
Known center of image and will countCalculating the internal and external parameters
Calculated distortion center, recorded as C' x ,C′ y The error between;
set distortion center C x ,C y And calculating C' x ,C′ y Is recorded as
Bringing the calculated internal and external parameters of the camera into
Calculating a point P in the world coordinate system wi Point P in the camera coordinate system ci Moving the calibration plate by a certain distance through the control shaft, and calculating the point P in the world coordinate system after moving again wi The set of points in the camera coordinate system is: p' ci The error at this time is denoted as E 3 ＝|D′-D|。
7. An analytic device based on Tsai camera plane calibration algorithm is characterized by comprising:
the acquisition module is used for acquiring a picture of the target;
the processing module is used for extracting the coordinate value of the two-dimensional image at the center of the original point of the photo and solving the distortion coefficient of the coordinate value of the two-dimensional image;
the solving module is used for solving the distortion coefficient matrix;
and the output module is used for evaluating the result.
8. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor, when executing the computer program, implements the steps of the method according to any of claims 1 to 6.
9. A computer-readable storage medium, on which a computer program is stored, which, when being executed by a processor, carries out the steps of the method according to any one of claims 1 to 6.
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN115830133A (en) * | 2022-08-03 | 2023-03-21 | 宁德时代新能源科技股份有限公司 | Camera calibration method, camera calibration device, computer equipment, storage medium and program product |
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| CN115830133A (en) * | 2022-08-03 | 2023-03-21 | 宁德时代新能源科技股份有限公司 | Camera calibration method, camera calibration device, computer equipment, storage medium and program product |
| CN115830133B (en) * | 2022-08-03 | 2023-11-03 | 宁德时代新能源科技股份有限公司 | Camera calibration method, camera calibration device, computer equipment, storage medium and program product |
| WO2024027179A1 (en) * | 2022-08-03 | 2024-02-08 | 宁德时代新能源科技股份有限公司 | Camera calibration method and apparatus, computer device, storage medium, and program product |
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