CN111009014A - Calibration method of orthogonal spectral imaging pose sensor of general imaging model - Google Patents
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Abstract
The invention relates to calibration of an orthogonal spectral imaging pose sensor, aims to solve the problems of distortion correction and an imaging model of the orthogonal spectral imaging pose sensor, and provides a calibration method based on a general imaging model and applied to calibration of a novel orthogonal spectral imaging pose sensor. The invention adopts the technical scheme that the calibration method of the orthogonal spectral imaging pose sensor of the universal imaging model utilizes orthogonal spectral imaging of a double-linear array CCD camera to realize pose measurement, wherein continuous vector value functions are used for representing a mapping relation, the vector value functions are fitted through radial basis function interpolation, control points are adaptively selected by combining a Kmeans clustering method, a CCD camera matrix is solved, and the linear coordinates of each point in a calibration data set are solved according to the CCD camera matrix to realize calibration. The invention is mainly applied to the calibration occasion of the pose sensor.
Description
Technical Field
The invention relates to calibration of an orthogonal spectral imaging pose sensor, in particular to a calibration method of an orthogonal spectral imaging pose sensor of a general imaging model.
Background
In visual measurement, the linear array CCD has higher resolution and faster speed than the area array CCD, but the linear array CCD can only acquire one-dimensional images. In order to realize the space target measurement, a multi-view measurement method based on a plurality of linear array CCDs is generally adopted to complete the measurement. The multi-view measurement method requires that the measured space target must be within the common view field range of all linear array CCDs, so the measurement range is greatly limited. In order to meet the measurement requirements of large range, high precision and high speed in vision measurement, the orthogonal spectral imaging pose sensor based on the twin-line array CCD is designed and realized. The novel sensor is measured by combining a special optical imaging system with a double-linear array CCD to simulate a monocular area array CCD, so that the sensor solves the problem of small measurement range of a multi-view measurement system, and simultaneously improves the resolution of the measurement system, namely the measurement precision.
The optical system of the pose sensor consists of an imaging system and a light splitting system. The imaging system is an objective lens with a large field of view, mainly comprises an aperture diaphragm and a spherical mirror group and is responsible for imaging a space point into a two-dimensional image. The light splitting system is responsible for splitting a two-dimensional image into two one-dimensional images which are respectively received by the linear array CCD in the corresponding direction, and the light splitting system consists of a light splitting prism and two cylindrical lens groups. According to the curvature of the cylindrical mirror, light beams parallel to the optical axis can be compressed to the focus of the cylindrical mirror group to form a linear real image in the same direction as a bus, and particularly, the linear array CCD is placed perpendicular to the bus direction of the cylindrical mirror, so that the image can be acquired in the largest range without losing the large field of view of the objective lens.
Due to a special optical structure, various types of distortion exist in an optical system of the orthogonal spectral pose sensor, including radial distortion caused by a large-field-of-view objective lens, one-way errors caused by a cylindrical mirror, linear and nonlinear errors caused by assembly and the like. These distortions affect the imaging geometry and therefore the actual optical system differs from the ideal pinhole model. The nonlinear distortion of the optical system with a large field of view mainly includes radial distortion and tangential distortion, and the tangential distortion is negligible. The commonly used calibration method considers the influence of radial distortion on the basis of a pinhole imaging model, and mainly comprises a Tsai two-step method, a Weng method and a Zhang-Zhengyou method. These calibration methods require that each object point in the world coordinate system corresponds to at least two image points in the image coordinate system.
The pinhole imaging model is established based on the assumption of a central projection method and is suitable for an optical system for projecting rays to intersect at one point. The actual optical system has pupil difference at the entrance pupil, so that rays cannot intersect at one point, and the larger the pupil difference is, the lower the precision of calibration by using the pinhole imaging model is. The orthogonal spectral imaging pose sensor provided by the invention has a special optical structure and has larger distortion. The pinhole imaging model therefore does not accurately describe the imaging system. The rotational symmetry model proposed by Tardif et al, although it can solve the problem of pupil difference, still cannot solve the influence of manufacturing assembly errors on the calibration accuracy.
Disclosure of Invention
In order to overcome the defects of the prior art and solve the problems of distortion correction and imaging models of the orthogonal spectral imaging pose sensor, the invention aims to provide a calibration method based on a general imaging model and apply the calibration method to the calibration of a novel orthogonal spectral imaging pose sensor. The invention adopts the technical scheme that the calibration method of the orthogonal spectral imaging pose sensor of the universal imaging model utilizes orthogonal spectral imaging of a double-linear array CCD camera to realize pose measurement, wherein continuous vector value functions are used for representing a mapping relation, the vector value functions are fitted through radial basis function interpolation, control points are adaptively selected by combining a Kmeans clustering method, a CCD camera matrix is solved, and the linear coordinates of each point in a calibration data set are solved according to the CCD camera matrix to realize calibration.
Introducing a Pluecker coordinate to represent incident light rays, enabling each incident light ray to have a unique coordinate, namely the incident light rays are represented as 6 homogeneous coordinates on a 5-dimensional projective space PR5, the corresponding relation between an object point under a world coordinate system and a pixel on a CCD camera image sensor is converted into a straight line under the Pluecker coordinate system, and the use (x is used for setting1，x2，x3) Representing a point in the 3-dimensional space R3, two points x ═ x (x)1，x2，x3)T，y＝(y1，y2，y3)TThe straight line has a Prock coordinate of lij＝xiyj-xjyiWherein x is0＝y00. The Prock coordinates are expressed in the form of a vector
All relations between object points in a world coordinate system and pixel points under an image coordinate system are expressed by using a vector value function f (x), and the vector value function is fitted by using the world coordinate values and the image coordinate values of part of known points by adopting an interpolation method based on a radial basis function:
wherein HcamIs a camera matrix, x is an image coordinate;
for any given radial basis function, the set of image points { x ] is knowni1, …, N, control point set ci1, … M and the camera matrix, where the set of image points and the set of control points are obtained by measurement, the vector value function f (x) can be estimated, and the camera matrix needs to be obtained by calibration:
according to the characteristics of the Prock line, the following expression is obtained
Wherein, { wi1, …, and N is the world coordinate set of the object point; { xi1, …, where N is the set of image coordinates of the image point;
from the above equation, the camera matrix is solved from the image coordinates x and world coordinates w of the known points, and if the image coordinates and world coordinates of the N points are known, the above equation is rewritten to
Mvec(Hcam)＝0
Order to
The problem is converted into a least squares solution for solving a homogeneous system of equations, and the matrix M is expressed as M ═ UD according to a singular value decomposition methodTV, where M is an M × n matrix, U is an M × M matrix, and V is an n × n matrix. I.e., vec (H)cam) Is the last column of matrix V;
thus, the set of calibration data { x is knowni→wiWhen i is 1, …, N, the camera matrix H is solvedcam。
The concrete steps are detailed as follows:
firstly, coordinate normalization processing: carrying out normalization processing on the image coordinate values and the world coordinate values of each point, wherein a normalization data set is used as data used in the subsequent steps;
secondly, selecting control points in a self-adaptive manner according to given data by adopting a K-means clustering method;
thirdly, selecting a proper radial basis function: selecting a MultiQuadric function and a Gaussian function with shape parameters as radial basis functions to calibrate a camera matrix, wherein the MultiQuadric function is called MQ function for short;
fourthly, solving a camera matrix HcamCalculating a calibration matrix M according to the image coordinate and world coordinate pair, and solving a camera matrix by using a singular value decomposition method;
fifthly, using the image coordinate value x of any point and the solved camera matrix HcamAnd fitting to obtain corresponding line coordinates, and converting the line coordinates obtained by interpolation fitting into original numerical values according to the following formula.
And sixthly, repeatedly executing the fifth step until the coordinate values of all the points in the data set are fitted.
The invention has the characteristics and beneficial effects that:
according to the calibration method provided by the invention, the vector value function is calibrated through interpolation fitting of the radial basis function, the fitting precision is improved by combining the self-adaptive selection of the control points by the Kmeans clustering method, and the problems of distortion correction and imaging model existing in the orthogonal spectral imaging pose sensor are solved. The universal imaging model does not consider distortion influence, only concerns the mapping relation between incident light and pixels to establish the corresponding relation between a world coordinate system and an image coordinate system, and is suitable for a special optical imaging system. The invention realizes a calibration method based on a general imaging model, and is applied to the calibration of a novel orthogonal spectral imaging pose sensor.
Description of the drawings:
FIG. 1 is a flow chart of a calibration method of an orthogonal spectral imaging pose sensor based on a general imaging model.
FIG. 2 sets of calibration samples. (a) Calibrating the collection result of the world coordinate data of the collection (b) calibrating the collection result of the image coordinates of the collection.
FIG. 3 tests the collection of data sets. (a) Test data set world coordinate acquisition results (b) test data set image coordinate acquisition results.
FIG. 4 different radial basis function interpolation fit error analysis. (a) RMS of the calibration results and test results interpolated using MQ functions (b) RMS of the calibration results and test results interpolated using gaussian functions.
Detailed Description
The invention is designed for calibration of an orthogonal spectral imaging pose sensor. The calibration method is based on a general imaging model, introduces a Prock straight line to represent the mapping relation between an image coordinate system and a world coordinate system, adopts a radial basis function interpolation method to fit the mapping relation, and adaptively selects a control point through a Kmeans clustering method to improve the fitting precision.
The invention aims to solve the problems of distortion correction and imaging model of an orthogonal spectral imaging pose sensor. The universal imaging model does not consider distortion influence, only concerns the mapping relation between incident light and pixels to establish the corresponding relation between a world coordinate system and an image coordinate system, and is suitable for a special optical imaging system. The invention realizes a calibration method based on a general imaging model, is applied to the calibration of a novel orthogonal spectral imaging pose sensor, uses a continuous vector value function to express a mapping relation, performs calibration by interpolating and fitting the vector value function through a radial basis function, improves the fitting precision by combining a Kmeans clustering method and adaptively selecting a control point, and realizes calibration.
The invention comprises an orthogonal spectral imaging pose sensor mathematical model based on a general imaging model and a calibration method of an orthogonal spectral imaging pose sensor.
The orthogonal spectral imaging pose sensor mathematical model based on the general imaging model introduces the Prockian coordinates to represent incident rays, so that each incident ray has unique coordinates, namely the incident rays can be represented as 6 homogeneous coordinates on a 5-dimensional projective space PR 5. The corresponding relation between the object point in the world coordinate system and the pixel on the image sensor is converted into a straight line in the Plucko coordinate system. Let use (x)1，x2，x3) Representing a point in the 3-dimensional space R3, two points x ═ x (x)1，x2，x3)T，y＝(y1，y2，y3)TThe straight line has a Prock coordinate of lij＝xiyj-xjyiWherein x is0＝y00. The prock coordinates may be expressed in the form of a vector
Assuming that the correspondence is continuously variable, the overall relationship between object points in the world coordinate system and pixel points in the image coordinate system can be represented using a vector value function f (x). The vector value function can be fitted by utilizing the world coordinate values and the image coordinate values of part of known points and adopting an interpolation method based on a radial basis function.
Wherein HcamIs the camera matrix and x is the image coordinates.
As can be seen from the above equation, for any given radial basis function, the set of image points { x ] is knowni1, …, N, control point set ci1, … M and the camera matrix, the vector value function f (x) can be estimated. Wherein the set of image points and the set of control points can be obtained by measurement, and the camera matrix needs to be obtained by calibration.
From the characteristics of the Prock line, the following expression can be obtained
Wherein, { wi1, …, and N is the world coordinate set of the object point; { xi1, …, and N is the set of image coordinates of the image point.
From the above equation, knowing the image coordinates x and world coordinates w of the points, the camera matrix can be solved. If the image coordinates and world coordinates of N points are known, the above formula can be rewritten as
Mvec(Hcam)＝0
Order to
The problem is converted to a least squares solution to solve a homogeneous system of equations. According to the singular value decomposition method, the matrix M may be expressed as M ═ UDTV, where M is an M × n matrix, U is an M × M matrix, and V is an n × n matrix. I.e., vec (H)cam) Is the last column of the matrix V.
Thus, the set of calibration data { x is knowni→wiI is 1, …, N, i.e. the camera matrix H can be solvedcam。
The calibration method provided by the invention comprises the following steps:
firstly, coordinate normalization processing is carried out. The selected radial basis interpolation function has shape parameters, the shape parameters are selected depending on the distribution of points under a coordinate system, and the image coordinate values and the world coordinate values of the points are normalized to avoid the influence of a scale factor of an optical imaging system on the coordinate values. The normalized data set serves as data for subsequent steps.
And secondly, adaptively selecting control points according to given data by adopting a K-means clustering method. The radial basis function is an interpolation method based on high-dimensional scattered data, the approximation degree and stability of the function are closely related to the distribution of control points, and the control points are selected in a random mode, so that the reasonable distribution of the control points cannot be ensured. Therefore, the selection of the control point is a very important content in the calibration method, and directly influences the measurement accuracy.
And thirdly, selecting a proper radial basis function. Because the interpolation effect of the radial basis function with the shape parameter is better, the invention selects a MultiQuadric function (MQ function for short) and a Gaussian function with the shape parameter as the radial basis function to calibrate the camera matrix.
Fourthly, solving a camera matrix Hcam. And calculating a calibration matrix M according to the image coordinate and the world coordinate pair, and solving the camera matrix by using a singular value decomposition method.
Fifthly, using the image coordinate value x of any point and the solved camera matrix HcamAnd fitting to obtain corresponding line coordinates. Since the normalized coordinate values change the coordinate values of the line space, the line coordinates obtained by interpolation fitting are converted into original values according to the following formula.
And sixthly, repeatedly executing the fifth step until the coordinate values of all the points in the data set are fitted.
The invention provides a calibration method of an orthogonal spectral imaging pose sensor based on a general imaging model. The method does not consider any distortion, establishes a mapping relation between an image coordinate system and a world coordinate system, and realizes the calibration of the novel orthogonal spectral imaging pose sensor. The calibration flow chart is shown in fig. 1.
The invention collects 358 point image coordinate data and world coordinate data as calibration set, and 364 point image coordinate data and world coordinate data as test set for test, the points of the test set and calibration set are not coincident. The distribution of the acquisition results of the calibration set and the test set is shown in fig. 2 and 3.
And performing interpolation fitting by respectively adopting two different radial basis functions and different shape parameter values, and respectively applying the calibration result to calibration data and test data for error evaluation. The error estimate is expressed in terms of the distance of the object point in the world coordinate system to the fitted Procko line, as shown in FIG. 4. And selecting the shape parameter which enables the difference value between the testing root mean square error value and the calibration root mean square error value to be minimum from the experimental data as the shape parameter of the MQ radial basis function to calibrate the orthogonal spectral imaging pose sensor. The RMS of the calibration data set and the test data set are shown in table 1. The experimental result shows that the calibration method based on the universal imaging model can meet the calibration requirement of the orthogonal spectral imaging pose sensor.
TABLE 1 comparison of different radial basis function errors
Aiming at an image data set acquired by the orthogonal spectral imaging pose sensor, a radial basis interpolation method is adopted to fit the mapping relation between an image coordinate system and a world coordinate system, and a proper shape parameter value is selected according to different radial basis functions to complete the calibration of the orthogonal spectral imaging pose sensor.
Claims (3)
1. A calibration method of an orthogonal spectral imaging pose sensor of a universal imaging model is characterized in that the orthogonal spectral imaging of a double-linear array CCD camera is utilized to realize pose measurement, wherein a continuous vector value function is used for representing a mapping relation, the vector value function is fitted through radial basis function interpolation, a Kmeans clustering method is combined to select control points in a self-adaptive mode, a CCD camera matrix is solved, and the linear coordinates of each point in a calibration data set are solved according to the CCD camera matrix to realize calibration.
2. The method for calibrating an orthogonal spectral imaging pose sensor of a universal imaging model as claimed in claim 1, wherein the incident light is represented by the Prockian coordinates, each incident light has unique coordinates, i.e. the incident light is represented by 6 homogeneous coordinates on the 5-dimensional projective space PR5, the correspondence between the object point under the world coordinate system and the pixel on the CCD camera image sensor is transformed into a straight line under the Prockian coordinate system, and the application (x) is set1，x2，x3) Representing a point in 3-dimensional space R3, then passes through two pointsx＝(x1，x2，x3)T，y＝(y1，y2，y3)TThe straight line has a Prock coordinate of lij＝xiyj-xjyiWherein x is0＝y0When the sum is 0, the Prock coordinate is expressed in the form of vector
All relations between object points in a world coordinate system and pixel points under an image coordinate system are expressed by using a vector value function f (x), and the vector value function is fitted by using the world coordinate values and the image coordinate values of part of known points by adopting an interpolation method based on a radial basis function:
wherein HcamIs a camera matrix, x is an image coordinate;
for any given radial basis function, the set of image points { x ] is knowni1, …, N, control point set ci1, … M and the camera matrix, where the set of image points and the set of control points are obtained by measurement, the vector value function f (x) can be estimated, and the camera matrix needs to be obtained by calibration:
according to the characteristics of the Prock line, the following expression is obtained
Wherein, { wi1, …, and N is the world coordinate set of the object point; { xi1, …, where N is the set of image coordinates of the image point;
from the above equation, the camera matrix is solved from the image coordinates x and world coordinates w of the known points, and if the image coordinates and world coordinates of the N points are known, the above equation is rewritten to
Mvec(Hcam)＝0
Order to
The problem is converted into a least squares solution for solving a homogeneous system of equations, and the matrix M is expressed as M ═ UD according to a singular value decomposition methodTV, where M is an M × n matrix, U is an M × M matrix, and V is an n × n matrix, i.e., vec (H)cam) Is the last column of matrix V;
thus, the set of calibration data { x is knowni→wiWhen i is 1, …, N, the camera matrix H is solvedcam。
3. The calibration method of the orthogonal spectral imaging pose sensor of the general imaging model as claimed in claim 1, characterized by comprising the following concrete steps:
firstly, coordinate normalization processing: carrying out normalization processing on the image coordinate values and the world coordinate values of each point, wherein a normalization data set is used as data used in the subsequent steps;
secondly, selecting control points in a self-adaptive manner according to given data by adopting a K-means clustering method;
thirdly, selecting a proper radial basis function: selecting a MultiQuadric function and a Gaussian function with shape parameters as radial basis functions to calibrate a camera matrix, wherein the MultiQuadric function is called MQ function for short;
fourthly, solving a camera matrix HcamCalculating a calibration matrix M according to the image coordinate and world coordinate pair, and solving a camera matrix by using a singular value decomposition method;
fifthly, using the image coordinate value x of any point and the solved camera matrix HcamFitting to obtain corresponding line coordinates, and converting the line coordinates obtained by interpolation fitting into original values according to the following formula:
and sixthly, repeatedly executing the fifth step until the coordinate values of all the points in the data set are fitted.
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| CN116047753A (en) * | 2022-12-30 | 2023-05-02 | 中国科学院长春光学精密机械与物理研究所 | Construction and optimization method of orthogonal optimization model of optical system |
| CN116758160A (en) * | 2023-06-20 | 2023-09-15 | 哈尔滨工业大学 | Method for detecting pose of optical element assembly process based on orthogonal vision system and assembly method |
| CN117119325A (en) * | 2023-08-24 | 2023-11-24 | 合肥埃科光电科技股份有限公司 | Area array sensor camera and mounting position adjusting method thereof |
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Cited By (7)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN111551917A (en) * | 2020-04-30 | 2020-08-18 | 中国科学院沈阳自动化研究所 | Calibration method of laser triangulation displacement sensor |
| CN116047753A (en) * | 2022-12-30 | 2023-05-02 | 中国科学院长春光学精密机械与物理研究所 | Construction and optimization method of orthogonal optimization model of optical system |
| CN116047753B (en) * | 2022-12-30 | 2024-03-12 | 中国科学院长春光学精密机械与物理研究所 | Construction and optimization method of orthogonal optimization model of optical system |
| CN116758160A (en) * | 2023-06-20 | 2023-09-15 | 哈尔滨工业大学 | Method for detecting pose of optical element assembly process based on orthogonal vision system and assembly method |
| CN116758160B (en) * | 2023-06-20 | 2024-04-26 | 哈尔滨工业大学 | Method for detecting pose of optical element assembly process based on orthogonal vision system and assembly method |
| CN117119325A (en) * | 2023-08-24 | 2023-11-24 | 合肥埃科光电科技股份有限公司 | Area array sensor camera and mounting position adjusting method thereof |
| CN117119325B (en) * | 2023-08-24 | 2024-03-12 | 合肥埃科光电科技股份有限公司 | Area array sensor camera and mounting position adjusting method thereof |
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Application publication date: 20200414 |