CN113781581A - Depth of field distortion model calibration method based on target loose attitude constraint - Google Patents
Depth of field distortion model calibration method based on target loose attitude constraint Download PDFInfo
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Abstract
The invention belongs to the field of computer vision measurement, and provides a depth of field distortion model calibration method based on target loose attitude constraint. In the aspect of image acquisition calibration, the camera is used for acquiring images of multiple postures of the target in the depth of field, the target plane is not required to be perpendicular to the optical axis when the postures are put, the target is only required to be ensured to cover the imaging field of view and the depth of field, and two types of features of straight lines and angular points on the target can be imaged. In the aspect of field depth distortion model calibration, firstly, the angular point distances of the central areas of all target images are used as constraints to calibrate an internal parameter matrix; secondly, calculating the object distance of the straight line point on the target according to the homography matrix; thirdly, establishing a minimized objective function containing the depth of field distortion model parameters by taking the minimum distance between the detected straight line point and the straight line where the detected straight line point is located as a constraint; and finally, optimizing an objective function by taking the pixel coordinates of the straight line points, the object distance of the straight line points and the focal length as input quantities to complete the solution of all parameters of the depth-of-field distortion model.
Description
Technical Field
The invention belongs to the field of computer vision measurement, and relates to a method for calibrating parameters of a depth of field distortion model, which is implemented without a target and a camera optical axis being in a vertical placing posture.
Background
The vision measurement technology quantitatively represents object information through image information and imaging model parameters, has the advantages of non-contact, real-time, high precision and full-field measurement, and is widely applied to various fields, wherein the imaging model parameters of a vision system comprise internal parameters, external parameters and distortion parameters. Wherein the distortion parameter has a strong correlation with the imaging depth of field. Therefore, the portability and the precision of the parameter calibration of the depth-of-field distortion model are ensured, and the method has important significance for improving the measurement precision and the practicability of the visual system.
The invention discloses a lens distortion model considering distortion partitions such as depth of field dimension and space, and discloses a lens distortion model with a patent number of CN 112258584A, namely Li Xiao et al of China Petroleum university (east China). In addition, in 2017, sunpeng, the university of beijing, published a paper entitled "modeling and calibration of depth-dependent distortion for large depth visual measurement" in Optics Express journal, and the paper proposed a depth distortion model suitable for large object distance, wide field imaging scenes, solved and calibrated the distortion amount on any defocusing plane perpendicular to the optical axis, and promoted the three-dimensional measurement accuracy of vision in 6m object distance, 7.0 × 3.5 × 2.5m space from 0.055mm to 0.028 mm. For the above calibration method for the depth-of-field distortion model, it is necessary to ensure that the target plane and the optical axis are always placed vertically during implementation, which puts high requirements on the experimental device and the operation flow, so that the whole calibration process is complicated, human errors are easy to introduce, and the practicability is poor.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a depth of field distortion model calibration method based on target loose attitude constraint. The method comprises the following steps: and calibrating image acquisition and field depth distortion model calibration. In the aspect of calibrating image acquisition, the camera is used for acquiring images of a plurality of postures of the target in the depth of field, the target placing posture is not required to be vertical to the optical axis of the camera, the target is only required to be ensured to cover the field of view and the depth of field of the camera, and two types of features, namely straight lines and angular points on the target can be imaged. In the aspect of field depth distortion model calibration, firstly, the inner parameters of a camera imaging model are calibrated by using the angular point distance constraint of the central areas of a plurality of target images; secondly, resolving the object distance of the straight line points on the target image according to the homography matrix; thirdly, establishing a minimized objective function containing the depth of field distortion model parameters by taking the minimum distance between the detected straight line point and the straight line where the detected straight line point is located as a constraint; and finally, optimizing an objective function by taking the pixel coordinates of the straight line points, the object distance of the straight line points and the focal length as input quantities to complete the solution of all parameters of the depth-of-field distortion model.
The invention relates to a depth of field distortion model calibration method based on target loose attitude constraint, which comprises the steps of sequentially completing image center angular point distance constraint-based imaging model internal parameter solution according to target images collected under a plurality of attitudes, and optimizing and solving depth of field distortion model parameters by taking the minimum square of the distance from points to straight lines as an objective function after image straight line point object distance solution based on a homography matrix. Different from the requirements of other depth-of-field model calibration methods on the placement of the vertical postures of the targets and the optical axis of the camera, the calibration method disclosed by the invention has loose constraint on the postures of the targets, only needs a plurality of targets placed in the postures to cover the field of view and the depth of field, and ensures that straight lines and angular points on the targets are visible. The method improves the calibration convenience and has low calibration cost on the premise of ensuring the calibration precision of the distortion model.
A field depth distortion model calibration method based on target loose attitude constraint comprises the following steps:
first step, image acquisition
The whole camera deep distortion model calibration experiment system consists of a camera, a lens and a target; the method comprises the following steps that a target for parameter calibration in a camera depth distortion model is a plane plate, two characteristics of straight lines and angular points are arranged on the target, and the intersection point of every two straight lines is the angular point to ensure that the distance between every two angular points is accurately known during machining; image acquisition is a precondition for solving parameters of a depth distortion model of a camera; firstly, opening a camera provided with a lens, setting the acquisition frame frequency, the exposure time, the focal length and the resolution of the camera, and finishing the focusing of the lens after adjusting the focusing distance; secondly, the target is placed in front of the camera in multiple postures, the target is not required to be perpendicular to the optical axis of the lens, the target postures are only required to cover the view field and the depth of field of the camera, and the angular points and the straight lines can be imaged. And after placing one target gesture, enabling the target to be in a static state, acquiring target images by using a camera, and finally acquiring the target images under a plurality of gestures.
Second, calibrating the depth distortion model of the camera
(1) Camera imaging model
The camera imaging model describes the one-to-one mapping relation between the object space point and the image space point, and records the object space point
Has homogeneous coordinates of (x, y, z,1)TIts undistorted projected point on the image
Has homogeneous coordinates of (u, v,1)T. Because the target plane and the image plane are both two-dimensional planes, the camera imaging model can be expressed as:
wherein s is a scale factor,
is an internal parameter matrix, C0＝(cx,cy)TAs the center of distortion of the image, fx、fyIs the equivalent focal length in the u and v directions. f. ofx＝f/dx，fy＝f/dy，dx and dyIs the physical size of the picture element in the horizontal and vertical directions. f is the focal length of the lens. r is1 and r2For world coordinate systems and faciesThe first two column vectors of the transformation matrix are rotated between the machine coordinate systems, and t is a translation vector between the world coordinate system and the camera coordinate system. H ═ s.M [. r ]1 r2 t]The conversion relation between the target plane and the image plane is expressed as a homography matrix.
(2) Camera depth distortion model
Manufacturing and assembly process defects cause radial distortion and decentration of the lens, so that the projection of a straight line on an image is a curve. A lens distortion model is expressed by a polynomial, and the formula is as follows:
wherein ,
for distorted image point coordinates, deltau、δvIs a distortion function of the image point in the u and v directions,
is the distortion radius, k, of an image point1 and k2First and second order radial distortion parameters, p, respectively1 and p2First and second order eccentric distortion parameters, respectively.
The magnitude of lens distortion is closely related to the depth of field, and particularly under the close-range condition, the relationship is stronger and the generated distortion is larger. Considering that the imaging distortion caused by different object distances is different, the object distances are connected with the distortion model to establish a depth-of-field distortion model, and the expression is as follows:
wherein ,
to enlarge the parameter, satisfy
Respectively, the object distance is sn、sm、 and skThe ith radial distortion parameter on the focal plane.
And
respectively, the object distance is focused to sn and smF is the focal length of the lens. The following formula can be obtained by referring to Duane C.Brown paper "Close-range camera calibration" and the client S.Fraser paper "Variation of diagnosis with the photopgraphic field":
wherein g is an empirical parameter,
and
when the lens is focused at the object distance s, the lens is at the object distance skThe ith radial distortion parameter and the eccentricity distortion parameter of the defocus plane,
the result of equation (4) is generalized to the i-th order eccentric distortion parameter for a focal plane at infinityn、sm and skThe distortion parameter relation between the defocus planes represented by the formula (5) is obtained:
wherein ,
and
when focusing on the object distance s, the object distance is snThe ith radial distortion parameter and the eccentric distortion parameter on the defocusing plane;
and
when focusing on the object distance s, the object distance is smAn ith-order radial distortion parameter and an eccentric distortion parameter on the defocusing plane; the radial distortion parameter and the eccentric distortion parameter in the formula (5) do not depend on the focal distance s and the distortion parameter on the focal plane, so that a camera depth distortion model of the lens is established.
(3) Camera depth distortion model calibration
1) Internal parameter calibration
Considering the characteristics that the lens distortion is small in the center and large in the periphery of the image, the method uses the known distances between the angular points of the central regions of all target images as constraints, and calibrates the internal parameter matrix of the camera by using the method in the paper A flexible new technique for camera calibration published in Zhang Zhen Yong 2000
And then pass through fx＝f/dxAnd obtaining the focal length f of the camera.
2) Linear point object distance solution
The distortion of the lens can distort an object-side straight line into a curve on an image, namely, the imaging of points on the straight line under the effect of the distortion of the lens can be distributed in a curve. First, the pixel coordinates of a straight line point on an image are located using a gray scale gravity center method, which can be expressed by equation (6):
wherein f (u, v) is a coordinate of (u, v)TThe gray value of the pixel point theta is over (u, v)TA set of pixel points with points in a straight-line vertical direction,
is the pixel coordinates of the located straight line point.
From the formula (5), the distortion parameter solution requires that the object distance of the straight line point is known, and therefore, the object distance of the straight line point is calculated on the basis of positioning the straight line point. Suppose that the coordinate of a certain straight line point p positioned on the image is
Order to
Wherein p ═ p (p)x,py,pz)T. The coordinates of the straight line points after the action of the homography matrix H are
The object distance of the straight line point p on the target image can be expressed by formula (7):
3) depth of field distortion model parameter solution
The change of the straightness generated by changing the action of the object-side straight line into a curve under the action of lens distortion can be expressed by a radial distortion parameter and an eccentric distortion parameter. Suppose there are n straight line points on a straight line, the jth straight line point is Ωj＝(uj,vj)T J 1,2, n, determined by the straight-line pointsThe regression line equation of (a) can be expressed as:
wherein ,
and gamma is the distance from the point to the regression line, the square of the distance from the point to the regression line can be expressed as:
wherein ,
α＝a-c，
on the basis, the depth distortion model is calibrated. Firstly, supposing that the camera acquires eta' images of the target in different postures, wherein the eta image has lηThe line on the ith' line of the ith image is detectedη,jThe number of the straight-line points is,ηΩi′is the set of all the straight line points on the ith' straight line of the ith image,ηΩi′,jandηsi′,jrespectively representing the jth straight line point on the ith' straight line of the ith image and the object distance of the straight line point. Then, the invention takes the minimum distance between the point and the regression line as the target, substitutes the depth of field distortion model shown in the formula (5) into the formula (2) and the formula (9), and optimizes and solves the distortion parameter
i is 1, 2. The established minimization objective function can be expressed as:
equation (5) is the radial distortion parameter and the eccentric distortion parameter of a straight line point with an arbitrary object distance, and the two types of distortion parameters are related to the object distance, the radial distortion parameter, the eccentric distortion parameter and the focal length f of the lens of the other two straight line points. For solving, two straight-line points are selected in the depth of field, the object distance is sk and sm. Then, the pixel coordinates of the straight line points on all the target images are usedηΩi′,jObject distance of straight line pointηsi′,jThe calibrated focal length f is used as An input quantity, and An objective function shown in a formula (10) is optimized by a Levenberg-Marquardt (LM) algorithm in a D.Marquardt published paper "An algorithm for space resolution on nonlinear parameters", so as to obtain a depth distortion model parameter
Therefore, the solving of each parameter of the depth-of-field distortion model is completed under the condition of target placement attitude loose constraint.
The invention has the beneficial effect of providing a depth of field distortion model calibration method without strict requirements on the placement posture of a target. For other depth-of-field distortion model calibration methods, in order to enable the calibration method to be carried out smoothly, the target and the camera optical axis are required to be kept in a vertical placing posture all the time, so that high requirements are provided for a calibration experimental device and an operation flow, the calibration time cost is high, human errors are easy to introduce, and the practicability is poor.
Drawings
Fig. 1 is a schematic diagram illustrating a method for calibrating a depth-of-field distortion model based on a target loose-posture constraint. The system comprises a camera 1, a lens 2, a target 3, an angular point 4 and a straight line 5.
Fig. 2 is a flowchart of a depth-of-field distortion model calibration method based on target loose-posture constraint.
Detailed Description
The following describes the embodiments of the present invention in detail with reference to the technical solutions and the accompanying fig. 1 and 2. FIG. 1 is a schematic diagram of a depth of field distortion model calibration method based on target loose pose constraints. FIG. 2 is a flow chart of a depth of field distortion model calibration method based on target loose pose constraints.
The invention relates to a depth of field distortion model calibration method based on target loose attitude constraint, which comprises image acquisition and solving of depth of field distortion model parameters. The whole calibration process can be summarized as follows: the lens 2 is arranged on the camera 1, and the camera 1 is used for collecting images of the target 2 in a plurality of postures to finish image collection; on the basis, parameters in the depth-of-field distortion model are calibrated, and firstly, an internal parameter matrix is solved by using the angular point distance constraint of all image central regions. Secondly, the object distance of the straight line point is calculated by utilizing the homography matrix. And finally, for the depth of field distortion model, optimizing and solving each parameter of the depth of field distortion model by taking the minimum distance from the point on the image to the regression line as constraint and taking the pixel coordinate of the linear point, the object distance of the linear point and the focal length of the camera as input quantities. The following detailed description is made of specific embodiments:
1. image acquisition
The whole camera distortion model calibration experiment system comprises a camera 1, a lens 2 and a target 3. The target 3 for calibrating the parameters of the depth-of-field distortion model of the camera is a plane plate, two characteristics of an angular point 4 and a straight line 5 are arranged on the plane plate, the intersection point of every two straight lines 5 is the angular point 4, the distance between every two angular points 4 is 7.5mm, and 16 straight lines 5 are distributed on the target in a transverse and vertical mode. When image acquisition is carried out, firstly, the camera 1 is connected and opened, the acquisition frame frequency of the camera 1 is set to be 30 frames, the exposure time is 0.3s, the theoretical focal length is 50mm, the imaging resolution is 4092 pixels multiplied by 3072 pixels, the focusing object distance is adjusted to be 420mm, and the focusing of the camera 1 is completed. Secondly, put a plurality of gestures with target 3 in front of camera 1, this process need not target 3 and camera 1's optical axis perpendicular, only need guarantee that target 3's gesture can cover camera 1's visual field and depth of field, and angular point 4 and straight line 5 can both form images can. After placing one target 2 gesture, keeping the target 2 still, and acquiring images of the target 2 by using the camera 1 to finally obtain target images under 12 gestures.
2. Depth of field distortion model calibration
(1) Imaging model
Program code for creating an imaging model represented by formula (1), and a homography matrix H ═ s · M · [ r ·1 r2 t]The expression code of (1);
(2) depth of field distortion model
Manufacturing and assembly process defects cause radial distortion and decentering distortion of the lens 2 such that the straight line 1 projects as a curve on the image. For this purpose, a polynomial distortion model shown in formula (2) is introduced into formula (1) to obtain a radial distortion parameter (k) with a first order and a second order1 and k2) And first and second order eccentric distortion parameters (p)1 and p2) And (3) imaging the model expression of the camera, and compiling corresponding program codes.
The lens distortion magnitude is closely related to the depth of field position, and the object distance is related to the distortion model to establish a depth of field distortion model on the focusing plane shown in formula (3) in consideration of the fact that the imaging distortion caused by different object distances is different. On the basis, the formula (3) is generalized according to the result of the formula (4), and the relational expression among the defocus plane distortion parameters represented by the formula (5) is obtained. Programming a depth of field distortion model program code of any object distance out-of-focus plane;
(3) depth of field distortion model calibration
1) Internal parameter calibration
Considering the characteristics that the lens distortion is small in the center of the image and large in the periphery, the known distance between the corner points 3 in the center area of all 12 target images is taken as constraint, and the internal parameter matrix of the camera is calibrated by using the method in the paper Aflex new technology for camera calibration published in Zhang Zhengyou 2000. The focal length f of the camera was found to be 49.66mm, the center of image distortion (c)x,cy)T＝(2043.1,1531.3)T。
2) Linear point object distance solution
The distortion of the lens 2 can distort an object-side straight line into a curve on an image, namely, the image of a straight line point under the distortion effect can be distributed in a curve, and the distortion parameter is solved by using the straight line point according to the fact. Firstly, the pixel coordinates of the straight line points on the image are positioned by utilizing a gray scale gravity center method shown in a formula (6), the formula (5) shows that the distortion parameter solving requires that the object distance of the straight line points is known, and therefore, the invention calculates the object distance of the straight line points on the basis of positioning the straight line points according to the formula (7).
3) Depth of field distortion model parameter solution
Under the action of lens distortion, the change of straightness generated by changing object space straight line into curve can be expressed by using a radial distortion parameter and an eccentric distortion parameter. For all the straight line points on a certain straight line on the image, solving regression straight line equations corresponding to the straight line points according to a formula (8), and further obtaining the distance from each straight line point to a regression straight line according to a formula (9).
On the basis, each parameter of the depth of field distortion model is solved, the camera 1 acquires 12 images of the target 3 in different postures, each image has 32 straight lines, the number range of the straight line points detected on each straight line is 1200-1688, and the object distance of each straight line point can be obtained according to the homography matrix. Taking the 3 rd image as an example, 32 straight lines were shared by the 3 rd image, 1600 straight line points were detected on the 6 th straight line, and the pixel coordinates of the 1200 th, 1300 th and 1400 th straight line points were (785,429)T、(857,436)TAnd (926,437)T. The object distances of the 1200 th, 1300 th and 1400 th straight line points are 443.5mm, 450.2mm and 456.7mm, respectively.
Two straight line points are arbitrarily selected in all images, and the object distances are respectively sk456.8mm and sm415.8 mm. For 12 collected images, with the minimum distance from the point to the regression line as the target, the depth distortion model shown in formula (5) is substituted into formula (2) and formula (9), and the pixel coordinates of all the detected line points are usedηΩi′,jObject distances of all straight line pointsηsi′,jMarquardt published paper "An algorithm for least squares estimation on nonlinear parameters"The Levenberg-Marquardt (LM) algorithm in (1) optimizes an objective function formula (10) to obtain distortion parameters
i is 1, 2. Object distance is sk456.8mm and smThe results for each distortion parameter at 415.2mm are:
and
thus, the calibration of each parameter of the depth-of-field distortion model is completed under the condition of target attitude loose constraint. After the distortion parameters are obtained, the radial distortion parameter and the eccentric distortion parameter of any object from the straight line point can be obtained according to the formula (5).
The depth of field distortion model calibration method based on the target loose posture constraint realizes high-precision calibration of the depth of field distortion model under the target loose posture constraint, and overcomes the dependence on the target and the camera optical axis always keeping the vertical posture when the traditional method is used for calibration. The method reduces the dependency of calibration on an experimental device and an operation process, improves the convenience of calibration on the premise of ensuring the calibration precision, and has good applicability.
Claims (1)
1. A field depth distortion model calibration method based on target loose attitude constraint is characterized by comprising the following steps:
first step, image acquisition
The whole camera depth distortion model calibration experiment system mainly comprises a camera, a lens and a target; the target for parameter calibration in the camera depth distortion model is a plane plate, two characteristics of straight lines and angular points are arranged on the plane plate, and the intersection point of every two straight lines is an angular point; ensuring that the distance between every two angular points is known during processing; image acquisition is a precondition for solving parameters of a depth distortion model of a camera; firstly, opening a camera provided with a lens, setting the acquisition frame frequency, the exposure time, the focal length and the resolution of the camera, and finishing the focusing of the lens after adjusting the focusing distance; secondly, placing a plurality of postures of the target in front of the camera without the target being perpendicular to the optical axis of the lens, and only ensuring that the postures of the target can cover the view field and the depth of field of the camera and angular points and straight lines can be imaged; after placing a target gesture, enabling the target to be in a static state, collecting target images by using a camera, and finally collecting and obtaining target images under a plurality of gestures;
second, depth of field distortion model calibration
(1) Camera imaging model
The camera imaging model describes the one-to-one mapping relation between the object space point and the image space image point, and records the object space point
Has homogeneous coordinates of (x, y, z,1)TIts undistorted projected point on the image
Has homogeneous coordinates of (u, v,1)T(ii) a Because the target plane and the image plane are both two-dimensional planes, the camera imaging model is expressed as:
wherein s is a scale factor,
is an internal parameter matrix, C0＝(cx,cy)TAs the center of distortion of the image, fx、fyEquivalent focal lengths in the u and v directions; f. ofx＝f/dx，fy＝f/dy，dx and dyIs the physical size of the picture element in the horizontal and vertical directions; r is1 and r2For world coordinate systems and faciesRotating the first two column vectors of the transformation matrix between the machine coordinate systems, wherein t is a translation vector between the world coordinate system and the camera coordinate system; h ═ s.M [. r ]1 r2 t]The homography matrix is used for expressing the conversion relation between the target plane and the image plane; f is the focal length of the lens;
(2) camera depth distortion model
Manufacturing and assembling process defects cause radial distortion and eccentric distortion of the lens, so that the projection of a straight line on an image is a curve; a polynomial is adopted to express a camera lens distortion model, and the formula is as follows:
wherein ,
for distorted image point coordinates, deltau、δvIs a distortion function of the image point in the u and v directions,
is the distortion radius, k, of an image point1 and k2First and second order radial distortion parameters, p, respectively1 and p2First and second order eccentric distortion parameters, respectively;
the lens distortion magnitude is closely related to the depth of field position, the object distance and the distortion model are related to establish a camera depth of field distortion model in consideration of different imaging distortions caused by different object distances, and the expression is as follows:
wherein ,
to enlarge the parameter, satisfy
Respectively, the object distance is sn、sm、 and skThe ith order radial distortion parameter on the focusing plane;
and
respectively, the object distance is focused to sn and smThe ith order eccentric distortion parameter on the two focusing planes further obtains the following formula:
wherein g is an empirical parameter,
and
when the lens is focused at the object distance s, the lens is at the object distance skThe ith radial distortion parameter and the eccentricity distortion parameter of the defocus plane,
the result of equation (4) is generalized to the i-th order eccentric distortion parameter for a focal plane at infinityn、sm and skThe distortion parameter relation between the defocus planes represented by the formula (5) is obtained:
wherein ,
and
when focusing on the object distance s, the object distance is snThe ith radial distortion parameter and the eccentric distortion parameter on the defocusing plane;
and
when focusing on the object distance s, the object distance is smAn ith-order radial distortion parameter and an eccentric distortion parameter on the defocusing plane; the radial distortion parameter and the eccentric distortion parameter in the formula (5) do not depend on the focusing distance s and the distortion parameter on the focusing plane, so that a camera depth of field distortion model of the lens is established;
(3) camera depth distortion model calibration
1) Internal parameter calibration
With the known distances between the corners in the central regions of all the target images as constraints, the method in the paper "A flexible new technique for camera calibration" published by Zhang Zhen Yong 2000 is used to calibrate the intrinsic parameter matrix of the camera
And then pass through fx＝f/dxObtaining a lens focal length f;
2) linear point object distance solution
The distortion of the lens can distort an object-side straight line into a curve on an image, namely, the imaging of points on the straight line under the distortion action of the lens can be distributed in a curve, and the distortion parameter is solved by using the straight line points according to the fact; first, the pixel coordinates of a straight line point on an image are located using a gray scale gravity center method, which is expressed by equation (6):
wherein f (u, v) is a coordinate of (u, v)TThe gray value of the pixel point theta is over (u, v)TA set of pixel points with points in a straight-line vertical direction,
pixel coordinates of the located straight line points;
according to the formula (5), the distortion parameter solution requires that the object distance of the straight line point is known, and therefore the object distance of the straight line point is calculated on the basis of positioning the straight line point; suppose that the coordinate of a certain straight line point p positioned on the image is
Order to
Wherein p ═ p (p)x,py,pz)T(ii) a The coordinates of the straight line points after the action of the homography matrix H are
The object distance of the straight line point p on the target image is expressed by formula (7):
3) camera depth distortion model parameter solution
The change of the straightness generated by changing the object-side straight line into a curve under the action of lens distortion is expressed by a radial distortion parameter and an eccentric distortion parameter; suppose there are n straight line points on a straight line, the jth straight line point is Ωj＝(uj,vj)TJ 1,2, n, where the straight points are locatedThe regression line equation determined is expressed as:
wherein ,
and gamma is the distance from the point to the regression line, the square of the distance from the point to the regression line can be expressed as:
wherein ,
α＝a-c，
on the basis, calibrating a depth distortion model of the camera; firstly, supposing that the camera acquires eta' images of the target in different postures, wherein the eta image has lηThe line on the ith' line of the ith image is detectedη,jThe number of the straight-line points is,ηΩi′is the set of all the straight line points on the ith' straight line of the ith image,ηΩi′,jand
respectively setting the jth straight line point on the ith' straight line of the ith image and the object distance of the straight line point; then, with the minimum distance from the point to the regression line as the target, the depth distortion model shown in the formula (5) is substituted into the formula (2) and the formula (9), and the distortion parameters are optimized and solved
The established minimization objective function is expressed as:
formula (5) is a radial distortion parameter and an eccentric distortion parameter of a straight line point with any object distance, and the two types of distortion parameters are related to the object distance, the radial distortion parameter and the eccentric distortion parameter of other two straight line points and the focal length f of the lens; for solving, two straight-line points are selected in the depth of field, the object distance is sk and sm(ii) a Then, the pixel coordinates of the straight line points on all the target images are usedηΩi′,jObject distance of straight line point
The calibrated focal length f is used as an input quantity, and an objective function shown in a formula (10) is optimized through a Levenberg-Marquardt algorithm, so that the parameters of a depth of field distortion model are obtained
Therefore, the solving of each parameter of the depth-of-field distortion model is completed under the condition of target placement attitude loose constraint.
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Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104156974A (en) * | 2014-09-05 | 2014-11-19 | 大连理工大学 | Camera distortion calibration method on basis of multiple constraints |
| US20150093042A1 (en) * | 2012-06-08 | 2015-04-02 | Huawei Technologies Co., Ltd. | Parameter calibration method and apparatus |
| CN109727291A (en) * | 2018-12-28 | 2019-05-07 | 北京航空航天大学 | A kind of high-precision online calibration method of zoom camera |
| CN111768451A (en) * | 2020-07-01 | 2020-10-13 | 江苏集萃智能光电系统研究所有限公司 | Large-size binocular vision defocusing calibration method based on mobile display screen |
-
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Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20150093042A1 (en) * | 2012-06-08 | 2015-04-02 | Huawei Technologies Co., Ltd. | Parameter calibration method and apparatus |
| CN104156974A (en) * | 2014-09-05 | 2014-11-19 | 大连理工大学 | Camera distortion calibration method on basis of multiple constraints |
| CN109727291A (en) * | 2018-12-28 | 2019-05-07 | 北京航空航天大学 | A kind of high-precision online calibration method of zoom camera |
| CN111768451A (en) * | 2020-07-01 | 2020-10-13 | 江苏集萃智能光电系统研究所有限公司 | Large-size binocular vision defocusing calibration method based on mobile display screen |
Non-Patent Citations (1)
| Title |
|---|
| 谭启蒙;胡成威;高升;: "空间机械臂视觉相机内参标定技术研究", 航天返回与遥感, no. 06 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117629106A (en) * | 2023-12-29 | 2024-03-01 | 中国人民解放军国防科技大学 | Multi-reference-surface structure target device, preparation method and testing method thereof |
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