CN113781581B - 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 target loose attitude constraint-based depth of field distortion model calibration method. In the aspect of image acquisition calibration, images of a target in a plurality of postures in the depth of field are acquired by using a camera, the placing postures do not need to be perpendicular to the optical axis, the target only needs to be ensured to cover the imaging view field and the depth of field, and two types of characteristics of straight lines and angular points on the target can be imaged. In the aspect of depth distortion model calibration, firstly, using angular point distances of central areas of all target images as constraint calibration inner parameter matrixes; secondly, calculating the object distance of a straight line point on the target according to the homography matrix; thirdly, taking the minimum distance from the detected straight line point to the straight line where the straight line point is located as constraint, and establishing a minimum objective function containing parameters of a depth distortion model; and finally, taking the pixel coordinates of the straight line points, the object distance and the focal length of the straight line points as input quantities, and optimizing an objective function to finish the solution of all parameters of the depth distortion model.
Description
Technical Field
The invention belongs to the field of computer vision measurement, and relates to a calibration method of depth of field distortion model parameters.
Background
The vision measurement technology quantitatively characterizes 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 the 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 accuracy of the parameter calibration of the depth distortion model are ensured, and the method has important significance for improving the measurement accuracy and the practicability of the vision system.
Li Xiao et al of China Petroleum university (Huadong) discloses a lens distortion model taking depth of field dimension, space and other distortion partitions into consideration, with the patent number of CN 112258584A. In addition, sun Peng of Beijing university of information published in the Optics Express journal under the heading "Modelling and calibration of depth-dependent distortion for large depth visual measurement", which proposes a depth of field distortion model suitable for large object distance, wide field imaging scenes, solving and calibrating the amount of distortion on any defocus plane perpendicular to the optical axis, improving the three-dimensional measurement accuracy of vision in a space of 6m object distance, 7.0m3.5m2.5m from 0.055mm to 0.028mm. For the depth of field distortion model calibration method, the target plane and the optical axis are required to be always vertically arranged in implementation, so that high requirements are put on experimental devices and operation flows, 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 discloses a depth of field distortion model calibration method based on target loose attitude constraint. Comprising the following steps: and (5) calibrating image acquisition and depth distortion model calibration. In the aspect of calibration image acquisition, images of a target in a plurality of postures in the depth of field are acquired by using a camera, the placement posture of the target does not need to be perpendicular to the optical axis of the camera, the target only needs to be ensured to cover the field of view and the depth of field of the camera, and two types of characteristics, namely a straight line and an angular point on the target can be imaged. In the aspect of field depth distortion model calibration, firstly, using angular point distance constraint of a central area of a plurality of target images to calibrate internal parameters of a camera imaging model; secondly, calculating the object distance of a straight line point on the target image according to the homography matrix; thirdly, taking the minimum distance from the detected straight line point to the straight line where the straight line point is located as constraint, and establishing a minimum objective function containing parameters of a depth distortion model; and finally, taking the pixel coordinates of the straight line points, the object distance and the focal length of the straight line points as input quantities, and optimizing an objective function to finish the solution of all parameters of the depth distortion model.
According to the target image acquired under a plurality of postures, the depth of field distortion model parameter is optimized and solved by taking the least square of the distance from point to straight line as an objective function after the internal parameter solving of the imaging model based on the distance constraint of the center angular point of the image and the object distance solving of the straight line point of the image based on the homography matrix are sequentially completed. Different from the vertical posture placing requirements of other depth-of-field model calibration methods on targets and camera optical axes, the calibration method of the invention has loose constraint on the target posture, only needs targets with a plurality of placing postures to cover the field of view and the depth of field, and ensures that straight lines and corner 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 depth of field distortion model calibration method based on target loose attitude constraint comprises the following steps:
first, image acquisition
The whole camera deep distortion model calibration experiment system consists of a camera, a lens and a target; the target for parameter calibration in the camera depth distortion model is a plane plate, two types of characteristics of straight lines and angular points are arranged on the plane plate, and the intersection point of every two straight lines is the angular point, so that the distance between every two angular points is accurately known during processing; the image acquisition is a precondition of solving parameters of a camera depth distortion model; firstly, opening a camera with a lens, setting a frame frequency, exposure time, focal length and resolution of the camera, and completing focusing of the lens after adjusting a focusing distance; secondly, placing a plurality of gestures on the front of the camera, the targets are not required to be perpendicular to the optical axis of the lens, only the targets are required to be ensured to cover the field of view and the depth of field of the camera, and the corner point and the straight line can be imaged. After one target gesture is put, the target is in a static state, a camera is used for collecting target images, and finally target images under a plurality of gestures are collected and obtained.
Second, calibrating a camera depth of field distortion model
(1) Camera imaging model
The camera imaging model describes the one-to-one mapping relationship between the object space point and the image space point, and records the object space pointThe homogeneous coordinates of (1) are (x, y, z) T Its undistorted projection point on the image +.>The homogeneous coordinates of (1, v, u) 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,as an internal reference matrix, C 0 ＝(c x ,c y ) T Is the distortion center of the image, f x 、f y Is the equivalent focal length in the u and v directions. f (f) x ＝f/d x ，f y ＝f/d y ，d x and dy Is the physical dimension of the picture element in the horizontal and vertical directions. f is the focal length of the lens. r is (r) 1 and r2 The first two column vectors of the rotation transformation matrix between the world coordinate system and the camera coordinate system are t is a translation vector between the world coordinate system and the camera coordinate system. H=s·m· [ r ] 1 r 2 t]The homography matrix expresses the conversion relation between the target plane and the image plane.
(2) Camera depth of field distortion model
Manufacturing and assembly process imperfections cause radial and decentration distortions of the lens, such that the projection of straight lines onto the image is curved. The lens distortion model is expressed by using a polynomial, and the formula is as follows:
wherein ,to distort the image point coordinates, delta u 、δ v Is a distortion function of the image point in the u, v direction,for the distortion radius of the image point, k 1 and k2 The radial distortion parameters of the first order and the second order, p 1 and p2 The first order and second order decentration distortion parameters, respectively.
The lens distortion is closely related to the depth of field position, and particularly under the condition of close range, the relationship is stronger and the generated distortion amount is larger. Taking different imaging distortions caused by different object distances into consideration, and building a depth distortion model by correlating the object distances with the distortion model, wherein the expression is as follows:
wherein ,to amplify parameters, satisfy-> Respectively focusing object distances s n 、s m、 and sk I-th order radial distortion parameter in the focal plane. /> and />The focusing object distances are s respectively n and sm The i-th order eccentric distortion parameter on the two focusing planes of the lens is f. Refer to Duane C.Brown paper "Close-range camera calibration"The Clive S.Fraser paper "Variation of distortion within the photographic field" can be given by the following formula:
wherein g is an empirical parameter, and />When the object distance of focusing the lens is s, the lens is at the object distance s k An ith order radial distortion parameter and an decentration distortion parameter of the defocus plane at +.>To the ith order eccentric distortion parameter of the focusing plane focusing in the infinite distance, the result of the formula (4) is generalized to be at any object distance s n 、s m and sk Obtaining a distortion parameter relation between the respective defocus planes represented by the formula (5):
wherein , and />To be at the object distance s when focusing on the object distance s n An i-th order radial distortion parameter and an eccentric distortion parameter on the defocus plane; /> and />To be at the object distance s when focusing on the object distance s m An ith order radial distortion parameter and an eccentric distortion parameter on the defocus plane; the radial distortion parameter and the eccentric distortion parameter in the formula (5) are independent of the focusing distance s and the distortion parameter on the focusing plane, so that a camera depth distortion model of the lens is established.
(3) Camera depth of field distortion model calibration
1) Internal parameter calibration
Considering the characteristics of small lens distortion in the center of an image and large periphery, the invention uses the known distances between the angular points on the center area of all target images as constraint, and calibrates the internal parameter matrix of the camera by using the method in the Zhang Zhengyou published paper A flexible new technique for camera calibrationAnd then pass through f x ＝f/d x The camera focal length f is obtained.
2) Linear point object distance solution
The distortion of the lens can lead the object side straight line to be distorted into a curve on the image, namely, the imaging of the point on the straight line under the action of the distortion of the lens can be distributed in a curve. First, the pixel coordinates of the straight line point on the image are located by using the gray-level gravity center method, which can be expressed as follows by equation (6):
wherein f (u, v) is the coordinate (u, v) T The gray value of the pixel point of (2) is theta (u, v) T A collection of pixel points with points in the vertical direction of the line,is the pixel coordinates of the located straight line point.
From the equation (5), the distortion parameter solution requires that the object distance of the straight line point is known, and for this purpose, the invention is used for locating the straight line pointThe object distance of the straight line point is calculated on the basis. Assume that the coordinates of a certain straight line point p positioned on the image areOrder theWhere p' = (p x ,p y ,p z ) T . The coordinates of the straight line points after the homography matrix H is acted are +.>The object distance of the straight line point p on the target image can be expressed as:
3) Depth of field distortion model parameter solving
The straightness change generated by changing the action of the object side straight line on lens distortion into a curve can be expressed by a radial distortion parameter and an eccentric distortion parameter. Assuming that n straight line points exist on a straight line, the j-th straight line point is omega j ＝(u j ,v j ) T J=1, 2, n, the regression line equation determined by these straight line points can be expressed as:
wherein ,for the included angle between the regression line and u, γ is the distance from the point to the regression line, and then 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, assume that a camera acquires images of eta' targets in different postures together, and the eta image has l η Straight line, N is detected on the ith straight line of the eta image η,j A point of the straight line is a point, η Ω i′ is the set of all straight line points on the ith straight line of the eta image, η Ω i′,j and η s i′,j the object distance is the j-th straight line point and the straight line point on the i' th straight line of the eta image. Then, the invention takes the minimum distance from the point to the regression line as the target, brings the depth distortion model shown in the formula (5) into the formula (2) and the formula (9), and optimizes and solves distortion parametersi=1, 2. The minimized objective function established can be expressed as:
equation (5) is a radial distortion parameter and an decentration distortion parameter of a straight line point having an arbitrary object distance, and the two kinds of distortion parameters are related to the object distances, the radial distortion parameters, the decentration distortion parameters, 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, and the object distances are s respectively k and sm . Then, the pixel coordinates of the straight line points on all target images are used η Ω i′,j Object distance of straight line point η s i′,j The focal length f which is already marked is taken as an input quantity, and an objective function shown in a formula (10) is optimized through a Levenberg-Marquardt (LM) algorithm in a D.Marquardt publication An algorithm for least squares estimation on nonlinear parameters to further obtainDepth of field distortion model parametersThe solution of each parameter of the depth of field distortion model is completed under the condition of loose constraint of the target placement posture.
The invention provides 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 optical axis of the camera are required to be kept in a vertical arrangement state all the time, so that very high requirements are put forward on a calibration experiment device and an operation flow, the defects of high calibration time cost, easiness in introducing human errors and poor practicality are overcome, the strong constraint dependence of the traditional calibration method on the target arrangement state is overcome, the calibration convenience is improved on the premise of ensuring the calibration precision, the calibration cost is low, and the field applicability is high.
Drawings
Fig. 1 is a schematic diagram of a depth of field distortion model calibration method based on target loose attitude constraint. Wherein, 1-camera, 2-camera, 3-target, 4-corner, 5-straight line.
Fig. 2 is a flow chart of a depth of field distortion model calibration method based on target loose pose constraint.
Detailed Description
The following describes the embodiments of the present invention in detail with reference to the technical scheme and fig. 1 and 2. Fig. 1 is a schematic diagram of a depth of field distortion model calibration method based on target loose attitude constraint. Fig. 2 is a flow chart of a depth of field distortion model calibration method based on target loose attitude constraint.
The invention discloses a target loose attitude constraint-based depth of field distortion model calibration method, which comprises image acquisition and solving of depth of field distortion model parameters. The whole calibration flow can be summarized as follows: the method comprises the steps that a lens 2 is installed on a camera 1, images of a target 2 in a plurality of postures are collected by the camera 1, and image collection is completed; on the basis, the parameters in the depth distortion model are calibrated, and firstly, the inner parameter matrix is solved by utilizing the angular point distance constraint of the central area of all images. And secondly, calculating the object distance of the straight line point by utilizing the homography matrix. And finally, for the depth distortion model, taking the minimum distance from the point on the image to the regression line as constraint, taking the pixel coordinates of the straight line point, the object distance of the straight line point and the focal length of the camera as input quantities, and optimizing and solving each parameter of the depth distortion model. The specific implementation is described in detail below:
1. image acquisition
The whole camera distortion model calibration experiment system consists of a camera 1, a lens 2 and a target 3. The target 3 for calibrating parameters of the camera depth distortion model is a plane plate, two types of characteristics of angular points 4 and straight lines 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. When image acquisition is performed, first, the camera 1 is connected and turned on, the acquisition frame frequency of the camera 1 is set to 30 frames, the exposure time is set to 0.3s, the theoretical focal length is set to 50mm, the imaging resolution is 4092 pixels×3072 pixels, the focusing object distance is set to 420mm, and focusing of the camera 1 is completed. Secondly, putting the target 3 in front of the camera 1 into a plurality of postures, the process does not need to be perpendicular to the optical axis of the camera 1, only the posture of the target 3 needs to be ensured to cover the field of view and the depth of field of the camera 1, and the corner point 4 and the straight line 5 can be imaged. After the pose of one target 2 is placed, keeping the target 2 still, acquiring images of the target 2 by using the camera 1, and finally obtaining target images under 12 poses.
2. Depth of field distortion model calibration
(1) Imaging model
Program code for programming an imaging model represented by equation (1) and a homography matrix h=s·m· [ r ] 1 r 2 t]Expression code of (a);
(2) Depth of field distortion model
Manufacturing and assembly process imperfections result in radial and decentration distortions of the lens 2 such that the straight line 1 is projected 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 model with first-order and second-order radial distortion parameters (k 1 and k2 ) And first and second order decentration distortion parametersNumber (p) 1 and p2 ) And corresponding program code is formulated.
The lens distortion is closely related to the depth of field position, and the depth of field distortion model on the focusing plane shown in the formula (3) is established by combining the object distance and the distortion model in consideration of imaging distortion caused by different object distances. On the basis, the formula (3) is generalized according to the result of the formula (4), and the relation between the defocusing plane distortion parameters represented by the formula (5) is obtained. According to the depth distortion model program code of the arbitrary object distance focal plane;
(3) Depth of field distortion model calibration
1) Internal parameter calibration
Considering the characteristic that the distortion of the lens is small in the center of the image and large in the periphery, the method uses the known distances among the corner points 3 in the center area of all 12 target images as constraints, and the method in the Zhang Zhengyou published paper Aflexible new technique for camera calibration is utilized to calibrate the internal reference matrix of the camera. The focal length f of the camera was 49.66mm, and the image distortion center (c x ,c y ) T ＝(2043.1,1531.3) T 。
2) Linear point object distance solution
The distortion of the lens 2 causes the object-side straight line to be distorted into a curve on the image, namely the imaging of straight line points under the distortion effect is distributed in a curve, and the distortion parameters are solved by utilizing the straight line points according to the fact. Firstly, the pixel coordinates of straight line points on an image are positioned by using a gray level gravity center method shown in a formula (6), the object distance of the straight line points is known by solving distortion parameters according to a formula (5), and therefore, the object distance of the straight line points is calculated on the basis of positioning the straight line points according to a formula (7).
3) Depth of field distortion model parameter solving
Under the action of lens distortion, straightness change generated by changing an object straight line into a curve can be expressed by a radial distortion parameter and an eccentric distortion parameter. And solving regression straight line equations corresponding to all straight line points on a certain straight line on the image according to the formula (8), and further obtaining the distance from each straight line point to the regression straight line according to the formula (9).
On the basis, each parameter of the depth 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 of the straight line points detected on each straight line ranges from 1200 to 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 are arranged on the 3 rd image, 1600 straight line points are detected on the 6 th straight line, and pixel coordinates of the 1200 th, 1300 th and 1400 th straight line points are respectively (785,429) T 、(857,436) T And (926,437) T . The object distances for 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 s respectively k = 456.8mm and s m = 415.8mm. For 12 acquired images, taking the minimum distance from the point to the regression line as a target, and taking the depth distortion model shown in the formula (5) into the formula (2) and the formula (9) to detect the pixel coordinates of all the linear points η Ω i′,j Object distance of all straight line points η s i′,j The focal length f which is already marked is taken as an input quantity, and an objective function formula (10) is optimized through a Levenberg-Marquardt (LM) algorithm in D.Marquardt publication An algorithm for least squares estimation on nonlinear parameters to obtain distortion parametersi=1, 2. The object distance is s k = 456.8mm and s m The results for each distortion parameter at =415.2 mm are: /> and />Under the condition of loose constraint of the target postureAnd the calibration of each parameter of the depth of field distortion model is completed. After the distortion parameters are obtained, the radial distortion parameters and the eccentric distortion parameters of any object distance straight line points can be obtained according to the formula (5).
According to the target loose attitude constraint-based depth of field distortion model calibration method, high-precision calibration of the depth of field distortion model under the target loose attitude constraint is realized, and the dependence on the vertical attitude of the target and the camera optical axis all the time when the traditional method calibration is implemented is overcome. The method reduces the dependence of calibration on experimental devices and operation flows, improves the convenience of calibration on the premise of ensuring the calibration precision, and has good applicability.
Claims (1)
1. A depth of field distortion model calibration method based on target loose attitude constraint is characterized by comprising the following steps:
first, image acquisition
The whole camera depth of field 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 types of characteristics of straight lines and angular points are arranged on the plane plate, and the intersection point of every two straight lines is the angular point; ensuring that the distance between every two corner points is known during processing; the image acquisition is a precondition of solving parameters of a camera depth distortion model; firstly, opening a camera with a lens, setting a frame frequency, exposure time, focal length and resolution of the camera, and completing focusing of the lens after adjusting a focusing distance; secondly, placing a plurality of gestures on the front of the camera, wherein the targets are not required to be perpendicular to the optical axis of the lens, and only the targets are required to be ensured to cover the field of view and depth of field of the camera, and the corner points and the straight lines can be imaged; after each target gesture is put, the target is in a static state, a camera is used for collecting target images, and finally target images under a plurality of gestures are collected and obtained;
second, calibrating the depth of field distortion model
(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 spaceIntermediate pointsThe homogeneous coordinates of (1) are (x, y, z) T Its undistorted projection point on the image +.>The homogeneous coordinates of (1, v, u) T The method comprises the steps of carrying out a first treatment on the surface of the 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,as an internal reference matrix, C 0 ＝(c x ,c y ) T Is the distortion center of the image, f x 、f y Equivalent focal lengths in the u and v directions; f (f) x ＝f/d x ，f y ＝f/d y ，d x and dy Is the physical dimension of the picture element in the horizontal and vertical directions; r is (r) 1 and r2 The first two column vectors of the rotation transformation matrix between the world coordinate system and the camera coordinate system are represented by t, which is a translation vector between the world coordinate system and the camera coordinate system; h=s·m· [ r ] 1 r 2 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 of field 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; the camera lens distortion model is expressed by using a polynomial, and the formula is as follows:
wherein ,to distort the image point coordinates, delta u 、δ v Is a distortion function of the image point in the u, v direction,for the distortion radius of the image point, k 1 and k2 The radial distortion parameters of the first order and the second order, p 1 and p2 The first-order eccentric distortion parameter and the second-order eccentric distortion parameter are respectively;
the lens distortion size is closely related to the depth of field position, and the object distance and the distortion model are related to establish a camera depth of field distortion model by considering the imaging distortion difference caused by different object distances, wherein the expression is as follows:
wherein ,to amplify parameters, satisfy-> Respectively focusing object distances s n 、s m、 and sk An i-th order radial distortion parameter on a focal plane; /> and />The focusing object distances are s respectively n and sm Is a combination of two of (2)The ith order eccentric distortion parameter on the focusing plane further obtains the following formula:
wherein g is an empirical parameter, and />When the object distance of focusing the lens is s, the lens is at the object distance s k An ith order radial distortion parameter and an decentration distortion parameter of the defocus plane at +.>To the ith order eccentric distortion parameter of the focusing plane focusing in the infinite distance, the result of the formula (4) is generalized to be at any object distance s n 、s m and sk Obtaining a distortion parameter relation between the respective defocus planes represented by the formula (5):
wherein , and />To be at the object distance s when focusing on the object distance s n An i-th order radial distortion parameter and an eccentric distortion parameter on the defocus plane; /> and />To be at the object distance s when focusing on the object distance s m An ith order radial distortion parameter and an eccentric distortion parameter on the defocus plane; the radial distortion parameter and the eccentric distortion parameter in the formula (5) are independent of the focusing distance s and the distortion parameter on the focusing plane, so that a camera depth distortion model of the lens is established;
(3) Camera depth of field distortion model calibration
1) Internal parameter calibration
Calibrating an internal reference matrix of the camera by using the method in the publication A flexible new technique for camera calibration of Zhang Zhengyou 2000 with known distances between corner points on central areas of all target images as constraintsAnd then pass through f x ＝f/d x Obtaining a lens focal length f;
2) Linear point object distance solution
The lens distortion causes the object side straight line to be distorted into a curve on the image, namely the imaging of the point on the straight line under the action of the lens distortion is distributed in a curve, and the distortion parameter is solved by utilizing the straight line point according to the fact; first, the pixel coordinates of the straight line point on the image are located by using a gray-scale gravity center method, which is expressed as formula (6):
wherein f (u, v) is the coordinate (u, v) T The gray value of the pixel point of (2) is theta (u, v) T A collection of pixel points with points in the vertical direction of the line,pixel coordinates of the located straight line point;
as known from equation (5), the distortion parameter solution requires that the linear point object distance be known, and for this purpose,calculating the object distance of the straight line point on the basis of positioning the straight line point; assume that the coordinates of a certain straight line point p positioned on the image areOrder theWhere p' = (p x ,p y ,p z ) T The method comprises the steps of carrying out a first treatment on the surface of the The coordinates of the straight line points after the homography matrix H acts are as followsThe object distance of the straight line point p on the target image is expressed as formula (7):
3) Camera depth of field distortion model parameter solving
The straightness change 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; assuming that n straight line points exist on a straight line, the j-th straight line point is omega j ＝(u j ,v j ) T J=1, 2, n, the regression line equation determined by these straight line points is expressed as:
wherein ,for the included angle between the regression line and u, γ is the distance from the point to the regression line, and then the square of the distance from the point to the regression line can be expressed as:
wherein ,α＝a-c，
calibrating a camera depth distortion model on the basis; firstly, assume that a camera acquires images of eta' targets in different postures together, and the eta image has l η Straight line, N is detected on the ith straight line of the eta image η,j A point of the straight line is a point, η Ω i′ is the set of all straight line points on the ith straight line of the eta image, η Ω i′,j andrespectively the object distance of the jth straight line point on the ith straight line of the eta image; then, taking the minimum distance from the point to the regression line as a target, introducing the depth of field distortion model shown in the formula (5) into the formula (2) and the formula (9), and optimizing and solving distortion parameters +.>The established minimized objective function is expressed as:
equation (5) is a radial distortion parameter and an eccentric distortion parameter of a straight line point with any object distance, and the two 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, and the object distances are s respectively k and sm The method comprises the steps of carrying out a first treatment on the surface of the Then, the pixel coordinates of the straight line points on all target images are used η Ω i′,j Straight lineObject distance of pointThe focal length f which is already marked is used as input quantity, and the objective function shown in the formula (10) is optimized through the Levenberg-Marquardt algorithm, so that the depth of field distortion model parameter ++>The solution of each parameter of the depth of field distortion model is completed under the condition of loose constraint of the target placement posture.
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