CN105096329B - Method for accurately correcting image distortion of ultra-wide-angle camera - Google Patents

Method for accurately correcting image distortion of ultra-wide-angle camera Download PDF

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CN105096329B
CN105096329B CN201510514238.0A CN201510514238A CN105096329B CN 105096329 B CN105096329 B CN 105096329B CN 201510514238 A CN201510514238 A CN 201510514238A CN 105096329 B CN105096329 B CN 105096329B
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刘晨曦
陈从华
叶德焰
杨磊
汤益明
叶志聪
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Xiamen Yaxon Networks Co Ltd
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Abstract

The invention relates to a method for accurately correcting distortion of an ultra-wide-angle camera image, which comprises the steps of firstly calculating a correction error based on a distortion model, then iteratively refining according to a descent algorithm, and finally correcting a distorted image according to internal parameters and distortion parameters of a camera lens obtained by refining.

Description

Method for accurately correcting image distortion of ultra-wide-angle camera
Technical Field
The invention relates to the technical field of image processing and computer vision, in particular to a method for accurately correcting image distortion of a super-wide-angle camera.
Background
In recent years, with the rapid development of digital signal processing and the rapid improvement of computer processing capability, a vision system based on a super-wide-angle lens is widely applied to the fields of virtual reality, video monitoring, intelligent transportation, medical treatment, robot navigation and the like. The range of angles of view of lens shots conventionally used in these applications is small, and the shot image does not reflect all the information of the shot scene. In order to acquire more information in the same scene, a plurality of cameras are mostly adopted to acquire information at different angles at present, or the cameras are controlled by a system to scan in a cruising way. The multiple camera systems not only increase the construction and maintenance cost of the equipment, but also greatly increase the wiring difficulty; the fast cruise system needs to be additionally provided with a camera moving and rotating platform, so that the cost is increased, and meanwhile, the stability and the service life of the system are also reduced. And the ultra-wide angle camera can well solve the problems.
Since images photographed by the ultra-wide angle camera are very distorted, if projection information of the severely distorted images is to be utilized, the distorted images need to be corrected to perspective projection images that conform to the human visual habits. Various correction algorithms are proposed, which can be summarized in two aspects: (1) imaging modeling, namely modeling an imaging surface of the ultra-wide-angle lens and calculating correction parameters by model constraint; (2) the image distortion is corrected from a 2-dimensional space and a 3-dimensional space, and the correction is realized through the conversion of 2-dimensional or 3-dimensional coordinates and the calibration of a distortion lens.
In the traditional correction method, firstly, a high-order polynomial model is adopted, forward or reverse Taylor expansion is carried out on a distortion function, and the expansion order is determined according to the required precision. The method is applied to lenses with small distortion such as a digital camera and the like, has high precision, and on wide-angle and ultra-wide-angle lenses, the model can only compensate the lens distortion near the center of an image, obvious system errors exist around the image, the distortion correction precision is not high, and the distortion at the edge is maximum; and secondly, converting the problem into a characteristic value to solve the problem by adopting a division model according to the stereoscopic vision matching constraint condition. The method improves the correction precision of the wide-angle lens distortion correction of about 130 degrees, and for a system with small distortion or larger distortion, the error of the solved distortion coefficient is very large, and the model is not suitable for distortion correction of ultra wide angle and high precision. For example, patent application No. 201410424349.8, "a method for correcting a fisheye image after calibrating a fisheye lens", has too high and too complex polynomial order, and has low correction accuracy near the edge of the fisheye image, and a small effective correction angle.
In these algorithms, there are the disadvantages of complicated modeling, difficult measurement and low correction precision: the simple distortion correction technology cannot correct the part with larger angle; complicated distortion correction techniques are difficult to measure and difficult to meet with real-time.
Disclosure of Invention
The invention aims to provide a method for accurately correcting the image distortion of a super-wide-angle camera, which is simple to realize, high in correction precision, strong in practicability, stable and reliable.
The invention discloses a method for accurately correcting distortion of an image of an ultra-wide angle camera, which comprises the following steps of firstly calculating a correction error based on a distortion model, then carrying out iterative refinement according to a descent algorithm, and finally correcting a distorted image according to internal parameters and distortion parameters of the camera obtained by the refinement, wherein the method specifically comprises the following steps:
step 1, establishing a corresponding position relation between a distorted image and a world coordinate system:
firstly, any point O in the world coordinate system is set as [ X, Y, Z,1 ]]TThe camera coordinate corresponding to the corrected image is P ═ Xc,Yc,Zc]TThe distortion image coordinates are Q ═ u, v, the correction image coordinates are Q ' ═ u ', v ', and the projection imaging model is described by the following formula:
P＝MO (1)
in the formula (1), M is a projection matrix,
Figure BDA0000785645740000031
M＝[R|T]，
Figure BDA0000785645740000032
in order to be a matrix of rotations,
Figure BDA0000785645740000033
is a translation vector;
then, establishing a relation model of the distorted image and the corrected image as follows:
Figure BDA0000785645740000034
Figure BDA0000785645740000035
in the formula, k1，k2，k3，k4，k5，k6As a radial distortion parameter, p1，p2As tangential distortion parameter, fx, fy, u0，v0R is the distance from a projection point under a camera coordinate system to the origin of the camera coordinate system as an internal parameter of the camera，xc＝Xc/Zc，yc＝Yc/Zc；
Step 2, shooting a plurality of pictures by using a planar calibration plate with black and white alternate rectangular or square checkerboards as a calibration image, detecting image coordinates of every four intersected checkerboards on the calibration plate, namely angular points, establishing a corresponding relation between the calibration plate and the calibration image according to the projection imaging model in the step 1, and calculating an image coordinate back projection error: and | l d-d '| |, wherein | | · | | represents a norm l2, d is an image coordinate of a calibration board angular point, d' is a world coordinate system coordinate of the calibration board angular point, and a target function is established through projection of the projection imaging model in the step 1 under the image coordinate:
Figure BDA0000785645740000041
determining whether the target function meets the preset precision requirement or not by using epsilon as the square of the back projection error, m as the total number of the angular points and j as the index number of the angular points, and if not, performing nonlinear optimization refinement by using a descent iteration algorithm to obtain optimized lens internal parameters and distortion parameters;
and 3, substituting the lens internal parameters and the distortion parameters obtained in the step 2 into a formula (2) and a formula (3) for calculation to obtain the spatial data of the corrected image, wherein the coordinates u ', v' and x of the corrected image are obtainedc、ycThe relationship between u' ═ xc·fx+u0，v'＝yc·fy+v0；
Step 4, assigning a value to the corrected image by using a nearest neighbor interpolation formula to finish correction, wherein the nearest neighbor interpolation formula comprises the following steps: g (u ', v ') -g (u 'int,v'int) G (u ', v ') is the pixel value, u ' of the image at (u ', v 'int,v′intIs the integer part of u ', v'.
The descending iterative algorithm is an LM descending iterative algorithm, and comprises the following specific steps:
1. initializing camera internal parameters (fx, fy, u)0，v0) Projection matrix M and distortion parameter c0Initializing step span v: -2;
2、calculating coordinates (u) of each calibration imagei,vi) For all distortion parameters ckPartial derivative matrix J:
Figure BDA0000785645740000051
3. calculating H: ═ JTJ，JTInitializing a step size lambda of max (diag (H)) for the transposed matrix of J, wherein diag is an element on a diagonal of the matrix;
according to the current lens internal parameters (fx, fy, u)0，v0) Projection matrix M and distortion parameter ckEstimating the coordinates of a calibration image, k representing the updating times of the parameters under the current iteration, and calculating an objective function
Figure BDA0000785645740000052
4. Solving equation (J)TJ+λI)δ＝-JTεkAnd I is a unit matrix, increment delta is obtained, and distortion parameter c is updatedk+1:＝ck+δ；
5. Calculating target function after updating distortion parameter
Figure BDA0000785645740000053
6. If epsilonk+1＝εkThen the iterative calculation is stopped and the current distortion parameter ckThe distortion parameter is the optimized distortion parameter; if epsilonk+1＜εkUpdating parameter c: ═ ck+1，ε:＝εk+1V:2, go to 2; if epsilonk+1＞εkUpdating parameter: ═ epsilonkλ ═ v × λ, go to 4.
Aiming at the defects of low correction precision and small effective angle of a polynomial model and a division model, the invention obtains the internal parameters and distortion parameters of the lens of the super-wide-angle camera by utilizing a nonlinear optimization technology, accurately corrects the super-wide-angle image according to the parameters of a calibrated image, and can obtain a larger available visual angle than other distortion correction technologies. The invention corrects the distorted image by using the parameters obtained by the lens calibration method, is not only suitable for the distortion correction of the ultra-wide-angle lens, but also suitable for the common lens and the wide-angle lens with smaller distortion, and has large angle and high precision for the integral distortion correction of the image. Furthermore, the invention uses the self-made plane calibration plate for calibration, and can correct the image in any environment only by once calibration, thereby being stable and reliable and having strong practicability.
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FIG. 1 is a schematic view of a self-made planar calibration plate according to the present invention;
FIG. 2 is a flow chart of the calibration according to the present invention;
FIG. 3 is a flow chart of image distortion correction in the present invention;
the invention is further described in detail below with reference to the figures and examples.
Detailed Description
The invention discloses a method for accurately correcting distortion of an image of an ultra-wide angle camera, which comprises the following steps of firstly calculating a correction error based on a distortion model, then carrying out iterative refinement according to a descent algorithm, and finally correcting a distorted image according to internal parameters and distortion parameters of the camera obtained by the refinement, wherein the method specifically comprises the following steps:
step 1, establishing a corresponding position relation between a distorted image and a world coordinate system:
firstly, any point O in the world coordinate system is set as [ X, Y, Z,1 ]]TThe camera coordinate corresponding to the corrected image is P ═ Xc,Yc,Zc]TThe distortion image coordinates are Q ═ u, v, the correction image coordinates are Q ' ═ u ', v ', and the projection imaging model is described by the following formula:
P＝MO (1)
in the formula (1), M is a projection matrix,
Figure BDA0000785645740000061
M＝[R|T]，
Figure BDA0000785645740000062
in order to be a matrix of rotations,
Figure BDA0000785645740000063
is a translation vector;
then, establishing a relation model of the distorted image and the corrected image as follows:
Figure BDA0000785645740000071
Figure BDA0000785645740000072
in the formula, k1，k2，k3，k4，k5，k6As a radial distortion parameter, p1，p2As tangential distortion parameter, fx, fy, u0，v0R is the distance from a projection point under a camera coordinate system to the origin of the camera coordinate system, x is the internal parameter of the camerac＝Xc/Zc，yc＝Yc/Zc；
Establishing a corresponding position relation between the distorted image and a world coordinate system according to the model, wherein parameters in the relation model of the distorted image and the corrected image can be obtained through a lens calibration algorithm in the step 2;
step 2, as shown in fig. 2, taking a plurality of pictures by using the planar calibration plate with black and white alternate rectangular or square checkerboards as shown in fig. 1, detecting image coordinates of the corner points, which are the intersecting points of every four checkerboards on the calibration plate, establishing the corresponding relation between the calibration plate and the calibration image according to the projection imaging model in the step 1, and calculating the back projection error of the coordinates of the calibration image: i | d-d '| |, where | · | | | represents the norm l2, d is the image coordinate of the corner point on the calibration board, d' is the world coordinate system coordinate of the corner point on the calibration board, and the target function is established through the projection of the projection imaging model in step 1 under the image coordinate system:
Figure BDA0000785645740000073
determining whether the target function meets the preset precision requirement or not by using epsilon as the square of the back projection error, m as the total number of the angular points and j as the index number of the angular points, and if not, utilizing a descending iterative algorithmCarrying out nonlinear optimization refinement to obtain optimized lens internal parameters and distortion parameters; the descending iterative algorithm is an LM descending iterative algorithm, and comprises the following specific steps:
1. initializing camera internal parameters (fx, fy, u)0，v0) Projection matrix M and distortion parameter c0Initializing step span v: -2;
2. calculating coordinates (u) of each calibration imagei,vi) For all distortion parameters ckPartial derivative matrix J:
Figure BDA0000785645740000081
3. calculating H: ═ JTJ，JTInitializing a step size lambda of max (diag (H)) for the transposed matrix of J, wherein diag is an element on a diagonal of the matrix;
according to the current lens internal parameters (fx, fy, u)0，v0) Projection matrix M and distortion parameter ckEstimating the coordinates of a calibration image, k representing the updating times of the parameters under the current iteration, and calculating an objective function
Figure BDA0000785645740000082
4. Solving equation (J)TJ+λI)δ＝-JTεkAnd I is a unit matrix, increment delta is obtained, and distortion parameter c is updatedk+1:＝ck+δ；
5. Calculating target function after updating distortion parameter
Figure BDA0000785645740000083
6. If epsilonk+1＝εkThen the iterative calculation is stopped and the current distortion parameter ckThe distortion parameter is the optimized distortion parameter; if epsilonk+1＜εkUpdating parameter c: ═ ck+1，ε:＝εk+1V:2, go to 2; if epsilonk+1＞εkUpdating parameter: ═ epsilonkλ ═ v × λ, go to 4;
step 3, as shown in fig. 3, obtaining the lens internal parameters (fx, fy, u) according to step 20，v0) And distortion parameters, which are calculated by using a formula (2) and a formula (3) to obtain the spatial data of the corrected image, wherein the coordinates u ', v' and x of the corrected imagec、ycThe relationship between u' ═ xc·fx+u0，v'＝yc·fy+v0；
Step 4, because the coordinates of the image are positive integers, and the coordinates of the image obtained in step 3 may have decimal numbers, the correction is completed by assigning a value to the corrected image by using a nearest neighbor interpolation method, and the nearest neighbor interpolation formula: g (u ', v ') -g (u 'int,v'int) G (u ', v ') is the pixel value, u ' of the image at (u ', v 'int,v’intIs the integer part of u ', v'.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the technical scope of the present invention, so that any minor modifications, equivalent changes and modifications made to the above embodiment according to the technical spirit of the present invention are within the technical scope of the present invention.

Claims (2)

1. A method for accurately correcting image distortion of an ultra-wide-angle camera is characterized by comprising the following steps: firstly, calculating a correction error based on a distortion model, then iteratively refining according to a descent algorithm, and finally correcting a distorted image according to internal parameters and distortion parameters of a camera obtained by refining, wherein the method specifically comprises the following steps:
step 1, establishing a corresponding position relation between a distorted image and a world coordinate system:
firstly, any point O in the world coordinate system is set as [ X, Y, Z,1 ]]TThe camera coordinate corresponding to the corrected image is P ═ Xc,Yc,Zc]TThe distortion image coordinates are Q ═ u, v, the correction image coordinates are Q ' ═ u ', v ', and the projection imaging model is described by the following formula:
P＝MO (1)
in the formula (1), M is a projection matrix,
Figure FDA0002276541880000011
M＝[R|T]，
Figure FDA0002276541880000012
in order to be a matrix of rotations,
Figure FDA0002276541880000013
is a translation vector;
then, establishing a relation model of the distorted image and the corrected image as follows:
Figure FDA0002276541880000014
Figure FDA0002276541880000015
in the formula, k1，k2，k3，k4，k5，k6As a radial distortion parameter, p1，p2As tangential distortion parameter, fx, fy, u0，v0R is the distance from a projection point under a camera coordinate system to the origin of the camera coordinate system, x is the internal parameter of the camerac＝Xc/Zc，yc＝Yc/Zc；
Step 2, shooting a plurality of pictures by using a planar calibration plate with black and white alternate rectangular or square checkerboards as a calibration image, detecting image coordinates of every four intersected checkerboards on the calibration plate, namely angular points, establishing a corresponding relation between the calibration plate and the calibration image according to the projection imaging model in the step 1, and calculating an image coordinate back projection error: and | l d-d '| |, wherein | | · | | represents l2 norm, d is the image coordinate of the calibration board angular point, d' is the world coordinate system coordinate of the calibration board angular point, and the target function is established through the projection of the projection imaging model in the step 1 under the image coordinate system:
Figure FDA0002276541880000021
epsilon is the inverse projection error planeJudging whether the target function meets the preset precision requirement or not by using m as the total number of the angular points and j as the index number of the angular points, and if not, performing nonlinear optimization refinement by using a descending iterative algorithm to obtain optimized lens internal parameters and distortion parameters;
and 3, substituting the lens internal parameters and the distortion parameters obtained in the step 2 into a formula (2) and a formula (3) for calculation to obtain the spatial data of the corrected image, wherein the coordinates u ', v' and x of the corrected image are obtainedc、ycThe relationship between u' ═ xc·fx+u0，v'＝yc·fy+v0；
Step 4, assigning a value to the corrected image by using a nearest neighbor interpolation formula to finish correction, wherein the nearest neighbor interpolation formula comprises the following steps: g (u ', v ') -g (u 'int,v'int) G (u ', v ') is the pixel value, u ' of the image at (u ', v 'int,v′intIs the integer part of u ', v'.
2. The method for accurately correcting the image distortion of the ultra-wide angle camera according to claim 1, wherein the method comprises the following steps: the descending iterative algorithm is an LM descending iterative algorithm, and comprises the following specific steps:
step 1, initializing internal parameters fx, fy and u of camera0，v0Projection matrix M and distortion parameter c0Initializing step span v: -2;
step 2, calculating coordinates (u) of each calibration imagei,vi) For all distortion parameters ckPartial derivative matrix J:
Figure FDA0002276541880000031
step 3, calculating H: ═ JTJ，JTInitializing a step size lambda of max (diag (H)) for the transposed matrix of J, wherein diag is an element on a diagonal of the matrix;
according to the current lens internal parameters fx, fy, u0，v0Projection matrix M and distortion parameter ckEstimating the coordinates of the calibration image, k denotesCalculating the target function according to the updating times of the parameters under the current iteration
Figure FDA0002276541880000032
Step 4, solving equation (J)TJ+λI)δ＝-JTεkAnd I is a unit matrix, increment delta is obtained, and distortion parameter c is updatedk+1:＝ck+δ；
Step 5, calculating the objective function after updating the distortion parameters
Figure FDA0002276541880000033
Step 6, if εk+1＝εkThen the iterative calculation is stopped and the current distortion parameter ckThe distortion parameter is the optimized distortion parameter; if epsilonk+1＜εkUpdating parameter c: ═ ck+1，ε:＝εk+1And v:2, turning to step 2; if epsilonk+1＞εkUpdating parameter: ═ epsilonkAnd λ ═ v × λ, go to step 4.
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