CN111383194B - Polar coordinate-based camera distortion image correction method - Google Patents
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Abstract
The invention discloses a camera distortion image correction method based on polar coordinates, which comprises the steps of generating a calibration standard image, manufacturing a plane calibration plate, collecting the calibration distortion image, carrying out corner detection on the calibration standard image and the calibration distortion image, converting the calibration standard image and the calibration distortion image into polar coordinates, establishing a distortion correction equation of polar diameter and polar angle, solving distortion parameters, and carrying out image correction. The method can realize the distortion correction of the camera without acquiring an internal reference matrix of the camera, thereby correcting the image acquired by the camera; the method adopts the polar coordinate form, simplifies the distortion correction formula, reduces the difficulty of solving distortion parameters, and can improve the distortion correction precision of the camera.
Description
Technical Field
The invention relates to an image processing technology, in particular to a method for correcting image distortion caused by camera distortion based on polar coordinates.
Background
Cameras produce distortion of the image during imaging due to machining and mounting errors. The distortion of the camera imaging mainly comprises three forms of radial distortion, tangential distortion and Bao Lengjing distortion. The calibration method is generally adopted as the checkerboard calibration method proposed by Zhang Zhengyou. In the calibration, according to the known size of the checkerboard, the rectangular coordinates of the corner points are determined, compared with the rectangular coordinates of the corner points in the distorted image of the camera, and the distortion coefficient is calculated.
Both radial and tangential aberrations are related to the distance of the image point from the center point. In practical applications, a quick correction of image distortion is required. According to the invention, radial and tangential distortion of the camera is directly analyzed and solved in a polar coordinate form, so that the image distortion caused by the camera distortion is corrected, the thought is clear, the distortion fitting formula is simplified, and the correction speed is improved.
Disclosure of Invention
The invention aims to: the invention aims to provide a novel polar coordinate-based camera calibration pattern and an image distortion correction method caused by camera distortion.
The technical scheme is as follows: the invention provides a camera distortion image correction method based on polar coordinates, which comprises the following steps:
(1) Manufacturing a calibration plate: drawing a calibration standard image PicCorrect. Jpg through computer programming, wherein the calibration standard image comprises two concentric circles and four rays starting from the circle center, and two of the four rays are vertical and two of the four rays are horizontal; manufacturing a plane calibration plate by using a calibration standard image;
(2) Collecting a calibration distortion image, extracting a calibration standard image and corner points of the calibration distortion image, and converting the calibration standard image and the corner points of the calibration distortion image into polar coordinates: the distorted image acquired by the plane calibration plate through the camera is a calibration distorted image PicCapt; respectively extracting pixel rectangular coordinates of corner points at the intersection points of concentric circles and four rays in the image by using a sub-pixel corner detection method; respectively taking the centers of concentric circles in PicCorrect. Jpg and PicCapt. Jpg as poles of polar coordinates, and constructing a polar coordinate system in the forward direction of the polar axis horizontally to the right; converting rectangular coordinates of the corner points obtained through detection into polar coordinates; matching the angular points detected in PicCorrect. Jpg and PicCapt. Jpg, and calibrating the polar coordinates of the angular points in the standard image to be
Calibrating polar coordinates of corner points in distorted images to be +.>
(3) Determining a distortion coefficient: the mean value of the polar paths of the angular points in PicCorrect. Jpg and PicCapt. Jpg are respectively counted and are respectively used for Mr c And Mr, the scaling factor of the two graphs is k 0 ＝Mr c Substituting polar coordinates of angular points except for the circle center in the two figures into the following correction equation respectively:
solving the equation to obtain a distortion correction coefficient k 1 ,k 2 ,k 3 ,k 4 ,k 5 ,k 6 And image deflection angle
/>
(4) Camera image distortion correction: collecting an image in the same plane as the calibration plate, recording as Pic2Revi. Jpg, taking the center of the Pic2Revi. Jpg image as a pole, constructing a polar coordinate system in a horizontal direction as a polar axis forward direction, and converting rectangular coordinates (x, y) of each pixel point into polar coordinates
Will->
Substituting into the correction equation to obtain corrected polar coordinates
Polar coordinates +.>
Converted into rectangular coordinates, denoted as (x) c ,y c ) And (5) making the pixel values before and after conversion equal, and interpolating the converted image to obtain a corrected image.
In the step (2), when the calibration distortion image is acquired, the center of the calibration distortion image is the center of a calibration circle in the calibration plate; the two sets of horizontal and vertical lines are as horizontal and vertical as possible.
In the step (3), the distortion correction coefficient k is calculated by a least square method 1 ,k 2 ,k 3 ,k 4 ,k 5 ,k 6 And image deflection angle
In the step (2), corner coordinates are extracted from the calibration standard image and the calibration distortion image by using a goodfeaturestrack () function in python software.
In the step (2), the corner points detected in the calibration standard image and the calibration distortion image are matched, and the specific steps are as follows:
ordering the angular points in PicCorrect. Jpg and PicCapt. Jpg according to the polar diameters from small to large, and ordering the angular points according to the polar angles with the same polar diameter from small to large; and after sorting, the corner numbers in PicCorrect. Jpg and PicCapt. Jpg are the same and are matched corner pairs.
The beneficial effects are that: compared with the prior art, the invention has the following advantages:
(1) The concentric circles and the rays from the circle center are used as the patterns of the calibration plate, so that the polar coordinate values of the corner points in the calibration standard image can be easily and accurately determined.
(2) The calibration standard image is also subjected to angular point detection and the polar coordinates of the angular points are obtained, so that the accuracy and the error of an angular point detection algorithm and coordinate conversion can be checked, and the error caused by the accuracy of the angular point detection algorithm is reduced.
(3) The ratio of the average value of the polar diameters of all the angular points in the calibration standard image and the calibration distortion image is used as the scaling factor of the two images, and compared with the scaling factor obtained by using the polar diameter of only one point, the error of scaling factor estimation is reduced.
(4) Since all the radial distortion correction formulas and tangential distortion correction formulas are in the form of polar coordinates, the radial distortion correction formulas and tangential distortion correction formulas can be directly expressed as correction formulas of polar diameter and polar angle:
the equation does not contain coupling terms any more, so that the solution of the coefficients is simplified, and the solution precision is improved. The center of the pattern is aligned with the "+" of the center of the image when photographing, thus eliminatingBesides the offset of the center point, the polar diameter correction formula is simplified; the two rays are as horizontal as possible, but still have small angle deviation, and parameters are added in the formula
The method is used for eliminating the deviation of the integral rotation of the pattern in the solving process, and ensures the accuracy of distortion parameter solving.
Drawings
FIG. 1 is a general flow chart of the present invention for a polar coordinate based camera distortion correction method;
FIG. 2 is a calibration standard image based on polar coordinates;
FIG. 3 is a schematic illustration of center alignment during calibration plate image acquisition;
fig. 4 is a schematic diagram of the result of corner detection on a calibration distorted image.
Detailed Description
The technical scheme of the present invention is described in detail below, but the scope of the present invention is not limited to the embodiments.
As shown in fig. 1, the method for correcting a camera distortion image based on polar coordinates of the present invention comprises the following steps:
(1) Manufacturing a calibration plate: two concentric circles and four rays from the center of the circle are drawn through computer programming, wherein two of the two rays are vertical and two of the two rays are horizontal. The standard image was saved as PicCorrect. Jpg picture, as shown in FIG. 2, which was later analyzed as an undistorted image; and printing the picture, adhering the picture on a wood board to serve as a calibration board, and collecting an image by a camera and correcting distortion.
(2) Extracting the coordinates of corner points of two images, and converting to obtain polar coordinates: the distorted image acquired by the calibration plate through the camera is stored as PicCapt. Jpg, the PicCorrect. Jpg and PicCapt. Jpg are utilized to simultaneously extract the pixel rectangular coordinates of the corner points at the intersection point of the concentric circles and the rays of the two images by using a sub-pixel corner point detection method, the circle center is used as the origin of the polar coordinates, and the polar coordinates of all the corner points in the two images are obtained through conversion from the rectangular coordinate system to the polar coordinate system and are respectively expressed as
And->
(3) Determining a distortion coefficient: the mean value of the polar paths of the corner points in PicCorrect. Jpg and PicCapt. Jpg is counted by Mr respectively c And Mr, the scaling factor of the two graphs is k 0 ＝Mr c And (2) Mr, sorting the polar coordinates of 8 angular points except for the circle center in the two graphs from small to large according to polar diameters, sorting the polar points with the same polar diameters from small to large according to polar angles, completing corresponding matching of the 8 angular points in the two graphs, and substituting the polar coordinates into the following two equations respectively:
solving the equation to obtain a distortion correction coefficient k 1 ,k 2 ,k 3 ,k 4 ,k 5 ,k 6 And image deflection angle
(4) Camera image distortion correction: collecting any image of the calibration plate in the same plane, marking as Pic2Revi. Jpg, taking the center of the image as the origin of coordinates, converting the rectangular coordinates (x, y) of each point into polar coordinates, substituting the polar coordinates into the correction equation obtained in the step (3), obtaining corrected polar coordinates, converting the polar coordinates into rectangular coordinates, marking as (x) c ,y c ) Let the pixel values before and after conversion be equal, i.e. f (x c ,y c ) =f (x, y), interpolates the converted image, resulting in a corrected image.
Example 1:
in this embodiment, the algorithm of python+opencv is used to implement design and distortion correction of the pattern.
The calibration standard pattern adopts two concentric circles with different radiuses and four rays which start from the circle center, two horizontal rays and two vertical rays, and is shown in figure 2. The calibration pattern drawn by the python software was saved as PicCorrect. Jpg. Printing the pattern, adhering the pattern on a flat wood board, and collecting an image of the pattern by using a camera. The center of the image acquisition area is set to be "+" through software, the calibration plate is moved to enable the circle center in the calibration plate to coincide with "+", and meanwhile, when two horizontal rays are horizontally placed as much as possible, an image is acquired, and in FIG. 3, the acquired image is stored as PicCapt.
And converting PicCorrect. Jpg and PicCapt. Jpg into gray images, setting the number of corner points to be 9, and extracting rectangular coordinates of sub-pixel corner points by using a goodfeaturesToTrack () function, wherein the corner point detection result of PicCapt. Jpg is shown in figure 4. And taking a corner point at the center of a circle as a pole, taking the horizontal direction as the positive direction of a polar axis, and respectively constructing a polar coordinate system in PicCorrect. Jpg and PicCapt.
The average value of the polar diameters of 9 angular points in PicCorrect. Jpg and PicCapt. Jpg is obtained respectively by Mr c And Mr, the scaling factor of the two graphs is k 0 ＝Mr c /Mr. The scaling factor reflects how far or how far the calibration plate is from the camera. The polar coordinates of 8 angular points except the circle center in the two figures are firstly ordered according to the polar diameters from small to large, the polar diameters are the same and ordered according to the polar angles from small to large, so that the 8 angular points in the two figures are matched correspondingly, and then the following calibration equations are substituted respectively:
solving the variable k for equation (1) 1 ,k 2 ,k 3 The coefficient matrix is
The equation is converted into:
then using lstqr to obtain k by least square method 1 ,k 2 ,k 3 Is a solution to (a).
For equation (2), to
And k 4 ,k 5 ,k 6 Solving as variables, the coefficient matrix is +>
The equation is converted into:
then using lstqr to obtain
And k 4 ,k 5 ,k 6 Is a solution to (a). In this embodiment, the coefficient k obtained by equations (1) and (2) 1 ,k 2 ,k 3 And k 4 ,k 5 ,k 6 The values differ slightly and are therefore regarded as identical parameters. If the distortion correction accuracy is high, the distortion correction parameters can be treated as different distortion correction parameters.
Any image in the same plane as the calibration plate is collected and marked as Pic2Revi. Jpg, and a polar coordinate system is constructed with the center of the image as a pole and the horizontal direction as the polar axis forward direction; converting rectangular coordinates (x, y) of each pixel point into polar coordinates, and recording as
Substituting into the previous correction equations (1) and (2) to obtain corrected polar coordinates +.>
The polar coordinates are converted into rectangular coordinates, which are denoted as (x) c ,y c ) Let the pixel values before and after conversion be equal, i.e. f (x c ,y c ) =f (x, y), interpolates the converted image, resulting in a corrected image. />
Claims (5)
1. A camera distortion image correction method based on polar coordinates is characterized by comprising the following steps: the method sequentially comprises the following steps of:
(1) Manufacturing a calibration plate: drawing two concentric circles and four rays from the circle center as standard images through computer programming, wherein the four rays are two vertical rays and two horizontal rays; storing the standard image as PicCorrect. Jpg picture, and analyzing the PicCorrect. Jpg picture as an undistorted image; printing the standard image, adhering the standard image on a wood board to serve as a calibration board, and collecting the image by a camera and correcting distortion;
(2) Extracting the coordinates of corner points of two images, and converting to obtain polar coordinates: the distorted image acquired by the calibration plate through the camera is stored as PicCapt. Jpg, the PicCorrect. Jpg and PicCapt. Jpg are utilized to simultaneously extract the pixel rectangular coordinates of the corner points at the intersection point of the concentric circles and the rays of the two images by using a sub-pixel corner point detection method, the circle center is used as the origin of the polar coordinates, and the polar coordinates of all the corner points in the two images are obtained through conversion from the rectangular coordinate system to the polar coordinate system and are respectively expressed as
And->
(3) Determining a distortion coefficient: the mean value of the polar paths of the corner points in PicCorrect. Jpg and PicCapt. Jpg is counted by Mr respectively c And Mr, the scaling factor of the two graphs is k 0 ＝Mr c And (2) substituting polar coordinates of angular points except for the circle center in the two figures into the following two correction equations respectively:
solving the equation to obtain a distortion correction coefficient k 1 ,k 2 ,k 3 ,k 4 ,k 5 ,k 6 And image deflection angle
(4) Camera image distortion correction: any image of the calibration plate in the same plane is collected and recorded as Pic2Revi. Jpg, and rectangular coordinates (x, y) of each point are converted into polar coordinates by taking the center of the image as the origin of coordinates
Will->
Substituting into the correction equation in the step (3) to obtain corrected polar coordinates +.>
Polar coordinates +.>
Converted into rectangular coordinates, denoted as (x) c ,y c ) Let the pixel values before and after conversion be equal, i.e. the pixel value at (x, y) is equal to (x) c ,y c ) Pixel values at the positions are equal; and interpolating the converted image to obtain a corrected image.
2. The method for correcting a camera distortion image based on polar coordinates according to claim 1, wherein: in the step (1), a radial combined pattern which is formed by concentric circles and starts from the circle center is used as a calibration plate pattern; the concentric circles and ray patterns generated by the program are stored as images, can be used as correction standards of undistorted images and can also be used as evaluation standards of the accuracy of subsequent algorithms; the printed pattern is used as a calibration plate, the center of an image is marked with a "+" when the camera collects, so that the pattern is aligned with the center of the pattern, two groups of horizontal lines and vertical lines are horizontal and vertical as much as possible, and the collected image is used for solving the distortion coefficient of the camera.
3. The method for correcting a camera distortion image based on polar coordinates according to claim 1, wherein: in the step (2), since the radius of each concentric circle and the polar angle of each ray in the standard pattern PicCorrect. Jpg drawn by the program are known, the polar coordinates of all the corner points of the concentric circles and the rays are known, and the polar coordinates can be used for subsequent camera calibration.
4. The method for correcting a camera distortion image based on polar coordinates according to claim 1, wherein: in the step (3), a formula is adopted
Describing a functional relation between the polar diameter of the camera and the polar angle before and after distortion correction; determining the scaling factor k of the statistics PicCorrect. Jpg and PicCapt. Jpg by the ratio of the mean values of the polar diameters of the same points 0 The method comprises the steps of carrying out a first treatment on the surface of the After the standard image and the distorted image are aligned by the "+" center, only parameters are needed
Describing a fixed deflection angle; parameter k 1 ,k 2 ,k 3 And k 4 ,k 5 ,k 6 The magnitude of the distortion of the pole diameter and the pole angle with the increase of the pole diameter and the pole angle order is reflected respectively.
5. The method for correcting a camera distortion image based on polar coordinates according to claim 1, wherein: in the step (4), the distortion correction of the image acquired by the camera is completed by adopting rectangular coordinates to polar coordinates and then adopting the conversion from the polar coordinates to the rectangular coordinates.
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