CN113554709A - Camera-projector system calibration method based on polarization information - Google Patents
Camera-projector system calibration method based on polarization information Download PDFInfo
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/2433—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures for measuring outlines by shadow casting
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- G06T2207/20004—Adaptive image processing
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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- G06T2207/20—Special algorithmic details
- G06T2207/20112—Image segmentation details
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Abstract
The invention provides a camera-projector system calibration method based on polarization information. Selecting a calibration plate, and pasting the printed black-white checkerboard to the left half part of the calibration plate; (2) projecting the black and white checkerboard to the right half part of the calibration plate through a projector; (3) collecting calibration pictures of different postures under the optimal polarization angle by utilizing a CCD camera provided with a linear polaroid; (4) calibrating the camera through the printed checkerboard; (5) and establishing a relation between the image coordinate system of the projector and the world coordinate system by using the projection checkerboard to finish the calibration of the projector. The camera-projector calibration method provided by the invention obtains a picture required by calibration by utilizing polarization information, extracts the angular points by using a sub-pixel angular point extraction algorithm mapped by a single-mapping matrix, greatly improves the extraction precision of the angular points of the checkerboard, and obviously improves the calibration accuracy of the system.
Description
Technical Field
The invention relates to a calibration method of a camera-projector system, in particular to a method for recovering texture and color information of a highlight area of a calibration picture by using polarization information of light so as to improve the calibration precision of the camera-projector system.
Background
The structured light three-dimensional measurement system composed of the camera and the projector is widely applied to the fields of industrial precision detection, quality control, entity modeling and the like due to the advantages of high measurement precision, simplicity in operation, rapidness in data processing and the like. The key to accurately reconstructing three-dimensional shapes is to precisely calibrate each element used in the structured light system, including internal parameters characterizing the projection transformation characteristics of the camera and projector, and external parameters of spatial position relationships. The calibration principle and method of the camera are very mature at present. The calibration problem of the projector is complicated because the projector cannot capture images by itself, and the relationship between the spatial coordinates of the object and the coordinates mapped to the projector space cannot be directly acquired by researchers. At present, the world coordinate method is widely used for calibrating the projector due to the advantages of simple principle, convenient adjustment, easy realization and the like. The key to this method is how to obtain the image coordinates of the projected image in the camera coordinate system. Therefore, a great deal of work is done by researchers, but most of the attention is how to separate the calibration plate and change the calibration pattern to improve the extraction precision of the feature points, so that the imaging process of the calibration picture is omitted, and experiments show that paper, plastics and other materials can generate highlight areas of different degrees due to focusing when being shot by a camera under natural conditions. These high light areas can cause loss of texture information of the calibration image, thereby causing inaccurate extraction of pixel coordinates of the diagonal points, and finally causing low calibration precision of the camera. In active optical inspection systems, it is important to obtain high quality images.
Disclosure of Invention
In view of the above background, the invention provides a calibration technique for a camera-projector system based on polarization information, thereby solving the actual problem that the texture details and color information of the corner points are lost in the corner point extraction process. The calibration equipment is simplified, the complexity of the process is reduced, and the calibration precision is obviously improved.
In order to achieve the purpose, the invention adopts the following specific technical scheme:
and S1, selecting a calibration plane.
S2 calculation of light polarization information.
And S3, acquiring a calibration picture.
And S4, preprocessing the picture.
And S5, extracting corner points.
And S6, calibrating the camera.
And S7, calibrating the projector.
The single-polarizer imaging system employed in the present invention is shown in fig. 1, and the polarization information of various polarization states of light can be described by Stokes variables. Stokes variation of polarized light state:
in the above formula
Corresponding to the polarized light of the different states,
representing the total intensity of the light waves received by the imaging system,
representing the light intensity difference between the polarized light component of the light wave in the x-direction and the polarized light component in the y-direction,
indicating the difference in light intensity in two diagonal directions,
indicating the difference in intensity between left-hand polarized light and right-hand polarized light. In the single polarizer imaging system of FIG. 1, when the transmission axis of the polarizer is at an angle to the x-axis
When it is, ignore
Component, the intensity of the image pixel location is:
I(x,y,θ)=
（2）
thereby: and obtaining the relation between the pixel intensity and the polarization angle of the calibration image according to the stokes variables of the three different polarization states.
The adaptive gamma correction employed by the present invention enhances the black and white color contrast of the board. The basic gamma correction formula is as follows:
S=c
（3）
pdf(k)=
， k=
,……..,
（4）
n represents the total number of pixels in the input image I, from which the value of y is obtained as:
the sub-pixel angular point extraction algorithm adopted by the invention is as follows: and extracting the corner of the calibration image by adopting a sub-pixel corner extraction algorithm mapped by a homography matrix. From corner point q to any point in fig. 3
All vectors of (a) are perpendicular to the point
The image gray scale gradient.
Wherein:
representing the gray scale gradient of the image pi points. q is minimum
The coordinates of (a). And establishing an equation of all pi nearby the point q to obtain the accurate coordinate of the point q.
A represents
Is n
2 is a matrix of
In n
A column vector of 1. When in use
And then, obtaining the minimum value of the q point by the above formula, and continuously iterating by taking the minimum value of the q point as a center to obtain a coordinate with higher precision. Calibrating four coordinates of starting point of board
(t =1,2,3,4) is updated to
(r =1,2,3, 4). The homography matrix can be obtained by the following equation:
αm=HM （8）
here, the
I =1, 2.. and n denotes the coordinates of the corner points extracted in the image.
I =1, 2.. and n denotes a world coordinate system to which the coordinates of the corner points correspond.
Is a homography matrix and alpha is a constant. Therefore only need to
The corresponding homography matrix H can be found. The coordinates of all corner points are mapped to pixel coordinates by a homography matrix H. And then obtaining the sub-pixel coordinates of all corner points.
The projector calibration method adopted by the invention comprises the following steps: calibrated camera parameters are used to solve the link between the calibration plate and the projection image. The calibrated external parameter matrix of the camera is as follows:
third column vector of camera extrinsic parameter matrix
A normal vector n of the calibration plane, the last column vector is provided
The coordinates of the origin P of the calibration plane are provided. The calibration plane is a set of all points r, an original point o represents coordinates of a known point on the calibration plane, n represents a nonzero normal vector of the calibration plane, and finally three linear equation sets of the calibration plate plane are obtained through the characteristics of a plane equation:
wherein:
for unit vectors, define d as the dot product:
from which a plane can be derived
The equation of (c):
in the above formula: a, b, c, d are known real numbers, and a, b, c are not all 0. The three-dimensional world coordinate points of the corner points are solved by finding the intersection points of the rays and the plane. To obtain a projection through an angle in the image plane of the picture
The three-dimensional ray is transformed by using the obtained camera parameters as follows:
where s is the scale factor of the ray (Rx, Ry, Rz). And determining the intersection point of the ray and the calibration plane to obtain the three-dimensional position of the projection angle. The values of the ray coordinates are brought in the calibration plane equation:
in the above formula, except for the parameter s, the other parameters are known, and thus the value of s can be obtained. And (4) solving a three-dimensional world coordinate value corresponding to the projection angle through the value of s, and converting the calibration of the projector into a mature camera calibration.
The calibration method of the camera-projector system based on the polarization information has the following advantages. Under the condition of natural light, any picture can generate high-light areas of different degrees when being acquired by a camera, a calibration image under the optimal polarization angle is obtained by utilizing the stokes variable, the high-light areas of the image can be well removed, and texture color information at the angle point is restored. The traditional Harris corner has the problem of inaccurate extraction when the corner is extracted, and the sub-pixel corner extraction algorithm based on single-mapping matrix mapping is more accurate than the corner pixel coordinate information extracted by the Harris corner extraction algorithm. Experiments prove that the method obviously improves the precision of system calibration.
Drawings
FIG. 1 is a single polarizer imaging system.
Fig. 2 gamma-corrected image gray scale changes.
Figure 3 sub-pixel coordinate extraction principle of corner points.
Fig. 4 projector calibration schematic.
Fig. 5 is a calibration picture in the best polarization state.
The sub-pixel corner extraction algorithm of the single mapping matrix mapping of fig. 6 is compared with the corner pixel coordinate information extracted by the Harris corner extraction algorithm.
FIG. 7 is a comparison of the extraction accuracy of corner point information of the projection checkerboard under natural light and under the optimal polarization angle.
Fig. 8 shows a comparison of the camera calibration results under natural light and under the optimal polarization angle.
Fig. 9 shows a comparison of the calibration results of the projector under natural light and the optimum polarization angle.
Detailed Description
In order to more clearly describe the technical contents of the present invention, the following further description is given in conjunction with specific embodiments. And a CCD camera with a polaroid is used for acquiring a calibration picture under the optimal polarization angle, so that the influence of a high light area of the picture is reduced. The method specifically comprises the following steps: firstly, a CCD camera provided with a linear polaroid is used for acquiring a calibration picture in the optimal polarization state. And then preprocessing the acquired calibration picture, enhancing the color contrast of black and white grids of the checkerboard in the picture by using self-adaptive gamma correction, and extracting the corner sub-pixel coordinate information of the printing checkerboard and the projection checkerboard based on a sub-pixel corner extraction algorithm mapped by a single mapping matrix. And finally, on the basis of obtaining the camera calibration parameters, solving the relation between the image coordinate system and the world coordinate system of the projector to finish the calibration of the projector.
By utilizing the principle, the calibration method of the camera-projector system based on the polarization information comprises the following specific steps:
s1: obtaining a calibration picture: the position of projector and camera is installed, the plane calibration board which is manufactured is arranged at a certain position in the common visual angle range of projector and camera, the projector is obliquely arranged, the checkerboard image which is printed and pasted on the left side of the calibration board and ensures that the checkerboard image projected to the right side of the calibration board by the projector can be simultaneously collected by the camera, the optimal polarization state of light under the space attitude of the calibration board is calculated, and the calibration picture is collected by the linear polaroid in front of the lens of the CCD camera. And changing the spatial attitude of the calibration plate to obtain the optimal polarization angle under different spatial attitudes, and repeatedly collecting. The 10 calibration pictures are shown in fig. 5.
S2: preprocessing a calibration picture: gamma correction has the characteristic of enhancing the characteristic information of an image, and fig. 2 shows the influence of different y values on the gray level of an output image. To adaptively adjust the gray value of the input image, the value of y is adjusted with the probability density function of the image. Thereby obtaining the most suitable value of y.
Extraction of corner S3: and extracting the corners of the calibration image by adopting a sub-pixel corner extraction algorithm mapped by the homography matrix, and extracting the corners of the calibration image by adopting a sub-pixel corner extraction algorithm mapped by the homography matrix. In fig. 3, the equations for all pi's around the point q are set up to find the exact coordinates of the point q. When in use
And then, the minimum value of the q point is obtained, and the coordinates with higher precision can be obtained by taking the minimum value of the q point as the center and continuing iteration. Calibrating four coordinates of starting point of board
Is updated to (t =1,2,3,4)
(r =1,2,3, 4). The homography matrix can be obtained by α m = HM. The coordinates of all corner points are mapped to pixel coordinates by a homography H. And then obtaining the sub-pixel coordinates of all corner points. In fig. 6, the sub-pixel corner extraction algorithm mapped by the single mapping matrix is compared with the corner pixel coordinate information extracted by the Harris corner extraction algorithm.
Calibration of the S4 camera: in matlab, the camera is calibrated using the zhang's calibration method. A comparative graph of the camera calibration results is shown in fig. 8.
Calibration of S5 projector: projector calibration schematics as shown in fig. 4, calibrated camera parameters are used to solve the relationship between the calibration plate and the projected image. Therefore, the relation between the two-position image coordinate of the projector image and the corresponding three-dimensional world coordinate value is solved, and the calibration of the projector is converted into the mature camera calibration. A comparison graph of projector calibration results is shown in fig. 9.
Claims (1)
1. A calibration method of a camera-projector system based on polarization information is characterized by comprising the following steps:
(1) selection of the calibration plane: selecting a plastic plane with high surface evenness and low manufacturing cost as a calibration surface; selecting a light and thin material for the material of the printed checkerboard to ensure that the printed checkerboard and the calibration plane are as horizontal as possible;
(2) calculation of light polarization information: the polarization information of various polarization states of the light can be described by Stokes variables; stokes variation of polarized light state:
in the above formula
Corresponding to the polarized light of the different states,
representing the total intensity of the light waves received by the imaging system,
representing the light intensity difference between the polarized light component of the light wave in the x-direction and the polarized light component in the y-direction,
indicating the difference in light intensity in two diagonal directions,
indicating the light intensity difference of the left-handed polarized light and the right-handed polarized light; since the components of circular polarization are very few, they are ignored herein
Composition and represents the polarized light Stokes variable as:
S=(x,y)=
=
（2）
according to the expression, the intensity I (x, y, theta) of the image pixel position depends on the corresponding polarization angle theta; in a single polarizer imaging system, when the polarizer pass axis is at an angle to the x-axis
The intensity at the image pixel location is then:
I(x,y,θ)=
（3）
at least three independent parameters are needed to completely determine the polarization state of a beam of light based on formula (3); when a calibration image is collected, the polaroid in front of the polarization lens is rotated to obtain the polarization angle
，
And
the calibration plate image of (a); obtaining the relation between the pixel intensity and the polarization angle of the calibration image according to the stokes variables of the three different polarization states;
(3) obtaining a calibration picture: projecting a checkerboard for camera calibration to the right half part of the calibration board through a projector; ensuring that the printing checkerboard and the projection checkerboard are both positioned in the camera view angle; finally, a CCD camera provided with a linear polaroid is used for collecting more than ten calibration pictures under different space postures under the optimal polarization angle;
(4) preprocessing the picture: adopting self-adaptive gamma correction to enhance the black-white contrast of the checkerboard angular points; the basic gamma correction formula is as follows:
S=c
(4)
pdf(k)=
， k=
,……..,
(5)
n represents the total number of pixels in the input image I, from which the value of y is obtained as:
(5) and (3) extracting angular points: respectively extracting angular points from the printing checkerboard and the projection checkerboard by utilizing a sub-pixel angular point extraction algorithm mapped by the single-mapping matrix;
(6) calibrating the camera: the extracted corner points of the printing checkerboard finish the calibration of the camera by using a Zhang-Zhengyou calibration method;
(7) using the calibrated camera parameters to solve the relation between the calibration plate and the projection image; the calibrated external parameter matrix of the camera is as follows:
wherein: third column vector of camera extrinsic parameter matrix
A normal vector n of the calibration plane, the last column vector is provided
Providing the coordinates of the origin P of the calibration plane; the calibration plane is a set of all points r, an original point o represents coordinates of a known point on the calibration plane, n represents a nonzero normal vector of the calibration plane, and finally three linear equation sets of the calibration plate plane are obtained through the characteristics of a plane equation:
wherein:
for unit vectors, define d as the dot product:
from which a plane can be derived
The equation of (c):
in the above formula: a, b, c, d are known real numbers, a, b, c are not all 0; three-dimensional world coordinate points of the angular points are solved by finding intersection points of the rays and the planes; to obtain a projection through an angle in the image plane of the picture
The three-dimensional ray is transformed by using the obtained camera parameters as follows:
wherein s is a scaling factor for the ray (Rx, Ry, Rz); determining the intersection point of the ray and the calibration plane to obtain the three-dimensional position of the projection angle; the values of the ray coordinates are brought in the calibration plane equation:
except for unknown parameter s, other parameters are known in the formula, so that the value of s can be obtained; after the value of s is determined, the three-dimensional world coordinate value corresponding to the projection angle can be obtained, and the calibration of the projector is converted into the mature camera calibration.
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| CN114866751A (en) * | 2022-04-15 | 2022-08-05 | 海信视像科技股份有限公司 | Projection equipment and trigger correction method |
| CN116778001A (en) * | 2023-08-24 | 2023-09-19 | 华东交通大学 | Camera-projector calibration method and system based on global optimal polarized image |
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Application publication date: 20211026 |