CN111429522B - Method and system for calibrating camera by using common pole polar line property of coplanar circles - Google Patents
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Abstract
The invention discloses a method and a system for calibrating a camera by utilizing the polar line property of a common pole of a coplanar circle. Respectively extracting edge points of the target images from the 3 images, and fitting by using a least square method to obtain a coefficient matrix of a quadratic curve; on the basis, according to the polar line properties of the common poles of the two coplanar circles at various positions, the common poles are located at the infinite straight line, and the polar line corresponding to the common poles passes through the centers of the two circles; when concentric, two common poles are infinite points, and when non-concentric circles, one common pole is an infinite point; therefore, a vanishing line is obtained by utilizing the polar line property of the common poles of the three coplanar circular templates, the intersection point of the vanishing line and the quadratic curve is an image of a circular point, and the three images provide images of three groups of circular points; and finally, solving the intrinsic parameters of the camera by using the constraint of the image pair absolute quadratic curve image of the circular ring points. The method has the advantages of simple test scene, wide applicability and quick calibration, and the calculation process is a linear process.
Description
Technical Field
The invention relates to the field of computer vision, in particular to a method and a system for calibrating a camera by utilizing the polar line property of a common pole of a coplanar circle.
Background
The central task of computer vision is to understand images, and its ultimate goal is to make the computer have the ability to recognize three-dimensional environmental information through two-dimensional images. This capability will not only enable the machine to perceive the geometric information of objects in a three-dimensional environment, including shape, pose, motion, etc., but also to describe, store, recognize and understand them. Camera calibration, which is the procedure necessary for many computer vision applications, is to determine the mapping from a three-dimensional point in space to its two-dimensional image point. In order to determine the mapping process, a geometric imaging model of the camera needs to be established, parameters of the geometric model are called as camera parameters, and the camera parameters can be divided into an internal parameter and an external parameter. The intrinsic parameters describe the imaging geometry of the imaging system and the extrinsic parameters describe the orientation and position of the imaging system with respect to the world coordinate system. Camera calibration can be divided into traditional calibration, self-calibration and calibration based on geometric entities. No matter which calibration method is used, the aim is to establish a constraint relation, particularly a linear constraint relation, between a two-dimensional image and parameters in a camera, which is a target pursued by the current camera calibration and is one of hot spots of research in the field of computer vision at present.
The pinhole camera imaging model is simple, is convenient to manufacture, does not need special mirror surfaces, and is one of the hotspots of the research in the panoramic vision field. Although the traditional Camera Calibration method can obtain higher precision, the Calibration block is difficult to manufacture and inconvenient to operate, and a method for replacing the traditional Calibration block by a plane grid is proposed in the documents of 'A Flexible New Technique for Camera Calibration', (Zhengyou Zhang, IEEE transactions on Pattern and Machine integrity, vol.22, No.11, pp.1330-1334,2000), and the method has the advantages of simplicity, low cost and high Calibration stability and precision relative to self-Calibration; the document "new easy camera calibration technique based on circular calibration", (x.meng and z.hu, Pattern Recognition, vol.36, No.5, pp.1155-1164,2003.) proposes to calibrate the camera based on circular points by using a circle and a plurality of straight lines passing through the center of the circle as calibration templates, and the method applies the properties of the circular points in the projective geometry to calibration, so that the circular points become the theoretical basis of the camera calibration method.
The documents "Camera alignment from the same square-after orientation of two Parallel Circles", (y.wu, h.zhu, z.hu, et al, European Conference on Computer Vision, vol.2021, No.1, pp.190-202,2004.) solve the image of a circle point based on quasi-affine invariance between two Parallel Circles, using at least two Parallel Circles, resulting in a circle point on the plane where it lies, but the method requires solving a set of non-linear equations, "European cluster Structure from N > -2 Parallel Circles 2006: the Theory and Algorithms", (g.pierce, s.peter and, y.wu, European Conference on Computer Vision, 238-252, pp) discusses the simultaneous formation of two Parallel bundles of Parallel and extended lines from two Parallel Circles, and the property of the two Parallel bundles of Parallel Circles, thus summarizing the two Parallel Circles and the property of the two Parallel Circles, and the property of the two Parallel Circles in the image. The documents "The common self-polar triangle of section circuits" ("Haifei Huang, Hui Zhang, Yiu-min Cheng, International Conference on Image Processing, pp.1170-1174, 2016") and "The common self-polar triangle of section circuits and site adaptation" Haifei Huang, Hui Zhang, Yiu-min Cheng, Conference on Computer Vision and Pattern Recognition, pp.4065-4072,2015) use The concept of a common polar triangle camera in calibration, with The triangle vertex at a distance from The polar coordinate. Therefore, a vanishing line of the support plane of the circle can be obtained in the image. The algorithm recovers the image of the circular ring points, compared with the traditional calibration method, the method avoids the problems of solving the quadratic equation and unstable numerical value, but two documents only discuss the separation circle and the concentric circle in the coplanar circle template.
Disclosure of Invention
The invention aims to: aiming at the existing problems, the method and the system for calibrating the camera by utilizing the polar line property of the common pole of the coplanar circle have wide applicability and good stability, and the calibration of the camera is completed by a simple scene arrangement and linear solving mode.
The invention utilizes the common pole polar line property of coplanar circles at various positions to calibrate the camera. Firstly, respectively extracting edge points of a target image from 3 (or more) images, and fitting by using a least square method to obtain a coefficient matrix of a quadratic curve; on the basis, according to the polar line properties of the common poles of the two coplanar circles at various positions, the common poles are located at the infinite straight line, and the polar line corresponding to the common poles passes through the centers of the two circles; when concentric, two common poles are infinite points, and when non-concentric circles, one common pole is an infinite point; therefore, a vanishing line is obtained by utilizing the polar line property of the common poles of the three (or more) coplanar circular templates, the intersection point of the vanishing line and the quadratic curve is the image of the circular points, and the three images provide the images of three groups of circular points; and finally, solving the intrinsic parameters of the camera by using the constraint of the image pair absolute quadratic curve image of the circular ring points.
The technical scheme adopted by the invention is as follows:
a method of calibrating a camera using common pole polar properties of coplanar circles, comprising the steps of:
respectively executing the following steps A-C for at least 3 different target images, wherein the target images are obtained by adopting a pinhole camera to acquire the target consisting of three coplanar circles;
A. respectively fitting a quadratic curve equation of each coplanar circle in the target image on an image plane;
B. randomly selecting two groups of quadric pairs from quadric equations of all coplanar circles, and calculating vanishing points on an image plane according to the common pole polar line relation of the selected quadric pairs so as to obtain corresponding vanishing lines;
C. calculating the image of the circular point according to the vanishing line;
D. and calculating the image of the absolute quadratic curve according to the images of the circular points corresponding to at least 3 target images and based on the linear constraint relation of the image pairs of the circular points to the image of the absolute quadratic curve, decomposing the image of the absolute quadratic curve, and calculating to obtain the internal parameters of the camera.
Further, in the step a, the method for fitting a quadratic curve equation of each coplanar circle in the target image in the image plane includes: and extracting pixel coordinates of edge points of the target image, and fitting a corresponding quadratic curve equation by adopting a least square method.
Further, in the step B, the method for calculating the vanishing point on the image plane according to the common pole-line relationship of the taken quadratic curve pair includes: and calculating generalized eigenvalues of the taken quadratic curve pairs, and determining vanishing points from eigenvectors of the generalized eigenvalues according to the number of public self-polar triangles between the taken quadratic curve pairs.
Further, the method for determining the vanishing points from the feature vectors of the generalized feature values according to the number of the common self-polar triangles between the taken quadratic curve pairs comprises the following steps:
when a unique common self-polar triangle exists between the taken quadratic curve pairs, determining the feature vector which is not in the quadratic curve as a vanishing point in the feature vectors of the generalized feature values;
when no public self-polar triangle exists between the two secondary curve pairs, determining a feature vector which is not equal to other feature vectors in the feature vectors of the generalized feature values as a vanishing point;
when countless common self-polar triangles exist between the taken quadratic curve pairs, the feature vectors with the same value in the feature vectors of the generalized feature values are determined as vanishing points.
Further, the method for calculating the image of the absolute quadratic curve based on the linear constraint relationship between the image of the circular ring point and the image of the absolute quadratic curve comprises the following steps:
the linear constraint relation of the image of the circular ring point to the image of the absolute quadratic curve is as follows:
where N is the number of target images, miIIs the image of the circular point, omega is the image of the absolute quadratic curve;
solving the image of the absolute quadratic curve according to the linear constraint relation of the image of the circular ring point to the image of the absolute quadratic curve;
and performing Cholesky decomposition on the image of the absolute quadratic curve and then inverting to obtain an internal parameter matrix, thereby obtaining the internal parameters of the camera.
Further, the method for solving the image of the absolute quadratic curve according to the linear constraint relationship of the image of the circular ring point to the image of the absolute quadratic curve comprises the following steps: and (3) optimally solving the linear constraint relation of the image pair of the circular ring points to the image of the absolute quadratic curve by adopting a least square method to obtain the image of the absolute quadratic curve.
Further, the 3 different target images are: and selecting at least 3 target images acquired under different orientations from the acquired at least 3 target images.
To solve the above problems, the present invention further provides a system for calibrating a camera using the common pole epipolar property of coplanar circles, which operates the above method for calibrating a camera using the common pole epipolar property of coplanar circles.
To solve the above problems, the present invention further provides a method for calibrating a camera using common pole line properties of coplanar circles, comprising the steps of:
A. acquiring images of a target consisting of three coplanar circles from at least 3 different directions by using a pinhole camera to obtain at least 3 target images;
B. and introducing at least 3 target images into the system for calibrating the camera by using the polar line property of the common pole of the coplanar circle to obtain the internal parameters of the camera.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
1. the target designed by the invention has simple structure and convenient manufacture, and only at least three coplanar circles at any positions need to be drawn on the plane.
2. The invention only needs a minimum of 3 target images containing a minimum of 3 coplanar circles, and is also applicable to more target images and targets.
3. The solving process of the invention is a linear calculation process, the calculation complexity and the calculation difficulty are low, the realization is easy, and the camera calibration can be rapidly completed.
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The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a schematic of the structure of three coplanar circular targets.
Fig. 2 is a projection of the target onto the image plane and its vanishing line recovered from the two sets of quadratic curves.
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification (including any accompanying claims, abstract) may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
Example one
In this embodiment, 3 target images are selected as an example, and the same principle is applied to the calculation of more than 3 target images. The embodiment discloses a method for calibrating a camera by utilizing the polar line property of a common pole of a coplanar circle, which comprises the following steps:
for 3 different target images in the acquired target images, the following steps a to C are respectively executed, where the target images are obtained by acquiring images of a target composed of three coplanar circles (or more than three, in this text, 3 are taken as an example, and the same is true for the coplanar circles of more than 3) by using a pinhole camera.
A. And respectively fitting to obtain a quadratic curve equation (namely a target projection equation) corresponding to each coplanar circle.
Three coplanar circles correspond to obtain three quadratic curve equations, and the corresponding coefficient matrix is Ci(i ═ 1,2, 3); in this context, for the sake of simplicity of presentation, the quadratic curve and its coefficient matrix are denoted by the same letters.
B. Two sets of quadratic curve pairs are selected from any one of the three quadratic curve equations. Calculating any two groups of quadratic curve pairs (C) in three quadratic curve equationsi,Cj) Generalized eigenvalues λ of (i ≠ 1,2, j ≠ 2,3, i ≠ j)ij(i, j ═ 1,2,3) which represents the j-th eigenvalue of the i-th group of quadratic curve pairs, and the eigenvector corresponding to the generalized eigenvalue is mij(i, j ═ 1,2, 3). Calculating vanishing points on an image plane according to the polar line relation of the public poles of the two sets of quadratic curve pairs, wherein at least two vanishing points v can be obtained by the two sets of quadratic curve pairs1、v2Thereby recovering the vanishing line l∞＝v1×v2. The calculation process is described in detail below.
Any point x and the quadratic curve C define a straight line l ═ Cx, l is called the epipolar line of point x with respect to C, and point x is called the pole of l with respect to C; if the point y is on the polar line l ═ Cx, then yTl＝yTCx ═ 0. Satisfy yTAny two points where Cx ═ 0 are referred to as being conjugate with respect to the quadratic curve C. A self-polar triangle, also known as a self-conjugate triangle, refers to any three vertices that are the poles of opposite sides with respect to a given conic. If any three vertices mi(i ═ 1,2,3) are conjugate points of each other with respect to a quadratic curve C, i.e., m is satisfiediCmj0, (i ≠ j) (i, j ═ 1,2,3), thatThree vertexes miOne three point formed by (i ═ 1,2,3) is in the shape of a self-polar triangle. Any one quadratic curve typically has a plurality of free triangles; if any two quadratic curves have two self-polar triangles which are completely equal, the self-polar triangle Δ m is determined1m2m3In the form of triangles with respect to their common poles, i.e. having a common pole-line relationship between them.
Two coplanar circles Q1And Q2Projected as a quadratic curve C on the image plane1And C2，C2 -1C1Has a characteristic value ofi(i is 1,2,3) corresponds to a feature vector of mi(i＝1,2,3)。
When the quadratic curve C1And C2When separated, contained (eccentric), crossed, then C2 -1C1Has a characteristic value of1≠λ2≠λ3,rank(C1-λiC2)＝2,(i＝1,2,3)，C1And C2There is a unique common self-pole triangle Δ m between1m2m3One vertex is located on the vanishing line, i.e. vanishing point v; when C is present1And C2At the tangent, then C2 -1C1Has a characteristic value of1＝λ2,rank(C1-λ1C2)＝2，λ3Corresponding feature vector m3Vanishing point v, there is no common epipolar triangle between them; when two C1And C2When concentric, then C2 -1C1Has a characteristic value of1＝λ2,rank(C1-λ1C2)＝1，λ1＝λ2Corresponding feature vector m1,m2For vanishing points v, v', there are an infinite number of common epipolar triangles. Therefore, at least two vanishing points can be obtained by selecting two groups of quadratic curve pairs.
C. According to the vanishing line l∞Calculating the image m of a circle pointI,mJ. Vanishing line l∞Image C of a circle coplanar with any onei(i-1, 2,3) intersecting at a circular pointImage m ofI,mJ。
D. According to the images of the circular points corresponding to the three target images, the image m based on the circular pointsiI,miJAnd (i is 1,2 and 3) calculating omega by linear constraint of the image omega of the absolute quadratic curve, and decomposing the image omega of the absolute quadratic curve to obtain the camera intrinsic parameters. In particular, the image m of a circular pointiI,miJ(i ═ 1,2,3) linear constraints on the image ω of the absolute quadratic curve, i.e.
Re and Im respectively represent the real part and the imaginary part of the complex number, the image omega of the absolute quadratic curve can be calculated according to the relation, Cholesky decomposition is carried out on the image omega of the absolute quadratic curve, and then inversion is carried out to obtain an internal parameter matrix
Namely, 5 intrinsic parameters of the camera are obtained, wherein fu,fvFor the scale factor of the camera in the direction of the two coordinate axes, s is called the tilt factor, [ u ]0,v0]Referred to as principal point coordinates.
In a specific embodiment, the method further comprises the step of acquiring at least 3 target images, and obtaining at least 3 target images from the acquired target images for the calculation.
Example two
The embodiment discloses a method for calibrating a camera by utilizing the polar line property of a common pole of a coplanar circle, which comprises the following steps:
A. and (3) extracting the pixel coordinates of the Edge points of the 3 (or more, the same calculation method as the same principle) target images by using an Edge function in a Matlab program, and fitting by using a least square method to obtain a corresponding target projection equation, wherein the target projection equation is a quadratic curve equation. The target image is obtained by acquiring an image of a target consisting of three coplanar circles (or more, and the same calculation method is used) by a pinhole camera. For each target image, three coplanar circles correspond to obtain three quadratic curve equations, and the corresponding coefficient matrix is Ci(i ═ 1,2, 3). As shown in fig. 1, the target plane hasThree coplanar circles Qi(i 1,2,3) projected on a pinhole camera as three conic curves Ci(i ═ 1,2,3), as shown in fig. 2, in this document, the quadratic curve and its coefficient matrix are represented by the same letters for the sake of simplicity of the description.
B. Two sets of quadric pairs (C) are calculated from (1) based on the common pole-line properties of the quadric pairsi,Ci+1) Characteristic value λ of (i ═ 1,2)ij(i-1, 2, j-1, 2,3) which represents the j-th eigenvalue of the i-th set of quadratic curve pairs, and the corresponding eigenvector is mij(i,j＝1,2,3)。
(Ci+1 -1Ci-λijI)mij＝0，(i＝1,2,j＝1,2,3) (1)
Wherein λijIs the jth eigenvalue of the ith set of quadratic curve pairs, and I is the identity matrix.
When C is presenti+1 -1CiThe characteristic value of (i ═ 1,2) is λ1≠λ2≠λ3,rank(C1-λjC2)＝2,(j＝1,2,3)，CiAnd Ci+1There is a unique common self-pole triangle Δ m between1m2m3One not in the quadratic curve, with the apex on the vanishing line, i.e. vanishing point vi(ii) a When lambda is1＝λ2,rank(Ci-λ1Ci+1) 2, there is no common dipole triangle, λ3Corresponding feature vector m3Is a vanishing point vi(ii) a When lambda is1＝λ2,rank(Ci-λ1Ci+1) At 1, there are an infinite number of common autocontrol triangles, λ1＝λ2Corresponding feature vector m1,m2Is a vanishing point vi，vi'。
As shown in fig. 2, two sets of quadratic curve pairs (C)i,Ci+1) (i-1, 2) obtaining at least two directional vanishing points v1,v2Then the line of disappearance l∞Comprises the following steps:
l∞＝v1×v2 (2)
C. according to disappearanceThread l∞Calculating the image m of a circle pointI,mJ。
Vanishing line l∞And the quadratic curve CiImage m both intersecting at two circular pointsI,mJSimultaneous vanishing line l∞And the quadratic curve Ci(i ═ 1,2,3) of:
wherein [ u v 1]TRepresenting homogeneous coordinates of points on the image plane. This second equation is preferably averaged because of the influence of noise.
Three images can obtain the image m of three groups of circular points1I,m1J、m2I,m2JAnd m3I,m3J。
D. And solving the internal parameters of the pinhole camera.
From the image m of the circle pointiI,miJ(i ═ 1,2,3) linear constraint relationship to the image ω of the absolute quadratic curve:
and (4) solving the formula (4) by adopting a least square method optimization, and obtaining an image omega of the quadratic curve. Then for ω ═ K-TK-1Cholesky decomposition to K-1Then inverse to obtain the internal parameter matrix K,
thereby obtaining 5 internal parameters of the camera and completing the calibration of the camera.
EXAMPLE III
In this embodiment, a specific case is adopted, and the calibration of the pinhole camera is completed by using the method of calibrating the camera by using the polar line property of the common pole of the coplanar circle in the second embodiment.
A. As shown in fig. 1, three coplanar circles Q1、Q2And Q3Constituting a targetAnd shooting the target in 3 different directions by using a pinhole camera to obtain three target images. Reading the three target images into Matlab, extracting the pixel coordinates of the Edge points of the target images by using an Edge function in the Matlab, and fitting by using a least square method to obtain an equation (target projection equation) of a secondary curve of each coplanar circle in each target image, wherein the result is as follows:
the coefficient matrixes of the three quadratic curves in the first image are respectively C1i(i ═ 1,2,3), the results were as follows:
the coefficient matrixes of the three quadratic curves in the second image are respectively C2i(i ═ 1,2,3), the results were as follows:
the coefficient matrixes of the three quadratic curves in the third image are respectively C3i(i ═ 1,2,3), the results were as follows:
B. and calculating the corresponding vanishing line of each target image.
Two sets of quadratic curve pairs (C) are selectedi,Ci+1) (i 1,2), calculating two sets of conic pairs (C) from (1) based on the common pole-line properties of the conici,Ci+1) Characteristic value λ of (i ═ 1,2)ij(i 1,2, j 1,2,3) with a corresponding feature vector of mij(i, j ═ 1,2,3), and further calculates vanishing points v in at least two directions of the taken pair of quadratic curvesi1，vi2(corresponding value is m)i1,mi2(i ═ 1,2, 3)). The corresponding calculation results are as follows:
two vanishing points in the first image, and the homogeneous coordinate matrix is as follows:
m11＝[0.797097678760242 0.797097678760242 -0.000056360785882]T， (14)
m12＝[-0.794182909366199 -0.607678675531815 -0.000365752016514]T， (15)
two vanishing points in the second image, and the homogeneous coordinate matrix is as follows:
m21＝[0.120143644537769 -0.992753784683627 0.002329736791298]T， (16)
m22＝[-0.602144757156308 -0.798386701894222 -0.000604704587210]T， (17)
two vanishing points in the third image, and the homogeneous coordinate matrix is as follows:
m31＝[0.797097678760242 -0.603850384893595 -0.00005.6360785880]T， (18)
m32＝[-0.794182909366337 -0.607678675531636 -0.000365752016514]T， (19)
obtaining the vanishing line l in each image according to the step (2)i∞(i ═ 1,2,3) homogeneous line coordinate matrix:
l1∞＝[0.0001.86610248231 0.0003.36300856271 -0.963946917196040]T， (20)
l1∞＝[0.002460353640654 -0.001330187381458 -0.693702574710390]T， (21)
l3∞＝[-0.0004.49974937546 0.001511670854165 -0.670293962842918]T， (22)
C. the image of the circle point is calculated.
Vanishing line li∞And the quadratic curve CiImage m both intersecting at two circular pointsiI,miJ(i 1,2,3), three sets of circle points m can be obtained for three images according to the formula (3)1I,m1J、m2I,m2JAnd m3I,m3JThe homogeneous coordinate matrix of (a) is:
D. and solving the internal parameters of the pinhole camera.
Substituting (24), (26) and (28) into (4) to obtain a linear equation system of the elements in ω, solving the linear equation system using SVD decomposition to obtain a coefficient matrix of ω, the results are as follows:
finally, K is obtained by performing Cholesky decomposition and inversion on ω in (29), and the results are as follows:
the five internal parameters of the obtained camera are respectively as follows: f. ofu＝1200.000000012，fv＝900.00000000514，s＝0.799999995844319，u0＝254.999999994824，v0＝255.00000001256。
Example four
The present implementation discloses a system for calibrating a camera using common pole epipolar properties of coplanar circles, which runs the method of calibrating a camera using common pole epipolar properties of coplanar circles in the above-described embodiments.
EXAMPLE five
The embodiment discloses a method for calibrating a camera by utilizing the polar line property of a common pole of a coplanar circle, which comprises the following steps:
A. and (3) acquiring images of the target consisting of three coplanar circles from 3 different directions by using a pinhole camera to obtain 3 target images.
B. And introducing the 3 target images into the system for calibrating the camera by utilizing the polar line property of the common pole of the coplanar circle in the embodiment to obtain the internal parameters of the camera.
EXAMPLE six
The embodiment discloses another method for calibrating a camera by using the polar line property of the common poles of coplanar circles, which comprises the following steps:
A. and acquiring images of the target consisting of three coplanar circles from at least 3 different directions by using a pinhole camera to obtain at least a plurality of target images.
B. At least 3 target images collected in different directions are selected from the obtained target images, and the system for calibrating the camera by using the polar line property of the common pole of the coplanar circle is introduced into the embodiment to obtain the internal parameters of the camera.
EXAMPLE seven
The embodiment discloses a computer readable storage medium, which stores a computer program, and the program can be run to execute the method for calibrating the camera by using the polar line property of the common pole of the coplanar circle in the first to third embodiments.
Example eight
The present embodiment discloses a system for calibrating a camera using common pole polar properties of coplanar circles, the system comprising a processor and the computer readable storage medium of embodiment seven, the processor being coupled to the computer readable storage medium for executing the computer program stored therein.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification and any novel method or process steps or any novel combination of features disclosed.
Claims (9)
1. A method for calibrating a camera using common pole polar properties of coplanar circles, comprising the steps of:
respectively executing the following steps A-C for at least 3 different target images, wherein the target images are obtained by adopting a pinhole camera to acquire images of a target consisting of at least 3 coplanar circles;
A. respectively fitting a quadratic curve equation of each coplanar circle in the target image on an image plane;
B. randomly selecting two groups of quadric pairs from quadric equations of all coplanar circles, and calculating vanishing points on an image plane according to the common pole polar line relation of the selected quadric pairs so as to obtain corresponding vanishing lines;
C. calculating the image of the circular point according to the vanishing line;
D. and calculating the image of the absolute quadratic curve according to the images of the circular points corresponding to at least 3 target images and based on the linear constraint relation of the image pairs of the circular points to the image of the absolute quadratic curve, decomposing the image of the absolute quadratic curve, and calculating to obtain the internal parameters of the camera.
2. The method for calibrating a camera using polar properties of common poles of coplanar circles as claimed in claim 1, wherein in said a, said method of fitting a quadratic curve equation at an image plane for each coplanar circle in the target image is: and extracting pixel coordinates of edge points of the target image, and fitting a corresponding quadratic curve equation by adopting a least square method.
3. The method for calibrating a camera using the common pole epipolar property of coplanar circles as claimed in claim 1, wherein in B, said calculating vanishing points on the image plane from the common pole epipolar relationship of the taken conic pairs comprises: and calculating generalized eigenvalues of the taken quadratic curve pairs, and determining vanishing points from eigenvectors of the generalized eigenvalues according to the number of public self-polar triangles between the taken quadratic curve pairs.
4. A method for calibrating a camera using common pole-line properties of coplanar circles as defined in claim 3, wherein said method of determining vanishing points from the eigenvectors of the generalized eigenvalues based on the number of common pole-triangles between the taken conic pairs comprises:
when a unique common self-polar triangle exists between the taken quadratic curve pairs, determining the feature vector which is not in the quadratic curve as a vanishing point in the feature vectors of the generalized feature values;
when no public self-polar triangle exists between the two secondary curve pairs, determining a feature vector which is not equal to other feature vectors in the feature vectors of the generalized feature values as a vanishing point;
when countless common self-polar triangles exist between the taken quadratic curve pairs, the feature vectors with the same value in the feature vectors of the generalized feature values are determined as vanishing points.
5. The method of calibrating cameras using common pole-line properties of coplanar circles as claimed in claim 1 wherein said method of calculating an image of an absolute conic based on a linear constraint relationship of the image of the circle points to the image of the absolute conic comprises:
the linear constraint relation of the image of the circular ring point to the image of the absolute quadratic curve is as follows:
where N is the number of target images, miIIs the image of the circular point, omega is the image of the absolute quadratic curve;
solving the image of the absolute quadratic curve according to the linear constraint relation of the image of the circular ring point to the image of the absolute quadratic curve;
and performing Cholesky decomposition on the image of the absolute quadratic curve and then inverting to obtain an internal parameter matrix, thereby obtaining the internal parameters of the camera.
6. The method of calibrating cameras using common pole-line properties of coplanar circles as claimed in claim 5 wherein said solving the image of the absolute quadratic curve based on the linear constraint relationship of the image of the circle points to the image of the absolute quadratic curve is by: and (3) optimally solving the linear constraint relation of the image pair of the circular ring points to the image of the absolute quadratic curve by adopting a least square method to obtain the image of the absolute quadratic curve.
7. The method of calibrating cameras with common pole-line properties of coplanar circles as claimed in claim 1, wherein said at least 3 different target images are: and selecting at least 3 target images acquired under different orientations from the acquired at least 3 target images.
8. A system for calibrating a camera using common pole epipolar properties of coplanar circles, said system operating a method for calibrating a camera using common pole epipolar properties of coplanar circles as claimed in any one of claims 1 to 7.
9. A method for calibrating a camera using common pole polar properties of coplanar circles, comprising the steps of:
A. acquiring images of a target consisting of three coplanar circles from at least 3 different directions by using a pinhole camera to obtain at least 3 target images;
B. introducing at least 3 of said target images into a system for calibrating cameras using common pole-line properties of coplanar circles as described in claim 8, resulting in camera intrinsic parameters.
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