CN111223149A - Method for calibrating camera internal parameters based on properties of two separation circles with same radius - Google Patents

Abstract

The invention discloses a method for calibrating intrinsic parameters of a camera based on the properties of two separating circles with the same radius, which comprises the following steps: fitting a target projection equation; estimating a vanishing line according to an equation; determining the image of the circular point according to the vanishing line; calculating intrinsic parameters of the camera according to the images of the circular points; the target of the invention is simple to manufacture, and only two circles with the same radius are needed; the physical scale of the target is not required, and the coordinates of the circle center under a world coordinate system and the radius of the circle do not need to be known; the image boundary points of the target can be almost completely extracted, so that the accuracy of curve fitting can be improved, and the calibration accuracy is improved; the method is a linear algorithm, is simple to calculate, and can finish calibration only by decomposing the feature value of the image square range.

Description

Method for calibrating camera internal parameters based on properties of two separation circles with same radius

Technical Field

The invention relates to the field of computer vision, in particular to a method for calibrating intrinsic parameters of a camera based on the properties of two separating circles with the same radius.

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 has simple imaging model, clear geometric principle, no need of some special mirror surfaces and important application in the field of vision. The documents "An algorithm for self calibration from sectional views", (R.Hartley, In Proc.IEEE Conference on Computer Vision and Pattern recognition, pages 908 and 912, June1994.) propose a pinhole camera self-calibration method which has the advantage that no calibration block is required and the disadvantage that the corresponding points between the images must be obtained. In computer vision, it is difficult to implement a very effective method for finding the corresponding point. The literature "Camera calibration by a single image of balls: From con to the absolute con", (Teramoto H.and Xu G., InProc. of 5th ACCV,2002, pp.499-506.) studies the relationship between spherical images and absolute quadratic curves under a pinhole Camera, calibrating the internal parameters by minimizing the reprojection error nonlinearity. This method requires a good initialization step, which would otherwise result in a local minimum during the minimization process. The literature, "Camera Calibration from Images of spheres", (Hui Zhang and KWan-Yee K., IEEE Transactions on Pattern Analysis & Machine Analysis, 2007, (29) (3): 499-. The documents "compressing Sphere Images Using the double-Contact Theorem", (X.Y, H.ZHa, spring Berlin Heidelberg,2006,3851(91):724-733) introduce the double-Contact principle, the relation between the three spherical Images and the image of the absolute quadratic curve can be determined by Using the double-Contact principle, the linear constraint of the internal parameters of the pinhole camera is established by Using the relation, and the internal parameters of the pinhole camera can be obtained by the linear constraint.

The circle is considered as one of the important image features similar to the point, line and quadratic curve, and the most important advantage is that the circle can be extracted from the image more accurately and provides acceptable calibration accuracy. Since circles have more geometric information, camera calibration using circles has been a direction of research in recent years. The documents "The Common self-polar triangle of centralized circuits and its application to a centralized triangle", (H.F.Huang and H.Zhang, in: Proceedings of IEEE International conference on Computer Vision and Pattern Recognition,2015, pp.4065-4072.) found that concentric circles have an infinite number of Common polar triangles, but that family of Common polar triangles share a vertex and a straight line. The vertex and the straight line are found to be the centers of the concentric circles and an infinite straight line on the supporting plane by analyzing the algebraic properties of the common self-polar triangle. Therefore, on the image plane, the image of the center of the circle and the vanishing line can be determined by using the generalized eigenvalue decomposition of the two concentric circle images. These allow good constraints on the IAC. The literature, "recording projected centers of circle-pairs with common variants", (Q.Chen, H.Y.Wu, in: Proceedings of IEEE International of Conference on mechanics and Automation,2017, pp.1775-1780.) describes a new method for restoring a circle-to-common tangent by decomposing a degenerate quadratic curve. Furthermore, two vanishing points are obtained using the properties of a circle, thereby determining a vanishing line on the support plane. Finally, the vanishing lines are used to determine the intrinsic parameters of the camera. The documents "Camera calibration with a twopolar coplanar circuits", (q. chen, h. y. wu, t. wada, in: proc. eccv,2004, pp.521-532.) hold a new calibration algorithm that can estimate both the external parameters and the focal length of the Camera using only the projection of two coplanar circles of any two radii. However, this method causes errors to accumulate and only part of the camera intrinsic parameters can be estimated.

Disclosure of Invention

The invention aims to: aiming at the existing problems, the method for calibrating the internal parameters of the camera based on the properties of the two separating circles with the same radius is provided; the invention solves the problem of large error of the internal parameters of the computer camera; the problem that the number of internal parameters of the camera is not complete is solved; solves the problem of complicated calculation method of the internal parameters of the camera

The technical scheme adopted by the invention is as follows:

a method for calibrating camera intrinsic parameters based on the properties of two separating circles with the same radius comprises the following steps: fitting a target projection equation; estimating a vanishing line according to an equation; determining the image of the circular point according to the vanishing line; and calculating the intrinsic parameters of the camera according to the images of the circular points.

Further, the fitting target projection equation is an equation for extracting pixel coordinates of Edge points of the target image by using an Edge function in a Matlab program, and fitting by using a least square method to obtain a circular image.

Further, the method for estimating the vanishing line comprises the following steps: with two separating circles C of the same radius in space₁And C₂Is a calibration object; if the order is O_cThe intrinsic parameter matrix of the camera with the optical center is

Wherein r is_cIs the aspect ratio, f_cIs the effective focal length, s is the tilt factor, [ u [ ]₀v₀1]^TIs in the form of a homogeneous coordinate matrix of a principal point p of the camera, where r_c,f_c,u₀,v₀S is 5 intrinsic parameters of the camera; then C is calculated by eigenvalue decomposition₁ ^*And C₂ ^*Three generalized eigenvectors L_kWhere k is 1,2,3, which represent the circle C₁And C₂And two of the sides L of the common self-polar triangle₁And L₂Is parallel toPerpendicular to the other side L₃(ii) a From the nature of the circle, the straight line L₁And the circle C₁With a real point of intersection M₁And M₂And the circle C₂Only the point of the complex intersection; for the same reason, straight line L₂And the circle C₂With a real point of intersection N₁And N₂And the circle C₁Only the point of the complex intersection; let a straight line L₁And a straight line L₃Intersect at E₁Straight line L₂And a straight line L₃Intersect at E₂Then point E is connected₁And N₁Form a straight line U₁Is connected to E₂And M₂Form a straight line U₁Is connected to E₂And M₁Form a straight line U₂Connecting point E₁And N₂Form a straight line V₂(ii) a According to the geometric properties of an isosceles triangle and a circle with the same radius, the other group of parallel straight lines U₁,V₁Or U₂,V₂Can also be obtained; two groups of parallel straight lines determine the infinite straight line L on the plane_∞(ii) a Extracting pixel coordinates of Edge points of the image target image by using an Edge function in Matlab, and fitting by using a least square method to obtain a corresponding quadratic curve equation; by c_niA coefficient matrix representing the ith circular image in the nth image, wherein n is 1,2,3, and i is 1, 2; equation of a circle c_niCan be represented by a homography matrix H_n＝K[r_n1r_n2T_n]Equation C with circle_iDetermination, i.e. of the relation λ_cnic_ni＝H_n ^-TC_iH_n ^-1Wherein λ is_cniIs a non-zero scale factor, r_n1And r_n2Are respectively a rotation matrix R_nFirst and second columns of (D), T_nIs a translation vector; taking two circular image equations c on the nth perspective image plane_n1,c_n2Then matrix pair (c)_n1 ^*,c_n2 ^*) Is equivalent to the matrix c_n2c_n1 ^-1By eigenvalue decomposition, matrix c_n2c_n1 ^-1Characteristic vector l of_nkCan be obtained, they represent L_kThe nth image of (1); therefore, it can be seen that,vanishing point v_n1∞Can be defined by a straight line l_n1And l_n2Determination, i.e. λ_nv1v_n1∞＝l_n1×l_n2Wherein λ is_nv1A non-zero scale factor, where x represents the cross product; if a straight line l_n1And the quadratic curve c_n1Intersect at two points m_n1And m_n2And a straight line l_n3Intersect at e_n1(ii) a Thus, it can be seen that the straight line l_n2And the quadratic curve c_n2Intersect at two points n_n1And n_n2And a straight line l_n3Intersect at e_n2(ii) a Through the connecting point e_n1And n_n1Form a straight line u_n1Connecting point e_n2And m_n2Form a straight line v_n1Then straight line u_n1And v_n1Vanishing point v of_n2∞Can be obtained, i.e. lambda_nv2v_n2∞＝u_n1×v_n1Wherein λ is_nv2A non-zero scale factor; thus, passing through point m_n1And e_n2Straight line u of_n2And pass through point e_n1And n_n2Straight line v of_n2Intersect at vanishing point v_n3∞I.e. λ_nv3v_n3∞＝u_n2×v_n2Wherein λ is_nv3A non-zero scale factor; connecting two vanishing points v_n1∞And v_n2∞The vanishing line l can be obtained_n∞I.e. λ_nll_n∞＝v_n1∞×v_n2∞Wherein λ is_nlA non-zero scale factor.

Further, the method for determining the image of the circle point comprises the following steps: on the nth perspective image, the plane pi is known₁Upper vanishing line l_n∞Then l is_n∞And the circle image c_n1Intersect at c_n1Image of a circular point on I_nAnd J_nThat is to say have

Further, the method for calculating the camera intrinsic parameters comprises the following steps: from the image I of the circle point_n,J_nThe linear constraint on the image ω of the absolute quadratic curve (n ═ 1,2,3) yields ω, i.e.:

wherein Re, Im represent the real and imaginary parts of the complex number, respectively; and performing Cholesky decomposition on omega and then inverting to obtain an internal parameter matrix K, namely obtaining 5 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 of the invention is simple to manufacture; the physical scale of the target is not required, and the coordinates of the circle center under a world coordinate system and the radius of the circle do not need to be known; the image boundary points of the target can be almost completely extracted, so that the accuracy of curve fitting can be improved, and the calibration accuracy is improved.

2. The method is a linear algorithm, is simple to calculate, and can finish calibration only by decomposing the feature value of the image square range.

Drawings

The invention will now be described, by way of example, with reference to the accompanying drawings, in which:

FIG. 1 is a flow chart of a method for calibrating camera intrinsic parameters based on the properties of two separate circles of the same radius.

Fig. 2 is a schematic view of a projection of a target under a pinhole camera.

FIG. 3 is a schematic diagram of a target for solving parameters within a pinhole camera.

Fig. 4 is a schematic view of a projection of a target onto an image plane.

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 1

A method for calibrating camera intrinsic parameters based on the properties of two separate circles with the same radius, as shown in fig. 1, includes:

s1: and fitting a target projection equation.

In the above step, the fitting target projection equation is an equation for obtaining a circle image by extracting the pixel coordinates of the Edge points of the target image by using an Edge function in a Matlab program and fitting by using a least square method.

S2: the vanishing line is estimated from the equation.

In the above step, the method for estimating the vanishing line includes: two separating circles with the same radius in the space are used as calibration objects. As shown in FIG. 2, if the point O is any point in space_wEstablishing a world coordinate system O for the origin_w-X_wY_wZ_wTwo of which are circles C₁And C₂The supporting plane is the world plane O_wX_wY_w. Algebraically, compute the matrix pairs (C)₁ ^*,C₂ ^*) Is also the problem of determining the matrix C₂C₁ ^*The eigenvector problem of (1), i.e. two circles C₁And C₂The generalized eigenvalue decomposition of (1) is satisfied by the following equation:

C₁ ^*L＝βC₂ ^*L， (1)

or

(C₁ ^*-βC₂ ^*)L＝0_3×3， (2)

Or

(C₂C₁ ^*-βI)L＝0_3×3， (3)

Where I is a 3 x 3 order identity matrix.

If C₁And C₂With a common autostart, then the vertex X and the edge L of the common autostart should satisfy the following relationship:

X＝C₁ ^*L， (4)

X＝βC₂ ^*L。 (5)

by combining the formulas (4) and (5), the following can be obtained:

C₁ ^*L＝X＝βC₂ ^*L。 (6)

the compounds of formulae (1) and (6) can be seen from₁ ^*,C₂ ^*) Is generalized eigenvector L_kIs a circle C₁And C₂Is common to three sides of the free triangle.

As shown in FIG. 3, one of the sides L in the common self-polar triangle₃Passing through the center O of two circles₁And O₂Because of the straight line L₁About circle C₁And C₂Is a straight line L₂And L₃Cross point of (E)₂Straight line L₂About circle C₁And C₂Is a straight line L₁And L₃Cross point of (E)₁Then, according to the principle of polarization, the straight line L₁Also through L₃About circle C₁And C₂I.e. the point of infinity V on the support plane_1∞. Similarly, a straight line L can be known₂Also passes through the point of infinity V_1∞. And from the nature of the circle, L₁⊥L₃,L₂⊥L₃. Straight line L₁And the circle C₁With a real point of intersection M₁And M₂And the circle C₂Only the point of the complex intersection. For the same reason, straight line L₂And the circle C₂With a real point of intersection N₁And N₂And the circle C₁Only the point of the complex intersection. From the definition of the intersection point, point M₁,M₂,N₁,N₂Can be determined by the following equation:

according to two circles C of the same radius₁And C₂The geometry of (a), we easily observe a property: isosceles triangle delta O₁M₁M₂And isosceles triangle Δ O₂N₁N₂Are congruent. Further, we have readily demonstrated that passing through point E₁And N₁Straight line U of₁And pass through point E₂And M₂Straight line V of₁Are parallel to each other. For the same reason, pass through point E₂And M₁Straight line U of₂And pass through point E₁And N₂Straight line V of₂Are parallel to each other. Then two further points of infinity V on the support plane_2∞,V_3∞May be determined.

Extracting the pixel coordinates of the Edge points of the target image in the 3 images by using an Edge function in Matlab, obtaining a corresponding quadratic curve equation by least square fitting, wherein c is used_niAnd a coefficient matrix representing an ith (i is 1,2) circular image in the nth (n is 1,2,3) image.

Then give a circle C₁A point on

Then the following equation holds:

as can be seen from the projection model,

satisfies the following conditions:

wherein λ_nmIs a non-zero scale factor, r_n1And r_n2Are respectively a rotation matrix R_nFirst and second columns of (D), T_nIs a translation vector. As shown in FIG. 1, with the camera optical center O_CEstablishing a camera coordinate system O for the origin_c-X_cY_cZ_cN and Z of image plane_cVertical axis, circle C₁,C₂The projections are respectively c_n1,c_n2The subscript n in FIG. 1, neglected, is denoted by c₁,c₂And (4) showing. Suppose a circle C₁Projection onto the image plane π is c_n1According to the homogeneity of projective transformation, the image point m_nIn the circle c_n1The method comprises the following steps:

m_n ^Tc_n1m_n＝0。 (11)

because of H_n＝K[r_n1r_n2T_n]Is a 3 × 3 order invertible matrix, then, by combining the equations (9), (10) and (11), we can obtain:

λ_nc1c_n1＝H_n ^-TC₁H_n ^-1， (12)

wherein λ_nc1A non-zero scale factor.

For the same reason, if circle C₂Is c on the image plane pi_n2Then, the following equation holds:

λ_nc2c_n2＝H_n ^-TC₂H_n ^-1， (13)

wherein λ_nc2A non-zero scale factor.

First consider a matrix pair (c)_n1 ^*,c_n2 ^*) Algebraically, because of the matrix pair (c)_n1 ^*,c_n2 ^*) Is equivalent to the matrix c_n2c_n1 ^-1The following equation is satisfied from the equation (12) and (13):

here. varies indicates a difference by a non-zero scale factor. Due to the quadratic curve pair (c)_n1 ^*,c_n2 ^*) And a pair of circles (C)₁ ^*,C₂ ^*) From a nonsingular homography H_nIs associated with, i.e. c_n2c_n1 ^-1∝H_n ^-TC₂C₁ ^-1H_n ^T. From the literature, "European Structure structural Confucial Consortium: Theoryand application to Camera Calibration ", (P.Gurdjos, J.S.Kim, and I.S.Kweon, In Proceeding of IEEE Conference on Computer Vision and Pattern Recognition,2006, pp.1214-1221.) two circles C₁And C₂Is a projective invariant, i.e., if L_k(k is 1,2,3) is a matrix C₁And C₂Is a generalized feature vector of, then l_nk＝H_nL_kMust be the matrix c_n1And c_n2The generalized eigenvectors of (3). On the image plane, vanishing point v_1∞Can be defined by a straight line l_n1And l_n2Determining, namely:

λ_nv1v_n1∞＝l_n1×l_n2， (15)

wherein λ_nv1A non-zero scale factor, where x represents the cross product.

As shown in fig. 4 (the subscript n in fig. 4 is ignored), if the straight line l_n1And the quadratic curve c_n1Intersect at two points m_n1And m_n2And a straight line l_n3Intersect at e_n1. By the same token, the straight line l_n2And the quadratic curve c_n2Intersect at two points n_n1And n_n2And a straight line l_n3Intersect at e_n2. Through the connecting point e_n1And n_n1Form a straight line u_n1Connecting point e_n2And m_n2Form a straight line v_n1. I.e. the following two equations hold:

λ_nu1u_n1＝e_n1×n_n1， (16)

λ_nv1v_n1＝e_n2×m_n2， (17)

wherein λ_nu1And λ_nv1A non-zero scale factor. Then, from the above discussion, the line u_n1And v_n1Vanishing point v of_n2∞Can be obtained, namely:

λ_nv2v_n2∞＝u_n1×v_n1，(18)

wherein λ_nv2A non-zero scale factor. For the same reason, pass through point m_n1And e_n2Straight line u of_n2And pass through point e_n1And n_n2Straight line v of_n2Intersect at vanishing point v_n3∞Namely:

λ_nu2u_n2＝m_n1×e_n2， (19)

λ_nv2v_n2＝e_n1×n_n2， (20)

λ_nv3v_n3∞＝u_n2×v_n2， (21)

wherein λ_nu2，λ_nv2，λ_nv3A non-zero scale factor. Connecting two vanishing points v_n1∞And v_n2∞The vanishing line l can be obtained_n∞I.e. λ_nll_n∞＝v_n1∞×v_n2∞(22) wherein λ_nlA non-zero scale factor.

S3: and determining the image of the circular point according to the vanishing line.

In the above step, the method for determining the image of the circle point comprises: known plane pi₁Upper vanishing line l_n∞Then l is_n∞And the circle image c_n1Intersect at c_n1Image of a circular point on I_nAnd J_nThen two equations can be obtained, one being:

the other one is that:

theoretically, the solution obtained by equation (23) is [ a + bi c + di1 ]]^TThe solution obtained by equation (24) is [ a-bi c-di1]^T. But they do not yield an ideal solution due to the effects of noise. Let us remember that the solution of equation (23) is [ a ]₁+b₁i c₁+d₁i 1]^TThe solution of equation (24) is [ a ]₂-b₂i c₂-d₂i 1]^T. Taking the mean value of the coefficients of the solutions of equation (23) and equation (24) as the image I of the circle point_nAnd J_nThe coefficients of (c) then have:

thus, a plane pi can be obtained₁Image of a circular point on I_nAnd J_n。

S4: and calculating the intrinsic parameters of the camera according to the images of the circular points.

In the above steps, the method for calculating the camera intrinsic parameters includes: 3 circular images can be estimated that the images of 3 groups of circular points are I respectively₁,J₁,I₂,J₂,I₃,J₃. Secondly, there is a linear constraint by the image of the circle point to the image ω of the absolute quadratic curve

Where Re, Im represent the real and imaginary parts of the complex number, respectively. ω can be obtained by solving equation set (26) by the SVD method. And finally, performing Cholesky decomposition on omega and then inverting to obtain K, namely obtaining the internal parameters of the pinhole camera.

Example 2

The embodiment performs the specific data substitution calculation according to the method of the embodiment 1, which is convenient for further understanding of the technical scheme.

A method for calibrating camera intrinsic parameters based on the properties of two separating circles with the same radius comprises the following steps:

s1: and fitting a target projection equation.

In the above steps, the size of the image used in this embodiment is 1038 × 1048. 3 experimental images of the target are shot by a pinhole camera, the images are read in, pixel coordinates of Edge points of the target image are extracted by utilizing an Edge function in Matlab, and an equation of a circular image is obtained by fitting with a least square method. The coefficient matrices of the equation for the ith (i ═ 1,2) circle image in the nth (n ═ 1,2,3) image are c respectively_niThe results are as follows:

s2: the vanishing line is estimated from the equation.

In the above step, because of the square range c of any two circular images_n1,c_n2Matrix pair (c)_n1 ^*,c_n2 ^*) Is equivalent to the matrix c_n2c_n1 ^-1The feature vector of (2). Therefore, we compute the matrix c₁₂c₁₁ ^-1,c₂₂c₂₁ ^-1,c₃₂c₃₁ ^-1The results are as follows:

decomposing the characteristic value of formula (33) to obtain three straight lines l_1kThe homogeneous matrix of coordinates of (a) is,the results are as follows:

l₁₁＝[0.0000131372232636 -0.00054538289497831]^T，(36)

l₁₂＝[0.0000202628469355 -0.00053375127317341]^T，(37)

l₁₃＝[-0.0008928788850378 0.00000010146350961]^T。(38)

decomposing the characteristic value of formula (34) to obtain three straight lines l_2kThe result of the homogeneous coordinate matrix of (a) is as follows:

l₂₁＝[0.0001787630326410 -0.00072278635956151]^T，(39)

l₂₂＝[-0.0000926813825859 -0.00098103194667671]^T，(40)

l₂₃＝[-0.0017096410841089 0.00086053258714201]^T。(41)

decomposing the characteristic value of formula (35) to obtain three straight lines l_3kThe result of the homogeneous coordinate matrix of (a) is as follows:

l₃₁＝[-0.0063150148065399 0.01056145988780411]^T，(42)

l₃₂＝[-0.0438145781588402 0.05112541987860161]^T，(43)

l₃₃＝[-0.0007246252546235 0.00091640975931321]^T。(44)

by substituting the expressions (36) and (37) into the expression (15), the vanishing point v can be obtained_11∞The result of the homogeneous coordinate matrix of (a) is as follows:

v_11∞＝[-2879.8267949194755601 1764.20471066060827071]^T。(45)

by substituting the expressions (39) and (40) into the expression (15), the vanishing point v can be obtained_21∞The result of the homogeneous coordinate matrix of (a) is as follows:

v_21∞＝[-1065.5406460551009786 1120.00000000000000001]^T。(46)

by substituting the expressions (42) and (43) into the expression (15), the vanishing point v can be obtained_31∞The result of the homogeneous coordinate matrix of (a) is as follows:

v_31∞＝[-289.9742893997091641 -268.06823688687074991]^T。(47)

when the formulae (27), (28), (36) and (37) are substituted into the formulae (7) and (8), the point m can be obtained₁₁,m₁₂,n₁₁,n₁₂The result of the homogeneous coordinate matrix of (a) is as follows:

m₁₁＝[617.7121596583361906 1848.45368609152978931]^T，(48)

m₁₂＝[1791.2521159172349598 1876.72200282111271001]^T，(49)

n₁₁＝[381.7200782616370702 1888.02310395718131981]^T，(50)

n₁₂＝[2290.9414414043790202 1960.50304394383579161]^T。(51)

when the formulae (29), (30), (39) and (40) are substituted into the formulae (7) and (8), the point m can be obtained₂₁,m₂₂,n₂₁,n₂₂The result of the homogeneous coordinate matrix of (a) is as follows:

m₂₁＝[866.65948134171651418 1597.88111919039806701]^T，(52)

m₂₂＝[2593.8444044523052980 2025.05688240540507641]^T，(53)

n₂₁＝[1783.7530719672731720 850.8176537222852851]^T，(54)

n₂₂＝[614.4301810556108875 961.28751414450596251]^T。(55)

substituting the expressions (31), (32), (42) and (43) into the expressions (7) and (8) can obtain the point m₃₁,m₃₂,n₃₁,n₃₂The result of the homogeneous coordinate matrix of (a) is as follows:

m₃₁＝[659.4095102552425942 299.59691694601320931]^T，(56)

m₃₂＝[1148.9010156011377148 592.27862352564613951]^T，(57)

n₃₁＝[482.8067068929873926 394.20648754828982871]^T，(58)

n₃₂＝[991.3482004413441472 830.02747579632330141]^T。(59)

from the formulae (36), (37) and (38), we can easily obtain the intersection point e₁₁,e₁₂The results are as follows:

e₁₁＝[1120.1841542350548479 1860.55726843202455711]^T，(60)

e₁₂＝[1120.1904611046218178 1916.05772061487232341]^T。(61)

from the formulae (39), (40) and (41), we can easily obtain the intersection point e₂₁,e₂₂The results are as follows:

e₂₁＝[1463.4968400320069576 1745.49383326770225721]^T，(62)

e₂₂＝[1048.1492373459368536 920.31261834519921191]^T。(63)

from the formulae (42), (43) and (44), we can easily obtain the intersection point e₃₁,e₃₂The results are as follows:

e₃₁＝[853.992796607284731 415.9441215438644691]^T，(64)

e₃₂＝[674.1267668088423761 558.16812812634088911]^T。(65)

by substituting the expressions (50) and (60), (49) and (61) into the expressions (16) and (17), respectively, a straight line u can be obtained₁₁,v₁₁The result of the homogeneous coordinate matrix of (a) is as follows:

u₁₁＝[0.0000762123717178 -0.00056646120841711]^T，(66)

v₁₁＝[0.0000483693633997 -0.00056659508004241]^T。(67)

by substituting the expressions (54) and (62), (53) and (63) into the expressions (16) and (17), respectively, a straight line u can be obtained₂₁,v₂₁The result of the homogeneous coordinate matrix of (a) is as follows:

u₂₁＝[-0.0007724041072318 -0.00020689189769491]^T，(68)

v₂₁＝[-0.0004788561528626 -0.00017141024949681]^T。(69)

by substituting expressions (58) and (64), (57) and (65) into expressions (16) and (17), respectively, a straight line u can be obtained₃₁,v₃₁Is prepared fromSecondary coordinate matrix, the results are as follows:

u₃₁＝[-0.0015567663119650 0.00008860742502071]^T，(70)

v₃₁＝[-0.0013966087241317 0.00046326845387831]^T。(71)

by substituting the expressions (66) and (67) into the expression (18), the vanishing point v can be obtained_12∞The result of the homogeneous coordinate matrix of (a) is as follows:

v_12∞＝[-8.4824509396292739 1764.20471066045638501]^T。(72)

by substituting the expressions (68) and (69) into the expression (18), the vanishing point v can be obtained_22∞The result of the homogeneous coordinate matrix of (a) is as follows:

v_22∞＝[1064.6669826047116202 8808.23836265052159431]^T。(73)

by substituting the expressions (70) and (71) into the expression (18), the vanishing point v can be obtained_32∞The result of the homogeneous coordinate matrix of (a) is as follows:

v_32∞＝[627.0993637878117397 -268.06823688688041321]^T。(74)

when the formulas (45) and (72) are respectively substituted into the formula (22), the vanishing line l can be obtained_1∞The result of the homogeneous coordinate matrix of (a) is as follows: l_1∞＝[-0.0000000000000000299 -0.00056682764418281]^T。(75)

When the formulas (46) and (73) are respectively substituted into the formula (22), the vanishing line l can be obtained_2∞The result of the homogeneous coordinate matrix of (a) is as follows: l_2∞＝[0.0009383786284404 -0.00000010663393501]^T。(76)

When the formulas (47) and (74) are respectively substituted into the formula (22), the vanishing line l can be obtained_3∞The result of the homogeneous coordinate matrix of (a) is as follows: l_3∞＝[0.0000000000000000393 0.00373039346851821]^T。(77)

S3: and determining the image of the circular point according to the vanishing line.

In the above step, the known plane pi₁Upper vanishing line l_1∞Then, the expressions (27) and (75) are substituted into the expressions (23), (24) and (25) to obtain c₁₁Image of a circular point on I₁And J₁The results are as follows:

I₁＝[320.17320507+1600.00000000i 1764.20471066-0.000000000084i1]^T，(78)

J₁＝[320.17320507-1600.00000000i 1764.20471066+0.000000000084i1]^T。(79)

known plane pi₁Upper vanishing line l_2∞Substituting the expressions (29) and (76) into the expressions (23), (24) and (25) to obtain c₂₁Image of a circular point on I₂And J₂The results are as follows:

I₂＝[-1065.64064605-0.20000000002i 240.00000000001-1760.00000000i1]^T，(80)

J₂＝[-1065.64064605+0.20000000002i 240.00000000001+1760.00000000i1]^T。(81)

known plane pi₁Upper vanishing line l_3∞C can be obtained by substituting the formulae (31) and (77) into the formulae (23), (24) and (25)₃₁Image of a circular point on I₃And J₃The results are as follows:

I₃＝[319.94226497+923.76043070i -268.06823688-0.0000000000097i1]^T，(82)

J₃＝[319.94226497-923.76043070i -268.06823688+0.0000000000097i1]^T。(83)

s4: and calculating the intrinsic parameters of the camera according to the images of the circular points.

In the above step, (78-83) is substituted into (26) to obtain a linear equation set of ω elements, and the linear equation set is solved by SVD 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 (84), and the results are as follows:

wherein the aspect ratio r_cK (1,1)/K (2,2) (K (1,1) denotes the element of the 1 st row and 1 st column of the matrix K, and K (2,2) denotes the element of the 2 nd row and 2 nd column of the matrix K), so the 5 intrinsic parameters of the pinhole camera are: r is_c＝0.9090909090909199，f_c＝880.0000000006186837，s＝0.0999999994974979，u₀＝319.9999999997619397，v₀＝239.9999999990701837。

The target of the invention is simple to manufacture, and only two circles with the same radius are needed; the physical scale of the target is not required, and the coordinates of the circle center under a world coordinate system and the radius of the circle do not need to be known; the image boundary points of the target can be almost completely extracted, so that the accuracy of curve fitting can be improved, and the calibration accuracy is improved; the method is a linear algorithm, is simple to calculate, and can finish calibration only by decomposing the feature value of the image square range.

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 (5)

1. A method for calibrating camera intrinsic parameters based on the properties of two separating circles with the same radius is characterized by comprising the following steps: fitting a target projection equation; estimating a vanishing line according to an equation; determining the image of the circular point according to the vanishing line; and calculating the intrinsic parameters of the camera according to the images of the circular points.

2. The method for calibrating camera intrinsic parameters based on the properties of two separating circles with the same radius as in claim 1, wherein the fitting target projection equation is an equation for extracting the pixel coordinates of the Edge points of the target image by using an Edge function in a Matlab program and fitting the extracted pixel coordinates to obtain the circle image by using a least square method.

3. The method for calibrating camera intrinsic parameters based on the properties of two separate circles of the same radius according to claim 1, wherein the method for estimating vanishing linesComprises the following steps: with two separating circles C of the same radius in space₁And C₂Is a calibration object; if the order is O_cThe intrinsic parameter matrix of the camera with the optical center is

Wherein r is_cIs the aspect ratio, f_cIs the effective focal length, s is the tilt factor, [ u [ ]₀v₀1]^TIs in the form of a homogeneous coordinate matrix of a principal point p of the camera, where r_c,f_c,u₀,v₀S is 5 intrinsic parameters of the camera; then C is calculated by eigenvalue decomposition₁ ^*And C₂ ^*Three generalized eigenvectors L_kWhere k is 1,2,3, which represent the circle C₁And C₂And two of the sides L of the common self-polar triangle₁And L₂Is parallel and perpendicular to the other side L₃(ii) a From the nature of the circle, the straight line L₁And the circle C₁With a real point of intersection M₁And M₂And the circle C₂Only the point of the complex intersection; for the same reason, straight line L₂And the circle C₂With a real point of intersection N₁And N₂And the circle C₁Only the point of the complex intersection; let a straight line L₁And a straight line L₃Intersect at E₁Straight line L₂And a straight line L₃Intersect at E₂Then point E is connected₁And N₁Form a straight line U₁Is connected to E₂And M₂Form a straight line U₁Is connected to E₂And M₁Form a straight line U₂Connecting point E₁And N₂Form a straight line V₂(ii) a According to the geometric properties of an isosceles triangle and a circle with the same radius, the other group of parallel straight lines U₁,V₁Or U₂,V₂Can also be obtained; two groups of parallel straight lines determine the infinite straight line L on the plane_∞(ii) a Extracting pixel coordinates of Edge points of the image target image by using an Edge function in Matlab, and fitting by using a least square method to obtain a corresponding quadratic curve equation; by c_niA coefficient matrix representing the ith circular image in the nth image, wherein n is 1,2,3, i is 1,2; equation of a circle c_niCan be represented by a homography matrix H_n＝K[r_n1r_n2T_n]Equation C with circle_iDetermination, i.e. of the relation λ_cnic_ni＝H_n ^-TC_iH_n ^-1Wherein λ is_cniIs a non-zero scale factor, r_n1And r_n2Are respectively a rotation matrix R_nFirst and second columns of (D), T_nIs a translation vector; taking two circular image equations c on the nth perspective image plane_n1,c_n2Then matrix pair (c)_n1 ^*,c_n2 ^*) Is equivalent to the matrix c_n2c_n1 ^-1By eigenvalue decomposition, matrix c_n2c_n1 ^-1Characteristic vector l of_nkCan be obtained, they represent L_kThe nth image of (1); thus, the vanishing point v is known_n1∞Can be defined by a straight line l_n1And l_n2Determination, i.e. λ_nv1v_n1∞＝l_n1×l_n2Wherein λ is_nv1A non-zero scale factor, where x represents the cross product; if a straight line l_n1And the quadratic curve c_n1Intersect at two points m_n1And m_n2And a straight line l_n3Intersect at e_n1(ii) a Thus, it can be seen that the straight line l_n2And the quadratic curve c_n2Intersect at two points n_n1And n_n2And a straight line l_n3Intersect at e_n2(ii) a Through the connecting point e_n1And n_n1Form a straight line u_n1Connecting point e_n2And m_n2Form a straight line v_n1Then straight line u_n1And v_n1Vanishing point v of_n2∞Can be obtained, i.e. lambda_nv2v_n2∞＝u_n1×v_n1Wherein λ is_nv2A non-zero scale factor; thus, passing through point m_n1And e_n2Straight line u of_n2And pass through point e_n1And n_n2Straight line v of_n2Intersect at vanishing point v_n3∞I.e. λ_nv3v_n3∞＝u_n2×v_n2Wherein λ is_nv3A non-zero scale factor; connecting two disappearsPoint v_n1∞And v_n2∞The vanishing line l can be obtained_n∞I.e. λ_nll_n∞＝v_n1∞×v_n2∞Wherein λ is_nlA non-zero scale factor.

4. The method for calibrating camera intrinsic parameters based on the properties of two separate circles with the same radius as in claim 1, wherein the method for determining the image of the circle point comprises the following steps: on the nth perspective image, the plane pi is known₁Upper vanishing line l_n∞Then l is_n∞And the circle image c_n1Intersect at c_n1Image of a circular point on I_nAnd J_nThat is to say have

5. The method for calibrating the camera intrinsic parameters based on the properties of the two separating circles with the same radius as the claim 1, wherein the method for calculating the camera intrinsic parameters comprises the following steps: from the image I of the circle point_n,J_nThe linear constraint on the image ω of the absolute quadratic curve (n ═ 1,2,3) yields ω, i.e.:

wherein Re, Im represent the real and imaginary parts of the complex number, respectively; and performing Cholesky decomposition on omega and then inverting to obtain an internal parameter matrix K, namely obtaining 5 internal parameters of the camera.

Images