Method for calibrating pinhole camera based on asymptote properties of two coplanar circles

Abstract

The invention relates to the technical field of computer vision and camera calibration, in particular to a method for calibrating a pinhole camera based on the asymptote property of two coplanar circles. The method comprises the following steps: taking two coplanar circles as targets, and shooting three images from different positions by using a pinhole camera; image edge points are extracted, and a coplanar circular image equation is fitted through a least square method; based on the relation between the asymptotes of the two coplanar circles and the position of the circle center, simultaneous projection constraint is carried out to solve images of the asymptotes; the image of the circular point is recovered by combining the pole-epipolar relation between the asymptote and the circular point and projective invariance; determining the image by using the image of the three groups of circular ring points and the constraint of the absolute conic; and internal parameters of the camera are obtained through decomposition and inversion. The target is easy to manufacture, the physical scale, the circle center and the radius do not need to be known, the asymptote closed solution can be obtained, the strict requirement of an existing method for circle center positioning and the limitation that multiple independent circles are needed are avoided, and the calibration precision, efficiency and applicability are improved.

Description

Technical Field

[0001] This invention relates to the field of computer vision and camera calibration technology, and more specifically to a method for calibrating a pinhole camera based on the asymptote properties of two coplanar circles. In particular, it relates to a method for calibrating the intrinsic parameters of a pinhole camera based on the geometric properties of the asymptotes of two coplanar circles. Background Technology

[0002] Camera calibration is a crucial step in computer vision for recovering 3D spatial information from 2D images. Pinhole camera calibration refers to the process of determining the intrinsic parameters of a pinhole camera. These parameters include the scale factor on the axes, tilt factor, and principal point coordinates, describing the camera's optical and geometric characteristics. Through specific methods and steps, using images taken at different positions with a calibration target (such as a checkerboard or circle), and combining theories of geometric projection relationships and projective invariance, these intrinsic parameters are solved to establish a projection model of the camera from 3D space to a 2D image. The accuracy of these parameters directly affects the accuracy of subsequent applications. In 3D reconstruction, accurate camera intrinsic parameters ensure that the 3D structure reconstructed from multiple 2D images matches the real scene; in target tracking, they improve the accuracy of calculating the target's trajectory in space. Calibration eliminates errors such as geometric distortion introduced by the camera's optical system and imaging process, providing reliable basic parameter support for various applications in computer vision.

[0003] Currently, camera calibration methods can be broadly categorized into two types: self-calibration methods, which do not require a specific calibration object but need to solve for the correspondence constraints between multiple images; and object-based calibration methods. While traditional geometric object-based calibration methods can achieve relatively accurate results, they require the fabrication of high-precision, high-cost 3D calibration objects. Therefore, some simple geometric objects have been used in camera calibration research. Conic sections, as common geometric elements, can be used as targets to avoid the noise sensitivity problem of feature point matching, thus helping to improve calibration stability.

[0004] In quadratic curve targets, the projection of the circle is easier to obtain in real-world scenarios, and there is an important projective geometry theory between the circle, its center, and the line at infinity. Specifically, the center and the line at infinity satisfy the polar-epoch relationship with respect to the circle, and this property is projectively invariant. Circle-based calibration methods can be divided into two categories: concentric circle targets and non-concentric circle targets. Specifically, Kim et al., in the paper "Geometric and algebraic constraints of projected concentric circles and their applications to camera calibration" (JS Kim, P. Gurdjos, and I.S. Kweon, IEEE Trans. Pattern Anal. Mach. Intell., vol. 27, no. 4, pp. 637-642, 2005), studied the projection properties of concentric circles, proved the geometric meaning and algebraic constraints of their projection, and proposed two calibration methods based on the homography of the image of the annular point and the image of the center of the circle, respectively; Wang et al., in the paper "Effective and automatic calibration using concentric circles" (L. Wang, H.X. Yao, and HD. Cheng, Int. J. Pattern In Recognit. Artif. Intell., vol. 22, no. 7, pp. 1379-1401, 2008, the geometric properties of the tangent of the concentric circle are used to locate the center of the circle, and geometric constraints are established based on orthogonality. Although this method does not require fitting a quadratic curve, the solution of the tangent of the center of the circle will introduce errors. Huang et al., in the paper "The common self-polar triangle of separate circles: Properties and applications to camera calibration", (HFHuang, H.Zhang, and YMCheung, in IEEE International Conference on Image Processing, pp. 1379-1401), used the geometric properties of the tangent of the concentric circle to locate the center of the circle and established geometric constraints based on orthogonality.In [1170-1174, 2016], the geometric properties of the common pole-polar triangle of separated circles were studied. Utilizing the property that one vertex of the common pole-polar triangle of separated circles lies at infinity, the image of the circle center and the vanishing line were recovered using at least three separated circles, thus proposing a linear calibration method based on separated circles. In the paper "Camera calibration based on the common pole-polar properties between two coplanar circles with various positions" (SXLiang, and Y.Zhao, Appl. Opt., vol. 59, no. 17, pp. 5167-5178, 2020), Liang et al. further proved algebraically that the common pole of all relative positions of two coplanar circles lies on a line at infinity, and the corresponding common polar line passes through the center of both circles. The key is that non-concentric circle pairs have a common pole at infinity, and the projection of the circle center and the vanishing line can be synchronously recovered through the relationship between the poles and polar lines of the two sets of coplanar circles.

[0005] Furthermore, the theory of asymptote calibration was first proposed by Yang et al. in the paper "Calibration of camera intrinsic parameters based on the properties of the polarity of circular points" (FLYang, Y. Zhao, and XCWang, Appl. Opt., vol. 58, no. 22, pp. 5901-5909, 2019), but their method involves the nonlinear solution of cubic polynomial equations. Liu et al. further studied the asymptote properties of conic sections in the paper "Calibration of intrinsic camera parameters with a conic and its asymptotes" (X. Liu, Y. Zhao, and X. Kou, Appl. Opt., vol. 60, no. 32, pp. 10024-10034, 2021), but the solution of asymptotes also presents difficulties.

[0006] The main problems with existing technologies include: although the concentric circle-based calibration method uses simple projective geometry properties, it imposes strict requirements on the precise positioning of the circle center, which is often difficult to meet in practical applications; the non-concentric circle-based calibration method requires the deployment of at least three independent circles, which greatly limits its applicability; the asymptote-based calibration method has problems with nonlinear solution or high solution difficulty, which affects the efficiency and stability of calibration. Summary of the Invention

[0007] In view of this, the present invention provides a method for calibrating a pinhole camera based on the asymptote properties of two coplanar circles. It aims to solve the problems of existing calibration methods based on concentric circles, which have strict requirements for precise positioning of the circle center and are difficult to meet in practical applications; calibration methods based on non-concentric circles, which require the deployment of at least three independent circles, thus limiting their applicability; and calibration methods based on asymptotes, which have problems such as nonlinear solutions or high solution difficulty. This invention improves the convenience, applicability, efficiency and stability of pinhole camera calibration, and provides a simple, widely applicable and stable method for solving the intrinsic parameters of a pinhole camera using two coplanar circles as targets.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A method for calibrating a pinhole camera based on the asymptote property of two coplanar circles, characterized by the following steps:

[0010] (1) Using two coplanar circles as targets, take three images containing the targets from different positions using a pinhole camera;

[0011] (2) Extract the edge points of the target image from the three images respectively, and obtain the equation of the coplanar circular image by fitting;

[0012] (3) Based on the relationship between the asymptotes of two coplanar circles and their positions relative to the center, the algebraic constraints of the asymptote projections are combined to obtain the image of the coplanar circle asymptotes;

[0013] (4) Based on the pole-polar relationship between the asymptote and the circular point about the circle and the projective invariance, the image of the circular point is recovered from the image of the asymptote;

[0014] (5) Based on the constraint that the circular points are located on the absolute conic section, the images of the three sets of circular points recovered from the three images are used to establish constraint relationships to determine the image of the absolute conic section.

[0015] (6) Decompose and inverse the image of the absolute quadratic curve to obtain the intrinsic parameters of the pinhole camera.

[0016] In one specific implementation, the two coplanar circles are coplanar circles at any position, including concentric circles or non-concentric circles.

[0017] In one specific implementation, in step (1), the pinhole camera captures images from different positions to obtain projection information of the target from different perspectives.

[0018] In a specific implementation, in step (2), the pixel coordinates of the edge points of the target image are extracted using an edge detection function, which is the Edge function in the MATLAB program.

[0019] In one specific implementation, in step (2), the equation of the coplanar circular image is fitted using the least squares method.

[0020] In a specific implementation scheme, in step (3), the relationship between the asymptotes of the two coplanar circles and their center positions is as follows: when the two coplanar circles are not concentric, the asymptotes of the two circles have a linear relationship; when the two coplanar circles are concentric, the asymptotes of the two circles are the same.

[0021] In a specific feasible implementation, when the two coplanar circles are not concentric, when solving for the image of the asymptote, the image of the asymptote of the other circle is obtained by solving for the asymptote of one circle through a linear transformation based on the linear relationship between the asymptotes of the two circles.

[0022] In a specific feasible implementation, when the two coplanar circles are concentric, when solving for the image of the asymptote, the image of the asymptote is obtained directly through the asymptote of one of the circles by utilizing the same property of the asymptotes of the two circles.

[0023] In a specific implementation scheme, in step (4), the annular point is the intersection of the plane containing the circle and the line at infinity, the asymptote is the tangent of the circle at the annular point, and the pole-polar relationship is that the annular point and the corresponding asymptote are poles and polars of each other with respect to the circle.

[0024] In one specific implementation scheme, the image of the absolute quadratic curve is decomposed by Cholesky and then inverted to obtain the intrinsic parameter matrix of the pinhole camera. The intrinsic parameters include the scale factor, tilt factor, and principal point coordinates on the x-axis and y-axis.

[0025] Compared with existing technologies, the method for calibrating a pinhole camera based on the asymptote properties of two coplanar circles described in this invention is used to solve for the intrinsic parameters of a pinhole camera. By using two coplanar circles at arbitrary positions as targets, the pinhole camera captures three images containing the targets from different positions. First, edge points are extracted from the images, and the equation of the coplanar circle image is obtained by fitting using the least squares method. Then, based on the relationship between the asymptotes of the two coplanar circles, which is only related to the center position, the algebraic constraints of the asymptote projection are solved to obtain the image of the asymptote. Combining the pole-epoch relationship satisfied by the asymptotes and the annulus points with respect to the circle and the projective invariance, the image of the annulus points is recovered. Furthermore, the image of the absolute conic section is determined by the constraint that the annulus points lie on the absolute conic section. Finally, the Cholesky decomposition is performed and the inverse is obtained to obtain the camera's intrinsic parameters, thus achieving the calibration of the pinhole camera's intrinsic parameters. This effectively improves the convenience, applicability, efficiency, and stability of the calibration, and has the following beneficial effects:

[0026] 1. It effectively avoids the limitations of existing technologies;

[0027] Compared to the calibration method based on concentric circles, it does not require precise positioning of the circle center, reducing the operational difficulty in practical applications;

[0028] Compared to calibration methods based on non-concentric circles, this method only requires two coplanar circles to complete the calibration, eliminating the need to deploy at least three independent circles and expanding its applicability.

[0029] Compared to other calibration methods based on asymptotes, this method can directly solve for the projection of the asymptotes through closed solutions, avoiding the problems of nonlinear solutions or high solution difficulty, and improving calibration efficiency.

[0030] 2. The target is simple to make, has no requirements on physical dimensions, and does not require knowledge of the center and radius, which further enhances the practicality and convenience of the method, improves calibration accuracy, and has good stability and wide applicability. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0032] Figure 1 This is an overall flowchart of the method for calibrating a pinhole camera based on the asymptote properties of two coplanar circles, as described in this invention.

[0033] Figure 2 This is a schematic diagram of the imaging process of a circle under a pinhole model.

[0034] Figure 3 This is a schematic diagram showing the relationship between a coplanar circle and its asymptote. Detailed Implementation

[0035] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] like Figure 1 As shown, the method for calibrating a pinhole camera based on the asymptote properties of two coplanar circles described in this invention is applied to solving the intrinsic parameters of a pinhole camera. It is simple to manufacture, widely applicable, and has good stability. It includes a target for solving the intrinsic parameters of the pinhole camera, which is composed of two coplanar circles in space. Its imaging under the pinhole model is as follows... Figure 2As shown, the target consists of two coplanar circles at arbitrary positions. To solve for the camera's intrinsic parameters, three images of the target captured by the pinhole camera are needed. Specifically, solving for the pinhole camera's intrinsic parameters using this target requires the following steps:

[0037] 1. Fitting the target projection equation

[0038] The pixel coordinates of the edge points of the target image are extracted using the Edge function in the MATLAB program, and the target projection equation is obtained by fitting the least squares method.

[0039] 2. Solving for the image of the asymptotes of coplanar circles

[0040] Let R and t be the world coordinate system O, respectively. W -X W Y W Z W To camera coordinate system O C -X C Y C Z C If the rotation matrix and translation vector are given, then a point M on the circle and its projection m onto the circular image satisfy μm=K[R t]M, where μ is a non-zero scaling factor and K is the camera intrinsic parameter matrix.

[0041] Camera intrinsic parameter matrix Among them, f u and f v Let be the scale factor on the u-axis and v-axis, and s be the skew factor, [u0 v0 1] T The coordinates of the main point.

[0042] Let (C1, C2) denote two coplanar circles. Then C1 and C2 intersect the line L at infinity. ∞ The intersection points of the two asymptotes of the circle are both points I and J on the annulus of the plane containing the circle. Since the two asymptotes of the circle intersect at the center, circle C... k The asymptotes of (k=1,2) intersect at the center O. k That is, circle C k The asymptote of IO is a straight line. k and JO k ,like Figure 2 As shown. Therefore, when two coplanar circles are concentric, they have the same two asymptotes. In this invention, for the sake of simplicity, the same letters are used to represent the curve and its coefficient matrix.

[0043] When a pair of coplanar circles (C1, C2) are not concentric, their asymptotes are not identical. Let L Ik and L Jk (k=1,2) is C k The tangent at the points I and J of the annulus, then Ck asymptote L Ik and L Jk Satisfy the equation:

[0044]

[0045] From formula (1), the asymptote L Ik and L Jk (k=1,2) satisfies the equation:

[0046]

[0047] And the circular point I is represented as:

[0048]

[0049] According to formulas (2) and (3), we get:

[0050] L I1 =C1C2 -1 L I2 (4)

[0051] Similarly, we can conclude that:

[0052] L J1 =C1C2 -1 L J2 (5)

[0053] Formulas (4) and (5) are the algebraic relationships between the asymptotes of coplanar circles C1 and C2.

[0054] Let A = C1C2 -1 Then the asymptote L of C1 I1 (L J1 It is possible to obtain the asymptote L of C2 through a linear transformation A. I2 (L J2 This shows that there is a linear relationship between the asymptotes of C1 and C2.

[0055] When a pair of coplanar circles (C1, C2) are concentric, the asymptotes of the two circles are the same. Let L I and L J Let the line be the tangent to the concentric circle (C1, C2) at points I and J on the annulus. Then we have:

[0056]

[0057] From equation (6), we know that the asymptotes L of the concentric circles (C1, C2) are... I and L J Satisfy the equation:

[0058]

[0059] Substituting equation (7) into equation (6), we get:

[0060]

[0061] From equation (8), the asymptote L I and L J Let be the tangent line to concentric circles C1 or C2 at points I and J on the annulus, and only depend on C1 or C2.

[0062] On the image plane π', the circular image pair (c1, c2) is the projection of the coplanar circular pair (C1, C2), m I and m J Let c be the images of points I and J on the circular ring, respectively. k (k=1,2) respectively at m I and m J The tangent at point l is denoted as l. Ik and l Jk Since the tangent point and tangent line of a conic section, as special pole-polar relationships, remain unchanged under projective transformation, the tangent line l... Ik and l Jk (k = 1, 2) represent the asymptotes L. Ik and L Jk The projection of the asymptote. Based on the relationship and properties between the asymptotes of two coplanar circles, and combined with the projective invariance, the image l of the asymptote is determined from the image pair (c1, c2). Ik and l Jk (k = 1, 2).

[0063] When the coplanar pair of circles (C1, C2) are not concentric, similar to formula (8), C k The asymptote L of (k=1,2) Ik and L Jk satisfy:

[0064]

[0065] From equations (4) and (9), the asymptote L I1 ,L I2 The projection l I1 , l I2 satisfy:

[0066]

[0067] Let l Ik The homogeneous coordinates of (k = 1, 2) are l Ik =[x k y k 1] T Then, from equation (10), we can obtain the information about l. Ik Algebraic constraints:

[0068]

[0069] Because l Ik and l Jk They are a pair of conjugate lines, therefore, solving the system of equations (11) yields the image l of the asymptotes of the non-concentric circle pair (C1,C2). Ik and l Jk (k = 1, 2).

[0070] When the coplanar pair of circles (C1, C2) are concentric, C1 and C2 have the same asymptote, i.e., L... I1 With L I2 Overlap, L J1 With L J2 They coincide. At this moment, the projection of the asymptote l I1 With l I2 Overlap, l J1 With l J2 Coincident. The projection of the asymptotes of the coplanar circle pair (C1, C2) onto the image plane π' is denoted as l. I and l J Then, from equation (8), we get:

[0071]

[0072] Without loss of generality, let the projection of the asymptote l I =[xy 1] T Then, from equation (12), we obtain the information about l. I Algebraic constraints:

[0073]

[0074] Solving the system of two quadratic equations in (13) yields a set of conjugate solutions, which are the images of the asymptotes of the concentric circle pair (C1, C2). I and l J .

[0075] 3. Restore the image of the circular points.

[0076] The asymptotes of a circle are the tangents to the circle at the annulus, and the points and lines of tangency are special poles and polars, meaning that the annulus and the asymptotes of the circle satisfy the pole-polar relation. Therefore, combining the projective invariance, the image l of the asymptotes... Ik and l Jk (k=1,2) Reconstruct the image m of the circular point. I and m J .

[0077] On the image plane π', the image m of the circular point I ,m JThese are the projections of the asymptotes l Ik ,l Jk (k=1,2) and the circular image c k The point of tangency (when c1 and c2 are images of concentric circles, l) I1 With l I2 Overlap, l J1 With l J2 (overlapping), then from equation (2), m I and m J Represented as:

[0078]

[0079] The image m of the circular point is recovered using formula (14). I and m J .

[0080] 4. Determine the image of an absolute conic section.

[0081] The images of three circular points are recovered from three images. Based on the fact that the circular points are located on the absolute conic, the constraint relationship between the image of the circular points and the image of the absolute conic is established to determine the image ω of the absolute conic.

[0082] Because the circular point lies on the absolute conic section, according to the projective invariance, the image m of the circular point... I and m J It should lie on the image of the absolute conic section. Because the image m of the circular point... I and m J It is a set of conjugate complex points; therefore, the image m of a set of circular points is... I and m J Only two linear constraint equations can be provided for the image of the absolute conic section:

[0083]

[0084] Where Re and Im represent the real and imaginary parts, respectively, and ω = K -T K -1 It is the image of an absolute conic section. Since ω has 5 degrees of freedom, at least three sets of images of the circular points determine ω, that is, at least three images are needed to recover the images of the three circular points.

[0085] 5. Solve for the intrinsic parameters of a pinhole camera.

[0086] According to ω=K -T K -1 The intrinsic parameter matrix K is obtained by performing Cholesky decomposition on the image ω of the absolute conic section and then inverting it.

[0087] This invention utilizes two coplanar circles as targets to solve for the intrinsic parameters of a pinhole camera. It requires capturing three images containing two coplanar circles from different positions using a pinhole camera. First, edge points of the target image are extracted from these three images, and the equation of the coplanar circle image is obtained using the least squares method. Since the relationship between the asymptotes of the two coplanar circles depends only on the position of the circle's center, this relationship is combined with the algebraic constraints of the asymptote projection to solve for the asymptote image. The asymptotes and the annulus satisfy the pole-epoch relationship with respect to the circle; combined with projective invariance, the image of the annulus is obtained. Then, the image of the absolute conic section is recovered from the constraint that the annulus lies on the absolute conic section. Finally, the Cholesky decomposition of the absolute conic section image is performed, and the inverse is used to solve for the pinhole camera's intrinsic parameters. The specific steps include: fitting the target projection equation, solving for the image of the coplanar circle asymptotes, recovering the image of the annulus, determining the image of the absolute conic section, and solving for the pinhole camera's intrinsic parameters.

[0088] This invention effectively avoids the aforementioned limitations by introducing linear constraints on asymptotes. The asymptotes of a circle are the tangents to the circle at the annulus, preserving geometric properties during projective transformation and providing a good geometric constraint for camera calibration.

[0089] This invention systematically analyzes the geometric relationship between the asymptotes of two coplanar circles, rigorously proving that concentric circles have the same asymptotes, while asymptotes of non-concentric circles have a linear relationship. This property allows the projection of the asymptotes to be directly solved using a closed-form solution, efficiently recovering the image of the circular points. Finally, a linear calibration method based on the properties of at least two coplanar circle asymptotes is proposed.

[0090] This invention proposes a method for solving the intrinsic parameters of an arbitrary pinhole camera using the asymptote property of two coplanar circles in space, with the target being at least two coplanar circles in space. The following example provides a more detailed description of the implementation of this invention, using two coplanar circles as the target. The method of this invention is then used to calibrate a pinhole camera used in an experiment; the specific steps are as follows:

[0091] 1. Fitting the target projection equation

[0092] Three images of the target were captured using a pinhole camera. These images were then read in, and the pixel coordinates of the target image's edge points were extracted using the Edge function in MATLAB. Finally, the equation of the quadratic curve was obtained by fitting the image using the least squares method. Here, c... nk (n = 1, 2, 3; k = 1, 2) represents the coefficient matrix of the k-th circular image in the n-th image, and the result is as follows:

[0093]

[0094]

[0095] 2. Solving for the image of the asymptotes of coplanar circles

[0096] Let R and t be the world coordinate system O, respectively. W -X W Y W Z W To camera coordinate system O C -X C Y C Z C If the rotation matrix and translation vector are given, then a point M on the circle and its projection m onto the circular image satisfy μm=K[R t]M, where μ is a non-zero scaling factor and K is the camera intrinsic parameter matrix;

[0097] Camera intrinsic parameter matrix Among them, f u and f v Let be the scale factor on the u-axis and v-axis, and s be the skew factor, [u0 v0 1] T Principal point coordinates;

[0098] Let (C1, C2) denote two coplanar circles, and let L be the asymptote. Ik and L Jk (k = 1, 2) represents circle C. k Tangents at points I and J of the annulus, respectively;

[0099] On the image plane π', the circular image pair (c1, c2) is the projection of the coplanar circular pair (C1, C2), m I and m J These are the images of points I and J of the circular ring, respectively;

[0100] Image c k (k=1,2) respectively at m I and m J The tangent at point l is denoted as l. Ik and l Jk Since the tangent point and tangent line of a conic section, as special pole-polar relationships, remain unchanged under projective transformation, the tangent line l Ik and l Jk (k = 1, 2) represent the asymptotes L. Ik and L Jk The projection;

[0101] Based on the relationship and properties between the asymptotes of two coplanar circles, and combined with the projective invariance, the image l of the asymptote can be solved from the image pair (c1, c2). Ik and l Jk (k = 1, 2), to simplify the description, the same letters are used to represent the curve and its coefficient matrix;

[0102] Solve for the image l of the asymptotes of coplanar circles using formulas (11) and (13). I1kand l J1k (k=1,2):

[0103]

[0104]

[0105] Similarly, we obtain the images of the asymptotes of the other two images:

[0106]

[0107] 3. Restore the image of the circular points.

[0108] The asymptotes of a circle are the tangents to the circle at the annulus, and the points and lines of tangency are special poles and polars, meaning that the annulus and the asymptotes of the circle satisfy the pole-polar relation. Therefore, combining the projective invariance, the image l of the asymptotes... Ik and l Jk (k=1,2) Obtain the image m of the circular point I and m J ;

[0109] The image m of the circular point is recovered using formula (14). I1 and m J1 :

[0110]

[0111]

[0112] Similarly, we obtain the images of the circular points in the other two images:

[0113]

[0114] 4. Determine the image of an absolute conic section.

[0115] The images of three circular points are recovered from three images. Based on the fact that the circular points are located on the absolute conic, the constraint relationship between the image of the circular points and the image of the absolute conic is established to determine the image ω of the absolute conic.

[0116] Substituting equations (34), (36), and (38) into equation (15) and solving them simultaneously, we obtain a system of linear equations about ω. By performing SVD decomposition on the system of equations, we can obtain the coefficient matrix of ω. The results are as follows:

[0117]

[0118] 5. Solve for the intrinsic parameters of a pinhole camera.

[0119] According to ω=K -T K -1The image ω of the absolute conic section in equation (40) is decomposed by Cholesky and then inverted to obtain the intrinsic parameter matrix K. The result is as follows:

[0120]

[0121] Therefore, the five intrinsic parameters of the pinhole camera are: f u =1599.99999999993, f v =1400.00000000017, s=0.500000000452278, u0=1199.99999999813v0=899.999999999215.

[0122] The various embodiments described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calibrating a pinhole camera based on the properties of two coplanar circular asymptotes, characterized in that, The method comprises the following steps: (1) using a pinhole camera to take three images containing two coplanar circles as targets from different positions; (2) extracting edge points of the target images from the three images respectively, and obtaining equations of the images of the coplanar circles by fitting; (3) based on the relationship between asymptotes of two coplanar circles and the positions of the circle centers, and the algebraic constraints of the asymptote projection, the images of the asymptotes of the coplanar circles are solved; (4) according to the pole and polar relationship of the circle ring points about the circle and the projective invariance, the images of the circle ring points are recovered from the images of the asymptotes; (5) according to the constraint that the circle ring points are located on an absolute conic, three sets of images of the circle ring points recovered by the three images are used to establish a constraint relationship to determine the image of the absolute conic; (6) the image of the absolute conic is decomposed and inverted to solve the internal parameters of the pinhole camera.

2. The method for calibrating a pinhole camera based on the properties of two coplanar circles asymptote according to claim 1, wherein, The two coplanar circles are coplanar circles at any position, including concentric circles or non-concentric circles.

3. The method for calibrating a pinhole camera based on the properties of two coplanar circles asymptote according to claim 1, wherein, In step (1), the pinhole camera takes images from different positions to obtain the projection information of the targets under different angles.

4. The method for calibrating a pinhole camera based on the properties of two coplanar circles asymptote according to claim 1, wherein, In step (2), an edge detection function is used to extract the pixel coordinates of the edge points of the target images, and the edge detection function is an Edge function in MATLAB program.

5. The method for calibrating a pinhole camera based on two coplanar circle asymptotes according to claim 1, wherein, In step (2), the least square method is used to fit the equations of the images of the coplanar circles.

6. The method for calibrating a pinhole camera based on two coplanar circular asymptotes according to claim 1, wherein, In step (3), the relationship between the asymptotes of the two coplanar circles and the positions of the circle centers is that when the two coplanar circles are non-concentric circles, the asymptotes of the two circles have a linear relationship; when the two coplanar circles are concentric circles, the asymptotes of the two circles are the same.

7. The method for calibrating a pinhole camera based on the properties of two coplanar circles asymptote according to claim 6, wherein, When the two coplanar circles are non-concentric circles, the image of the asymptote is solved based on the linear relationship between the asymptotes of the two circles, and the image of the asymptote of the other circle is solved from the asymptote of one circle by linear transformation.

8. The method for calibrating a pinhole camera based on the properties of two coplanar circles asymptote according to claim 6, wherein, When the two coplanar circles are concentric circles, the image of the asymptote is solved by using the property that the asymptotes of the two circles are the same.

9. The method for calibrating a pinhole camera based on two coplanar circular asymptotes according to claim 1, wherein, In step (4), the circle ring points are the intersection points of the plane of the circle and the infinite straight line, the asymptote is the tangent line of the circle at the circle ring point, and the pole and polar relationship is that the circle ring point and the corresponding asymptote are the pole and polar about the circle.

10. The method for calibrating a pinhole camera based on two coplanar circular asymptotes according to claim 1, wherein, After Cholesky decomposition and inversion of the image of the absolute conic, the internal parameter matrix of the pinhole camera is obtained, and the internal parameters include the scale factors, the tilt factors and the principal point coordinates on the x-axis and the y-axis.

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