CN102999896B - Method for linearly solving intrinsic parameters of camera by aid of three tangent circles - Google Patents

Abstract

The invention relates to a method for calibrating a camera by means of solving two vanishing points in orthogonal directions by the aid of three externally or internally tangent circles on a plane. The method includes that three images are taken for a target from different directions, equations of various curves on the images and coordinates of tangent points of the images are extracted, projection coordinates of centers of the various circles are solved, a corresponding point of an image of each tangent point relative to an image of each circle center on a projection curve and a tangent line of the image of the tangent point and the corresponding point relative to the projection curve are solved, and the two vanishing points in the orthogonal directions are solved according to a principle of cross-ratio invariance and intersection points of the tangent lines; and the two vanishing points in the two orthogonal directions on the three images are computed, constraint equations of intrinsic parameters of the camera are established, and the five intrinsic parameters of the camera are linearly solved. The method has the advantages that full-automatic calibration can be realized owing to the target, and errors caused by measurement in a calibration procedure are reduced; and as the quadratic curves are concise and comprehensive elements, the calibration precision is improved in the camera calibration procedure.

Description

Utilize three tangent circle linear solution camera intrinsic parameters

Technical field

The invention belongs to computer research field, relating to a kind of three tangent circle targets for solving camera intrinsic parameter.Utilize any three mutual circumscribed circles or two circumscribed and with three circles of a round inscribe as calibrating template, by solving shadow point that orthogonal directions disappears three width images, linearly determine camera intrinsic parameter.

Background technology

One of basic task of computer vision, the two-dimensional image information obtained from video camera exactly recovers object geological information in three dimensions, thus identifies and the geometric configuration of object in reconstruction of three-dimensional space.The mutual relationship between the corresponding point in the three-dimensional geometry position of space object point and its image must be determined in the process, and this relation is determined by the geometric model of video camera imaging, the parameter of these geometric models is exactly camera parameters.In most conditions, these parameters obtain all by experiment, Here it is camera calibration.It is generally divided into tradition to demarcate and self-calibration two kinds of methods, no matter which kind of scaling method, and demarcating object is all adopt some special geometric models, such as: plane square, triangle, round, spatial cuboids, cylinder etc.How setting up relation especially certain the linear relation between these geometric model and camera parameters, is the target that current camera calibration is pursued, and is also one of focus of current computer vision field research.

Although traditional camera marking method can obtain higher precision, calibrating block makes difficulty, is not easy to operation.For this problem document " A flexible new technique for camera calibration ", (Zhengyou Zhang, IEEETransactions on Pattern Analysis and Machine Intelligence, vol.22, no.11, pp.1330-1334,2000.) propose the method replacing traditional calibrating block with plane template, this method is simple and convenient, cost is low, and can higher precision be obtained, but need the physical coordinates of dot matrix on accurate locating template.Document " Planar conic based camera calibration ", (Changjiang Yang, Fengmei Sun, Zhanyi Hu, In Proceedings of International Conference onPattern Recognition, vol.1, pp.555-558,2000.) this method is done popularization, carried out calibrating camera by the quafric curve correspondence between image and template, instead of utilize correspondence between points.Because quafric curve is that the more succinct more globalize of one obtains primitive, the stability of method thus can be improved further.So solve problem of calibrating with curve to be widely studied.Document " A new easy camera calibration technique based on circular points ", (Xiaoqiao Meng, ZhanyiHu, Pattern Recognition, vol.36, no.5, pp.115-1164, 2003.) calibrating template with a circle and some the straight lines formations by the center of circle is proposed, utilize circular point to solve the method for camera intrinsic parameter, circular point in projective geometry is dissolved in camera calibration by the method first, so circular point has become the theoretical foundation (HartleyRichard of camera self-calibration method, Zisserman Andrew, " Multiple view geometry in computer vision ", Cambridge UniversityPress, Cambridge, 2000.)

Circle is a special quafric curve in plane, and circles all in plane all passes through circular point.Utilize circle as calibrating template, the method that the theory in conjunction with circular point carries out camera calibration is promoted gradually.Document (Yihong Wu, Haijiang Zhu, Zhanyi Hu, Fuchao Wu, " Camera calibration from the quasi-affine invariance of two parallelcircles ", In Proceedings ofthe ECCV, pp.190-202,2004.) proposing the method for demarcating with parallel circle, is that the intersection point of the picture of circular point direct solution two parallel circles completes demarcation according to the intersection point of parallel circle.Document (Yihong Wu, Xinju Li, Fuchao Wu, Zhanyi Hu, " Coplanar circle; quasi-affine invariance and calibration ", Image andVision Computing, vol.24, no.4, pp.319-326,2006.) discuss the position relationship of any two circles in plane, try to achieve the picture of circular point according to the intersection point of quafric curve in the position relationship computed image of circle.

Summary of the invention

The invention provides a kind of making simple, widely applicable, the target for solving camera intrinsic parameter of good stability.This target circle that is mutually circumscribed by three or inscribe forms.In the process solving camera intrinsic parameter, only need video camera to take 3 width images from different azimuth and just can go out 5 camera intrinsic parameters by linear solution.

The present invention adopts following technical scheme:

The present invention is the target for camera self-calibration that circle that is mutually circumscribed by three or inscribe is formed.Concrete step comprises: extract each bar curvilinear equation on image, solve the coordinate of the picture in each center of circle, solve the picture corresponding point on the drop shadow curve of this circle of picture about the center of circle at the point of contact on a circle, the shadow point that disappears in the diametric(al) at this point of contact of mistake is solved according to Cross ration invariability, solve the shadow point that disappears in this point of contact tangential direction of a mistake, solve the intrinsic parameter of video camera according to the shadow point Linear that disappears on pairwise orthogonal direction.

(1) drop shadow curve's equation of matching Circle in Digital Images

Utilize the function in the OpenCV program of VC++6.0 platform to extract the coordinate of image characteristic point, and with each bar curve in least-squares algorithm fitted figure picture, obtain each bar curvilinear equation on image.

(2) coordinate of the picture in each center of circle of tangent circle is solved

If circle Q ₁, Q ₂, Q ₃mutually circumscribed, they have the different centers of circle, its mid point A, and B, C are point of contact.Under the homograph H of world's coordinate plane to the plane of delineation, they on the image plane picture C _imeet: C _i=λ _ih ^-Tq _ih ^-1, i=1,2,3.Wherein radius is r, and central coordinate of circle is (X ₀, Y ₀) round Q, the some X on it meets equation X ^tqX=0, its matrix form is

$Q=\left[\begin{array}{ccc}1& 0& {-X}_0\\ 0& 1& -Y_0\\ -X_0& {-Y}_0& X_0^2+Y_0^2-r^2\end{array}\right].$

Suppose circle Q ₁the center of circle overlap with world coordinates initial point, the curve of the existence on the plane of delineation can be expressed as the linear combination of the drop shadow curve of three circles, namely (j=2,3), and meet β ≠ 0, det Δ _j=0.This be one about a cubic equation of β, have three roots.Pass through equation β can be solved ₁=λ _j/ λ ₁, ${\mathrm{\β}}_{\mathrm{2,3}}=\frac{{\mathrm{\λ}}_j}{{2\mathrm{\λ}}_1{r}_1^2}[(r_1^2+r_j^2-X_{0j}^2-Y_{0j}^2)\±\sqrt{({(r_1^2-r_j^2)}^2+(X_{0j}^2+Y_{0j}^2)-2(r_1^2+r_j^2)(X_{0j}^2+Y_{0j}^2))}].$ Wherein, circle Q _jcentral coordinate of circle, β _2,3it is the double root of equation.By β ₁substitute into it is the matrix of 1 that (j=2,3) formula obtains an order, and it represents the straight line by the picture in the center of circle, thus can obtain wherein, o ₁, o _jrepresent circle Q ₁, Q _jthe projection in the center of circle.Cross the straight line of the picture in the center of circle it is Δ _jeigenwert β ₁corresponding generalized eigenvector, so circle Q ₁the coordinate o of picture in the center of circle ₁=l ₁₂× l ₁₃.Same, o ₂, o ₃coordinate can calculate.

(3) of solving in diametric(al) disappears shadow point

When calculating round Q ₁the center of circle picture o ₁coordinate, and detect round Q ₁and Q ₃the coordinate m of picture of point of contact A _a, and then can m be calculated _aabout the picture o in the center of circle ₁in curve C ₁corresponding point m _d(as Fig. 3).Therefore m _a, o ₁, m _dplace straight line is circle Q ₁the projection of a upper diameter, can be obtained by harmonic conjugates and Cross ration invariability: (m _am _d, o ₁v ₁)=-1.Wherein, v ₁it is the shadow point that disappears in this diametric(al).

(4) the shadow point that disappears in the tangential direction at round point of contact was solved

Calculated some m _a, m _dabout curve C ₁tangent line l ₁, l ₂, then their intersection point v ₂it is the shadow point that disappears in diameter two-end-point tangential direction.Because on space plane, tangent line and the diameter of diameter two-end-point are vertical, so v on the image plane ₁, v ₂that the shadow point that disappears on two orthogonal directionss is asked.

(5) camera intrinsic parameter is calculated

Obtain the shadow point that disappears on three width images on orthogonal directions, utilize Cholesky to decompose and just can calculate camera intrinsic parameter K.

Advantage of the present invention:

(1) this target makes simple, draws the circle of three mutually circumscribed or inscribes with compasses in the plane.

(2) to the physical size not requirement of this target, without the need to knowing round position and the world coordinates in the center of circle.

(3) only 3 width images need be taken with video camera from different azimuth and just 5 intrinsic parameters of video camera can be gone out by linear solution.

Accompanying drawing explanation

Fig. 1 is three mutual circumscribed target construction schematic diagram for solving camera intrinsic parameter.

Fig. 2 is that two circles for solving camera intrinsic parameter are mutually circumscribed and in the target construction schematic diagram of a round inscribe.

Fig. 3 is the shadow point resolution principle that disappears on two orthogonal directionss.

Embodiment

For solving a target for camera intrinsic parameter, its circle that is mutually circumscribed by three or inscribe forms, as Fig. 1,2.Completing solving of camera intrinsic parameter with this target needs through following steps:

(1) drop shadow curve's equation of matching Circle in Digital Images

The present invention utilizes the function in the OpenCV program of VC++6.0 platform to extract the coordinate of image characteristic point, and with each bar curve in least-squares algorithm fitted figure picture, obtains each bar curvilinear equation on image.

(2) coordinate of the picture in each center of circle of tangent circle is solved

If circle Q ₁, Q ₂, Q ₃mutually circumscribed, they have the different centers of circle, its mid point A, and B, C are point of contact.Under the homograph H of world's coordinate plane to the plane of delineation, they on the image plane picture C _imeet: C _i=λ _ih ^-Tq _ih ^-1, i=1,2,3.Wherein radius is r, and central coordinate of circle is (X ₀, Y ₀) round Q, the some X on it meets equation X ^tqX=0, its matrix form is

$Q=\left[\begin{array}{ccc}1& 0& {-X}_0\\ 0& 1& -Y_0\\ -X_0& {-Y}_0& X_0^2+Y_0^2-r^2\end{array}\right].$

Suppose circle Q ₁the center of circle overlap with world coordinates initial point, the curve of the existence on the plane of delineation can be expressed as the linear combination of the drop shadow curve of three circles, namely (j=2,3), and meet β ≠ 0, det Δ _j=0.This be one about a cubic equation of β, have three roots.Pass through equation β can be solved ₁=λ _j/ λ ₁, ${\mathrm{\β}}_{\mathrm{2,3}}=\frac{{\mathrm{\λ}}_j}{{2\mathrm{\λ}}_1{r}_1^2}[(r_1^2+r_j^2-X_{0j}^2-Y_{0j}^2)\±\sqrt{({(r_1^2-r_j^2)}^2+(X_{0j}^2+Y_{0j}^2)-2(r_1^2+r_j^2)(X_{0j}^2+Y_{0j}^2))}].$

Wherein, circle Q _jcentral coordinate of circle, β _2,3it is the double root of equation.By β ₁substitute into it is the matrix of 1 that (j=2,3) formula obtains an order, and it represents the straight line by the picture in the center of circle, thus can obtain wherein, o ₁, o _jrepresent circle Q ₁, Q _jthe projection in the center of circle.Cross the straight line of the picture in the center of circle it is Δ _jeigenwert β ₁corresponding generalized eigenvector, so circle Q ₁the coordinate o of picture in the center of circle ₁=l ₁₂× l ₁₃.Same, o ₂, o ₃coordinate can calculate.

(3) of solving in diametric(al) disappears shadow point

When calculating round Q ₁the center of circle picture o ₁coordinate, and detect round Q ₁and Q ₃the coordinate m of picture of point of contact A _a, and then can m be calculated _aabout the picture o in the center of circle ₁in curve C ₁corresponding point m _d(as Fig. 3).Therefore m _a, o ₁, m _dplace straight line is circle Q ₁the projection of a upper diameter, can be obtained by harmonic conjugates and Cross ration invariability: (m _am _d, o ₁v ₁)=-1.

Wherein, v ₁it is the shadow point that disappears in this diametric(al).

(4) the shadow point that disappears in the tangential direction at round point of contact was solved

Calculated some m _a, m _dabout curve C ₁tangent line l ₁, l ₂, then their intersection point v ₂it is the shadow point that disappears in diameter two-end-point tangential direction.Because on space plane, tangent line and the diameter of diameter two-end-point are vertical, so v on the image plane ₁, v ₂it is the shadow point that disappears on two orthogonal directionss.

(5) camera intrinsic parameter is calculated

Obtain the shadow point that disappears on three width images on orthogonal directions, utilize Cholesky to decompose and just can calculate camera intrinsic parameter K.

Embodiment

The present invention proposes and utilize any three circles that are mutually circumscribed or inscribe in plane linearly to determine the target of camera intrinsic parameter.Without loss of generality, the experiment module structural representation of the present invention's employing as shown in Figure 1.With an example, description is specifically made to embodiment of the present invention below:

The experiment module adopted based on the camera marking method of three tangent circles is the circle of arbitrary three mutually circumscribed or inscribes in plane, and without loss of generality, we adopt three circumcircles as shown in Figure 1 as calibrating template at this.Q ₁, Q ₂, Q ₃be three mutually circumscribed circles, A, B, C are point of contacts, and utilize the method in the present invention to demarcate the video camera for testing, concrete steps are as follows:

(1) drop shadow curve's equation of matching Circle in Digital Images

The image resolution ratio that the present invention adopts is 640 × 480 pictures, several experiment pictures are taken from different directions with video camera, choose three width picture comparatively clearly, read in image, function in OpenCV is utilized to extract the coordinate of image characteristic point, and with each bar curve in least-squares algorithm fitted figure picture, obtain curvilinear equation C _j.

(2) coordinate of the picture in each center of circle of tangent circle is solved

If circle Q ₁, Q ₂, Q ₃mutually circumscribed, they have the different centers of circle, its mid point A, and B, C are point of contact.Under the homograph H of world's coordinate plane to the plane of delineation, they on the image plane picture C _imeet: C _i=λ _ih ^-Tq _ih ^-1, i=1,2,3.Wherein radius is r, and central coordinate of circle is (X ₀, Y ₀) round Q, the some X on it meets equation X ^tqX=0, its matrix form is

$Q=\left[\begin{array}{ccc}1& 0& {-X}_0\\ 0& 1& -Y_0\\ -X_0& {-Y}_0& X_0^2+Y_0^2-r^2\end{array}\right].$

Suppose circle Q ₁the center of circle overlap with world coordinates initial point, the curve of the existence on the plane of delineation can be expressed as the linear combination of the drop shadow curve of three circles, namely (j=2,3), and meet β ≠ 0, det Δ _j=0.This be one about a cubic equation of β, have three roots.Pass through equation β can be solved ₁=λ _j/ λ ₁, ${\mathrm{\β}}_{\mathrm{2,3}}=\frac{{\mathrm{\λ}}_j}{{2\mathrm{\λ}}_1{r}_1^2}[(r_1^2+r_j^2-X_{0j}^2-Y_{0j}^2)\±\sqrt{({(r_1^2-r_j^2)}^2+(X_{0j}^2+Y_{0j}^2)-2(r_1^2+r_j^2)(X_{0j}^2+Y_{0j}^2))}].$

Wherein, circle Q _jcentral coordinate of circle, β _2,3it is the double root of equation.By β ₁substitute into it is the matrix of 1 that (j=2,3) formula obtains an order, and it represents the straight line by the picture in the center of circle, thus can obtain wherein, o ₁, o _jrepresent circle Q ₁, Q _jthe projection in the center of circle.Cross the straight line of the picture in the center of circle it is Δ _jeigenwert β ₁corresponding generalized eigenvector, so circle Q ₁the coordinate o of picture in the center of circle ₁=l ₁₂× l ₁₃.Same, o ₂, o ₃coordinate can calculate.

On the three width images that above method calculates for being tested, the projection coordinate in three tangent circle centers of circle is respectively

o ₁＝(363，293，1) ^T，o ₂＝(238，116，1) ^T，o ₃＝(427，120，1) ^T；

o ₁′＝(288，323，1) ^T，o ₂′＝(300，114，1) ^To ₃′＝(451，220，1) ^T；

o ₁″＝(242，297，1) ^T，o ₂″＝(422，111，1) ^T，o ₃″＝(463，310，1) ^T。

(3) of solving in diametric(al) disappears shadow point

When calculating round Q ₁the center of circle picture o ₁coordinate, and detect round Q ₁and Q ₃the coordinate m of picture of point of contact A _a, and then can m be calculated _aabout the picture o in the center of circle ₁in curve C ₁corresponding point m _d(as Fig. 3).Therefore m _a, o ₁, m _dplace straight line is circle Q ₁the projection of a upper diameter, can be obtained by harmonic conjugates and Cross ration invariability: (m _am _d, o ₁v ₁)=-1.

The corresponding point of trying to achieve in three width experimental image through above process are respectively m _d=(307,426.6364,1) ^t, m _d'=(173,128.4059,1) ^t, m _d"=(119,259.2824,1) ^t.And then the shadow point v that disappears tried to achieve on three width images ₁=(372.5032,268.7538,1) ^t, v ₁'=(127.4359,421.5641,1) ^t, v ₁"=(216.9909,274.9901,1) ^t.Wherein, v ₁it is the shadow point that disappears in this diametric(al).

(4) the shadow point that disappears in the tangential direction at round point of contact was solved

Calculated some m _a, m _dabout curve C ₁tangent line l ₁, l ₂, then their intersection point v ₂it is the shadow point that disappears in diameter two-end-point tangential direction.Because on space plane, tangent line and the diameter of diameter two-end-point are vertical, so v on the image plane ₁, v ₂it is the shadow point that disappears on two orthogonal directionss.

V is respectively through another the shadow point that disappears calculated on three width images ₂=(427.4638 ,-593.0786,1) ^t, v ₂'=(573.1879 ,-174.5117,1) ^t, v ₂"=(323.9964 ,-256.6133,1) ^t.

(5) camera intrinsic parameter is calculated

Obtain the shadow point that disappears on three width images on orthogonal directions, utilize Cholesky decomposition computation to go out camera intrinsic parameter K.The camera intrinsic parameter obtained in this experimentation $K=\left[\begin{array}{ccc}651.8619& 0.3248& 323.2858\\ 0& 651.9809& 242.9000\\ 0& 0& 1\end{array}\right].$

Claims (1)

1., based on the method solving camera intrinsic parameter of three tangent circle targets, it is characterized in that this target is made up of three mutual three circumscribed circles; The concrete steps of described method comprise: take three width images of target from different directions with video camera and read in image, extract each bar curvilinear equation on image, solve the coordinate of the picture in each center of circle, solve the picture corresponding point on the drop shadow curve of this circle of picture about the center of circle at the point of contact on a circle, the shadow point that disappears in the diametric(al) at this point of contact of mistake is solved according to Cross ration invariability, solve the shadow point that disappears in this point of contact tangential direction of a mistake, solve the intrinsic parameter of video camera according to the shadow point Linear that disappears on pairwise orthogonal direction;

(1) drop shadow curve's equation of matching Circle in Digital Images

Utilize the function in the OpenCV program of VC++6.0 platform to extract the coordinate of image characteristic point, and with each bar curve in least-squares algorithm fitted figure picture, obtain each bar curvilinear equation on image;

(2) coordinate of the picture in each center of circle of tangent circle is solved

If circle Q ₁, Q ₂, Q ₃mutually circumscribed, they have the different centers of circle, its mid point A, and B, C are point of contact; Under the homograph H of world's coordinate plane to the plane of delineation, they on the image plane picture C _imeet: C _i=λ _ih ^-Tq _ih ^-1, i=1,2,3; Wherein radius is r, and central coordinate of circle is (X ₀, Y ₀) round Q, the some X on it meets equation X ^tqX=0, its matrix form is

$Q=\left[\begin{array}{ccc}1& 0& -X_0\\ 0& 1& -Y_0\\ -X_0& -Y_0& X_0^2+Y_0^2-r^2\end{array}\right];$

Suppose circle Q ₁the center of circle overlap with world coordinates initial point, the curve of the existence on the plane of delineation can be expressed as the linear combination of the drop shadow curve of three circles, namely j=2,3, and meet β ≠ 0, det Δ _j=0; This be one about a cubic equation of β, have three roots; Pass through equation β can be solved ₁=λ _j/ λ ₁, ${\mathrm{\β}}_{\mathrm{2,3}}=\frac{{\mathrm{\λ}}_j}{2{\mathrm{\λ}}_1{r_1}^2}[({r_1}^2+r_j^2-X_{0j}^2-Y_{0j}^2)\±\sqrt{({({r_1}^2-r_j^2)}^2+(X_{0j}^2+Y_{0j}^2)-2({r_1}^2+r_j^2)(X_{0j}^2+Y_{0j}^2))};$ Wherein, (X _0j, Y _0j) be circle Q _jcentral coordinate of circle, r ₁, r _jrepresent circle Q respectively ₁, Q _jradius, β _2,3it is the double root of equation; By β ₁substitute into obtaining an order is the matrix of 1, and it represents the straight line by the picture in the center of circle, thus can obtain wherein, o ₁, o _jrepresent circle Q ₁, Q _jthe projection in the center of circle; Cross the straight line π of the picture in the center of circle _1j=o ₁× o _jit is Δ _jeigenwert β ₁corresponding generalized eigenvector, so circle Q ₁the coordinate o of picture in the center of circle ₁=π ₁₂× π ₁₃; Same, o ₂, o ₃coordinate can calculate;

(3) of solving in diametric(al) disappears shadow point

When calculating round Q ₁the center of circle picture o ₁coordinate, and detect round Q ₁and Q ₃the coordinate m of picture of point of contact A _a, and then can m be calculated _aabout the picture o in the center of circle ₁in curve C ₁corresponding point m _d; Therefore m _a, o ₁, m _dplace straight line is circle Q ₁the projection of a upper diameter, can be obtained by harmonic conjugates and Cross ration invariability: (m _am _d, o ₁v ₁)=-1; Wherein, v ₁it is the shadow point that disappears in this diametric(al);

(4) the shadow point that disappears in the tangential direction at round point of contact was solved

Calculated some m _a, m _dabout curve C ₁tangent line π ₁, π ₂, then their intersection point v ₂it is the shadow point that disappears in diameter two-end-point tangential direction; Because on space plane, tangent line and the diameter of diameter two-end-point are vertical, so v on the image plane ₁, v ₂it is the shadow point that disappears on two orthogonal directionss;

(5) camera intrinsic parameter is calculated

Obtain the shadow point that disappears on three width images on orthogonal directions, utilize Cholesky to decompose and just can calculate camera intrinsic parameter K.