CN115388874B - Round target pose estimation method based on monocular camera - Google Patents
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Abstract
The invention provides a monocular camera-based circular target pose estimation method, which comprises the following steps: step one, solving a target imaging elliptic equation; step two, calculating a target normal vector; thirdly, calculating a three-dimensional coordinate of the center of the target; step four, decoupling the normal vector of the target; and fifthly, optimizing the target pose. The invention provides a complete analysis form for solving the target position and plane normal vector, can complete the solution within a single millisecond, has the characteristics of high speed and high precision, simultaneously reduces the requirement of measurement on system hardware equipment by adopting a monocular camera, and improves the flexibility and adaptability of the system. The method of cooperative targets is adopted in the system, so that the problem of normal vector decoupling can be solved with high robustness, the accuracy of target plane normal vector calculation can be improved, and the method has wide application prospect in cooperative measurement because the cooperative target configuration scheme is easy to realize in measurement and is a common measurement strategy in actual measurement.
Description
Technical Field
The invention discloses a circular target pose estimation method based on a monocular camera, and belongs to the field of image processing.
Background
The prior pose estimation algorithm based on monocular vision can be mainly divided into three types, namely an algorithm based on points and angular points, an algorithm based on straight lines and an algorithm based on ellipses.
The central idea of the algorithm based on the points and the corner points is that a homography matrix between a camera imaging plane and an object plane is calculated by detecting the corner points in an image, rotation and translation parameters of the object plane are obtained from the homography matrix, and the method is commonly called as a PnP (perspective-n-points) problem. The method has been successfully applied by NASA to the calibration and verification of advanced guided video sensors for in-orbit automated rendezvous in (A.Heaton,R.Howard,and R.Pinson,Orbital express AVGS validation and calibration for automated rendezvous,In Proc.AIAA/AAS Astrodyn.Spec.Conf.Exhibit,2008,pp.6937-6954( andelu f. Schwann, richard t. Hopand robin m. Ping Sen in-orbit cooperative satellite attitude measurement experiments, AIAA/AAS astronomical expert conference and exhibition, 2008, page numbers, 6937-6954)). However, in a real environment, the number of corner points contained in a target is very large, and the corner points of the target are greatly influenced by illumination, so that the difficulty of corner point detection and matching is increased, and meanwhile, the instability based on a PnP algorithm is also increased.
The central idea based on the straight line algorithm is similar to the idea of the corner points, except that the former calculates the homography matrix through the matched corner points, the latter calculates by adopting the matched straight lines, and the algorithm by adopting the straight lines is classified into PnL problems (perspetive-n-lines). Representative algorithms are the three-line based algorithm P3L(M.Dhome,M.Richetin,J.-T.Lapreste,and G.Rives,Determination of the attitude of 3D objects from a single perspective view,IEEETransactions on Pattern Analysis and Machine Intelligence,vol.11,no.12,pp.1265-1278,Dec.1989( Michigan, rickel, let-Di Ehrlich Lapraise and G Riviet, based on the 3D object pose of a single view, electrical and electronic Engineer pattern recognition and machine intelligence journal, volume 11, 12, pages 1265-1278, 12 months 1989)), the four-line based algorithm P4L(F.A.Van Den Heuvel,Exterior orientation using coplanar parallel lines,In Proc.Scand.Conf.Image Anal.,1997,vol.1,pp.71-78(F.A. Fan Denghe Vir, based on the external directions of coplanar parallel lines, the tenth Scan Navier image analysis conference, la Peng Landa, first volume, pages 71-78)), and the 8-line based algorithm P8L(Y.Liu,T.S.Huang,and O.D.Faugeras,Determination of camera location from 2-D to 3-D line and point correspondences,IEEE Trans.Pattern Anal.Mach.Intell.,vol.12,no.1,pp.28-37,Jan.1990( Liu Yuncai, thgash yellow, olivir D Fuguy, based on the camera position estimation of the correspondence between 2-dimensional lines and three-dimensional lines, the electrical and electronic Engineer pattern recognition and machine intelligence journal, volume 12, pages 1, pages 28-37, 1 month 1990). Although the robustness of the algorithm based on the straight lines is greatly enhanced, in a real scene, the number of interference straight lines is great, and the problem of accurately finding the matched straight lines is still a problem of spacing.
The central idea of the ellipse-based algorithm is to reversely deduce the normal vector of the plane where the circular marker point is located by using the imaging principle of the camera and using the parameters of the imaging ellipse. Pose estimation algorithms (Y.C.Shiu and S.Ahmad,3D location of circular and spherical features by monocular model-based vision,In Proc.IEEE Int.Conf.Syst.,Man Cybern.,1989,pp.576-581(Y.C.Shiu and s.eihatmaide based on monocular single ellipses, circular and spherical feature location determination based on monocular vision, international conference on electrical and electronic engineers and control theory, page 576-581, 1989)), can give one analytical solution, but the solved normal vector has two non-decouples. To focus much of this next effort on how to solve for the true normal vector from the two normal vectors found, representative efforts are: solving the motion circular feature normal vector dual problem by adding coplanar-line constraints (D.He and B.Benhabib,Solving the orientation-duality problem for a circular feature in motion,IEEE Trans.Syst.,Man,Cybern.A,Syst.Humans,vol.28,no.4,pp.506-515,Jul.1998(D.He and Bei Nuo present halibut, international conference on the institute of electrical and electronics engineers and control theory, volume 28, 4, page 506-515, 7 months 1998)), or calculating the international conference on the basis of the single-order pose estimation of the circular and line features by adding coplanar-line constraints (C.Meng,J.Xue,and Z.Hu,Monocular position-pose measurement based on circular and linear features,In Proc.IEEE Int.Conf.Digit.Image Comput.,Techn.Appl.,2015,pp.1-8( Meng, xue Jiao and Hu Zhan: technology and application, 2015, page 1-8)).
Disclosure of Invention
The invention provides a monocular camera-based circular target pose estimation technology, which is characterized in that a camera imaging process is studied under a projective geometric framework, a circular target and a projected ellipse are regarded as affine images formed by projecting the same algebraic manifold on Z axes under different projective coordinate systems, a target position and normal plane estimation problem is simplified into a projective coordinate system orthogonal transformation matrix solving problem, and then a real plane normal vector is obtained by utilizing the constraint of a coplanar target. The method gives a complete analysis form for solving the target position and plane normal vector, can complete the solution within a single millisecond, has the characteristics of high speed and high precision, simultaneously reduces the requirement of measurement on system hardware equipment by adopting a monocular camera, and improves the flexibility and adaptability of the system.
The invention adopts the following technical scheme:
step one, solving a target imaging elliptic equation;
And (3) giving an ellipse projected by the circular target, extracting edge points of the ellipse, performing ellipse fitting on the edge points to obtain a parameter equation of the ellipse, and converting the parameter equation of the ellipse into a quadratic form.
Step two, calculating a target normal vector;
transforming the quadratic form under the pixel coordinate system into the quadratic form under the projection coordinate system, and then transforming the quadratic form under the projection coordinate system into the quadratic form under the target coordinate system by constructing an orthogonal transformation matrix containing three variables, wherein the quadratic form has the characteristic of a circle, and solving the constraint to obtain the three variables so as to obtain the normal vector of the plane where the ellipse is located.
Thirdly, calculating a three-dimensional coordinate of the center of the target;
According to the orthogonal transformation matrix obtained by the second calculation, an algebraic manifold in a projective coordinate system where the target circle is located can be obtained, an affine graph of the algebraic manifold is assumed to be the plane where the circle is located, the coordinate of the radial graph on the Z axis is assumed to be known, the distance from the center of the circular mark point to the projective coordinate system is obtained by calculation, and the back projection ray in the projective coordinate system where the center of the circle is located can be obtained according to the center point of the projective ellipse and the internal parameters of the camera, so that the three-dimensional coordinate of the center of the target circle in the projective coordinate system can be obtained.
Fourth, target normal vector decoupling
The normal vector and the three-dimensional coordinate of the two coplanar targets are calculated respectively through the three steps, the true normal vector of each mark point is calculated by utilizing the constraint that the central connecting line of the two target points is perpendicular to the normal vector of the targets, and the optimal normal plane vector of the targets is obtained through a least square method.
Step five, target pose optimization
The initial pose information of the target is obtained through the steps, the ellipse formed by projection of the initial pose and diameter information of the target in a camera is calculated, the error of the ellipse edge point obtained in the step one on the calculated projection ellipse equation is used as an objective function, the three-dimensional coordinate of the target is used as an optimization parameter, and the three-dimensional coordinate of the target with the minimum objective function is obtained by adopting an optimization method.
Pose information of the circular target is obtained comprehensively.
The invention comprises the following detailed steps:
step one, solving a target imaging elliptic equation;
Given an elliptical edge point coordinate pair sequence (x i,yi) (i=1, 2,.., n), where x i,yi is the pixel coordinate value of the ith edge point on the horizontal and vertical axes, respectively, and n is the total number of edge pixels. Let the parametric equation of an ellipse be Ax 2+Bxy+Cy2 +dx+ey+f=0, where a=1, [ B, C, D, E, F ] is an unknown quantity. Then there is an equation for any edge point pair (x i,yi) For all edge points, the equation set H [ B, C, D, E, F ] T = -B is available, where/>And obtaining [ B, C, D, E, F ] T＝-inv(HTH)HT B by adopting a least square method, wherein inv (·) is matrix inversion operation, and [ A, B, C, D, E, F ] T＝sign(C)[A,B,C,D,E,F]T is obtained, wherein sign (·) is a sign function. The parametric equation for an ellipse can be expressed in the form of a quadratic form [ x, y,1] f [ x, y,1] T =0, where/>If C|F| is not less than 0, the ellipse is a normal vector of a circle plane where the degraded non-solved mark circle is located, wherein|and| are matrix determinant operations; when the ellipse is non-degenerate, i.e., c|F| < 0, it is known from C > 0 that |F| < 0. The pixel homogeneous coordinate where the ellipse center is located can BE obtained by using the parameter equation Ax 2+Bxy+Cy2 +dx+ey+f=0 as po= ((2 CD-BE)/(B 2-4AC),(2AE-BD)/(B2 -4 AC), 1), and further, the back projection ray vector of the target center under the camera projection coordinate system can BE obtained by using the camera imaging principle as pv=po x inv (M), wherein the function inv (·) is the matrix inversion operation, and the matrix M is the internal parameter matrix of the camera.
Step two, calculating a target normal vector;
as shown in fig. 2, assuming that the camera projection coordinate system is ozz 1, the corresponding coordinate is denoted as XYZ 1, the coordinate system after the coordinate system is projectively transformed is ozz 2, the corresponding coordinate is denoted as XYZ 2, such that the vector [0, 1] is parallel to the normal vector of the plane in which the circle lies, wherein the photographic transformation is denoted as orthogonal transformation matrix TR, such that XYZ 1＝XYZ2 RT is solved for X 0,y0,z0, θ are respectively unknown variables, andGiven an in-camera parameter matrix M, we can obtain/>, from [ X, y,1] = [ X 1/Z1,Y1/Z1, 1] M and [ X, y,1] f [ X, y,1] T =0The homogeneous equation is an algebraic manifold of homogeneous coordinates of the round edge points in a projective coordinate system OXYZ 1. Algebraic manifold/>, under the projective coordinate system OXYZ 2, of the homogeneous coordinates of the circular edge points can be obtained through projective transformation TRLet MFM T＝QλQT, where Q is the orthogonal matrix,For the matrix MFM T eigenvalue matrix, given |f| < 0 from step one, it can be known that |qλq T|＝|Q|2|λ|＝|MFMT|＝|M|2 |f| < 0, and |λ| < 0, and since F is quadratic, λ 1≥λ2＞0＞λ3. TMFM TTT＝(TQ)λ(TQ)T is obtained from above, and the matrix T and Q are orthogonal matrices, and the matrix TQ is also orthogonal matrix, so thatWhere x 2+y2+z2 =1, z+.1, thenWherein the value of the symbol-in-place is not used in the method to omit writing. Since the vector [0, 1] is parallel to the normal vector of the plane of the circle in the coordinate system OXYZ 2, the quadratic matrix SλS T is a symmetric matrix and satisfies the system of equationsWherein f 1,f2 is the label of the two equations, respectively. Because the equation set contains three unknowns and only two nonlinear equations, the analytic solution of the equation set is solved by adopting a branch-and-bound method, namely: as can be seen from equation f 1, the conditions for establishing this are λ 1＝λ2, x=0, y=0, and z=0. Assuming λ 1＝λ2, λ 1z2+λ3(x2+y2)＝λ1 from equation f 2, λ 1(x2+y2)＝λ3(x2+y2 from x 2+y2+z2 =1, and λ 1＝λ3 from x 2+y2 +.0, which contradicts λ 1＞λ3, hence λ 1≠λ2; when x=0, λ 2y2z2+λ3y4＝λ1y2, y+.0 is obtained from equation f 2 (λ 3-λ2)y2＝λ1-λ2, since λ 3-λ2＜0,λ1-λ2 < 0, the equation is not true, x+.0; when z=0, λ 1y2+λ2x2＝λ3 is obtained from equation f 2, and x 2+y2+z2 =1 (λ 2-λ1)x2＝λ3-λ1, i.e. >)Not, so z+.0; when y=0, λ 1x2z2+λ3x4＝λ2x2 is obtainable from equation f 2, available/>As is available from x 2+y2+z2 = 1,From tq=s, t=sq T is available, then [ x 0,y0,z0]＝[x,y,z]QT, since [ x, y, z ] has four sets of solutions, there are also four sets of normal vectors [ x 0,y0,z0 ] to the plane of the target. Because the vector [ x 0,y0,z0 ] is the coordinate of the normal vector of the plane where the circle is located in the coordinate system OXYZ 2, and the obtuse angle setting is adopted between the normal vector direction and the Z axis direction of the coordinate system, two groups of solutions/>, under the coordinate system OXYZ 1, of the plane vector where the target is located can be obtainedWherein V 1,V2 is the normal vector of the plane of the target, let/>Then/>
Thirdly, calculating a three-dimensional coordinate of the center of the target;
From the second step, it can be known that the homogeneous coordinates of the circular edge point in the coordinate system OXYZ 2 satisfy algebraic manifold Let XYZ 3＝XYZ2 R have/>Wherein T is the feasible solution obtained in the second step, let/>Wherein a, c, d and f are parameters, can be obtainedObtaining affine graph of the manifold at Z-axis k under coordinate system OXYZ 3 Let/>Affine coordinates of the homogeneous coordinates of the circular edge points on the affine graph are respectively, and/>I.e./> The center coordinates of the circle under affine coordinates can be known as/>The diameter of the circle is/>Since the target diameter is known to be r, then/>Get/>Distance from center of circle to center of coordinate system O/>According to the back projection ray vector PV obtained in the step one and the distance d from the center of the target to the projection center obtained by the calculation, the three-dimensional coordinate vector/>, under the projection coordinate system, of the target can be obtained
Fourth, target normal vector decoupling
Given two circular targets C 1,C2 in the same plane, respectively obtaining corresponding imaging elliptical back projection ray vectors PV 1,PV2 according to the first calculation, obtaining a normal vector group V 1,V2 corresponding to the target plane according to the second calculation, and obtaining a three-dimensional coordinate vector Coor 1,Coor2 of the target in a projection coordinate system according to the third calculation. Because the targets C 1,C2 are in the same plane, the true normal vector in the normal vector group V 1,V2 should be perpendicular to the connecting line of the centers of the targets C 1,C2, so that CV= Coor 1-Coor2, and the length normalization processing is performed to obtainFor vector group V 1,V2 of any one target, respectively finding out the vector closest to 90 degrees with the vector CV as the normal vector of the target, namely:
And fitting the obtained target normal vector VT 1、VT2 with an optimal target plane normal vector VO by adopting a least square method, wherein the analysis solution is VO= (VT 1+VT2)/2, and the target plane normal vector after modulo normalization is VO=VO/|VO|. Taken together, the center coordinates Coor 1,Coor2 of the targets C 1,C2, and the normal vector VO they lie in the plane, are obtained.
Step five, target pose optimization
For any target C E (C 1,C2) in the fourth step, the calculated initial pose is: three-dimensional coordinates Coor e (Coor 1,Coor2), normal vector VO. Let (x 0,y0,z0)＝VO,TC＝Coor*RT, then the rotation matrix between coordinate system OXYZ 1 and coordinate system OXYZ 2 beLet the coordinate system CXYZ 1 be the coordinate system with the center of the target point as the origin of coordinates and the normal vector of the target point as the Z axis, let the coordinate system CXYZ 2 be the coordinate system with the intersection point of the Z axis of the coordinate system OXYZ 2 and the plane of the target point as the origin and the normal vector of the target point as the Z axis, the coordinates C xyz1,Cxyz2 of the coordinate systems CXYZ 1 and CXYZ 2 satisfy C xyz2＝Cxyz1+TC, wherein T C＝Coor*RT. In the coordinate system CXYZ 1, the target edge point satisfies the equation [ C x1,Cy1,Cz1]F[Cx1,Cy1,Cz1]T =0, where/>R is the radius of the circular target, which is represented in the coordinate system CXYZ 2 asWherein/>Which is expressed in the coordinate system OXYZ 2 as/>Let/>ThenLet P xyz2＝[Px2,Py2,Pz2 ], thenWhich is denoted/>, in CXYZ 1 Let Q xyz＝Pxyz1 M, where M is the camera's internal matrix of parameters, then/>For the edge point (x i,yi) of the ellipse in step one (i=1, 2..once, n), its homogeneous coordinates [ y i,xi, 1] (i=1, 2..once, n) are constructed, let/>For the optimized objective function, the optimization variables are Coor and VO, and an optimization problem/> isconstructedWherein the symbol is a vector modulo value. For the optimization problem, adopting an interior point method to carry out iterative solution, wherein the obtained optimal value Coor opt and the VO opt are three-dimensional coordinates and plane normal vectors of the target point.
The invention has the advantages and effects that: the method comprises the steps of calculating the space position and plane normal vector of a target under a camera coordinate system based on a single camera and two coplanar circular targets, calculating a target plane normal vector group by adopting projective transformation, obtaining the distance between the center of a target circle and a projection center through the transformation relation between algebraic manifold and affine graph, further obtaining the three-dimensional coordinate of the center of the target circle in the camera coordinate system, decoupling the correct target plane normal vector by utilizing the orthogonal relation between the connecting line of the center of the coplanar target and the target plane, projecting the target onto a camera imaging plane to obtain a calculated projection elliptic equation for the initial value of the obtained target pose, and optimizing the target pose by utilizing the error of a real elliptic edge point on the calculated projection elliptic as a target function. The invention provides a complete analysis form for solving the target position and plane normal vector, can complete the solution within a single millisecond, has the characteristics of high speed and high precision, simultaneously reduces the requirement of measurement on system hardware equipment by adopting a monocular camera, and improves the flexibility and adaptability of the system. The method of cooperative targets is adopted in the system, so that the problem of normal vector decoupling can be solved with high robustness, the accuracy of target plane normal vector calculation can be improved, and the method has wide application prospect in cooperative measurement because the cooperative target configuration scheme is easy to realize in measurement and is a common measurement strategy in actual measurement.
Drawings
Fig. 1 shows an example of an application of the present invention for implementing the description.
FIG. 2 is a schematic diagram of a coordinate system in the method.
Fig. 3a is an original input image of a circular target to be detected for experiment 1.
Fig. 3b is a representation of the result of the calculation based on the invention after projection in an image. Wherein the center of a circle represents the projection of the three-dimensional coordinates on the imaging plane, and the arrow represents the projection of the normal vector on the imaging plane.
Fig. 4a is an original input image of a circular target to be detected for experiment 2.
Fig. 4b is a representation of the result of the calculation based on the present invention after projection in an image. Wherein the center of a circle represents the projection of the three-dimensional coordinates on the imaging plane, and the arrow represents the projection of the normal vector on the imaging plane.
Detailed Description
For a better understanding of the technical solution of the present invention, the following description will further describe the embodiment of the present invention with reference to the specific application example in fig. 1, in which only the target C 1C2 in fig. 1 is processed in the step one to the step three, and other targets are processed in this way. To further demonstrate the effectiveness of the method, we show the results of two experiments of the method in fig. 3 and 4, respectively, wherein fig. 3 (a) and fig. 4 (a) are input images of targets to be detected for the two experiments, respectively, fig. 3 (b) and fig. 4 (b) are center positions and normal vector display diagrams of targets detected by the method for the two experiments,
The method comprises the following specific implementation steps:
step one, solving a target imaging elliptic equation
Given the sequence of imaged elliptical edge point coordinate pair pairs (x i,yi) of target C 1 in fig. 1 (i=1, 2,., n), where x i,yi is the pixel coordinate value of the ith edge point on the horizontal and vertical axes, respectively, and n is 200 in the example. Let the parametric equation of an ellipse be Ax 2+Bxy+Cy2 +dx+ey+f=0, where a=1, [ B, C, D, E, F ] is an unknown quantity. Then there is an equation for any edge point pair (x i,yi)For all edge points, the equation set H [ B, C, D, E, F ] T = -B is available, where/>Using least squares to obtain [ B, C, D, E, F ] T＝-inv(HTH)HT B, where inv (·) is the matrix inversion, let [ a, B, C, D, E, F ] =sign (C) [ a, B, C, D, E, F ], where sign (·) is a sign function, in this example the values of the parameters [ a, B, C, D, E, F ] are [1, -0.042,0.8767, -129.4594, -93.3336, 5657.9]. The parametric equation for an ellipse can be expressed in the form of a quadratic form [ x, y,1] f [ x, y,1] T =0, where/>When the obtained ellipse is degenerated into a circle, namely |F|=0, wherein |·| is matrix determinant operation, and the normal vector of the plane where the circle is located is [0, -1]; if the ellipse is degenerated to be a straight line |F| > 0, the normal vector of the plane where the target is located cannot be obtained; when the ellipse is non-degenerate, i.e., c|F| <0, it is known from C > 0 that |F| <0. When |f|= -1020.2 in this example, the ellipse is non-degenerate. From the parameter equation Ax 2+Bxy+Cy2 +dx+ey+f=0 of the ellipse, the pixel homogeneous coordinate of the ellipse center can BE obtained as po= [ (2 CD-BE)/(B 2-4AC),(2AE-BD)/(B2 -4 AC), 1] = [723.881, 926.8062,1], further, from the camera imaging principle, the back projection ray vector of the target center under the camera projection coordinate system can BE obtained as pv=po x inv (M) = [0.0751, -0.0287,0.9968], wherein the function inv (·) is the matrix inversion operation, and the matrix M is the internal parameter matrix of the camera, in this example
Step two, calculating normal vector of the target plane;
as shown in fig. 2, assuming that the camera projection coordinate system is ozz 1, the corresponding coordinate is denoted as XYZ 1, the coordinate system after the coordinate system is projectively transformed is ozz 2, the corresponding coordinate is denoted as XYZ 2, such that the vector [0, 1] is parallel to the normal vector of the plane in which the circle lies, wherein the photographic transformation is denoted as orthogonal transformation matrix TR, such that XYZ 1＝XYZ2 RT is solved for X 0,y0,z0, θ are respectively unknown variables, andGiven an in-camera parameter matrix M, we can obtain/>, from [ X, y,1] = [ X 1/Z1,Y1/Z1, 1] M and [ X, y,1] f [ X, y,1] T =0The homogeneous equation is algebraic manifold of homogeneous coordinates of the edge points of the target circle under a projective coordinate system OXYZ 1. Algebraic manifold/>, under the projective coordinate system OXYZ 2, of the homogeneous coordinates of the circular edge points can be obtained through projective transformation TRLet MFM T＝QλQT, where Q is the orthogonal matrix,Is a matrix of MFM T eigenvalues, in this exampleFrom |F| < 0 given in step one, it can be seen that |QλQ T|＝|Q|2|λ|＝|MFMT|＝|M|2 |F| < 0, and |λ| < 0, and since F is a quadratic form, λ 1≥λ2＞0＞λ3. TMFM TTT＝(TQ)λ(TQ)T is obtained from above, and the matrix T and Q are orthogonal matrices, and the matrix TQ is also orthogonal matrix, so thatWhere x 2+y2+z2 =1, z+.1, then/> Wherein the value of the symbol-in-place is not used in the method to omit writing. Since the vector [0, 1] is parallel to the normal vector of the plane in which the circle lies in the coordinate system OXYZ 2, the quadratic matrix SλS T is a symmetric matrix and satisfies the system of equations/>Wherein f 1,f2 is the label of the two equations, respectively. Because the equation set contains three unknowns and only two nonlinear equations, the analytic solution of the equation set is solved by adopting a branch-and-bound method. As can be seen from equation f 1, the conditions for establishing them are a combination of four cases of λ 1＝λ2, x=0, y=0, z=0, assuming λ 1＝λ2, λ 1z 2+λ3(x2+y2)＝λ1 is obtained from equation f 2, λ 1(x2+y2)＝λ3(x2+y2 is obtained from x 2+y2+z2 =1), and λ 1＝λ3 is contradictory to λ 1＞λ3 by x 2+y2 +.0, and hence λ 1≠λ2; when x=0, λ 2y2z2+λ3y4＝λ1y2, y+.0 is obtained from equation f 2 (λ 3-λ2)y2＝λ1-λ2, since λ 3-λ2＜0,λ1-λ2 +.0, the equation is not true, x+.0; when z=0, λ 1y2+λ2x2＝λ3 is obtained from equation f 2, and x 2+y2+z2 =1 (λ 2-λ1)x2＝λ3-λ1, namelyNot, so z+.0; when y=0, λ 1x2z2+λ3x4＝λ2x2 can be obtained from equation f 2, which can be obtainedAvailable from x 2+y2+z2 =1,/>In this example x= ±0.4354, z= ± 0.9002. From tq=s, t=sq T, then [ x 0,y0,z0]＝[x,y,z]QT ] has four sets of solutions, since [ x, y, z ] has four sets of solutions, in this example [ x 0,y0,z0 ] of [ x, y, z ] of [0.3599,0, -0.933], [0.3599,0,0.933], [ -0.3599,0, -0.933] and [ -0.3599,0,0.933], the corresponding four sets of [ x 0,y0,z0 ] of solutions are [ -0.1501,0.1428, -0.9783], [0.1501, -0.1428,0.9783], [0.5403,0.2475, -0.8042] and [ -0.5403, -0.2475,0.8042]. Because the vector [ x 0,y0,z0 ] is the coordinate of the normal vector of the plane where the circle is located in the coordinate system OXYZ 2, and the obtuse angle setting is adopted between the normal vector direction and the Z axis direction of the coordinate system, two groups of solutions/>, under the coordinate system OXYZ 1, of the plane vector where the target is located can be obtainedWherein V 1,V2 is the normal vector to the plane in which the target lies, in this example V 1＝[0.5403,0.2475,-0.8042],V2 = [ -0.1501,0.1428, -0.9783]. Order theThen/>
Thirdly, calculating a three-dimensional coordinate of the center of the target;
From the second step, it can be known that the homogeneous coordinates of the circular edge point in the coordinate system OXYZ 2 satisfy algebraic manifold Let XYZ 3＝XYZ2 R have/>Where T is any feasible solution that has been obtained in step two, in this case/>Order theWherein a, c, d, f are parameters, the/>In this example a=1.9198 e7, c= -0.7405e7, d=0, f=0.2855e 7. Obtaining affine graph of the manifold at Z-axis k under coordinate system OXYZ 3 Let/>Affine coordinates of the homogeneous coordinates of the circular edge points on the affine graph are respectively, and/>I.e./> The center coordinates of the circle under affine coordinates can be known as/>The diameter of the circle isSince the target diameter is known to be r, then/>Get/>The radius of the target circle in this example is 25mm. Distance from center of circle to center of coordinate system 0/> In this example d= 3360.9mm. According to the back projection ray vector PV= [0.0753, -0.0288,1] obtained in the step one and the distance d= 3360.9mm from the center of the target to the projection center obtained by the calculation, the three-dimensional coordinate vector/>, under the projection coordinate system, of the target can be obtained
Fourth, target normal vector decoupling
Giving two circular targets C 1,C2 in the same plane, respectively obtaining corresponding imaging elliptic back projection ray vectors PV 1＝[-0.0751,-0.0287,0.9968],PV2 = [ -0.0192, -0.0222,0.9996] according to the calculation of the step one, and obtaining a normal vector group of the corresponding target plane according to the calculation of the step two And calculating according to the third step to obtain a three-dimensional coordinate vector Coor 1＝[-252.3,96.5,3350],Coor2 = [ -66.1, -76.5, 3448.2] of the target under the projection coordinate system. Because the targets C 1,C2 are in the same plane, the real normal vector in the normal vector group V 1,V2 should be perpendicular to the line connecting the centers of the targets C 1,C2, so that CV= Coor 1-Coor2 = [ -186.1665, -20.0332, -98.2164], and the length normalization processing is performed to obtain For vector group V 1,V2 of any one target, respectively finding out the vector closest to 90 degrees with the vector CV as the normal vector of the target, namely:
In this example, VT 1＝0.5403,0.2476,-0.8042,VT2 = 0.6139,0.2319, -0.7546.
Fitting the obtained target normal vector to obtain an optimal target plane normal vector VO by adopting a VT 1、VT2 least square method, wherein VO=min VO(∑i＝1,2(VTi-VO)(VTi-VO)T),
The analytical solution is VO= (VT 1+VT2)/2= [0.5771,0.2398, -0.7794], and the normal vector of the target plane after modulo normalization is VO=VO/|VO|= [0.5777,0.24, -0.7802].
The pose information of the target C 1,C2, namely the center coordinates Coor 1,Coor2, and the normal vector VO they sit on the plane are obtained.
Step five, target pose optimization
For any target C E (C 1,C2) in the fourth step, the calculated initial pose is: three-dimensional coordinates Coor e (Coor 1,Coor2), normal vector VO. Let (x 0,y0,z0)＝VO,TC＝Coor*RT, then the rotation matrix between coordinate system OXYZ 1 and coordinate system OXYZ 2 beLet the coordinate system CXYZ 1 be the coordinate system with the center of the target point as the origin of coordinates and the normal vector of the target point as the Z axis, let the coordinate system CXYZ 2 be the coordinate system with the intersection point of the Z axis of the coordinate system OXYZ 2 and the plane of the target point as the origin and the normal vector of the target point as the Z axis, the coordinates C xyz1,Cxyz2 of the coordinate systems CXYZ 1 and CXYZ 2 satisfy C xyz2＝Cxyz1+TC, wherein T C＝Coor*RT. In the coordinate system CXYZ 1, the target edge point satisfies the equation [ C x1,Cy1,Cz1]F[Cx1,Cy1,Cz1]T =0, where/>R is the radius of the circular target, which is represented in the coordinate system CXYZ 2 asWherein/>Which is expressed in the coordinate system OXYZ 2 as/>Let/>ThenLet P xyz2＝[Px2,Py2,Pz2 ], thenWhich is denoted/>, in CXYZ 1 Let Q xyz＝Pxyz1 M, where M is the camera's internal matrix of parameters, then/>For the edge points (xi, yi) of the ellipse in step one (i=1, 2..once, n), constructing its homogeneous coordinates [ yi, xi,1] (i=1, 2..once, n), let/>For the optimized objective function, the optimization variables are Coor and VO, and an optimization problem/> isconstructedWherein the symbol is a vector modulo value. For the optimization problem, adopting an interior point method to carry out iterative solution, wherein the obtained optimal value Coor opt and the VO opt are three-dimensional coordinates and plane normal vectors of the target point.
The pose of the target point C 1,C2 in this example is respectively ：Coor1＝[-251.3,95.2,3351.1],Coor2＝[-66.3,-76.1,3449.9],VO1＝[0.5765,0.232,-0.7813],VO2＝[0.5765,0.232,-0.7813].
Claims (7)
1. A monocular camera-based circular target pose estimation method is characterized by comprising the following steps of: the method comprises the following steps:
step one, solving a target imaging elliptic equation;
giving an ellipse projected by a circular target, extracting edge points of the ellipse, performing ellipse fitting on the edge points to obtain an ellipse parameter equation, and converting the ellipse parameter equation into a quadratic form;
Step two, calculating a target normal vector;
Transforming the quadratic form under the pixel coordinate system into the quadratic form under the projection coordinate system, and then transforming the quadratic form under the projection coordinate system into the quadratic form under the target coordinate system by constructing an orthogonal transformation matrix containing three variables, wherein the quadratic form has the characteristic of a circle, and solving the constraint to obtain the three variables so as to obtain the normal vector of the plane where the ellipse is located;
Thirdly, calculating a three-dimensional coordinate of the center of the target;
Obtaining an algebraic manifold in a projective coordinate system where a target circle is located according to the orthogonal transformation matrix obtained in the second step, setting a plane where the circle is located as an affine graph of the algebraic manifold, setting that the coordinate of the affine graph on a Z axis is known, obtaining the distance from the center of a circular mark point to the projective coordinate system through calculation, obtaining a back projection ray in the projective coordinate system where the center of the circle is located according to the center point of the projective ellipse and the internal parameter of the camera, and further obtaining the three-dimensional coordinate of the center of the target circle in the projective coordinate system;
fourth, target normal vector decoupling
Respectively calculating normal vectors and three-dimensional coordinates of two coplanar targets through the three steps, calculating the real normal vector of each mark point by utilizing the constraint that the central connecting line of the two target points is perpendicular to the normal vector of the target, and obtaining the optimal normal plane vector of the target through a least square method;
step five, target pose optimization
The initial pose information of the target is obtained through the steps, the ellipse formed by projection of the initial pose and diameter information of the target in a camera is calculated, the error of the ellipse edge point obtained in the step one on the calculated projection ellipse equation is used as an objective function, the three-dimensional coordinate of the target is used as an optimization parameter, and the three-dimensional coordinate of the target with the minimum objective function is obtained by adopting an optimization method; finally, pose information of the round target is obtained.
2. The monocular camera-based circular target pose estimation method of claim 1, wherein: in the first step, specifically: given a sequence of elliptical edge point coordinate pairs (x i,yi), i=1, 2, n; wherein x i,yi is the pixel coordinate value of the ith edge point on the horizontal axis and the vertical axis, and n is the total number of edge pixels; setting the parameter equation of the ellipse as Ax 2+Bxy+Cy2 +Dx+Ey+F=0, wherein A=1, [ B, C, D, E, F ] is an unknown quantity; then there is an equation for any edge point pair (x i,yi)For all edge points, the equation set H [ B, C, D, E, F ] T = -B is derived, where/>Obtaining [ B, C, D, E, F ] T＝-inv(HTH)HT B by adopting a least square method, wherein inv (& gt) is matrix inversion operation, and [ A, B, C, D, E, F ] T＝sign(C)[A,B,C,D,E,F]T is obtained, wherein sign (& gt) is a sign function; the parametric equation for an ellipse is expressed in quadratic form [ x, y,1] f [ x, y,1] T =0, where/>If C|F| is not less than 0, the ellipse is a normal vector of a circle plane where the degraded non-solved mark circle is located, wherein|and| are matrix determinant operations; when the ellipse is non-degenerate, namely C|F| <0, obtaining |F| <0 from C > 0; obtaining a pixel homogeneous coordinate where an ellipse center is located as PO= ((2 CD-BE)/(B 2-4AC),(2AE-BD)/(B2 -4 AC), 1) according to a parameter equation Ax 2+Bxy+Cy2 +Dx+Ey+F=0 of the ellipse, and obtaining a back projection ray vector of a target circle center under a camera projection coordinate system as PV=PO x inv (M) according to a camera imaging principle, wherein a function inv (·) is a matrix inversion operation, and the matrix M is an internal parameter matrix of the camera.
3. The monocular camera-based circular target pose estimation method of claim 1, wherein: in the second step, specifically: setting a camera projection coordinate system as OXYZ 1, wherein the corresponding coordinate is represented as XYZ 1, the coordinate system after projective transformation of the coordinate system is represented as OXYZ 2, and the corresponding coordinate is represented as OXYZ 2, so that vectors [0, 1] are parallel to the normal vector of the plane in which the circle is located; wherein the photographic transformation is represented as an orthogonal transformation matrix TR such that XYZ 1＝XYZ2 RT is solvedX 0,y0,z0, θ are respectively unknown variables, and/>Z 0 is not equal to 0; given an in-camera parameter matrix M, we find/>, from [ X, y,1] = [ X 1/Z1,Y1/Z1, 1] M and [ X, y,1] Fx, y,1] T =0The homogeneous equation is an algebraic manifold of homogeneous coordinates of the round edge points under a projective coordinate system OXYZ 1; algebraic manifold/>, under the projective coordinate system OXYZ 2, of homogeneous coordinates of circular edge points are obtained through projective transformation TRLet MFM T＝QλQT, where Q is the orthogonal matrix,Lambda 1≥λ2≥λ3 is a matrix MFM T eigenvalue matrix, and given |F| < 0 in the step one, |QλQ T|＝|Q|2|λ|＝|MFMT|＝|M|2 |F| < 0 is obtained, and |lambda| < 0 is obtained, and meanwhile, because F is quadratic, lambda 1≥λ2＞0＞λ3 is obtained; TMFM TTT＝(TQ)λ(TQ)T is obtained from above, and matrix T and Q are orthogonal matrices to obtain matrix TQ which is also orthogonal matrix, so thatWhere x 2+y2+z2 =1, z+.1, thenSince the vector [0, 1] is parallel to the normal vector of the plane in which the circle lies in the coordinate system OXYZ 2, the quadratic matrix SλS T is a symmetric matrix and satisfies the system of equations/>Wherein f 1,f2 is the label of each of the two equations; because the equation set contains three unknowns and only two nonlinear equations, the analytic solution of the equation set is solved by adopting a branch-and-bound method.
4. A monocular camera-based circular target pose estimation method according to claim 3, wherein: the conditions for satisfying the equation f 1 are represented by λ 1＝λ2, x=0, y=0, and z=0; let λ 1＝λ2, λ 1z2+λ3(x2+y2)＝λ1 from equation f 2, λ 1(x2+y2)＝λ3(x2+y2 from x 2+y2+z2 =1), and λ 1＝λ3 from x 2+y2 +.0, which contradicts λ 1＞λ3, hence λ 1≠λ2; when x=0, λ 2y2z2+λ3y4＝λ1y2 is obtained from equation f 2, y+.0, and (λ 3-λ2)y2＝λ1-λ2, since λ 3-λ2＜0,λ1-λ2 < 0, the equation is not true, x+.0, and when z=0, λ 1y2+λ2x2＝λ3 is obtained from equation f 2, and x 2+y2+z2 =1, and (λ 2-λ1)x2＝λ3-λ1, namelyNot, so z+.0; when y=0, λ 1x2z2+λ3x4＝λ2x2 is obtained from equation f 2, resulting in/>Obtained from x 2+y2+z2 = 1,Obtaining t=sq T from tq=s, then [ x 0,y0,z0]＝[x,y,z]QT, since [ x, y, z ] has four sets of solutions, the normal vector of the plane in which the target lies [ x 0,y0,z0 ] also has four sets; because the vector [ x 0,y0,z0 ] is the coordinate of the normal vector of the plane where the circle is located in the coordinate system OXYZ 2, and the obtuse angle setting is carried out between the normal vector direction and the Z-axis direction of the coordinate system, two groups of solutions/>, under the coordinate system OXYZ 1, of the plane vector where the target is located are obtainedWherein V 1,V2 is the normal vector of the plane of the target, let/>Then/>
5. The monocular camera-based circular target pose estimation method according to claim 3 or 4, wherein: in the third step, the homogeneous coordinates of the round edge points obtained in the second step in the coordinate system OXYZ 2 satisfy algebraic manifoldLet XYZ 3＝XYZ2 R have/>Wherein T is the feasible solution obtained in the second step, let/>Wherein a, c, d and f are parameters to obtainObtaining affine graph of the manifold at Z-axis k under coordinate system OXYZ 3 Let/>Affine coordinates of the homogeneous coordinates of the circular edge points on the affine graph are respectively, and/>I.e./> Obtaining circle center coordinates of a circle under affine coordinates as/>The diameter of the circle is/>Since the target diameter is known to be r, then/>Get/>Distance from center of circle to center of coordinate system O/>Obtaining a three-dimensional coordinate vector/>, under a projection coordinate system, of the target according to the back projection ray vector PV obtained in the step one and the distance d from the center of the target to the projection center obtained through the calculation
6. The monocular camera-based circular target pose estimation method according to claim 1 or 2 or 5, wherein: in the fourth step, two circular targets C 1,C2 in the same plane are given, corresponding imaging elliptic back projection ray vectors PV 1,PV2 are obtained through calculation according to the first step, normal vector groups V 1,V2 of corresponding target planes are obtained through calculation according to the second step, and three-dimensional coordinate vectors Coor 1,Coor2 of the targets in a projection coordinate system are obtained through calculation according to the third step; because the targets C 1,C2 are in the same plane, the true normal vector in the normal vector group V 1,V2 should be perpendicular to the connecting line of the centers of the targets C 1,C2, so that CV= Coor 1-Coor2, and the length normalization processing is performed to obtainFor vector group V 1,V2 of any one target, respectively finding out the vector closest to 90 degrees with the vector CV as the normal vector of the target, namely: Fitting the obtained target normal vector VT 1,VT2 to obtain an optimal target plane normal vector VO by adopting a least square method, wherein VO=mim VO(∑i＝1,2(VTi-VO)(VTi-VO)T), the analytic solution is VO= (VT 1+VT2)/2, and the target plane normal vector after modulo normalization is VO=VO/|VO|. The center coordinates Coor 1,Coor2 of the target C 1,C2, as well as the normal vector VO of the plane, are obtained.
7. The monocular camera-based circular target pose estimation method of claim 6, wherein: in the fifth step, for any target C e (C 1,C2) in the fourth step, the calculated initial pose is: three-dimensional coordinates Coor e (Coor 1,Coor2), normal vector VO; let (x 0,y0,z0)＝VO,TC＝Coor*RT, then the rotation matrix between coordinate system OXYZ 1 and coordinate system OXYZ 2 beLet the coordinate system CXYZ 1 be the coordinate system with the center of the target point as the origin of coordinates and the normal vector of the target point as the Z axis, let the coordinate system CXYZ 2 be the coordinate system with the intersection point of the Z axis of the coordinate system OXYZ 2 and the plane of the target point as the origin and the normal vector of the target point as the Z axis, then the coordinates C xyz1,Cxyz2 of the coordinate systems CXYZ 1 and CXYZ 2 satisfy C xyz2＝Cxyz1+TC, wherein T C＝Coor*RT; in the coordinate system CXYZ 1, the target edge point satisfies the equation [ C x1,Cy1,Cz1]F[Cx1,Cy1,Cz1]T =0, where/>R is the radius of the circular target, which is represented in the coordinate system CXYZ 2 asWherein/>Which is expressed in the coordinate system OXYZ 2 as/>Let/>ThenLet P xyz2＝[Px2,Py2,Pz2 ], thenWhich is denoted/>, in CXYZ 1 Let Q xyz＝Pxyz1 M, where M is the camera's internal matrix of parameters, then/>For the edge point (x i,yi) of the ellipse in step one (i=1, 2..once, n), its homogeneous coordinates [ y i,xi, 1] (i=1, 2..once, n) are constructed, let/>For the optimized objective function, the optimization variables are Coor and VO, and an optimization problem/> isconstructedWherein the symbol I; for the optimization problem, adopting an interior point method to carry out iterative solution, wherein the obtained optimal value Coor opt and the VO opt are three-dimensional coordinates and plane normal vectors of the target point.
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