CN106651950A - Single-camera pose estimation method based on perspective projection invariance of quadratic curve - Google Patents

Abstract

The invention discloses a single-camera pose estimation method based on perspective projection invariance of a quadratic curve, which comprises the steps of S101, estimating a homography matrix between a camera imaging plane and a space plane object according to corresponding information of the quadratic curve; and S102, solving a rotation matrix and a translation vector in pose parameters according to the homography matrix. According to the invention, the pose is estimated directly on the basis of a quadratic curve equation, so that an error transport chain is shortened, and the robustness of the pose estimation method is improved; and solving for a nonlinear equation set is transformed into solving for a linear equation set, solving is performed without a need of constructing a nonlinear objective optimization function, and solving can be completed in the linear algorithm time complexity O(n).

Description

A kind of one camera position and orientation estimation method based on conic section perspective projection consistency

Technical field

The present invention relates to computer vision field, more particularly to it is a kind of based on the single-phase of conic section perspective projection consistency Seat in the plane orientation estimation method.

Background technology

One camera pose estimation problem is computer vision, one, photogrammetry field is important studies a question.This is asked The basic description of topic can be attributed to：The feature corresponding informance of image space and physical space, solves and determine under two spaces Pose constraint between the different coordinates of justice, that is, estimate rotation parameter and translation parameters.And one camera position and orientation estimation method What accuracy directly influenced the tasks such as the visual pursuit in computer vision research field, photogrammetric, camera calibration completes matter Amount.

Because during planar target perspective projection, point, straight line and conic section have consistency, existing one camera The feature corresponding informance that position and orientation estimation method is adopted mainly has Feature point correspondence, characteristic straight line correspondence and the secondary song of feature Three kinds of line correspondence.For the method for estimation of distinguished point based correspondence, the acquisition of Feature point correspondence information easily receives image The impact of noise and image coordinates extracting method precision, remote-effects have arrived the precision of pose estimation.Document " Fast and Globally Convergent Pose Estimation from Video Images”(C.P.Lu,G.D.Hager,and E.Mjolsness.IEEE Transactions on Pattern Analysis&Machine Intelligence, Vol.22, pp.610-622,2000.) propose that one kind utilizes spin matrix Orthogonal Parameter, set up suitable object function.Should Method estimated accuracy is high, and computational efficiency is high, little to the degree of dependence of initial value.But spin matrix Orthogonal Parameterization is easily subject to defeated Enter the impact of the noise of data, cause its iterative process to be degenerated.Document " EPnP:An Accurate O(n)Solution to the PnP Problem”(V.Lepetit,F.Moreno-Noguer,and P.Fua.International Journal of Computer Vision, vol.81, pp.155-166,2009.), the method is by the actual control point being input into by four virtual controls System point conversion of equal value, and then problem is attributed to estimate coordinate of four virtual controlling points under camera coordinates system, it can be Complete in linear algorithm time complexity O (n), but due to the impact of data noise, the result of many solutions usually occurs.For The method of estimation of feature based line correspondences, the uncertainty of straight length result in and be imaged on image line segment feature with not Certainty, meanwhile, linear feature is relatively simple, it is easy to affected by Noise texture error detection in environment.And compared to straight Line has the conic section of higher order time, such as oval, and its textural characteristics compares straight line, and easily identification is separated from environment texture Out, while in terms of feature extraction, with more sane characteristic.

The content of the invention

It is an object of the invention to by a kind of one camera pose estimation side based on conic section perspective projection consistency Method is mentioned solving the problems, such as background section above.

It is that, up to this purpose, the present invention is employed the following technical solutions：

A kind of one camera position and orientation estimation method based on conic section perspective projection consistency, the method includes following step Suddenly：

S101, according to conic section corresponding informance, estimate the homography between camera imaging plane and space plane object Matrix；

S102, according to the homography matrix, solve the spin matrix and translation vector in pose parameter.

Especially, step S101 includes：The homography matrix refers to point and camera on a two dimensional surface object The mapping relations between picture point on imaging plane；

The perspective projection model of camera is：

Wherein,For on imaging plane under camera coordinates system put homogeneous coordinates, For the homogeneous coordinates put on world coordinate system lower plane object；K is the Intrinsic Matrix of camera, its specifically include principal point coordinate, Focal length parameter, s is scale factor；If the pose parameter that [R t] is transformed under camera coordinates system for world coordinate system；Spin matrix R can carry out the form of column vector to represent, then：

[R t]=[r₁ r₂ r₃ t] (2)

Because object is planar object, thereforeThen formula (1) is expressed as：

IfH=K [r₁r₂T], formula (3) is expressed as

H is the homography of world coordinate system plane and the plane of delineation；

In plane, the algebraic equation of conic section is represented by：

Ax²+Bxy+Cy²+ Dx+Ey+F=0 (5)

Using the form expression formula (5) of matrix, specially：

According to formula (6), the relation of point and quadratic curve equation in planar object on conic section is expressed as formula：

According to conic section perspective projection consistency, perspective projection of the conic section on imaging plane under world coordinate system Imaging is also conic section；In the same manner, according to formula (7), the pass of point and quadratic curve equation on imaging plane on conic section System can be expressed as formula：

Wherein, C ' represents the matrix parameter of imaging plane conic section algebraic equation；

Bring formula (4) into formula (8), can obtain：

Simultaneous formula (7), (9), draw between the conic section in the conic section and imaging plane in world coordinate system Relation, i.e.,：

C=sH^TC'H (10)

Without loss of generality, in the case of two matrix determinants of restriction are worth, (10) are expressed as：

C=H^TC'H (11)

Wherein：Det (H)=1, det (C)=1, det (C')=1.

Especially, step S101 also includes：Two groups of conic section correspondence equation equations in simultaneous same plane, will Homography matrix equation is solved by the linear equation solution of non-linear equation, process is as follows：

If there is n conic section C in space_i, i=1,2,3....n, all of space conic section in one plane, its Corresponding conic section on imaging plane is C_i', i=1,2,3....n, and the n conic section in space is in same generation Under boundary's coordinate system；For two groups of conic section corresponding informances, following equation is set up：

C_i ^-1C_j=H^-1C_i'^-1C_j'H (12)

Can be obtained by formula (12),

C_i'^-1C_j'H-HC_i ^-1C_j=0 (13)

It can be converted into linear equation：

M_ijH=0 (14)

Wherein：H=[H₁₁ H₂₁ H₃₁ H₁₂ H₂₂ H₃₂ H₁₃ H₂₃ H₃₃]^T,

Setting

When conic section corresponding informance number is more than two, the solution of formula (14) should be attributed to determined linear equation The solution of group；The optimal solution of homography matrix is obtained using least square method.

Especially, step S102 includes：The Intrinsic Matrix of camera is K, and homography matrix is H, then：

[r₁ r_{2 t}]=HK^-1 (15)

Because spin matrix is orthogonal matrix, each column vector is all unit vector, and pairwise orthogonal, i.e.,

r₃=r₁×r₂ (16)

Then according to formula (15), the first row column vector of spin matrix, secondary series column vector are solved, and be translated towards Amount；According to formula (16), the first row column vector and secondary series column vector of spin matrix are carried out into multiplication cross computing, obtain spin moment 3rd row column vector of battle array.

One camera position and orientation estimation method based on conic section perspective projection consistency proposed by the present invention is directly secondary Pose is estimated on the basis of curvilinear equation, the transfer chain of error is shortened, the robustness of position and orientation estimation method is improve；To solve Solving Linear is changed into by Solving Nonlinear Systems of Equations, goes to solve without the need for constructing Nonlinear Parameter majorized function, and energy It is enough to complete in linear Algorithms T-cbmplexity O (n).

Description of the drawings

Fig. 1 is the one camera position and orientation estimation method based on conic section perspective projection consistency provided in an embodiment of the present invention Flow chart；

Fig. 2 is the survey rod fast calibration device structural representation estimated based on pose provided in an embodiment of the present invention.

Specific embodiment

For the ease of understanding the present invention, the present invention is described more fully below with reference to relevant drawings.In accompanying drawing Give presently preferred embodiments of the present invention.But, the present invention can be realized in many different forms, however it is not limited to this paper institutes The embodiment of description.On the contrary, the purpose for providing these embodiments is made to the more thorough of the disclosure understanding Comprehensively.It should be noted that when an element is considered as " connection " another element, it can be directly to another Element may be simultaneously present centering elements.Unless otherwise defined, all of technology used herein and scientific terminology with The implication that the those skilled in the art for belonging to of the invention are generally understood that is identical.Made in the description of the invention herein Term is intended merely to describe the purpose of specific embodiment, it is not intended that of the invention in limiting.Term as used herein " and/or " including the arbitrary and all of combination of one or more related Listed Items.

Refer to shown in Fig. 1, Fig. 1 is provided in an embodiment of the present invention based on the single-phase of conic section perspective projection consistency Seat in the plane orientation estimation method flow chart.

In the present embodiment based on conic section perspective projection consistency one camera position and orientation estimation method specifically include it is as follows Step：

S101, according to conic section corresponding informance, estimate the homography between camera imaging plane and space plane object Matrix.

Circular feature 203 as a example by shown in Fig. 2, on the camera plane object 202 of camera 201.Because planar object 202 can Imaging plane can be not parallel to, imaging features may be oval.Oval feature is extracted in shooting image, it is many obtained from Group conic section corresponding informance.

Based on conic section perspective projection consistency, by solving homography matrix, set up single two under world coordinate system Transformational relation between secondary curve algebraic equation matrix and the conic section algebraic equation matrix under corresponding camera coordinates system.

In computer vision, homography matrix be for describing the projection mapping from a plane to another plane, Homography matrix described in this enforcement refers to reflecting between the picture point on point and camera imaging plane on a two dimensional surface object Penetrate relation；

The perspective projection model of camera is：

Wherein,For on imaging plane under camera coordinates system put homogeneous coordinates, For the homogeneous coordinates put on world coordinate system lower plane object；K is the Intrinsic Matrix of camera, its specifically include principal point coordinate, Focal length parameter, s is scale factor；If the pose parameter that [R t] is transformed under camera coordinates system for world coordinate system；Spin matrix R can carry out the form of column vector to represent, then：

[R t]=[r₁ r₂ r₃ t] (2)

Because object is planar object, thereforeThen formula (1) is expressed as：

IfH=K [r₁ r₂T], formula (3) is expressed as

H is the homography of world coordinate system plane and the plane of delineation；

In plane, the algebraic equation of conic section is represented by：

Ax²+Bxy+Cy²+ Dx+Ey+F=0 (5)

Using the form expression formula (5) of matrix, specially：

According to formula (6), the relation of point and quadratic curve equation in planar object on conic section is expressed as formula：

According to conic section perspective projection consistency, perspective projection of the conic section on imaging plane under world coordinate system Imaging is also conic section；In the same manner, according to formula (7), the pass of point and quadratic curve equation on imaging plane on conic section System can be expressed as formula：

Wherein, C ' represents the matrix parameter of imaging plane conic section algebraic equation；

Bring formula (4) into formula (8), can obtain：

Simultaneous formula (7), (9), draw between the conic section in the conic section and imaging plane in world coordinate system Relation, i.e.,：

C=sH^TC'H (10)

Without loss of generality, in the case of two matrix determinants of restriction are worth, (10) are expressed as：

C=H^TC'H (11)

Wherein：Det (H)=1, det (C)=1, det (C')=1.

For homography matrix H is solved, the solution of formula (11) is nonlinear, and the solution of nonlinear equation easily falls into Enter the mistaken ideas of locally optimal solution.

Two groups of conic section correspondence equation equations in simultaneous same plane in the present embodiment, will solve homography matrix side Journey is by the linear equation solution of non-linear equation, and process is as follows：

If there is n conic section C in space_i, i=1,2,3....n, all of space conic section in one plane, its Corresponding conic section on imaging plane is C_i', i=1,2,3....n, and the n conic section in space is in same generation Under boundary's coordinate system；For two groups of conic section corresponding informances, following equation is set up：

C_i ^-1C_j=H^-1C_i'^-1C_j'H (12)

Can be obtained by formula (12),

C_i'^-1C_j'H-HC_i ^-1C_j=0 (13)

It can be converted into linear equation：

M_ijH=0 (14)

Wherein：H=[H₁₁ H₂₁ H₃₁ H₁₂ H₂₂ H₃₂ H₁₃ H₂₃ H₃₃]^T,

Setting

When conic section corresponding informance number is more than two, the solution of formula (14) should be attributed to determined linear equation The solution of group；The optimal solution of homography matrix is obtained using least square method.

S102, according to the homography matrix, solve the spin matrix and translation vector in pose parameter.

The Intrinsic Matrix of camera is K, and homography matrix is H, then：

[r₁ r_{2 t}]=HK^-1 (15)

Because spin matrix is orthogonal matrix, each column vector is all unit vector, and pairwise orthogonal, i.e.,

r₃=r₁×r₂ (16)

Then according to formula (15), the first row column vector of spin matrix, secondary series column vector are solved, and be translated towards Amount；According to formula (16), the first row column vector and secondary series column vector of spin matrix are carried out into multiplication cross computing, obtain spin moment 3rd row column vector of battle array.

Technical scheme directly estimates pose on the basis of quadratic curve equation, shortens the transmission of error Chain, improves the robustness of position and orientation estimation method；Solving Linear, nothing are changed into by Solving Nonlinear Systems of Equations by solving Nonlinear Parameter majorized function need to be constructed to go to solve, and can be completed in linear Algorithms T-cbmplexity O (n).

One of ordinary skill in the art will appreciate that realizing all or part of flow process in above-described embodiment method, can be Related hardware is instructed to complete by computer program, described program can be stored in a computer read/write memory medium In, the program is upon execution, it may include such as the flow process of the embodiment of above-mentioned each method.Wherein, described storage medium can be magnetic Dish, CD, read-only memory (Read-Only Memory, ROM) or random access memory (Random Acces s Memory, RAM) etc..

Note, above are only presently preferred embodiments of the present invention and institute's application technology principle.It will be appreciated by those skilled in the art that The invention is not restricted to specific embodiment described here, can carry out for a person skilled in the art various obvious changes, Readjust and substitute without departing from protection scope of the present invention.Therefore, although the present invention is carried out by above example It is described in further detail, but the present invention is not limited only to above example, without departing from the inventive concept, also More other Equivalent embodiments can be included, and the scope of the present invention is determined by scope of the appended claims.

Claims (4)

1. a kind of one camera position and orientation estimation method based on conic section perspective projection consistency, it is characterised in that including as follows Step：

S101, according to conic section corresponding informance, estimate the homography matrix between camera imaging plane and space plane object；

S102, according to the homography matrix, solve the spin matrix and translation vector in pose parameter.

2. the one camera position and orientation estimation method based on conic section perspective projection consistency according to claim 1, it is special Levy and be, step S101 includes：The homography matrix refers to point and camera imaging plane on a two dimensional surface object On picture point between mapping relations；

The perspective projection model of camera is：

$s\tilde{m}=K\[\begin{array}{cc}R& t\end{array}\]\tilde{P}---\left(1\right)$

Wherein,For on imaging plane under camera coordinates system put homogeneous coordinates,For generation The homogeneous coordinates put on boundary's coordinate system lower plane object；K is the Intrinsic Matrix of camera, and it specifically includes principal point coordinate, focal length Parameter, s is scale factor；If the pose parameter that [R t] is transformed under camera coordinates system for world coordinate system；Spin matrix R can Carry out the form of column vector to represent, then：

[R t]=[r₁ r₂ r₃ t] (2)

Because object is planar object, thereforeThen formula (1) is expressed as：

$s\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=K\[\begin{array}{ccc}{r}_1& r_2& t\end{array}\]\left[\begin{array}{c}X\\ Y\\ 1\end{array}\right]---\left(3\right)$

IfH=K [r₁ r₂T], formula (3) is expressed as

$s\tilde{m}=H\tilde{M}---\left(4\right)$

H is the homography of world coordinate system plane and the plane of delineation；

In plane, the algebraic equation of conic section is represented by：

Ax²+Bxy+Cy²+ Dx+Ey+F=0 (5)

Using the form expression formula (5) of matrix, specially：

$\[\begin{array}{ccc}x& y& 1\end{array}\]\left[\begin{array}{ccc}A& \frac{B}{2}& \frac{D}{2}\\ \frac{B}{2}& C& \frac{E}{2}\\ \frac{D}{2}& \frac{E}{2}& F\end{array}\right]\left[\begin{array}{c}x\\ y\\ 1\end{array}\right]=0---\left(6\right)$

According to formula (6), the relation of point and quadratic curve equation in planar object on conic section is expressed as formula：

${\tilde{M}}^{T}C\tilde{M}=0$

$C=\left[\begin{array}{ccc}A& \frac{B}{2}& \frac{D}{2}\\ \frac{B}{2}& C& \frac{E}{2}\\ \frac{D}{2}& \frac{E}{2}& F\end{array}\right]---\left(7\right)$

According to conic section perspective projection consistency, perspective projection imaging of the conic section on imaging plane under world coordinate system It is also conic section；In the same manner, according to formula (7), the relation of point and quadratic curve equation on imaging plane on conic section can To be expressed as formula：

${\tilde{m}}^T{C}^{\′}\tilde{m}=0---\left(8\right)$

Wherein, C ' represents the matrix parameter of imaging plane conic section algebraic equation；

Bring formula (4) into formula (8), can obtain：

$s{\tilde{M}}^T{H}^T{C}^{\′}H\tilde{M}=0---\left(9\right)$

Simultaneous formula (7), (9), draw the pass between the conic section in the conic section and imaging plane in world coordinate system System, i.e.,：

C=sH^TC'H (10)

Without loss of generality, in the case of two matrix determinants of restriction are worth, (10) are expressed as：

C=H^TC'H (11)

Wherein：Det (H)=1, det (C)=1, det (C')=1.

3. the one camera position and orientation estimation method based on conic section perspective projection consistency according to claim 2, it is special Levy and be, step S101 also includes：Two groups of conic section correspondence equation equations in simultaneous same plane, will solve single answering Property matrix equation is by the linear equation solution of non-linear equation, and process is as follows：

If there is n conic section C in space_i, i=1,2,3....n, all of space conic section in one plane, its into Corresponding conic section in image plane is C_i', i=1,2,3....n, and the n conic section in space sit in the same world Under mark system；For two groups of conic section corresponding informances, following equation is set up：

C_i ^-1C_j=H^-1C_i ^'-1C_j'H (12)

Can be obtained by formula (12),

C_i ^'-1C_j'H-HC_i ^-1C_j=0 (13)

It can be converted into linear equation：

M_ijH=0 (14)

Wherein：H=[H₁₁ H₂₁ H₃₁ H₁₂ H₂₂ H₃₂ H₁₃ H₂₃ H₃₃]^T,

$M_{ij}=\left[\begin{array}{ccccccccc}{A}_{11}-B_{11}& A_{12}& A_{13}& -B_{21}& 0& 0& -B_{31}& 0& 0\\ A_{21}& A_{22}-B_{11}& A_{23}& 0& -B_{21}& 0& 0& -B_{31}& 0\\ A_{31}& A_{32}& A_{33}-B_{11}& 0& 0& -B_{21}& 0& 0& -B_{31}\\ -B_{12}& 0& 0& A_{11}-B_{22}& A_{12}& A_{13}& -B_{32}& 0& 0\\ 0& -B_{12}& 0& A_{21}& A_{22}-B_{22}& A_{23}& 0& -B_{32}& 0\\ 0& 0& -B_{12}& A_{31}& A_{32}& A_{33}-B_{22}& 0& 0& -B_{32}\\ -B_{13}& 0& 0& -B_{23}& 0& 0& A_{11}-B_{33}& A_{12}& A_{13}\\ 0& -B_{13}& 0& 0& -B_{23}& 0& A_{21}& A_{22}-B_{33}& A_{23}\\ 0& 0& -B_{13}& 0& 0& -B_{23}& A_{31}& A_{32}& A_{33}-B_{33}\end{array}\right].$

Setting

When conic section corresponding informance number is more than two, the solution of formula (14) should be attributed to overdetermined linear system Solve；The optimal solution of homography matrix is obtained using least square method.

4. the one camera position and orientation estimation method based on conic section perspective projection consistency according to claim 3, it is special Levy and be, step S102 includes：The Intrinsic Matrix of camera is K, and homography matrix is H, then：

[r₁ r₂T]=HK^-1 (15)

Because spin matrix is orthogonal matrix, each column vector is all unit vector, and pairwise orthogonal, i.e.,

r₃=r₁×r₂ (16)

Then according to formula (15), the first row column vector of spin matrix, secondary series column vector, and translation vector are solved；Root According to formula (16), the first row column vector and secondary series column vector of spin matrix are carried out into multiplication cross computing, obtain spin matrix 3rd row column vector.