CN112163309B - Method for rapidly extracting space circle center of single plane circle image - Google Patents
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Abstract
The invention discloses a method for rapidly extracting the spatial circle center of a single plane circle image, which comprises a first step, a second step, a third step and a fourth step. The invention relates to the technical field of vision measurement systems, in particular to a method for quickly extracting the space circle center of a single plane circle image, which aims at solving the problem that the space coordinate extraction precision and efficiency of the current circle center target circle center are low.
Description
Technical Field
The invention relates to the technical field of vision measurement systems, in particular to a method for rapidly extracting the spatial circle center of a single plane circle image.
Background
With the development of computer technology and mapping technology, optical three-dimensional measurement technology is increasingly widely applied, and accurate and rapid extraction of circular target circle center space coordinates in the process is an important aspect affecting measurement accuracy and efficiency.
A plurality of research data show that the current space circle center coordinate extraction mainly depends on a stereoscopic vision method, firstly, an ellipse center is extracted, then, the space circle center coordinate is solved by utilizing a binocular imaging principle, and because the ellipse center is often not a projection point of the space circle center in the perspective projection transformation process, the reconstructed space circle center coordinate has low precision, and particularly, the problem is obvious when facing a large-scale circle center target. Many scholars have proposed various solutions to this problem, which are mainly divided into two categories: firstly, a distortion compensation method is that a mathematical model for circle center compensation is given according to the analysis design of the included angle between a known mark point and an image plane and the distance between the mark point and the image plane, and the extracted circle center of an ellipse is compensated according to the mathematical model; secondly, optimizing the pose by using a nonlinear optimization method, namely shooting two view images, solving the camera pose transformation according to epipolar matching, and then carrying out reprojection of the edge contour according to the initial pose, and constructing a least square model to minimize the edge reprojection error; the document proposes a method for solving the circle center based on a dual quadratic curve, solves the circle center projection vector between any two circle centers according to 3 coplanar mark points, and solves the circle center projection through vector cross multiplication. In general, the current method needs a plurality of view angle pictures or a plurality of mark points to finish the extraction of the three-dimensional coordinates of the center of the circular target, and the precision is unreliable, and particularly, the method is difficult to obtain better effects in the requirements of large-scale circular target positioning application such as robot positioning, circular pipeline measurement and the like.
Disclosure of Invention
In order to solve the existing problems, the invention provides a method for quickly extracting the space circle center of a single plane circle image, which aims at solving the problem that the space coordinate of the current circle center target circle center is low in extraction precision and efficiency, builds a space cone equation by utilizing a camera optical center and an imaging ellipse, builds a cone front bottom surface, solves a parallel plane equation of the space circle according to the front bottom surface, and finally finds a correct space circle equation according to a parallel plane and an actual radius, thereby avoiding the problem of solving the space circle center projection coordinate, solving the space circle center coordinate by only needing a single image, and being stable and reliable.
The technical scheme adopted by the invention is as follows:
the conic curve is a curve obtained by intersecting a plane and a secondary conical surface, the curve has the characteristic of mirror symmetry, and according to the conic curve theory and the imaging model, the following two conclusions are provided:
i. the unique acute angle theta exists, and the conical right bottom surface rotates clockwise and anticlockwise around the long axis by theta to obtain two circular sections;
if the intersection line of the plane A and the cone is a circle, for any plane B parallel to the plane A, if the intersection line exists, the intersection line is a circle.
According to the conclusion, the method for rapidly extracting the space circle center of the single plane circle image comprises the following steps:
step one: constructing a conical right bottom surface;
step two: rotating the plane of the bottom surface around the long axis to find an angle theta with a circular cross section, and recording the plane as alpha;
step three: finding a plane beta which is parallel to alpha and has a cross-sectional circle diameter D;
step four: solving a section circle equation at the moment, and solving a circle center coordinate.
Further, in the first step, constructing the conical right bottom surface includes the following steps:
(1) Solving an elliptic cone equation under a coordinate system:
elliptic cone image coordinate system P-X p Y p Z p The lower elliptic cone equation is
Wherein y= (Y) 0 ,y 1 ,y 2 )，/>
Is a 3 x 3 symmetric matrix->
Is 3 x 1 vector, ">
As scalar, take a= [ a ] ij ]，B＝[b i ]，c＝1，
Since the ellipse is in the XOY plane, then y 2 Is set to be 0, the number of the components is set to be 0,
let Q (Y) =0 at this time may be the following equation:
as can be seen from the standard equation (2) for ellipses,
assuming that the major axis radius of the ellipse is d 0 Short axis radius d 1 ，
Then
The gradient being 0 at the apex of the elliptical cone, i.e
And is also provided with
On the elliptical cone there is +.>
The availability of the combination of formula (1) and formula (2)
At this time
The solution is shown as formula (3):
(2) Solving an elliptic cone equation under a camera coordinate system:
assume that a set of orthonormal basis of an image coordinate system under a camera coordinate system is re= [ Ue Ve Ne]Re can also be considered as a rotation transformation matrix between two coordinate systems, assuming C e For a certain point on the disk surface to be in a camera coordinate system, X is an ellipse coordinate under an image coordinate system, Y is an ellipse coordinate under the camera coordinate system, and the following formula (4) is shown:
the general elliptic cone equation is therefore derived as shown in the following equation (5):
wherein:
assuming that there is a projection plane with origin C p The unit normal vector is N p Constructing the other two orthogonal unit vectors U p And V p The rotation matrix is R p ＝[U p V p N p ]The plane intersects with the elliptical cone, the intersection line is an ellipse,
the point on the ellipse can be defined by X p ＝C p +y2U p +y3，N p ＝C p +J p Y p The elliptic equation is expressed by the following formula (7):
(7) Wherein the method comprises the steps of
The elliptic equation can be reconstructed into the following form:
(Y p -K) T M(Y p -K)＝1 (8)
(8) Wherein the method comprises the steps of
Is the center of the circle coordinate,
SVD decomposition of RDR on M T ＝M，
Where R is a 2 x 2 matrix representing orthogonal basis vectors,
(3) Constructing a right bottom surface:
the symmetry of the elliptical cone is easy to know, and the coneThe connection line between the vertex and the center of the circle of the front bottom surface is necessarily perpendicular to the front bottom surface, and any point c is taken on the projection contour 1 C 1 Line c is the origin 1 E is normal vector direction construction plane pi 1 Intersecting the cone with the ellipse l, and obtaining the center coordinates c according to the algorithm of the steps (1) and (2) 2 Judging the connection line c 2 E is smaller than a threshold value, which is generally E -6 If not, continuing to use c 2 E is the intersection of the normal construction plane and the cone until the right bottom surface is found.
Further, in the second, third and fourth steps, the method solves a circular target plane, and includes the following steps:
s1: the plane alpha intersects with the elliptical cone to form an ellipse, the radius of the long and short axes of the ellipse can be obtained according to the steps in the process of constructing the right and bottom surfaces of the cone in the step one,
the process is perturbed by a minimum increment Δθ as shown in equation (9):
(λ 0 ,λ 1 )＝f(θ+ηΔθ)
wherein η represents a learning rate, and is used to control a disturbance step length, and construct a least squares problem searching parameter θ to minimize a difference between radii of the ellipse long and short axes, as shown in equation (10):
s2: the plane equation when the intersection line is a circle can be obtained through S1, the plane is recorded as beta, the origin is the center coordinate c, the center of a circular target is easy to know and is necessarily on the ray Ec, the center is assumed to be distant from the point c, the point coordinate can be obtained according to linear transformation, the point is taken as the origin to construct a plane beta 'parallel to the plane beta, the diameter D of the circle intersected by the beta' and the elliptical cone is obtained according to the steps in the process of constructing the right bottom surface of the cone in the step one, the diameter D of the circular target is known, and the least square problem can be constructed as shown in the following formula (11) and the formula (12):
d＝f(l+ηΔl) (11)
s3: the correct value is obtained through iteration, and then a space circular target equation and a circle center coordinate are obtained.
The beneficial effects obtained by the invention by adopting the structure are as follows: according to the method for quickly extracting the space circle center of the single plane circle image, aiming at the problem that the current space coordinate extraction precision and efficiency of the circle center target circle center are low, firstly, a space cone equation is built by utilizing a camera optical center and an imaging ellipse, then a cone right bottom surface is built, the space circle equation is solved according to the right bottom surface, finally, a correct space circle equation is found according to a parallel plane and an actual radius, the problem of solving the space circle center projection coordinate is avoided, the space circle center coordinate can be solved only by a single image, the method is stable and reliable, and the method has good practicability in the problems of robot positioning, circular pipeline measurement and the like. The scheme can also be applied to the field of photogrammetry, and the adjustment of the beam method is performed by utilizing the observation data of a plurality of visual angles, so that the measurement accuracy is improved.
Drawings
FIG. 1 is a schematic diagram of a target imaging model of a method for rapidly extracting the spatial center of a single plane circle image;
FIG. 2 is a schematic diagram of the construction front and bottom surfaces of the method for rapidly extracting the spatial circle centers of the single plane circle image;
FIG. 3 is an analysis schematic diagram of learning rate of the method for rapidly extracting spatial circle centers of single plane circle images;
FIG. 4 is a schematic structural diagram of a pipeline surveying instrument and a pipeline detection robot in an embodiment 1 of the method for rapidly extracting the spatial circle center of a single plane circle image;
FIG. 5 is a graph showing the comparison of the results of the pipeline length measurement in example 1 of the method for rapidly extracting the spatial center of a circle of a single plane circle image according to the present invention;
fig. 6 is a schematic diagram of a circular target in embodiment 2 of the method for rapidly extracting the spatial center of a single plane circle image according to the present invention.
FIG. 7 is a graph showing the comparison of the results of the pipe length measurement in example 1 of the method for rapidly extracting the spatial center of a circle of a single plane circle image according to the present invention;
fig. 8 is a schematic diagram of a circular target in embodiment 2 of the method for rapidly extracting the spatial center of a single plane circle image according to the present invention.
The accompanying drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate the invention and together with the embodiments of the invention, serve to explain the invention.
In FIG. 1, the E point is the viewpoint, E-X e Y e Z e The point P is the main point of the camera, and the point P-X is the coordinate system of the camera p Y p Z p Is an image coordinate system; in FIG. 2, c 1 Is the origin, pi 1 Is a straight line c 1 Plane constructed in E normal vector direction, c 2 Is the center coordinates of pi 2 Is a straight line c 2 E, constructing a plane in the normal vector direction; in fig. 6, (a) is a pipe mapper and (b) is a pipe mapping robot; in fig. 7, (a) represents a simulation environment, (b) represents a physical environment, and (c) is a measurement comparison diagram of the simulation environment and the physical environment.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention; all other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1-8, the method for rapidly extracting the spatial circle center of a single plane circle image comprises the following steps:
step one: constructing a conical right bottom surface;
step two: rotating the plane of the bottom surface around the long axis to find an angle theta with a circular cross section, and recording the plane as alpha;
step three: finding a plane beta which is parallel to alpha and has a cross-sectional circle diameter D;
step four: solving a section circle equation at the moment, and solving a circle center coordinate.
In the first step, constructing the conical right bottom surface comprises the following steps:
(1) Solving an elliptic cone equation under a coordinate system:
elliptic cone image coordinate system P-X p Y p Z p The lower elliptic cone equation is
Wherein y= (Y) 0 ,y 1 ,y 2 )，/>
Is a 3 x 3 symmetric matrix->
Is 3 x 1 vector, ">
As scalar, take a= [ a ] ij ]，B＝[b i ]，c＝1，
Since the ellipse is in the XOY plane, then y 2 Is set to be 0, the number of the components is set to be 0,
let Q (Y) =0 at this time may be the following equation:
as can be seen from the standard equation (2) for ellipses,
assuming that the major axis radius of the ellipse is d 0 Short axis radius d 1 ，
Then
The gradient being 0 at the apex of the elliptical cone, i.e
And is also provided with
On the elliptical cone there is +.>
The availability of the combination of formula (1) and formula (2)
At this time
The solution is shown as formula (3):
(2) Solving an elliptic cone equation under a camera coordinate system:
assume that a set of orthonormal basis of an image coordinate system under a camera coordinate system is re= [ Ue Ve Ne]Re can also be considered as a rotation transformation matrix between two coordinate systems, assuming C e For a certain point on the disk surface to be in a camera coordinate system, X is an ellipse coordinate under an image coordinate system, Y is an ellipse coordinate under the camera coordinate system, and the following formula (4) is shown:
the general elliptic cone equation is therefore derived as shown in the following equation (5):
wherein:
assuming that there is a projection plane with origin C p The unit normal vector is N p Constructing the other two orthogonal unit vectors U p And V p The rotation matrix is R p ＝[U p V p N p ]The plane intersects with the elliptical cone, the intersection line is an ellipse,
the point on the ellipse can be defined by X p ＝C p +y2U p +y3，N p ＝C p +J p Y p The elliptic equation is expressed by the following formula (7):
wherein the method comprises the steps of
The elliptic equation can be reconstructed into the following form:
(Y p -K) T M(Y p -K)＝1 (8)
(8) Wherein the method comprises the steps of
Is the center of the circle coordinate,
SVD decomposition of RDR on M T ＝M，
Where R is a 2 x 2 matrix representing orthogonal basis vectors,
λ 0 and lambda (lambda) 1 Respectively representing the long and short axes of the ellipse;
(3) Constructing a right bottom surface:
as apparent from the symmetry of the elliptical cone, the connecting line between the conical point and the center of the circle of the right bottom surface is necessarily perpendicular to the right bottom surface, and any point c is taken on the projection contour 1 C 1 Line c is the origin 1 E is normal vector direction construction plane pi 1 Crossing with each otherConical in ellipse l, and calculating center coordinates c according to the algorithm of the steps (1) and (2) 2 Judging the connection line c 2 E is smaller than a threshold value, which is generally E -6 If not, continuing to use c 2 E is the intersection of the normal construction plane and the cone until the right bottom surface is found.
In the second, third and fourth steps, solving a circular target plane, including the following steps:
s1: the plane alpha intersects with the elliptical cone to form an ellipse, the radius of the long and short axes of the ellipse can be obtained according to the steps in the process of constructing the right and bottom surfaces of the cone in the step one,
the process is perturbed by a minimum increment Δθ as shown in equation (9):
(λ 0 ,λ 1 )＝f(θ+ηΔθ)
wherein η represents a learning rate, and is used to control a disturbance step length, and construct a least squares problem searching parameter θ to minimize a difference between radii of the ellipse long and short axes, as shown in equation (10):
s2: the plane equation when the intersection line is a circle can be obtained through S1, the plane is recorded as beta, the origin is the center coordinate c, the center of a circular target is easy to know and is necessarily on the ray Ec, the center is assumed to be distant from the point c, the point coordinate can be obtained according to linear transformation, the point is taken as the origin to construct a plane beta 'parallel to the plane beta, the diameter D of the circle intersected by the beta' and the elliptical cone is obtained according to the steps in the process of constructing the right bottom surface of the cone in the step one, the diameter D of the circular target is known, and the least square problem can be constructed as shown in the following formula (11) and the formula (12):
d＝f(l+ηΔl) (11)
s3: the correct value is obtained through iteration, and then a space circular target equation and a circle center coordinate are obtained.
In the above steps, the parameter η represents the learning rate, which is generally called a super parameter, the value of which affects the optimization solution of the least square problem, it is easy to know that the least square problem in the circular target plane is a convex optimization problem, so that the extremum can be obtained by using the gradient descent method, and experiments show that when the value is constant, that is, when the least square model is disturbed by a constant step length, the convergence is slower if the value is smaller, and when the value is larger, the oscillation convergence occurs, as shown in fig. 3, and the η can be better attenuated gradually along with the solving process.
As shown in fig. 3-5, the initial descent speed is faster, and the number of iterations is smaller as the decay of the learning rate gradually converges to the minimum value.
Example 1, applied in pipe length measurement:
the device shown in fig. 6 is a pipeline surveying instrument and a pipeline detection robot, the surveying instrument is used for static measurement scenes, the pipeline detection robot is used for pipeline measurement in a narrow space, two measuring devices comprise an illumination device and a camera, the camera is calibrated by an internal reference through a Zhang calibration method, the real pipeline measurement is compared with a three-dimensional simulation environment, the pipeline length is 2m, the caliber of the pipeline is known to be 0.4m, the central coordinates of two circular ports are respectively obtained through algorithm steps in the scheme, the pipeline length is obtained again, the angles are obtained for 20 times, statistical data are obtained as shown in fig. 7, the algorithm can accurately obtain the pipeline length, the actual measurement average error is about 2cm, the actual measurement variance in the data is larger than the simulation environment measurement variance, because the circular target edge noise in the actual environment is more, the extraction precision is lower than that of the simulation environment, and the measured value variance can be reduced through multi-measurement averaging in the actual measurement.
to measure the accuracy of the circle center extraction in this scheme, a marker circle as shown in fig. 8 was used as a target for testing. The radius of the circle to be measured is 5cm, the middle angular point is the actual circle center, images are acquired at different distances when the image plane and the target plane form an included angle of 45 degrees, the sub-pixel coordinates of the angular point are extracted as a reference, the three-dimensional coordinates of the circle center are solved by the scheme and projected to the imaging plane through the camera model to obtain pixel coordinates, and then the sub-pixel coordinates of the circle center of the fitting ellipse are extracted.
The results of the three are shown in table 1 below,
table 1 circle center coordinates comparison results
The difference between the center coordinates extracted by the scheme and the reference coordinates is about 0.1-2 pixels, but the difference between the center of the ellipse and the reference is 5-12 pixels, so that the center coordinates obtained by the method are more accurate and have very small error with the actual coordinates.
The invention and its embodiments have been described above with no limitation, and the actual construction is not limited to the embodiments of the invention as shown in the drawings. In summary, if one of ordinary skill in the art is informed by this disclosure, a structural manner and an embodiment similar to the technical solution should not be creatively devised without departing from the gist of the present invention.
Claims (1)
1. The method for rapidly extracting the space circle center of a single plane circle image is characterized in that a pipeline surveying instrument and a pipeline detection robot are adopted to measure a real object pipeline, the pipeline surveying instrument and the pipeline detection robot both comprise a lighting device and a camera, the camera finishes internal reference calibration by a Zhang's calibration method, and the pipeline length measurement comprises the following steps:
s1: firstly, acquiring a single image by a camera, forming a space cone equation by using a camera optical center and an imaging ellipse, and then constructing a cone right bottom surface;
s2: solving a parallel plane equation of a space circle according to the front bottom surface of the cone;
s3: finally, finding out a correct space circle equation according to the parallel plane and the actual radius;
the establishment of the space circle equation specifically comprises the following steps:
step one: constructing a conical right bottom surface;
step two: rotating the plane of the bottom surface around the long axis to find an angle theta with a circular cross section, and recording the plane as alpha;
step three: finding a plane beta which is parallel to alpha and has a cross-sectional circle diameter D;
step four: solving a section circle equation at the moment, and solving a circle center coordinate;
in the first step, constructing the conical right bottom surface comprises the following steps:
(1) Solving an elliptic cone equation under a coordinate system:
elliptic cone image coordinate system P-X p Y p Z p The lower elliptic cone equation is
Wherein y= (Y) 0 ,y 1 ,y 2 )，/>
Is a 3 x 3 symmetric matrix->
Is 3 x 1 vector, ">
As scalar, take a= [ a ] ij ]，B＝[b i ]C=1, since the ellipse is in XOY plane, then y 2 Let Q (Y) =0 at 0, the following equation can be used:
in the formula (1), Y is an elliptical coordinate under a camera coordinate system, and y= (Y) 0 ,y 1 ,y 2 ) Y in the XOY plane 2 Is 0, A= [ a ] ij ]Simplified to a 2 x 2 matrix, b= [ B ] i ]Reduced to 2* A matrix 1;
as can be seen from the standard equation (2) for ellipses,
in the formula (2), y 0 、y 1 Is the coordinates of the x-axis and the Y-axis of Y in the XOY plane; assuming that the major axis radius of the ellipse is d 0 Short axis radius d 1 ，
Then
The gradient being 0 at the apex of the elliptical cone, i.e
And->
On the elliptical cone there is +.>
The combination of formula (1) and formula (2) is as follows:
at this time
The solution is shown as formula (3):
(2) Solving an elliptic cone equation under a camera coordinate system:
assume that a set of orthonormal bases of an image coordinate system under a camera coordinate system isRe＝[Ue Ve Ne]Re can also be considered as a rotation transformation matrix between two coordinate systems, assuming C e For a certain point on the disk surface to be in a camera coordinate system, X is an ellipse coordinate under an image coordinate system, Y is an ellipse coordinate under the camera coordinate system, and the following formula (4) is shown:
the general elliptic cone equation is therefore derived as shown in the following equation (5):
wherein:
assuming that there is a projection plane with origin C p The unit normal vector is N p Constructing the other two orthogonal unit vectors U p And V p The rotation matrix is R p ＝[U p V p N p ]The plane intersects with the elliptical cone, the intersection line is an ellipse,
the point on the ellipse can be defined by X p ＝C p +y2U p +y3，N p ＝C p +J p Y p The elliptic equation is expressed by the following formula (7):
wherein:
the elliptic equation can be reconstructed into the following form:
(Y p -K) T M(Y p -K)＝1 (8)
wherein the method comprises the steps of
As the center coordinates, carrying out SVD decomposition on M to obtain RDR T =m, where R is a 2×2 matrix representing orthogonal basis vectors, +.>
λ 0 And lambda (lambda) 1 Respectively representing the long and short axes of the ellipse;
(3) Constructing a right bottom surface:
as apparent from the symmetry of the elliptical cone, the connecting line between the conical point and the center of the circle of the right bottom surface is necessarily perpendicular to the right bottom surface, and any point c is taken on the projection contour 1 C 1 Line c is the origin 1 E is normal vector direction construction plane pi 1 Intersecting the cone with the ellipse l, and obtaining the center coordinates c according to the algorithm of the steps (1) and (2) 2 Judging the connection line c 2 E is smaller than a threshold value, which is generally E -6 If not, continuing to use c 2 E is the intersection of a normal construction plane and a cone until a right bottom surface is found;
in the second, third and fourth steps, solving a cross-section circle equation, including the following steps:
s1: the plane alpha intersects with the elliptical cone to form an ellipse, the radius of the long and short axes of the ellipse can be obtained according to the steps in the process of constructing the right and bottom surfaces of the cone in the step one,
the process is perturbed by a minimum increment Δθ as shown in equation (9):
(λ 0 ,λ 1 )＝f(θ+ηΔθ) (9)
wherein η represents a learning rate, and is used to control a disturbance step length, and construct a least squares problem searching parameter θ to minimize a difference between radii of the ellipse long and short axes, as shown in equation (10):
s2: the plane equation when the intersection line is a circle can be obtained through S1, the plane is recorded as beta, the origin is the center coordinate c, the center of a space circle of an easily known target is necessarily on the ray Ec, the center is assumed to be distant from the point c, the coordinate is obtained according to linear transformation, the point is taken as the origin to construct the plane beta 'parallel to the plane beta, the diameter D of the intersection circle of beta' and the elliptical cone is obtained according to the steps in the process of constructing the right bottom surface of the cone in the step one, the diameter of the circle to be obtained is known to be D, and the least square problem can be constructed as shown in the following formula (11) and formula (12):
d＝f(l+ηΔl) (11)
s3: the correct value is obtained through iteration, and then the cross-section circle equation and the circle center coordinate are obtained.
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