CN106815872B - Monocular vision space positioning method based on conical projection transformation - Google Patents

Monocular vision space positioning method based on conical projection transformation Download PDF

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CN106815872B
CN106815872B CN201710011372.8A CN201710011372A CN106815872B CN 106815872 B CN106815872 B CN 106815872B CN 201710011372 A CN201710011372 A CN 201710011372A CN 106815872 B CN106815872 B CN 106815872B
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丁雅斌
梅江平
章点
刘彦敏
贺媛
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Wuhu Irobsys Robot Co ltd
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Abstract

The invention relates to a monocular vision space positioning method based on conical projection transformation, which comprises the following steps: (1) constructing a circular target, wherein black and white color blocks are uniformly alternated in a radial shape, the circle center position is obvious, and the circular radius is known; (2) the camera shoots a circular target under any posture to obtain an image which is an ellipse, and the pixel coordinates of a circumferential point group and the circle center of the ellipse are extracted; (3) according to the circumferential image, establishing an oblique elliptical cone model with the vertex as the optical center of the camera and the bottom edge as the elliptical circumference and equation expression, and further mapping the oblique elliptical cone expression into a straight elliptical cone expression; (4) based on the geometric relation in the straight elliptic cone, the distance between the optical center of the camera and the circle center is obtained by utilizing the radius constraint of the circular target, and the space coordinate of the circle center in the coordinate system of the camera is further obtained by utilizing the circle center constraint. The invention can realize the measurement of the position of the space object by only using one camera, and has strong economy; meanwhile, the spatial position measurement is realized by utilizing the projection transformation of the cone in the space.

Description

Monocular vision space positioning method based on conical projection transformation
Technical Field
The invention relates to the technical field of image positioning methods, in particular to a monocular vision space positioning method based on conical projection transformation.
Background
With the rapid development of sensor technology, computer technology and image processing technology, the vision-based positioning technology is more and more widely applied to the navigation of robots, the target positioning of industrial robots and the virtual reality, and becomes a new subject of rapid development.
The vision system is generally classified into a monocular vision system, which is generally used for two-dimensional measurement due to loss of depth information, and a binocular vision system, which can perform three-dimensional measurement using parallax of two cameras. The monocular vision single image avoids the problem that a plurality of images need to be matched with an algorithm to determine the corresponding relation of the characteristic points, and can be widely applied if the purpose of measuring the three-dimensional pose can be achieved through auxiliary equipment or design. The method is an effective method for measuring the monocular vision three-dimensional pose by taking a geometric figure with known parameters as a positioning target and increasing constraint conditions by utilizing the rule of projection transformation of the geometric figure in space. The standard circle is used as a positioning target, and the calculation of the three-dimensional pose by solving the projection transformation relation of the standard circle in the imaging process is simple in operation and strong in robustness, and has high engineering application value.
Disclosure of Invention
Aiming at the defects of the technology, the invention provides a monocular vision space positioning method based on conical projection transformation.
The monocular vision space positioning method based on conical projection transformation is characterized by specifically comprising the following steps of:
(1) constructing a circular target, uniformly and radially alternating black and white color blocks, enabling the circle center position to be obvious, and obtaining the circular radius in advance;
(2) a camera shoots a circular target at any posture, an obtained image is an ellipse, and pixel coordinates of a circumferential point group and a circle center of the ellipse are extracted;
(3) according to the circumferential image, establishing an oblique elliptical cone model with the vertex as the optical center of the camera and the bottom edge as the elliptical circumference and equation expression, and further mapping the oblique elliptical cone expression into a straight elliptical cone expression;
(4) based on the geometric relation in the straight elliptic cone, the distance between the optical center of the camera and the circle center is obtained by utilizing the radius constraint of the circular target, and the space coordinate of the circle center in the coordinate system of the camera is further obtained by utilizing the circle center constraint.
The method for establishing the oblique elliptical cone model with the vertex being the optical center of the camera and the bottom edge being the elliptical circumference and the equation expression in the step (3) further mapping the oblique elliptical cone expression to the straight elliptical cone expression comprises the following steps:
the image coordinate system is a rectangular coordinate system established by taking pixels as units, and (u)i,vi) The image coordinates of the circle point group are shown, wherein i is 1,2,3.. n, and n is the total number of the circle points; the camera coordinate system is a space coordinate system with the origin at the optical center, an XOY plane established and parallel to the imaging plane and the Z axis as the camera optical axis, and O-X is setcYcZcFor camera coordinate system, let P1To image a plane, let (x)i,yi1) homogeneous camera coordinates obtained by converting image coordinates of a circumferential point group are obtained, the circumferential point group presents an ellipse in an image, an oblique elliptical cone is formed by an optical center of the camera and the circumference of the ellipse, and a generatrix of the oblique elliptical cone is a light projection direction;
mapping the oblique elliptical cone into a straight elliptical cone along the light projection direction, firstly adjustingNode zciThe length of all rays is scaled to equal length α0Obtaining transformed circular point group coordinates (x)ci,yci,zci) Wherein
Figure GDA0002154869740000021
And is
Figure GDA0002154869740000022
α0The mean value of the coordinates of the above-mentioned circle point groups is obtained as the center O of the bottom surface of the straight elliptic cone0；
Then rotating the Z axis of the camera coordinate system to OO0Forming a new camera coordinate system O-Xc'Yc'Zc', grouping the circumferential points in homogeneous coordinates (x)i,yi1) rotoconversion to O-X'cY′cZ′cIn, and adjust z'ciValue of (2), all points Z'cThe axis coordinates are consistent, thus obtaining the transformed circumferential point group coordinates (x'ci,y'ci,z'ci) Wherein z'ci＝χ0The transformed points are all located in the new imaging plane P'1Above, P'1The intersection point with the imaging ray forms an ellipse, and the circumference of the ellipse and the optical center of the camera form a straight elliptic cone.
3. The specific algorithm for solving the space coordinate of the camera in the camera coordinate system based on the geometric relationship in the right elliptic cone and the circular target by utilizing the radius constraint of the circular target in the step (4) and further combining the circle center constraint:
defining the plane formed by the optical center and the ellipse long axis as the long axis plane, the plane formed by the optical center and the ellipse short axis as the short axis plane, O1Is the midpoint of the intersection of the major axis plane and the circular object, O2Is the center of a circle, r is the radius of the circular object, O1O2A, A, B are points of tangency between two generatrixes in the minor axis plane and the circular target, ∠ OAB is γ, α is the base angle of the major axis plane isosceles triangle, β is the base angle of the minor axis plane isosceles triangle, andthe optical center and the major axis of the ellipse form a plane having the following relationship:
Figure GDA0002154869740000031
Figure GDA0002154869740000032
Figure GDA0002154869740000033
after the value of γ is obtained by equations (1) and (2), the OA length is obtained by the sine equation in Δ OAB, and the calculation procedure is as follows:
Figure GDA0002154869740000034
then at Δ OO2In A, the cosine formula is used to obtain OO2The calculation process is as follows:
OO2＝r2+|OA|2-2r|OA|cosγ (4)
solving the OO in the formulas (3) and (4)2According to the camera coordinates (x) of the center of the circle of the circular objecto,yo1) finding the coordinates of the center of a circle in the actual camera coordinate system:
Figure GDA0002154869740000035
the x0From 2 to 5 object distances.
Center O of the bottom surface of the straight elliptic cone0The calculation process of (2) is as follows:
Figure GDA0002154869740000036
Figure GDA0002154869740000041
the circle point group coordinate (x'ci,y'ci,z'ci) The calculation steps of (1) are as follows:
Figure GDA0002154869740000042
Figure GDA0002154869740000043
R＝R2R1(10)
Figure GDA0002154869740000044
Figure GDA0002154869740000045
from point X'cFitting the ellipse can result in:
Figure GDA0002154869740000046
the invention has the beneficial effects that:
compared with the prior art, the invention has the advantages that the object in the space can be positioned only by one camera, thereby having good economy; the pose of the space object is calculated by utilizing the geometric relation of projection transformation of the circle in the space, the calculation is simple, and the calculation time is short.
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The invention is further illustrated with reference to the following figures and examples.
FIG. 1 is a schematic view of the present invention in use;
FIG. 2 is a flow chart of an embodiment of the present invention;
FIG. 3 is a diagram of a computational model of the present invention;
FIG. 4 is a schematic diagram of the spatial projection relationship of the present invention;
FIG. 5 is a schematic of the geometry of the present invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further explained below.
As shown in fig. 1, the hardware involved in implementing the spatial localization method includes a camera 3, a planar target 1, and a circular target 2. Wherein the camera 3 is calibrated, 4 round targets 2 are uniformly fixed on the plane of the space object 1, and the circle center is distributed in a square vertex.
When the method is applied, the camera acquires images of the circular targets, and after the space coordinates of the circular targets are obtained through the method, the space coordinates are fitted into a plane where the circular targets are located, so that the space postures of the circular targets can be obtained.
In the monocular visual space positioning method based on conical projection transformation provided by the invention, a monocular camera shoots a constrained circular target image once, so that the spatial position relationship between the camera and the circular target can be obtained, as shown in fig. 2, the method comprises the following steps:
(1) constructing a circular target, wherein black and white color blocks are uniformly alternated in a radial shape, the circle center position is obvious, and the circular radius is known;
(2) the camera shoots a circular target under any posture to obtain an image which is an ellipse, and the pixel coordinates of a circumferential point group and the circle center of the ellipse are extracted;
(3) establishing an oblique elliptical cone model with the vertex as the optical center of the camera and the bottom edge as the elliptical circumference and equation expression, and then mapping the oblique elliptical cone expression into a straight elliptical cone expression, wherein the specific algorithm is as follows:
rectangular coordinate system (u) established by taking pixel as unit in image coordinate systemi,vi) Is the image coordinate of the circle point group (i is 1,2,3.. n, n is the total number of the circle points), the camera coordinate system is a space coordinate system with the origin at the optical center, the XOY plane is parallel to the imaging plane and the Z axis is the optical axis of the camera, and O-X is setcYcZcAs camera coordinate system, P1Is an imaging plane, (x)i,yi1) homogeneous camera coordinates obtained by converting image coordinates of a circumferential point group, wherein the circumferential point group appears as an ellipse in an image, and the optical center of the camera is equal to that of the cameraThe ellipse forms an oblique elliptical cone, and the generatrix of the oblique elliptical cone is the light projection direction;
mapping the oblique elliptical cone into a straight elliptical cone along the light projection direction, firstly adjusting zciThe length of all rays is scaled to equal length α0Obtaining transformed circular point group coordinates (x)ci,yci,zci) (i.e. the
Figure GDA0002154869740000051
And is
Figure GDA0002154869740000052
α0An arbitrary value other than zero), and the average value of the coordinates of the circumferential point group is determined as the center O of the bottom surface of the straight elliptic cone0The calculation process is as follows:
Figure GDA0002154869740000061
Figure GDA0002154869740000062
then rotating the Z axis of the camera coordinate system to OO0Forming a new camera coordinate system O-X'cY′cZ′cGrouping the homogeneous coordinates (x) of the circumferential pointsi,yi1) rotoconversion to O-X'cY′cZ′cIn, and adjust z'ciValue of (2), all points Z'cThe axis coordinates are consistent, thus obtaining the transformed circumferential point group coordinates (x'ci,y'ci,z'ci) (i.e. z'ci＝χ0，χ0Preferably about 2 to 5 object distances), the transformed points are all located in the new imaging plane P'1Above, P'1The intersection point of the imaging light ray and the imaging light ray forms an ellipse, the ellipse periphery and the optical center of the camera form a straight elliptic cone, and the calculation steps are as follows:
Figure GDA0002154869740000063
Figure GDA0002154869740000064
R＝R2R1
Figure GDA0002154869740000065
Figure GDA0002154869740000066
from point X'cFitting the ellipse can result in:
Figure GDA0002154869740000067
(4) based on the geometric relationship in the right elliptical cone, the distance between the optical center of the camera and the circle center is obtained by utilizing the radius constraint of the circular target, and the space coordinate specific algorithm in the camera coordinate system is further obtained by utilizing the circle center constraint: as shown in FIGS. 4 and 5, the plane formed by the optical center and the ellipse major axis is defined as the major axis plane, the plane formed by the optical center and the ellipse minor axis is defined as the minor axis plane, and O1Is the midpoint of the intersection of the major axis plane and the circular object, O2Is the center of a circle, r is the radius of the circular object, O1O2The distances of (a) and (A, B) are the tangent points between the two generatrices in the minor axis plane and the circular object, respectively, where ∠ OAB is γ, α is the base angle of the isosceles triangle in the major axis plane, and β is the base angle of the isosceles triangle in the minor axis plane, the relationship between the optical center and the major axis of the ellipse is as follows:
Figure GDA0002154869740000071
Figure GDA0002154869740000072
Figure GDA0002154869740000073
after the value of γ is determined by the above formula, the OA length is determined by the sine formula in Δ OAB, and then Δ OO is determined2In A, the cosine formula is used to obtain OO2The calculation process is as follows:
Figure GDA0002154869740000074
OO2＝r2+|OA|2-2r|OA|cosγ
solving the above equation to obtain OO2According to the camera coordinates (x) of the center of the circle of the circular objecto,yo1) finding the coordinates of the center of a circle in the actual camera coordinate system:
Figure GDA0002154869740000075
the first embodiment is as follows:
4 circular objects are arranged on a flat plate in space, and the centers of the 4 circular objects are 4 vertexes of a square with the side length of 50 mm. Fixing the camera, placing the flat plate in the view field of the camera, then rotating the flat plate by 0 degree, 10 degrees, 20 degrees and 30 degrees along any side line respectively, and capturing images of each pose. The coordinates of the obtained circular target and the included angle between two adjacent poses are shown in table 1, the circle center of the circular target in each image can form a square with the side length of about 50mm, the normal included angle between two adjacent poses is 10 degrees, and the method provided by the invention has high reliability according to the structure of table 1.
Table 1 verification of experimental results
0° 10°
Mark 1 (-24.6581，23.8483，150.8) (-25.3319，-23.3091，146.234)
Mark 2 (-25.6738，-25.3295，160.316) (-24.278，24.9297，144.725)
Mark 3 (25.513，-26.2338，166.441) (25.1083，27.3183，156.171)
Mark 4 (24.6698，25.2593，159.465) (26.2765，-24.2031153.063)
Side length (50.1003，51.5607，51.9704，50.1031) (48.2739，50.7516，51.6283，52.066)
Included angle 0° 10.1522°
20° 30°
Mark 1 (-24.0413，-20.0446，131.852) (-23.9375，-12.2803，116.544)
Mark 2 (-23.8324，25.9062，139.387) (-23.5742，29.4638，133.972)
Mark 3 (25.462，29.3033，151.251) (25.493，32.7866，145.712)
Mark 4 (28.1308，-20.6534，142.782) (28.2491，-13.2206，130.999)
Side length (46.5649，50.8157，50.7398，53.3081) (45.2374，50.5613，48.3809，54.1595)
Included angle 9.3908° 10.0179°
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (5)

1. The monocular vision space positioning method based on the cone projection transformation is characterized in that: the method specifically comprises the following steps:
(1) constructing a circular target, uniformly and radially alternating black and white color blocks, enabling the circle center position to be obvious, and obtaining the circular radius in advance;
(2) a camera shoots a circular target at any posture, an obtained image is an ellipse, and pixel coordinates of a circumferential point group and a circle center of the ellipse are extracted;
(3) according to the circumferential image, establishing an oblique elliptical cone model with the vertex as the optical center of the camera and the bottom edge as the elliptical circumference and equation expression, and further mapping the oblique elliptical cone expression into a straight elliptical cone expression;
(4) based on the geometric relation in the straight elliptic cone, the distance between the optical center of the camera and the circle center is obtained by utilizing the radius constraint of the circular target, and the space coordinate of the circle center in a camera coordinate system is further obtained by utilizing the circle center constraint;
the method for establishing the oblique elliptical cone model with the vertex being the optical center of the camera and the bottom edge being the elliptical circumference and the equation expression in the step (3) further mapping the oblique elliptical cone expression to the straight elliptical cone expression comprises the following steps:
the image coordinate system is a rectangular coordinate system established by taking pixels as units, and (u)i,vi) The image coordinates of the circle point group are shown, wherein i is 1,2,3.. n, and n is the total number of the circle points; the camera coordinate system is a space coordinate system with the origin at the optical center, an XOY plane established and parallel to the imaging plane and the Z axis as the camera optical axis, and O-X is setcYcZcFor camera coordinate system, let P1To image a plane, let (x)i,yi1) homogeneous camera coordinates obtained by converting image coordinates of a circumferential point group are obtained, the circumferential point group presents an ellipse in an image, an oblique elliptical cone is formed by an optical center of the camera and the circumference of the ellipse, and a generatrix of the oblique elliptical cone is a light projection direction;
mapping the oblique elliptical cone into a straight elliptical cone along the light projection direction, firstly adjusting zciBy scaling the length of all raysIs of equal length α0Obtaining transformed circular point group coordinates (x)ci,yci,zci) Wherein
Figure FDA0002154869730000011
And is
Figure FDA0002154869730000012
α0The mean value of the coordinates of the above-mentioned circle point groups is obtained as the center O of the bottom surface of the straight elliptic cone0；
Then rotating the Z axis of the camera coordinate system to OO0Forming a new camera coordinate system O-X'cY′cZ′cGrouping the homogeneous coordinates (x) of the circumferential pointsi,yi1) rotoconversion to O-X'cY′cZ′cIn, and adjust z'ciValue of (2), all points Z'cThe axis coordinates are consistent, thus obtaining the transformed circumferential point group coordinates (x'ci,y'ci,z'ci) Wherein z'ci＝χ0The transformed points are all located in the new imaging plane P'1Above, P'1The intersection point with the imaging ray forms an ellipse, and the circumference of the ellipse and the optical center of the camera form a straight elliptic cone.
2. The monocular visual space positioning method based on conical projection transform of claim 1, wherein: the specific algorithm for solving the space coordinate of the camera in the camera coordinate system based on the geometric relationship in the right elliptic cone and the circular target by utilizing the radius constraint of the circular target in the step (4) and further combining the circle center constraint:
defining the plane formed by the optical center and the ellipse long axis as the long axis plane, the plane formed by the optical center and the ellipse short axis as the short axis plane, O1Is the midpoint of the intersection of the major axis plane and the circular object, O2Is the center of a circle, r is the radius of the circular object, O1O2Let A, B be two generatrices in the minor axis plane and a circleFor the target tangent points, let ∠ OAB be γ, α be the base angle of the major axis plane isosceles triangle, and β be the base angle of the minor axis plane isosceles triangle, the following relationships are found in the plane formed by the optical center and the major axis of the ellipse:
Figure FDA0002154869730000021
Figure FDA0002154869730000022
Figure FDA0002154869730000023
after the value of γ is obtained by equations (1) and (2), the OA length is obtained by the sine equation in Δ OAB, and the calculation procedure is as follows:
Figure FDA0002154869730000024
then at Δ OO2In A, the cosine formula is used to obtain OO2The calculation process is as follows:
OO2＝r2+|OA|2-2r|OA|cosγ (4)
solving the OO in the formulas (3) and (4)2According to the camera coordinates (x) of the center of the circle of the circular objecto,yo1) finding the coordinates of the center of a circle in the actual camera coordinate system:
Figure FDA0002154869730000031
3. the monocular visual space positioning method based on conical projection transform of claim 1, wherein: the x0From 2 to 5 object distances.
4. The base of claim 1The monocular vision space positioning method based on the cone projection transformation is characterized in that: center O of the bottom surface of the straight elliptic cone0The calculation process of (2) is as follows:
Figure FDA0002154869730000032
Figure FDA0002154869730000033
5. the monocular visual space positioning method based on conical projection transform of claim 1, wherein: the circle point group coordinate (x'ci,y'ci,z'ci) The calculation steps of (1) are as follows:
Figure FDA0002154869730000034
Figure FDA0002154869730000035
R＝R2R1(10)
Figure FDA0002154869730000036
Figure FDA0002154869730000037
from point X'cFitting the ellipse can result in:
Figure FDA0002154869730000038
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