CN106815872A - Monocular vision space-location method based on conical projection conversion - Google Patents

Abstract

Monocular vision space-location method the present invention relates to be based on conical projection conversion, comprises the following steps：(1) circular target is constructed, it is characterized by black and white color lump radially uniformly replaces, home position is obvious, known to circular radius；(2) it is ellipse that video camera shoots image obtained by circular target under any attitude, extracts the pixel coordinate in its circumference point group and the center of circle；(3) according to circumference image, summit is set up for video camera photocentre, base is oblique oval Based On The Conic Model and the equation expression in oval week, and then the expression of oblique elliptic cone is mapped as into straight elliptic cone expression；(4) based on the geometrical relationship in straight elliptic cone, the distance of video camera photocentre and the center of circle is tried to achieve using the Radius Constraint of circular target, space coordinates of the center of circle in camera coordinate system is tried to achieve further with center of circle constraint.The present invention can be achieved with the measurement to space object position using only a video camera, economical strong；Spatial position measuring is realized in projective transformation using circular cone in space simultaneously.

Description

Monocular vision space-location method based on conical projection conversion

Technical field

The present invention relates to image position method technical field, the specifically monocular vision based on conical projection conversion is empty Between localization method.

Background technology

With the fast development of sensor technology, computer technology and image processing techniques, the positioning skill of view-based access control model Art has obtained increasingly being widely applied in the navigation of robot, the target positioning of industrial robot and virtual reality, into It is a new discipline for fast development.

Vision system is generally divided into single camera vision system and binocular vision system, and monocular vision is logical due to Damage degree information It is usually used in two-dimensional measurement, binocular vision system can carry out three-dimensional measurement using two parallaxes of video camera.Monocular vision single width figure Matching algorithm is needed to determine the problem of feature point correspondence as avoiding multiple image, if can be reached by auxiliary equipment or design To the purpose of three-dimensional pose measurement, it will be widely used.Using geometric figure known to parameter as positioning target, utilize Geometric figure in space projective transformation rule increase constraints realize three-dimensional pose ask for be monocular vision three-dimensional position The effective ways of appearance measurement.Using standard round as positioning target, by resolving its Transformation Relation of Projection reality in imaging process Show three-dimensional pose asks for simple to operate, strong robustness, with engineering application value very high.

The content of the invention

For the defect of above-mentioned technology, the present invention proposes the monocular vision space-location method based on conical projection conversion.

Monocular vision space-location method based on conical projection conversion, it is characterised in that specifically include following steps：

(1) circular target is constructed, black and white color lump is radially uniformly replaced, and cause home position substantially, and in advance Draw circular radius；

(2) video camera shoots circular target under any attitude, and gained image is ellipse, extracts its circumference point group and the center of circle Pixel coordinate；

(3) according to circumference image, summit is set up for video camera photocentre, base is the oblique oval Based On The Conic Model and equation in oval week Expression, and then the expression of oblique elliptic cone is mapped as straight elliptic cone expression；

(4) based on the geometrical relationship in straight elliptic cone, video camera photocentre and circle are tried to achieve using the Radius Constraint of circular target The distance of the heart, space coordinates of the center of circle in camera coordinate system is tried to achieve further with center of circle constraint.

Summit is set up for video camera photocentre described in step (3), and base is the oblique oval Based On The Conic Model and equation in oval week Expression, and then be by the algorithm that the expression of oblique elliptic cone is mapped as straight elliptic cone expression：

Image coordinate system is the direct coordinate system set up in units of pixel, makes (u_i,v_i) it is the image seat of circumference point group Mark, wherein i=1,2,3...n, n are the total number of circumferential point；Camera coordinate system be origin in photocentre, set up XOY plane, and It is parallel with imaging plane, to set Z axis be the space coordinates of camera optical axis, if O-X_cY_cZ_cIt is camera coordinate system, makes P₁It is into Image plane, makes (x_i,y_i, 1) and the homogeneous camera coordinates that are obtained for the image coordinate of circumference point group is converted, circumference point group is in figure Ellipse is rendered as in, video camera photocentre is light projection with an oblique elliptic cone, the bus of oblique cone is formed ellipse week Direction；

The oblique elliptic cone is mapped as straight elliptic cone along light projecting direction, z is adjusted first_ciValue, by all light Length scale is equal length α₀, the circumference point group coordinate (x after being converted_ci,y_ci,z_ci), whereinAndα₀It is the arbitrary value being not zero, asks for the coordinate average value of above-mentioned circumference point group as straight elliptic cone bottom The center O in face₀；

Then camera coordinate system Z axis are rotated to OO₀, form new camera coordinate system O-X '_cY′_cZ′_c, by circumference Homogeneous coordinates (the x of point group_i,y_i, 1) and rotation transformation is to O-X '_cY′_cZ′_cIn, and adjust z'_ciValue, make have point Z '_cAxial coordinate Unanimously, you can the circumference point group coordinate (x' after must converting_ci,y'_ci,z'_ci), wherein z'_ci=χ₀, then convert after point be all located at New imaging plane P '₁On, P '₁Intersection point with imaging light then forms ellipse, and the oval circumference is formed centrally directly with camera light Elliptic cone.

3rd, described in step (4) based on the geometrical relationship in straight elliptic cone, tried to achieve using the Radius Constraint of circular target Video camera photocentre and the distance in the center of circle, its space coordinates coordinate in camera coordinate system is tried to achieve further combined with center of circle constraint Specific algorithm：

The plane for defining photocentre and transverse formation is long shaft plane, and photocentre is short axle with the plane that ellipse short shaft is formed Plane, O₁It is long shaft plane and the midpoint of circular target intersection, O₂It is the center of circle of circular target, r is the radius of circular target, O₁O₂Distance be a, make the point of contact of two buses and circular target in A, B respectively short axis plane, make ∠ the OAB=γ, α be The base angle of long shaft plane isosceles triangle, β is the base angle of short axis plane isosceles triangle, then formed in photocentre and transverse There is following relation in plane：

After trying to achieve the value of γ using formula (1), formula (2), the length of OA, calculating process are tried to achieve using sine formula in Δ OAB It is as follows：

Again in Δ OO₂In A OO is tried to achieve using cosine formula₂, calculating process is as follows：

OO₂=r²+|OA|²-2r|OA|cosγ (4)

Solution formula (3), formula (4) try to achieve OO₂Distance, according to the camera coordinates (x in the circular target center of circle_o,y_o, 1) and try to achieve circle Coordinate of the heart in actual camera coordinate system：

The χ₀It is 2 times of object distances to 5 times of object distances.

The center O of the straight elliptic cone bottom surface₀Calculating process it is as follows：

The circumference point group coordinate (x'_ci,y'_ci,z'_ci) to ask for calculation procedure as follows:

R=R₂R₁ (10)

Using point X '_cFitted ellipse can be obtained：

The beneficial effects of the invention are as follows：

Compared with prior art, the beneficial effects of the invention are as follows only passing through the thing that video camera can be in located space Body, with good economy；Space object pose is calculated using the geometrical relationship of round projective transformation in space, letter is calculated Single, operation time is short.

Brief description of the drawings

The present invention is further described with reference to the accompanying drawings and examples.

Fig. 1 is use state schematic diagram of the invention；

Fig. 2 is implementing procedure figure of the invention；

Fig. 3 is computation model figure of the invention；

Fig. 4 is space projection relation schematic diagram of the invention；

Fig. 5 is geometrical relationship schematic diagram of the invention.

Specific embodiment

In order that the technological means realized of the present invention, creation characteristic, reached purpose and effect are easy to understand, below it is right The present invention is expanded on further.

As shown in figure 1, realizing that the hardware that the space-location method is related to has video camera 3, plane target 1 and circular mesh Mark 2.Wherein video camera 3 has been demarcated, and 4 circular targets 2 are uniformly fixed in the plane of space object 1, the square top in the center of circle Point distribution.

Using when, the image of camera acquisition circular target, by methods described try to achieve each circular target space sit After mark, the plane where being fitted to circular target, you can try to achieve the spatial attitude of circular target.

In monocular vision space-location method based on conical projection conversion proposed by the present invention, monocular-camera is once clapped Take the photograph the circular target image containing constraint, you can obtain the spatial relation between video camera and circular target, as shown in Fig. 2 Comprise the following steps：

(1) circular target is constructed, it is characterized by black and white color lump radially uniformly replaces, substantially, circle is partly for home position Known to footpath；

(2) it is ellipse that video camera shoots image obtained by circular target under any attitude, extracts its circumference point group and the center of circle Pixel coordinate；

(3) summit is set up for video camera photocentre, and base is oblique oval Based On The Conic Model and the equation expression in oval week, then will be oblique Elliptic cone expression is mapped as straight elliptic cone expression, and specific algorithm is：

The direct coordinate system that image coordinate system is set up in units of pixel, (u_i,v_i) it is the image coordinate (i=of circumference point group 1,2,3...n, n are the total number of circumferential point), camera coordinate system is origin photocentre, XOY plane be parallel with imaging plane, Z Axle is the space coordinates of camera optical axis, if O-X_cY_cZ_cIt is camera coordinate system, P₁It is imaging plane, (x_i,y_i, 1) and it is circle The homogeneous camera coordinates that the image coordinate of all point groups is converted to, circumference point group is rendered as ellipse, camera light in the picture The heart forms an oblique elliptic cone with the ellipse, and tiltedly ellipse element of a cone is light projecting direction；

The oblique elliptic cone is mapped as straight elliptic cone along light projecting direction, z is adjusted first_ciValue, by all light Length scale is equal length α₀, the circumference point group coordinate (x after being converted_ci,y_ci,z_ci) (i.e.Andα₀It is the arbitrary value being not zero), the coordinate average value of above-mentioned circumference point group is asked for as straight elliptic cone bottom The center O in face₀, calculating process is as follows：

Then camera coordinate system Z axis are rotated to OO₀, form new camera coordinate system O-X '_cY′_cZ′_c, by circumference Homogeneous coordinates (the x of point group_i,y_i, 1) and rotation transformation is to O-X '_cY′_cZ′_cIn, and adjust z'_ciValue, make have point Z '_cAxial coordinate Unanimously, you can the circumference point group coordinate (x' after must converting_ci,y'_ci,z'_ci) (i.e. z'_ci=χ₀, χ₀About 2 times object distances are to 5 times of things Away from being preferred), then the point after converting is all located at new imaging plane P₁' on, P₁' ellipse is then formed with the intersection point of imaging light, this is ellipse Circumference then forms straight elliptic cone with video camera photocentre, and calculation procedure is as follows:

R=R₂R₁

Using point X '_cFitted ellipse can be obtained：

(4) based on the geometrical relationship in straight elliptic cone, video camera photocentre and circle are tried to achieve using the Radius Constraint of circular target The distance of the heart, its space coordinates coordinate specific algorithm in camera coordinate system is tried to achieve further with center of circle constraint：As schemed 4th, shown in Fig. 5, the plane for defining photocentre and transverse formation is long shaft plane, and photocentre is short with the plane that ellipse short shaft is formed Axial plane, O₁It is long shaft plane and the midpoint of circular target intersection, O₂It is the center of circle of circular target, r is the radius of circular target, O₁O₂Distance be a, A, B be respectively the point of contact of two buses and circular target in short axis plane, makes ∠ OAB=γ, and α is to grow The base angle of axial plane isosceles triangle, β is the base angle of short axis plane isosceles triangle, then in putting down that photocentre and transverse are formed There is following relation in face：

After the value of γ is tried to achieve using above formula, the length of OA can be tried to achieve using sine formula in Δ OAB, then in Δ OO₂Profit in A OO is tried to achieve with cosine formula₂, calculating process is as follows：

OO₂=r²+|OA|²-2r|OA|cosγ

Solution above formula tries to achieve OO₂Distance, according to the camera coordinates (x in the circular target center of circle_o,y_o, 1) and the center of circle is tried to achieve in reality Coordinate in the camera coordinate system on border：

Embodiment one：

4 circular targets are arranged on the flat board in space, 4 centers of circle of circular target are that the length of side is the foursquare of 50mm 4 summits.Video camera is fixed, flat board is placed in the visual field of video camera, then flat board is distinguished along any one sideline 0 °, 10 °, 20 °, 30 ° of rotation, and capture the image of each pose.The method provided according to the present invention implements each step, gained circle As shown in table 1, the circular target center of circle in each image can shape for angle between the coordinate of shape target and two neighboring pose It is about the square of 50mm into the length of side, the normal direction angle of two neighboring pose is 10 °, and it can be seen from the structure according to table 1, the present invention is carried The method of confession has high reliability.

The confirmatory experiment result of table 1

	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)
			The length of side	(50.1003,51.5607,51.9704,50.1031)	(48.2739,50.7516,51.6283,52.066)
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)
The length of side	(46.5649,50.8157,50.7398,53.3081)	(45.2374,50.5613,48.3809,54.1595)
			Angle	9.3908°	10.0179°

General principle of the invention, principal character and advantages of the present invention has been shown and described above.The technology of the industry Personnel it should be appreciated that the present invention is not limited to the above embodiments, the simply present invention described in above-described embodiment and specification Principle, without departing from the spirit and scope of the present invention, various changes and modifications of the present invention are possible, these change and Improvement is both fallen within claimed invention.The claimed scope of the invention is by appending claims and its equivalent circle. It is fixed.

Claims (6)

1. the monocular vision space-location method for being converted based on conical projection, it is characterised in that：Specifically include following steps：

(1) circular target is constructed, black and white color lump is radially uniformly replaced, and cause home position substantially, and drawn in advance Circular radius；

(2) video camera shoots circular target under any attitude, and gained image is ellipse, extracts the picture in its circumference point group and the center of circle Plain coordinate；

(3) according to circumference image, summit is set up for video camera photocentre, base is the oblique oval Based On The Conic Model and equation table in oval week Reach, and then the expression of oblique elliptic cone is mapped as straight elliptic cone expression；

(4) based on the geometrical relationship in straight elliptic cone, video camera photocentre is tried to achieve with the center of circle using the Radius Constraint of circular target Distance, space coordinates of the center of circle in camera coordinate system is tried to achieve further with center of circle constraint.

2. it is according to claim 1 based on conical projection conversion monocular vision space-location method, it is characterised in that：Step Suddenly summit is set up for video camera photocentre described in (3), base is oblique oval Based On The Conic Model and the equation expression in oval week, and then will The algorithm that oblique elliptic cone expression is mapped as straight elliptic cone expression is：

Image coordinate system is the direct coordinate system set up in units of pixel, makes (u_i,v_i) it is the image coordinate of circumference point group, its Middle i=1,2,3...n, n are the total number of circumferential point；Camera coordinate system be origin in photocentre, set up XOY plane, and with into It is the space coordinates of camera optical axis that image plane is parallel, set Z axis, if O-X_cY_cZ_cIt is camera coordinate system, makes P₁For imaging is flat Face, makes (x_i,y_i, 1) and the homogeneous camera coordinates that are obtained for the image coordinate of circumference point group is converted, circumference point group is in the picture Ellipse is rendered as, video camera photocentre forms an oblique elliptic cone with ellipse week, and the bus of oblique cone is light projecting direction；

The oblique elliptic cone is mapped as straight elliptic cone along light projecting direction, z is adjusted first_ciValue, by the length of all light It is scaled equal length α₀, the circumference point group coordinate (x after being converted_ci,y_ci,z_ci), whereinAndα₀It is the arbitrary value being not zero, asks for the coordinate average value of above-mentioned circumference point group as straight elliptic cone bottom The center O in face₀；

Then camera coordinate system Z axis are rotated to OO₀, form new camera coordinate system O-X '_cY′_cZ′_c, by circumference point group Homogeneous coordinates (x_i,y_i, 1) and rotation transformation is to O-X '_cY′_cZ′_cIn, and adjust z'_ciValue, make have point Z '_cAxial coordinate is consistent, i.e., Circumference point group coordinate (x' after can converting_ci,y'_ci,z'_ci), wherein z'_ci=χ₀, then convert after point be all located at new imaging Plane P₁' on, P₁' ellipse is then formed with the intersection point of imaging light, the oval circumference is formed centrally straight elliptic cone with camera light.

3. it is according to claim 1 based on conical projection conversion monocular vision space-location method, it is characterised in that：Step Suddenly described in (4) based on the geometrical relationship in straight elliptic cone, using the Radius Constraint of circular target try to achieve video camera photocentre with The distance in the center of circle, its space coordinates coordinate specific algorithm in camera coordinate system is tried to achieve further combined with center of circle constraint：

The plane for defining photocentre and transverse formation is long shaft plane, and the plane that photocentre is formed with ellipse short shaft is flat for short axle Face, O₁It is long shaft plane and the midpoint of circular target intersection, O₂It is the center of circle of circular target, r is the radius of circular target, O₁O₂ Distance be a, make the point of contact of two buses and circular target in A, B respectively short axis plane, it is major axis to make ∠ OAB=γ, α The base angle of plane isosceles triangle, β is the base angle of short axis plane isosceles triangle, then the plane for being formed in photocentre and transverse In have following relation：

$\mathrm{\α}=\frac{\mathrm{\π}}{2}-\arctan \mathrm{\σ}/{\mathrm{\α}}_0$

$\mathrm{\β}=\frac{\mathrm{\π}}{2}-\arctan \mathrm{\τ}/{\mathrm{\α}}_0---\left(1\right)$

$\left\{\begin{array}{c}\frac{cos\mathrm{\β}}{r+a}=\frac{sin\mathrm{\γ}}{\sqrt{r^2-a^2}tan\mathrm{\α}}\\ \frac{cos\mathrm{\β}}{r-a}=\frac{sin(2\mathrm{\β}-\mathrm{\γ})}{\sqrt{r^2-a^2}\tan \mathrm{\α}}\end{array}\right.---\left(2\right)$

After trying to achieve the value of γ using formula (1), formula (2), the length of OA is tried to achieve using sine formula in Δ OAB, calculating process is as follows：

$\frac{2r}{sin(\mathrm{\π}-2\mathrm{\β})}=\frac{\left|OA\right|}{sin(2\mathrm{\β}-\mathrm{\γ})}---\left(3\right)$

Again in Δ OO₂In A OO is tried to achieve using cosine formula₂, calculating process is as follows：

OO₂=r²+|OA|²-2r|OA|cosγ (4)

Solution formula (3), formula (4) try to achieve OO₂Distance, according to the camera coordinates (x in the circular target center of circle_o,y_o, 1) try to achieve the center of circle and exist Coordinate in actual camera coordinate system：

$\left[\begin{array}{c}{X}_o\\ Y_o\\ Z_o\end{array}\right]=\frac{\left|{\mathrm{OO}}_1\right|}{\sqrt{x_o^2+y_o^2+1}}\left[\begin{array}{c}{x}_o\\ y_o\\ 1\end{array}\right]---\left(5\right).$

4. it is according to claim 2 based on conical projection conversion monocular vision space-location method, it is characterised in that：Institute State χ₀It is 2 times of object distances to 5 times of object distances.

5. it is according to claim 2 based on conical projection conversion monocular vision space-location method, it is characterised in that：Institute State the center O of straight elliptic cone bottom surface₀Calculating process it is as follows：

$X_i^c=\sqrt{{\mathrm{\α}}_0^2/(x_i^2+y_i^2+1)}\×{\left[\begin{array}{ccc}{x}_i& y_i& 1\end{array}\right]}^{\′}={\left[\begin{array}{ccc}{x}_{ci}& y_{ci}& z_{ci}\end{array}\right]}^{\′}---\left(6\right)$

$X_{O_1}=\frac{{\mathrm{\Σ}}_{i=1}^n{X}_i^c}{n}={\left[\begin{array}{ccc}{\stackrel{\‾}{x}}_c& {\stackrel{\‾}{y}}_c& {\stackrel{\‾}{z}}_c\end{array}\right]}^{\′}---\left(7\right).$

6. it is according to claim 2 based on conical projection conversion monocular vision space-location method, it is characterised in that：Institute State circumference point group coordinate (x'_ci,y'_ci,z'_ci) to ask for calculation procedure as follows:

$\begin{array}{cc}\mathrm{\α}=atan2({\stackrel{\‾}{y}}_c,{\stackrel{\‾}{z}}_c)& \mathrm{\β}=atan2({\stackrel{\‾}{x}}_c,{\stackrel{\‾}{y}}_{c}sin\mathrm{\α}+\stackrel{\‾}{z_c}cos\mathrm{\α})\end{array}---\left(8\right)$

$\begin{array}{cc}{R}_1=\left[\begin{array}{ccc}1& 0& 0\\ 0& \cos \mathrm{\α}& -sin\mathrm{\α}\\ 0& \sin \mathrm{\α}& \cos \mathrm{\α}\end{array}\right]& R_2=\left[\begin{array}{ccc}cos\mathrm{\β}& 0& -sin\mathrm{\β}\\ 0& 1& 0\\ sin\mathrm{\β}& 0& \cos \mathrm{\β}\end{array}\right]\end{array}---\left(9\right)$

R=R₂R₁ (10)

${\hat{X}}_c=R{\left[\begin{array}{ccc}{x}_i& y_i& 1\end{array}\right]}^{\′}---\left(11\right)$

$X_c^{\′}=\frac{{\hat{X}}_c}{{\hat{X}}_{c3}}{\mathrm{\χ}}_0={\left[\begin{array}{ccc}{x}_{ci}^{\′}& y_{ci}^{\′}& z_{ci}^{\′}\end{array}\right]}^{\′}---\left(12\right)$

Using point X_c' fitted ellipse can obtain：

$\frac{{\mathrm{\μ}}^2}{{\mathrm{\σ}}^2}+\frac{{\mathrm{\δ}}^2}{{\mathrm{\τ}}^2}=1---\left(13\right).$