CN101813465A - Monocular vision measuring method of non-contact precision measuring corner - Google Patents

Abstract

The invention discloses a monocular vision measuring method of a non-contact precision measuring corner, belonging to the technical field of photoelectric detection and aiming at realizing wider measuring range, high measuring precision and more convenient operation. Based on a monocular vision principle, the method comprises the following steps of: fixing a test target with a double-circle sign on an object to be measured parallel to a rotating shaft; photographing a target surface by using a position-fixed digital camera; selecting a group of characteristic points and characteristic parameters of an image surface to establish a set of computing method and formula for solving the corner by taking an image of the double-circle sign as an oval; processing photos by using a sub-pixel processing method, solving an equation of an image surface oval and image surface coordinates of the characteristic points and solving a plane equation of the target surface and a corner of the object to be measured; accurately solving the position of an image point in the center of a circle without marking the position of the center of a circle of the target surface; and correcting a measuring error caused by unparallel relations of the target surface and the rotating shaft by using data obtained in the measuring process. The invention has the advantages of simple installation and adjustment of equipment, high measuring precision, high practicability and capability of being used for marking angular displacement transducers such as a rudder, a horizontal rudder of an aircraft and the like on site of an airport.

Description

Non-contact precision is surveyed the monocular vision measuring method of corner

Technical field

The present invention relates to a kind of non-contact precision and survey the monocular vision measuring method of corner, belong to photoelectric detection technology field.

Background technology

In fields such as Aeronautics and Astronautics and navigations, often need use method and technology that the big non-contact precision of measurement range is surveyed corner.For example, when development type aircraft or production aircraft, after aircraft completes, need take a flight test to detect its flying quality.For obtaining performance test data accurately, before taking a flight test, need the angular displacement sensor of aileron, wing flap, diving rudder and yaw rudder on airport on-site proving aircraft.Because in the process of this demarcation, do not allow the inner structure of aircraft is done any change, so will use non-contacting measuring method.Document " based on the high precision face inside lock measuring method of digital picture " (Chinese Industrial Standards (CIS) number of the edition CN31-1252/04 " optics journal " in April, 2005,25 (4)) reported that a kind of non-contact precision surveys the method for corner, under breadboard experiment condition, the precision of surveying corner can reach 5 ", the angle measurement scope is 0 °～360 °.This method is based on the computer monocular vision principle, and the sign that adopts straight-line segment to do target surface is made the test target, will test target during measurement and be fixed on the testee, requires the target surface while strictly perpendicular to the rotating shaft of the primary optical axis and the object under test of camera.When this method is used for yaw rudder angular displacement sensor on airport on-site proving aircraft, owing to be difficult to the accurate position and the definite direction of the central shaft of definite rudder of aircraft rotating shaft at the scene, make that the installation adjusting of its measuring equipment will be very difficult, be difficult to reach requirement, make that also being difficult to revise its equipment installs caused measuring error not in place, its practicality is very poor.Also there is same problem in the method that the non-contact precision that existing other measurement ranges are big is surveyed corner.For solving these difficult problems, we had once studied a kind of method of surveying corner based on the non-contact precision of computer monocular vision.(" demarcating the vision measurement method of rudder of aircraft angular displacement " Chinese Industrial Standards (CIS) number of the edition CN51-1346/04 " photoelectric project " Dec 36 (12) in 2009).This method adopts the center of circle of three circles of coplane to do the outstanding feature of target surface, and its circumference is done auxiliary sign.At the characteristics of three circle signs at the picture of image planes, design digital picture sub-pix disposal route and handled photo in real time, the accuracy of surveying corner is than higher (do not counting under the situation that camera becomes phase error effect and other interference, computer simulation experiment result is better than 0.01 °); Survey angle range big (± 85 °), measuring equipment is installed and is regulated easily, has tentatively solved problem.But the texture ratios of three circle signs are than complex loose, and will accurately indicate the home position of each circle with the intersection point that intersects two straight-line segments, make that the Digital Image Processing difficulty is big, and the processing time is long; Because adopt the method for " determining a plane " to ask the plane equation of target surface at 3, this method anti-jamming capacity is not strong, measuring accuracy is not high enough; Especially, the angle of the normal of target surface and the primary optical axis of camera is during near 0 °, and its measuring error enlarges markedly; This method also must be known the centre distance of camera pixel, just can obtain required result during data processing.Do not having under the situation of photogrammetric special-purpose digital camera, when measuring with ordinary digital camera, the general centre distance that is difficult to accurately know camera pixel must be obtained the intrinsic parameter of camera through complicated, accurate demarcation, and its use is convenient not enough.

Summary of the invention

The objective of the invention is for overcoming the deficiency of above-mentioned prior art, provide that a kind of measurement range big (± 85 °), measuring accuracy height (being better than 0.005 °), Digital Image Processing are easier to, measuring equipment install regulate simpler, use non-contact precision more easily to survey the monocular vision measuring method of corner.

The inventive method is:

(1) do the target surface sign with the two with one heart round circumference of coplane and make the test target, be referred to as two circle targets, the rotating shaft that is parallel to object under test is fixed on this object under test.

(2) with the digital camera of a stationkeeping two round targets are taken pictures, when taking pictures, only require target surface in the apparent field of camera, the relative position attitude of camera and target surface is not had strict requirement, make that the installation site of camera is very flexible, regulate very simple.The view data of digital camera sends Computer Processing to by USB interface.

(3) picture according to two circle signs is oval characteristics, the end points, " characteristic diameter " of selecting the image planes ellipse short shaft as end points and the picture point in the center of circle as a group of feature point of image planes, the long stack features parameter of the picture of their image coordinates and characteristic diameter as image planes.

Said " characteristic diameter " refers to: suppose to do a plane parallel with image planes by the center of circle of this circle, this plane and the intersection of circle are called the characteristic diameter of this circle.Therefore, characteristic diameter is parallel with image planes, can be used to simplify and accelerates to ask the computation process of image planes unique point in the former picture point of target surface.

Character according to pin-hole imaging principle and similar triangles, utilize the characteristic diameter characteristics parallel with image planes, based on a correspondence and straight line correspondence, set up and asked the formula of image planes unique point at the world coordinates of the former picture point of target surface, obtain the world coordinates of corresponding former picture point, obtain the plane equation of target surface:

1. calculate the world coordinates (x of the center of circle C of two circle signs _C, y _C, z _C) formula:

$\left\{\begin{array}{c}{x}_C=X_{C}d{R}_1/r_{1}d=X_C{R}_1/r_1;\\ y_C=Y_{C}d{R}_1/r_{1}d=Y_C{R}_1/r_{1_1};\\ z_C=F{R}_1/r_{1}d=\mathrm{fd}{R}_1/r_{1}d=f{R}_1/r_1\end{array}\right.$

Wherein: R ₁Be the little radius of a circles of two circle signs, X _C, Y _CBe the image coordinates of center of circle picture point C ', d is the centre distance of camera pixel, r ₁Be to be that the picture of characteristic radius of roundlet of unit representation is long with the pixel, F is the focal length of camera, f=F/d.The image coordinates of putting on the image planes is unit representation with the pixel.

2. calculated characteristics diameter terminal A ₁, A ₂World coordinates (x _A1, y _A1, z _A1), (x _A2, y _A2, z _A2) formula:

$\left\{\begin{array}{ccc}{x}_{A1}=\frac{R_1}{r_1}\·X_{A1},& y_{A1}=\frac{R_1}{r_1}\·Y_{A1},& z_{A1}=z_C\\ x_{A2}=\frac{R_1}{r_1}\·X_{A2},& y_{A2}=\frac{R_1}{r_1}\·Y_{A2},& z_{A2}=z_C\end{array}\right.$

Wherein: X _A1, Y _A1, X _A2, Y _A2Be respectively A ₁, A ₂Picture point A ' ₁, A ' ₂Image coordinates.

Use the same method and obtain calculating A ₃(x _A3, y _A3, z _A3), A ₄(x _A4, y _A4, z _A4) formula.

3. ask image planes ellipse short shaft terminal B ' ₁, B ' ₂Former picture point B at target surface ₁, B ₂World coordinates (x _B1, y _B1, z _B1), (x _B2, y _B2, z _B2) formula:

According to the corresponding relation of each point shown in Figure 3, utilize the character of similar triangles, and relational expression

Try to achieve: z ₁/ z ₂=r ₁₂/ r ₁₁

$\left\{\begin{array}{ccc}{x}_{B1}=\frac{2r_{12}{R}_1}{(r_{11}+r_{12})r_1}{X}_{B1},& y_{B1}=\frac{2r_{12}{R}_1}{(r_{11}+r_{12})r_1}{Y}_{B1},& z_{B1}=\frac{2r_{12}{R}_1}{(r_{11}+r_{12})r_1}f\\ x_{B2}=\frac{2r_{11}{R}_1}{(r_{11}+r_{12})r_1}{X}_{B2},& y_{B2}=\frac{2r_{11}{R}_1}{(r_{11}+r_{12})r_1}{Y}_{B2},& z_{B2}=\frac{2r_{11}{R}_1}{(r_{11}+r_{12})r_1}f\end{array}\right.;$

$f=F/d=\sqrt{{\left(\frac{r_{11}+r_{12}}{r_{11}-r_{12}}{r}_1\right)}^2-\frac{{(r_{11}{X}_{B2}-r_{12}{X}_{B1})}^2+{(r_{11}{Y}_{B2}-r_{12}{Y}_{B1})}^2}{{(r_{11}-r_{12})}^2}}$

X wherein _B1, Y _B1, X _B2, Y _B2Be respectively B ₁, B ₂Picture point B ' ₁, B ' ₂Image coordinates; C ', B ' ₂Distance C ' the B ' of point-to-point transmission ₂=r ₁₂D; B ' ₁, C ' point-to-point transmission apart from B ' ₁C '=r ₁₁D; r ₁₁, r ₁₂Be to be the distance of corresponding point-to-point transmission on the image planes of unit representation with the pixel.

Use the same method to obtain and calculate B ₃(x _B3, y _B3, z _B3), B ₄(x _B4, y _B4, z _B4) formula.

From above-mentioned 1. to 3. computing formula as seen, if known d and F then ask the formula of the world coordinates of corresponding former picture point according to the image coordinates of unique point, all be simple one to one and accurate linear functional relation formula.Compare with other monocular vision measuring method, the calculating of this method not only simply but also accurate.

If can't know F and d, also can obtain f according to the characteristic parameter of image planes, obtain required result, the scheme that has overcome existing three circle targets must know that the pixel center of camera is apart from the shortcoming that just can obtain required result.

4. obtain the direction cosine of the plane equation and the normal thereof of target surface:

If the plane equation of target surface is ax+by+cz=1.Set up objective function:

Q＝∑(Ax _i+By _i+Cz _i-1) ²

Order

Set up equation

$\left[\begin{array}{ccc}\mathrm{\Σ}{x}_i^2& \mathrm{\Σ}{x}_i{y}_i& \mathrm{\Σ}{x}_i{z}_i\\ \mathrm{\Σ}{x}_i{y}_i& \mathrm{\Σ}{y}_i^2& \mathrm{\Σ}{y}_i{z}_i\\ \mathrm{\Σ}{x}_i{z}_i& \mathrm{\Σ}{y}_i{z}_i& \mathrm{\Σ}{z}_i^2\end{array}\right]\left[\begin{array}{c}a\\ b\\ c\end{array}\right]=\left[\begin{array}{c}\mathrm{\Σ}{x}_i\\ \mathrm{\Σ}{y}_i\\ \mathrm{\Σ}{z}_i\end{array}\right]$

With the C that has obtained on the target surface, A ₁, A ₂, A ₃, A ₄, B ₁, B ₂, B ₃, B ₄The above-mentioned equation of world coordinates substitution of 9 points is obtained the parameter a of the plane equation of target surface, b, and c, then the direction cosine of target surface normal are:

$\cos \mathrm{\α}=\frac{a}{\sqrt{a^2+b^2+c^2}},$ $\cos \mathrm{\β}=\frac{b}{\sqrt{a^2+b^2+c^2}},$ $\cos \mathrm{\γ}=\frac{c}{\sqrt{a^2+b^2+c^2}}.$

Adopt this computing method, its anti-jamming capacity is strong, and the computational solution precision height is important measures that improve measuring accuracy, is that its measuring accuracy is better than one of reason that has now three circle target schemes.

So, utilize the known radius of characteristic parameter and two circle signs of image planes, need not know the pixel center distance of camera and the real focal length of camera when taking pictures, also can obtain the direction cosine of the plane equation and the target surface normal of target surface.Therefore, do not having photogrammetric special-purpose digital camera, and, adopting ordinary digital camera can measure yet without complicated accurate demarcation under the yet not really high situation of the requirement of measuring accuracy.This method is convenient to the penetration and promotion application.

(4) according to the feature of the oval image of image planes, designed special-purpose digital picture sub-pix disposal route, be used for handling in real time pair digital photos of circle targets, obtain the equation of image planes ellipse, obtain the image coordinates of ellipse short shaft end points, obtain image coordinates and the endpoint location of characteristic diameter picture and the picture length of characteristic diameter of center of circle picture point again.Method is as follows:

1. ask the equation of image planes ellipse

Two circles indicate the picture in image planes, the corresponding ellipse of each circle.During Digital Image Processing, ask its oval equation respectively.If the image planes elliptic equation is X ²+ BXY+CY ²+ DX+EY+F=0.

Set up objective function: $Q=\mathrm{\Σ}{(X_i^2+{\mathrm{BX}}_i{Y}_i+{\mathrm{CY}}_i^2{+\mathrm{DX}}_i+{\mathrm{EY}}_i+F_i)}^2.$

Order: Set up equation:

$\left[\begin{array}{ccccc}\mathrm{\Σ}{X}_i^2{Y}_i^2& \mathrm{\Σ}{X}_i{Y}_i^3& \mathrm{\Σ}{X}_i^2{Y}_i& \mathrm{\Σ}{X}_i{Y}_i^2& \mathrm{\Σ}{X}_i{Y}_i\\ \mathrm{\Σ}{X}_i{Y}_i^3& \mathrm{\Σ}{Y}_i^4& \mathrm{\Σ}{X}_i{Y}_i^2& \mathrm{\Σ}{Y}_i^3& \mathrm{\Σ}{Y}_i^2\\ \mathrm{\Σ}{X}_i^2{Y}_i& \mathrm{\Σ}{X}_i{Y}_i^2& \mathrm{\Σ}{X}_i^2& \mathrm{\Σ}{X}_i{Y}_i& \mathrm{\Σ}{X}_i\\ \mathrm{\Σ}{X}_i{Y}_i^2& \mathrm{\Σ}{Y}_i^3& \mathrm{\Σ}{X}_i{Y}_i& \mathrm{\Σ}{Y}_i^2& \mathrm{\Σ}{Y}_i\\ \mathrm{\Σ}{X}_i{Y}_i& \mathrm{\Σ}{Y}_i^2& \mathrm{\Σ}{X}_i& \mathrm{\Σ}{Y}_i& N\end{array}\right]\left[\begin{array}{c}B\\ C\\ D\\ E\\ F\end{array}\right]=-\left[\begin{array}{c}\mathrm{\Σ}{X}_i^3{Y}_i\\ \mathrm{\Σ}{X}_i^2{Y}_i^2\\ \mathrm{\Σ}{X}_i^3\\ \mathrm{\Σ}{X}_i^2{Y}_i\\ \mathrm{\Σ}{X}_i^2\end{array}\right]$

Adopt digital picture sub-pix disposal route, obtain this equation of image coordinates substitution of tens points on one of them oval circumference of image planes, obtain this elliptic equation B parameter, C, D, E, F, obtain this oval equation, obtain the image coordinates of this ellipse short shaft end points again.Use the same method and handle another ellipse, obtain required result.

2. ask the image coordinates X of center of circle picture point C ' _C, Y _C:

Keeping collinear point according to interplanar central projection still be collinear point, the double ratio that conllinear is 4 character such as remain unchanged, and the minor axis terminal B of two ellipses of selection image planes ' ₁(X _B1, Y _B1), B ' ₂(X _B2, Y _B2), B ' ₃(X _B3, Y _B3), B ' ₄(X _B4, Y _B4) in any 3 and center of circle picture point C ' (X _C, Y _C), all can set up the double ratio relational expression of asking center of circle image point position, can set up the double ratio relational expression of 4 equivalences altogether.For reducing measuring error, the double ratio relational expression of available 4 equivalences is obtained the image coordinates of C ' respectively, is used for obtaining X again _CAnd Y _CMean value.To select B ' ₁, B ' ₂, B ' ₄And C ' is example, sets up the double ratio relational expression:

R wherein ₂=2R ₁Set when being design.Set up the image coordinates X that following equation is obtained center of circle picture point C ' according to following formula _C, Y _C:

$\frac{(X_{B1}-X_C)}{(X_{B2}-X_C)}/\frac{(X_{B1}-X_{B4})}{(X_{B2}-X_{B4})}=\frac{(X_{B1}-X_C)(X_{B2}-X_{B4})}{(X_{B2}-X_C)(X_{B1}-X_{B4})}=\frac{3}{2}$

$\frac{(Y_{B1}-Y_C)}{(Y_{B2}-Y_C)}/\frac{(Y_{B1}-Y_{B4})}{(Y_{B2}-Y_{B4})}=\frac{(Y_{B1}-Y_C)(Y_{B2}-Y_{B4})}{(Y_{B2}-Y_C)(Y_{B1}-Y_{B4})}=\frac{3}{2}$

So, do not need accurately to mark the position in the target surface center of circle with tangible sign, also can obtain the image coordinates of center of circle picture point rapidly, exactly.Because the picture of characteristic diameter is parallel with long axis of ellipse, utilize the image coordinates of center of circle picture point and the equation of image planes ellipse, the picture of obtaining the image coordinates of end points of characteristic diameter picture and characteristic diameter is long.Compare with the scheme of existing three circle targets, during Flame Image Process, saved with the sub-pix disposal route and asked the complicated processes of the equation of crossing two straight-line segments in three ellipses of image planes respectively, saved a large amount of Flame Image Process time in the hope of center of circle image point position.

(5), respectively the two targets of justifying when position I and the position II are taken pictures the plane equation of target surface when obtaining correspondence position with the digital camera of a stationkeeping if object under test turns over one when arriving another location II less than 180 ° angle from position I.The corner that the included angle on these two planes is exactly an object under test when above-mentioned position I forwards position II to.

(6) if the rotating shaft of target surface and object under test is not parallel, then will promptly there be systematic error in the φ value of obtaining with said method less than the actual value of object under test corner, need to revise.Utilize the world coordinates in target surface target surface center of circle when a plurality of diverse location of obtaining in the measuring process, can obtain rotating shaft direction, obtain the angle of target surface normal and rotating shaft, and be used for obtaining the actual value of corner.Therefore, during measurement, target surface only need be generally parallel to the rotating shaft of object under test; The stationkeeping of camera is only required target surface in the apparent field of camera, and the relative position attitude of target surface and camera is not had strict requirement.So, realizing measuring system of the present invention, the installation of its measuring equipment is regulated and is easy to, and operation is very convenient, and the measuring accuracy height is practical.

The invention has the beneficial effects as follows: it is simple and compact for structure that the two with one heart circles of the coplane of design indicate, fabrication and installation easily, and the image processing process that helps simplifying and accelerate to ask the equation of image planes ellipse and ask center of circle image point position help improving the precision of surveying corner.Under the situation that does not count camera imaging error effect and other interference, computer simulation experiment is surveyed the error of corner less than 0.0005 °.It is loose to have solved the existing target surface sign structure more complicated that exists based on the monocular vision measuring method of three circle targets, also needs accurately to indicate the home position of each circle with intersecting two straight-line segments, and its Digital Image Processing difficulty is big, the processing time is long; With and anti-jamming capacity is poor, measuring accuracy is not high enough, and when the angle of the primary optical axis of the normal of target surface and camera during near 0 °, its measuring error such as enlarges markedly at problem; And overcome it and must know the shortcoming of camera pixel centre distance.Realize measuring system of the present invention, when measuring at the scene, can utilize the not parallel measuring error that causes of measuring process gained data correction target surface and rotating shaft, measuring equipment is installed to regulate and is easy to, and operation is very convenient, and the measuring accuracy height is practical.Can be used to the angular displacement sensor of aileron, wing flap, diving rudder and yaw rudder on airport on-site proving aircraft.Having overcome the big non-contact precision of existing other measurement ranges surveys measuring equipment that the method for corner exists and installs at the scene to regulate and be difficult to reach requirement, use very inconvenient, but also be difficult to revise its equipment the measuring error that causes not in place, the shortcoming of poor practicability are installed.

Description of drawings

Fig. 1 is for realizing measuring system integral layout synoptic diagram of the present invention;

Fig. 2 is the position view of the group of feature point selected on the digital photos of two round targets;

Fig. 3 is that the target surface roundlet is in the minor axis end points of the oval image of image planes and the equivalent schematic of the relation of the central projection between center of circle picture point and its former picture point.

Embodiment

1. make the sign of target surface of the two with one heart round circumference of coplane, make the test target that is referred to as two circle targets (1), be parallel to the rotating shaft (3) of object under test (2), and be fixed on the object under test (2).Rotating shaft (3) is installed on the base (6).Also can in the roundlet of two circle signs, draw a radius again and make auxiliary sign, to test target perpendicular to the rotating shaft (3) of object under test (2) and be fixed on the object under test (2), make the installation of test target have greater flexibility, but some difference of its computing method when measuring.If there is a fritter plane domain on the surface of object under test, also two circle signs directly can be drawn in above it, perhaps be printed on the film, be attached to above it again; Even the both not parallel also out of plumb of rotating shaft of two circle signs and object under test still can accurately be measured.

2. with the digital camera (4) of a stationkeeping target surface of two round targets (1) is taken pictures.When taking pictures, only require target surface in the apparent field of camera, the relative position attitude of camera and target surface is not had strict demand.The view data of digital camera (4) sends microcomputer (5) to by USB interface and handles.

3. the picture according to two circle signs is oval characteristics, select the end points of image planes ellipse short shaft, the end points of characteristic diameter picture and the picture point in the center of circle are as a group of feature point of image planes, the long stack features parameter of the picture of their image coordinates and characteristic diameter as image planes, character according to pin-hole imaging principle and similar triangles, utilize the characteristic diameter characteristics parallel with image planes, based on a correspondence and straight line correspondence, computing method of overlapping the new plane equation of asking target surface have been designed, set up relevant computing formula, need not know the pixel center distance of camera and the real focal length of camera when taking pictures, just can obtain the direction cosine of the plane equation and the target surface normal of target surface.

4. according to the characteristics of the oval image of image planes, design digital picture sub-pix disposal route, be used for handling in real time pair digital photos of circle targets, obtained the equation of two ellipses of image planes, obtained the image coordinates of the minor axis end points of two ellipses of image planes shown in figure (2).Keep collinear point still to be characteristics such as the double ratio of 4 of collinear point and conllinear remains unchanged according to interplanar central projection again, utilize the image coordinates of ellipse short shaft end points, obtain the image coordinates of center of circle picture point, further obtain the position of end points of the picture of characteristic diameter on image planes of each circle and the length of picture thereof.Then, utilize the known radius of this stack features parameter and two circle signs,, obtain the world coordinates of the former picture point of this group of feature point on target surface according to newly-designed computing method; Use least square fitting again, obtain the direction cosine of the normal on the plane equation of target surface and this plane.

5. object under test turns over one when arriving another location II less than 180 ° angle from position I, respectively the target surfaces of the two circle targets when position I and the position II are taken pictures, and the direction cosine of the normal on the plane equation of target surface and this plane when calculating correspondence position.The corner that the included angle on these two planes is exactly an object under test when above-mentioned position I forwards position II to.

6. if the rotating shaft of target surface and testee is not parallel, then there is systematic error in The above results, needs to revise.During measurement, two round targets rotate synchronously with testee, and it is the circumference of central shaft with the rotating shaft that the movement locus in the target surface center of circle is one.Utilize the world coordinates in target surface center of circle when a plurality of diverse location of obtaining in the measuring process, use least square fitting, obtain the plane equation on this plane, locus circle place, and be used for obtaining rotating shaft direction, obtain the angle of target surface normal and rotating shaft, and obtain the actual value of corner.

7. relevant calculation: because in measuring process the stationkeeping of camera, desirable world coordinate system overlaps with camera coordinates system, promptly getting camera coordinates is as world coordinate system: the photocentre of getting camera is the initial point o of world coordinate system, the z axle is along the primary optical axis direction of camera, the x axle is parallel to the capable direction of image planes CCD, the y axle is parallel to the direction of image planes CCD row, sets up rectangular coordinate system o-xyz.Image coordinates be O-XY the coordinate of initial point O in world coordinate system for (0,0 ,-F), get OX//ox, OY//oy.

The position view of the group of feature point that Fig. 2 selects on the digital photos of two round targets for this programme.C ' is the picture point in the center of circle, A ' ₁, A ' ₂, A ' ₃, A ' ₄Be respectively the end points of the picture of two characteristic diameters of justifying; B ' ₁, B ' ₂, B ' ₃, B ' ₄Be respectively the end points of two ellipse short shafts of image planes; Their former picture points on target surface are respectively C, A ₁, A ₂, A ₃, A ₄B ₁, B ₂, B ₃, B ₄

(1) asks the image coordinates X of center of circle picture point C ' _C, Y _C:

The little radius of circle of known target surface is R ₁, big radius of circle is R ₂, calculate for simplifying during design, get R ₂=2R ₁=2R.According to the character that interplanar central projection keeps collinear point still to remain unchanged for the double ratio of 4 of collinear point, conllinear, set up the double ratio relational expression of the position of asking center of circle picture point C '.Capture face ellipse short shaft terminal B ' ₁, B ' ₂, B ' ₃, B ' ₄In any 3 and center of circle picture point C ' all can set up the double ratio relational expression of the position of asking center of circle picture point C ', can set up the double ratio relational expression of 4 equivalences altogether.For reducing measuring error, the double ratio relational expression of available these 4 equivalences is obtained one group of image coordinates X of center of circle picture point C ' respectively _C, Y _C, and then be used for asking X _C, Y _CMean value.To get B ' ₁, B ' ₂, B ' ₄And C ' is example, sets up the double ratio relational expression:

$\frac{\left(B_1^{\′}{B}_2^{\′}{C}^{\′}\right)}{\left(B_1^{\′}{B}_2^{\′}{B}_4^{\′}\right)}=\frac{B_1^{\′}{C}^{\′}}{B_2^{\′}{C}^{\′}}/\frac{B_1^{\′}{B}_4^{\′}}{B_2^{\′}{B}_4^{\′}}=\frac{B_1^{\′}{C\×}^{\′}{B}_2^{\′}{B}_4^{\′}}{B_2^{\′}{C}^{\′}\×B_1^{\′}{B}_4^{\′}}=\frac{R_2(R_1+R_2)}{R_1\×2R_2}=\frac{3}{2}---\left(1\right);$

Set up one group of image coordinates X that following equation is obtained center of circle picture point C ' according to formula (1) _C, Y _C:

$\frac{(X_{B1}-X_C)}{(X_{B2}-X_C)}/\frac{(X_{B1}-X_{B4})}{(X_{B2}-X_{B4})}=\frac{(X_{B1}-X_C)(X_{B2}-X_{B4})}{(X_{B2}-X_C)(X_{B1}-X_{B4})}=\frac{3}{2};$

$\frac{(Y_{B1}-Y_C)}{(Y_{B2}-Y_C)}/\frac{(Y_{B1}-Y_{B4})}{(Y_{B2}-Y_{B4})}=\frac{(Y_{B1}-Y_C)(Y_{B2}-Y_{B4})}{(Y_{B2}-Y_C)(Y_{B1}-Y_{B4})}=\frac{3}{2}.$

(2) ask the world coordinates x of center of circle C _C, y _C, z _C

Utilize the character of characteristic diameter characteristic parallel and similar triangles, obtain the world coordinates in the target surface center of circle with image planes:

$\left\{\begin{array}{c}{x}_C=X_C\mathrm{dR}/r_{1}d=X_{C}R/r_1;\\ y_C=Y_C\mathrm{dR}/r_{1}d=Y_{C}R/r_{1_1};\\ z_C=\mathrm{FR}/r_{1}d=\mathrm{fdR}/r_{1}d=\mathrm{fR}/r_1\end{array}\right.---\left(2\right);$

If known F and d, then the world coordinates in the target surface center of circle only determine and other monocular vision measuring methods relatively, the calculating of this method is not only simply but also accurate.If can't accurately know F and d, then also demand goes out f.

Fig. 3 is that target surface roundlet sign is in the minor axis end points of the oval image of image planes and the equivalent schematic of the relation of the central projection between center of circle picture point and its former picture point.Based on a correspondence and straight line correspondence, utilize the character of similar triangles, try to achieve: z ₁/ z ₂=r ₁₂/ r ₁₁Again in conjunction with following fundamental relation formula:

(x _B2-x _B1) ²+(y _B2-y _B1) ²+(z _B2-z _B1) ²＝4R ²，

Obtain: $f=F/d=\sqrt{{\left(\frac{r_{11}+r_{12}}{r_{11}-r_{12}}{r}_1\right)}^2-\frac{{(r_{11}{X}_{B2}-r_{12}{X}_{B1})}^2+{(r_{11}{Y}_{B2}-r_{12}{Y}_{B1})}^2}{{(r_{11}-r_{12})}^2}}$

With f substitution formula (2), so, utilizing the characteristic parameter that extracts from the digital photos of two round targets and the radiuss of a circle of two circle signs, the real focal length F of the pixel center that need not know camera camera apart from d with when taking pictures also can obtain the world coordinates x in the target surface center of circle _C, y _C, z _C

(3) ask A ₁(x _A1, y _A1, z _A1), A ₂(x _A2, y _A2, z _A2),

Utilize the character of characteristic diameter characteristic parallel and similar triangles equally, try to achieve with image planes:

$\left\{\begin{array}{ccc}{x}_{A1}=\frac{R_1}{r_1}\·X_{A1},& y_{A1}=\frac{R_1}{r_1}\·Y_{A1},& z_{A1}=z_C\\ x_{A2}=\frac{R_1}{r_1}\·X_{A2},& y_{A2}=\frac{R_1}{r_1}\·Y_{A2},& z_{A2}=z_C\end{array}\right.---\left(3\right)$

Use the same method and obtain A ₃(x _A3, y _A3, z _A3), A ₄(x _A4, y _A4, z _A4).

(4) ask B ₁(x _B1, y _B1, z _B1), B ₂(x _B2, y _B2, z _B2)

According to the corresponding relation of each point shown in Figure 3, utilize the character of similar triangles, try to achieve:

$\left\{\begin{array}{c}{x}_{B1}=\frac{2r_{12}R}{(r_{11}+r_{12})r_1}{X}_{B_1},y_{B_1}=\frac{2r_{12}R}{(r_{11}+r_{12})r_1}{Y}_{B_1},z_{B_1}=\frac{2r_{12}R}{(r_{11}+r_{12})r_1}f\\ x_{B2}=\frac{2r_{11}R}{(r_{11}+r_{12})r_1}{X}_{B_2},y_{B_2}=\frac{2r_{11}R}{(r_{11}+r_{12})r_1}{Y}_{B_2},z_{B_2}=\frac{2r_{11}R}{(r_{11}+r_{12})r_1}f\end{array}\right.---\left(4\right)$

Use the same method and obtain B ₃(x _B3, y _B3, z _B3), B ₄(x _B4, y _B4, z _B4).

(5) ask the plane equation of target surface

If the plane equation of target surface is ax+by+cz=h.Characteristics according to this measuring method can make h=1, and the plane equation of promptly establishing target surface is ax+by+cz=1.Utilize the C that has obtained on the target surface ₁, A ₁, A ₂, A ₃, A ₄, B ₁, B ₂, B ₃, B ₄World coordinates, use least square fitting, obtain the parameter a of the plane equation of target surface, b, c obtains the direction cosine of target surface normal.This method is summarized as follows:

Set up objective function S=∑ (ax _i+ by _i+ cz _i-1) ²

Order: Set up equation:

$\left[\begin{array}{ccc}\mathrm{\Σ}{x}_i^2& \mathrm{\Σ}{x}_i{y}_i& \mathrm{\Σ}{x}_i{z}_i\\ \mathrm{\Σ}{x}_i{y}_i& \mathrm{\Σ}{y}_i^2& \mathrm{\Σ}{y}_i{z}_i\\ \mathrm{\Σ}{x}_i{z}_i& \mathrm{\Σ}{y}_i{z}_i& \mathrm{\Σ}{z}_i^2\end{array}\right]\left[\begin{array}{c}a\\ b\\ c\end{array}\right]=\left[\begin{array}{c}\mathrm{\Σ}{x}_i\\ \mathrm{\Σ}{y}_i\\ \mathrm{\Σ}{z}_i\end{array}\right]---\left(5\right)$

With C on the target surface, A ₁, A ₂, A ₃, A ₄, B ₁, B ₂, B ₃, B ₄World coordinates substitution equation (5), obtain the parameter a of the plane equation of target surface, b, c, and obtain the direction cosine of target surface normal:

$\cos \mathrm{\α}=\frac{a}{\sqrt{a^2+b^2+c^2}},$ $\cos \mathrm{\β}=\frac{b}{\sqrt{a^2+b^2+c^2}},$ $\cos \mathrm{\γ}=\frac{c}{\sqrt{a^2+b^2+c^2}}---\left(6\right)$

Adopt this computing method, its anti-jamming capacity is strong, and the precision of calculation results height is important measures that improve measuring accuracy, but calculates slightly complexity a bit.

Also can adopt the method for " determine a plane " to ask the direction cosine of target surface normal at 3.For example, make C on the target surface, A ₁, B ₁3 position vector:

$\stackrel{\→}{C}=x_C\stackrel{\←}{i}+y_C\stackrel{\→}{j}+z_C\stackrel{\→}{k},{\stackrel{\→}{A}}_1=x_{A1}\stackrel{\←}{i}+y_{A1}\stackrel{\→}{j}+z_{A1}\stackrel{\→}{k},{\stackrel{\→}{B}}_1=x_{B1}\stackrel{\←}{i}+y_{B1}\stackrel{\→}{j}+z_{B1}\stackrel{\→}{k};$

Then the normal direction of target surface can be determined by following formula:

$\stackrel{\→}{N}=N_1\stackrel{\→}{i}+N_2\stackrel{\→}{j}+N_3\stackrel{\→}{k}=\left|\begin{array}{ccc}\stackrel{\→}{i}& \stackrel{\→}{j}& \stackrel{\→}{k}\\ (x_{B1}-x_C)& (y_{B1}-y_C)& (z_{B1}-z_C)\\ (x_{A1}-x_C)& (y_{A1}-y_C)& (z_{A1}-z_C)\end{array}\right|$

Wherein: $N_1=\left|\begin{array}{cc}(y_{B1}-y_C)& (z_{B_1}-z_C)\\ (y_{A1}-y_C)& (z_{A_1}-z_C)\end{array}\right|,$ $N_2=-\left|\begin{array}{cc}(x_{B1}-y_C)& (z_{B_1}-z_C)\\ (x_{A1}-y_C)& (z_{A_1}-z_C)\end{array}\right|,$

$N_3=-\left|\begin{array}{cc}(x_{B1}-x_C)& (y_{B_1}-y_C)\\ (x_{A1}-x_C)& (y_{A_1}-y_C)\end{array}\right|;$

Then the direction cosine of target surface normal are:

$\cos \mathrm{\α}=\frac{N_1}{\sqrt{N_1^2+N_2^2+N_3^2}},$ $\cos \mathrm{\β}=\frac{N_2}{\sqrt{N_1^2+N_2^2+N_3^2}},$ $\cos \mathrm{\γ}=\frac{N_3}{\sqrt{N_1^2+N_2^2+N_3^2}}---\left(6^{\′}\right)$

This method is calculated fairly simple, but the precision of its anti-jamming capacity and measurement is less better.

(6) ask corner

When object under test when position I forwards position II to, at position I and position II two round targets are taken pictures respectively, through Digital Image Processing, the direction cosine of target surface normal when obtaining correspondence position, establish and be respectively: cos α ₁, cos β ₁, cos γ ₁Cos α ₂, cos β ₂, cos γ ₂The corner that is exactly object under test when position I forwards position II to of the included angle between these two planes then.φ is determined by following formula:

cosφ＝cosα ₁cosα ₂+cosβ ₁cosβ ₂+cosγ ₁cosγ ₂ (7)

(7) revise target surface and the not parallel systematic error that causes of rotating shaft

If the rotating shaft of target surface and object under test is not parallel, then there is systematic error in The above results, needs to revise.If the direction cosine of its rotating shaft of object under test are cos α _P, cos β _P, cos γ _PThe direction cosine of object under test target surface normal when position 1 are cos α ₁, cos β ₁, cos γ ₁, then the angle ψ between the rotating shaft of target surface normal and object under test is determined by following formula:

cosψ＝cosα ₁cosα _P+cosβ ₁cosβ _P+cosγ ₁cosγ _P

Object under test rotates in fixed axis, and the angle ψ in rotation process between target surface normal and the rotating shaft remains unchanged, so utilize the ψ angle to revise the systematic error of surveying corner, the actual value φ of corner when object under test forwards position II to from position I _aTry to achieve by following formula:

φ _a＝2arcsin(sin(φ/2)/sinψ) (8)

During measurement, it is the circumference of central shaft with the rotating shaft that the movement locus in the target surface center of circle is one.Utilize the world coordinates in target surface center of circle when a plurality of diverse location of having obtained in the measuring process, use least square fitting, obtain the equation of this locus circle, obtain the position and the direction of rotating shaft.

Because when revising the said system error, only need know the direction cosine of testee rotating shaft, be to simplify to calculate, only need to adopt the same method of direction cosine of the normal on the above-mentioned plane equation of asking target surface and this plane, obtain the normal direction on plane, locus circle place.For example,, obtain the plane equation on plane, locus circle place, utilize formula (6) to obtain the direction cosine of rotating shaft again the world coordinates substitution formula (5) in the target surface obtained in the measuring process center of circle when a plurality of diverse location.

This modification method calculates accurately, and can utilize in the measuring process to such an extent that data are revised, make realize its equipment of measuring system of the present invention install regulate very simple, operation easily, the measuring accuracy height makes it have very strong practicality.

Designed a computer simulation experiment software at above-mentioned measurement scheme, under the situation of the influence that does not count the camera imaging error and other interference, if object under test progressively forwards 85 ° to since 1 °, carried out series of computation machine emulation testing test, in below table 1 of main outcome record, the table 2.

Computer simulation experiment result, the error of surveying corner is less than 0.0005 °.The error of camera imaging, influence survey corner accuracy mainly be its " an axle magnification hangs down " error.When measuring at the scene, camera is far away to the distance of target surface generally speaking, and " the axle magnification hangs down " error mainly shows as " pincushion type distortion " at this moment.Its pincushion type distortion rate of the camera of ordinary consumption level is about 0.4%, adopts middle-grade above camera or adopts photogrammetric this error of special-purpose digital camera littler.And this error belongs to systematic error, if require the accuracy of measuring very high, can this system's error be revised by camera is demarcated accurately.

Table 1: Computer Simulation is measured axle and is rotated corner experimental measurement result: the measured value of target surface central coordinate of circle during rotation

Setup parameter: x _c=0mm, y _c=0mm, z _c=2000mm, F=20mm.It is a that target surface is rotated counterclockwise angle around the y axle ₁, being rotated counterclockwise angle around the x axle is a ₂(a in table 1 and the table 2 ₂=0), α, β, γ are target surface normal direction angles.

Table 2: the measured value at target surface normal direction angle when Computer Simulation Measuring Object dead axle rotates

(when establishing target surface and xoy plane parallel, the direction angle alpha of target surface normal=90 °, β=90 °, γ=180 °)

Claims (2)

1. non-contact precision is surveyed the monocular vision measuring method of corner, it is characterized in that this method mainly is made up of following step:

(1) sign of doing target surface with the two with one heart round circumference of coplane is made the test target, and the rotating shaft that is parallel to object under test is fixed on this object;

(2) with the digital camera of a stationkeeping test target is taken pictures, when taking pictures, only require target surface in the apparent field of camera, the relative position attitude of camera and target surface is not had strict requirement; The view data of this digital camera sends Computer Processing to by USB interface;

(3) picture according to two circle signs is oval characteristics, select the end points of image planes ellipse short shaft, end points and two circle of characteristic diameter picture to indicate the group of feature point of the picture point in the center of circle, the long stack features parameter of the picture of their image coordinates and characteristic diameter as image planes as image planes; Characteristic diameter refers to: a plane parallel with image planes is done in the center of circle by this circle, this plane and the intersection of circle is called the characteristic diameter of this circle; According to the pin-hole imaging principle, utilize the characteristic diameter characteristics parallel,, set up and asked the formula of image planes unique point at the world coordinates of the former picture point of target surface based on a correspondence and straight line correspondence with image planes, obtain the world coordinates of corresponding former picture point, be used for obtaining the plane equation of target surface;

(4) according to the characteristics of the oval image of image planes, adopt digital picture sub-pix disposal route to handle digital photos in real time, obtain the equation of two ellipses of image planes, obtain the image coordinates of ellipse short shaft end points; The characteristic that the double ratio that still is 4 of collinear point and conllinear according to interplanar central projection maintenance collinear point remains unchanged, set up the formula of asking center of circle image point position, obtain the image coordinates of center of circle picture point, further obtain the image coordinates of end points of characteristic diameter picture and the length of characteristic diameter picture;

(5), respectively the target surface of the test target when position I and the position II is taken pictures the plane equation of target surface when obtaining correspondence position with the digital camera of a stationkeeping if object under test turns over one less than 180 ° angle in-position II from position I; The corner that the included angle on these two planes is exactly an object under test when above-mentioned position I forwards position II to;

(6) if the rotating shaft of target surface and testee is not parallel, then promptly there is systematic error in the φ value of obtaining with said method less than the actual value of testee corner, needs to revise; During measurement, it is the circumference of central shaft with the rotating shaft that the movement locus in the target surface center of circle is one; Utilize the world coordinates in target surface center of circle when a plurality of diverse location of having obtained in the measuring process, use least square fitting, obtain the plane equation on this plane, locus circle place, obtain the direction cosine of rotating shaft, obtain the angle ψ between the rotating shaft of target surface normal and testee; Utilize the ψ angle to revise the systematic error of surveying corner, obtain the actual value φ of corner _a, its computing formula is as follows: φ _a=2arcsin (sin (φ/2)/sin ψ).

2. non-contact precision according to claim 1 is surveyed the monocular vision measuring method of corner, it is characterized in that the characteristic that keeps collinear point still to remain unchanged according to interplanar central projection, set up the formula of asking center of circle image point position for the double ratio of 4 of collinear point and conllinear: select image planes ellipse short shaft terminal B ' ₁(X _B1, Y _B1), B ' ₂(X _B2, Y _B2), B ' ₃(X _B3, Y _B3), B ' ₄(X _B4, Y _B4) in any 3 and center of circle picture point C ' (X _C, Y _C), all can set up the double ratio relational expression of asking center of circle image point position, can set up the relational expression of 4 equivalences altogether; For reducing measuring error, obtain the image coordinates X of center of circle picture point C ' respectively with the double ratio relational expression of 4 equivalences _C, Y _C, be used for obtaining X again _CAnd Y _CMean value; To select B ' ₁, B ' ₂, B ' ₄, these 4 of C ' are example, set up the double ratio relational expression:

$\frac{\left(B_1^{\′}{B}_2^{\′}{C}^{\′}\right)}{\left(B_1^{\′}{B}_2^{\′}{B}_4^{\′}\right)}=\frac{B_1^{\′}{C}^{\′}}{B_2^{\′}{C}^{\′}}/\frac{B_1^{\′}{B}_4^{\′}}{B_2^{\′}{B}_4^{\′}}=\frac{B_1^{\′}{C}^{\′}\×B_2^{\′}{B}_4^{\′}}{B_2^{\′}{C}^{\′}\×B_1^{\′}{B}_4^{\′}}=\frac{R_2(R_1+R_2)}{R_1\×{2R}_2}=\frac{3}{2},$

R wherein ₂=2R ₁Set when being design; Set up one group of coordinate figure X that following equation is obtained center of circle picture point C ' again according to following formula _C, Y _C:

$\frac{(X_{B1}-X_C)}{(X_{B2}-X_C)}/\frac{(X_{B1}-X_{B4})}{(X_{B2}-X_{B4})}=\frac{(X_{B1}-X_C)(X_{B2}-X_{B4})}{(X_{B2}-X_C)(X_{B1}-X_{B4})}=\frac{3}{2};$

$\frac{(Y_{B1}-Y_C)}{(Y_{B2}-Y_C)}/\frac{(Y_{B1}-Y_{B4})}{(Y_{B2}-Y_{B4})}=\frac{(Y_{B1}-Y_C)(Y_{B2}-Y_{B4})}{(Y_{B2}-Y_C)(Y_{B1}-Y_{B4})}=\frac{3}{2}.$

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