CN103913131A - Free curve method vector measurement method based on binocular vision - Google Patents

Abstract

The invention relates to a free curve method vector measurement method based on the binocular vision, and belongs to the field of computer vision measurement. According to the measurement method, a projection pattern from a laser projection device to a free curve is composed of two orthogonal straight lines and four round light spots on the two straight lines; the two straight lines are intersected at one point; the four round light spots are the same in size and are evenly distributed on the same circumference. The image of the projection pattern is collected by a binocular vision system, through the threshold judgment condition based on the distance, the curvature of one point of the curve within the small neighborhood range is estimated, and different normal vector measurement schemes are selected. The measurement method considers the curvature of the neighborhood of the point to be tested, the measurement flexibility is high, the adaptability is high, and online efficient measurement of a normal vector of any point of the free curve can be achieved. The measurement method is simple, and the algorithm is easy to implement.

Description

A kind of free form surface method vector measurement method based on binocular vision

Technical field

The invention belongs to computer vision measurement field, relate to a kind of Surface Method vector measurement method based on binocular vision.

Background technology

Curved surface parts become the indispensable important composition part of each application product just day by day as turbo blade, loudspeaker, curved surface cavity, train covering etc.For these parts, Surface Method is vowed becomes important measurement parameter.Covering as Typical Aircraft compound substance curved surface part have that wall is thin, complex-shaped, the feature such as random deformation is large, material character anisotropy, range of size are large.Covering flexible drilling riveter skill has high requirements to boring riveting verticality, and aircraft skin riveting parts when boring, during by processing prefabricated component lay, hot-press solidifying and the caused distortion of part self gravitation and location, coordination, clamping, the accumulation of various errors makes the actual theory method vector generation deviation in riveting point place's method vector and three-dimensional digital model for the treatment of.If riveting point normal direction precision goes beyond the scope, can make that hole crudy declines, type of attachment for forcing connections, junction generation stress is concentrated and skin-surface is rough, and then affect riveting quality and Aerodynamic Configuration of Aireraft, and finally cause aircraft usage hydraulic performance decline.Therefore the online high precision, the high-level efficiency measurement that, how to realize aircraft skin surface any point method vector become the important problem of needing solution badly.

" a kind of device of measuring normal vector of arbitrary point of free-form surface " that Lee is former, the patent No. of Yu Jianfeng invention is CN201120358775 invented and a kind ofly utilized spherical contact on curved surface, to draw crossing curve, utilizes cutting of curve to vow the measuring method of asking for normal vector.This kind of method is contact type measurement, asks for ratio of precision lower for its method vector of random deformation curved surface." for larger radius of curvature curved surface normal vector method for quick " that the patent No. of Yao Zhenqiang, Hu Yongxiang invention is CN102248450A invented and utilized optical measuring technique to realize obtaining of two imaginary orthogonal planes and surfaces intersection, utilize these two intersections to ask for any normal vector of curved surface at the cross product of the method vector of tested point, but the method is not considered any amount of curvature at place of curved surface, and single utilization one method is asked for method vector, efficiency is low, flexibility is poor.

Summary of the invention

The technical barrier that the present invention will solve is the defect that overcomes prior art, invent a kind of free form surface method vector measurement method based on binocular vision, adopt the measuring system being formed by binocular vision system and projection pattern to carry out the measurement of free form surface any point method vector.Arrive the distance size of fit Plane by more set threshold value and tested point, choose the high-precision rapid survey of different measuring scheme Completion Techniques vector.The size of the curvature of the tested point neighborhood that this measuring method is considered, flexibility is higher, can realize online high precision and the high-level efficiency of curved surface any point method vector and measure.

The technical solution used in the present invention is a kind of free form surface method vector measurement method based on binocular vision, it is characterized in that: in measuring method, by laser projection device to the projection pattern of free form surface projection by two orthogonal straight lines L ₁, L ₂form with four circular light spot G that are positioned on two lines; Two straight-line intersections are P, four circular light spot equal and opposite in directions and being distributed on same circumference; Utilize the image of binocular vision system acquired projections pattern; By the threshold determination condition based on distance, estimate the amount of curvature of some small neighbourhood scopes of curved surface, to choose different method vector measurement schemes: in the time of d≤ε, select the normal vector of fit Plane to approach curved surface tested point method vector; In the time of d > ε, utilize two space curves after matching to ask for the method vector at tested point place at the cross product of tested point place tangent vector; The concrete steps of measuring method are as follows:

(1) spot center based on threshold value grey scale centre of gravity method is extracted

The present invention adopts Canny operator, in conjunction with grey scale centre of gravity method, spot center is carried out to extracted with high accuracy, and in gray level image I (i, j), the grey scale centre of gravity of target S is:

$\left\{\begin{array}{c}{X}_k=\frac{\underset{(i,j)\∈S}{\mathrm{\Σ}}i\×W(i,j)}{\underset{(i,j)\∈S}{\mathrm{\Σ}}W(i,j)}\\ Y_k=\frac{\underset{(i,j)\∈S}{\mathrm{\Σ}}j\×W(i,j)}{\underset{(i,j)\∈}{\mathrm{\Σ}}W(i,j)}\end{array}\right.---\left(1\right)$

In formula, (X _k, Y _k) be the image coordinate of k spot center point; The weights of W (i, j) for setting; Consider the half-tone information situation between real background and target, the present invention adopts threshold value grey scale centre of gravity method, and its weights W (i, j) are defined as:

$\begin{array}{c}W(i,j)=\left\{\begin{array}{c}I(i,j)\\ 0\end{array}\right.\\ (I(i,j)>T)\\ (I(i,j)\≤T)\end{array}---\left(2\right)$

Wherein, T is the threshold value of distinguishing target and background; Grey scale centre of gravity is got W (i, j)=I (i, j);

(2) coupling of spot center point and reconstruction

After the extraction that completes spot center point, the spot center point on the image of left and right cameras collection mated and rebuild; Matching process is as follows:

First adopt 8 normalization algorithms of improvement of Hartley proposition to calculate the fundamental matrix F of left and right cameras, then between the two-dimensional digital image gathering by left and right two high-speed cameras, polar curve restriction relation is carried out the first coupling of spot center point, supposes left image spot central point x _i' and right image spot central point x _i'' match, 2 spot center points meet limiting constraint, and limit equation of constraint can be expressed as follows:

$x_i^{\′T}F{x_{i^{\′}}}^{\′}=0---\left(3\right)$

Wherein, x _i' be the image coordinates of the image spot central point of left camera acquisition; x _i' ' be and x _i' matching is gathered the image coordinates of image spot central point by right video camera; F is the fundamental matrix between two video cameras;

On this basis all spot center points that meet limiting constraint in the image of left and right are carried out to three-dimensional reconstruction to obtain the D coordinates value of spot center point under world coordinate system, reconstruction formula is as follows:

$\left\{\begin{array}{c}{x}_i=\frac{{\mathrm{zX}}_i^{\′}}{f_1}\\ y_i=\frac{{\mathrm{zY}}_i^{\′}}{f_1}\\ z_i=\frac{f_1(f_2{t}_y-{Y_{i^{\′}}}^{\′}{t}_z)}{Y_1(r_7{X}_i^{\′}+r_8{Y}_i^{\′}+r_9{f}_1)-f_2(r_4{X}_i^{\′}+r_5{Y}_i^{\′}+r_6{f}_1)}\end{array}\right.---\left(4\right)$

Wherein, x _i'=(X _i', Y _i'), X _i', Y _i' be respectively the image spot central point x of left camera acquisition _i' horizontal stroke, ordinate under image coordinates system; x _i''=(X _i'', Y _i''), X _i'', Y _i'' be respectively the image spot central point x of right camera acquisition _{i '}' horizontal stroke, ordinate under image coordinates system; (x _i, y _i, z _i) be by two coupling spot center point x _i', x _{i '}' rebuild the three-dimensional coordinate of free token point out; f ₁, f ₂be respectively the focal length of left and right cameras; for connecting the rotation matrix of left and right cameras relation, [t _xt _yt _z] be the translation matrix of right video camera with respect to left video camera;

(3) curvature is judged

1) least square fitting space plane

Take four spot center points reconstructing in the D coordinates value of world coordinate system as basis, utilize least square fitting space plane, step is as follows:

The general expression of plane equation is:

$\left\{\begin{array}{c}\mathrm{Ax}+\mathrm{By}+\mathrm{Cz}+D=0,(C\≠0)\\ z=-\frac{A}{C}x-\frac{B}{C}y-\frac{D}{C}\end{array}\right.---\left(5\right)$

The normal vector that wherein (A, B, C) is plane; D is the distance that initial point arrives plane; Note $a_0=-\frac{A}{D},a_1=-\frac{B}{D},a_2=-\frac{C}{D};$ Z=a ₀x+a ₁y+a ₂;

Select least square method to utilize n point (n>=3): (x _i, y _i, z _i), i=0,1 ...,, the above-mentioned plane of n-1 matching, makes: $S=\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{(a_{0}x+a_{1}y+a_2-z)}^2$ Minimum;

Wherein S is the quadratic sum that a little arrives the distance of straight line;

Make S obtain minimum value, should meet: k=0,1,2; That is:

$\left\{\begin{array}{c}\mathrm{\Σ}2(a_0{x}_i+a_1{y}_i+a_2-z_i)x_{i=0}\\ \mathrm{\Σ}2(a_1{x}_i+a_1{y}_i+a_2-z_i)y_i=0\\ \mathrm{\Σ}2(a_1{x}_i+a_1{y}_i+a_2-z_i)=0\end{array}\right.---\left(6\right)$

Rebuild the 3 d space coordinate (x of spot center by four _i, y _i, z _i), i=0,1,2,3 bring above-mentioned system of equations into tries to achieve a ₀, a ₁, a ₂;

The equation that is fit Plane is: z=a ₀x+a ₁y+a ₂; The normal vector of spatial fit plane is:

2) ask the distance of tested point P ' to fit Plane

Space a bit can be expressed as to the range formula of plane:

Wherein, S _planefor the equation of spatial fit plane; D is the distance that tested point arrives plane; P '=(x ', y ', z ') be the coordinate of tested point under world coordinate system; Q=(x _q, y _q, z _q) be any point in fit Plane; ε is set threshold value; In the time of d≤ε, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes little; In the time of d > ε, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes greatly;

(4) method vector solves

Based on the method vector measurement Scheme Choice criterion of distance threshold constraint, situation one: if the tested point P ' being positioned on curved surface meets d≤ε to the distance of spatial fit plane, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes little, now think the normal vector of plane be exactly the method vector of tested point on curved surface, $\stackrel{\→}{n}=(a_0{a}_1,-1);$

Situation two: if tested point P ' is to the distance d > ε of spatial fit plane on curved surface, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes greatly, its Proximal surface may be other quadric surfaces such as sphere, parabola, saddle face, now selects two space curves that project on curved surface to carry out solving of method vector; Its step is as follows:

1) extraction of laser stripe centerline points, coupling and reconstruction

The present invention adopts the laser stripe center line detecting method based on direction template, respectively in level, vertical, left bank 45., right bank 45.In direction, arrange the template that big or small fixed-direction is variable, be designated as respectively K ₀, K ₁, K ₂, K ₃, the every a line of two-dimensional digital image is processed respectively by these four templates; With right _irow is treated to example, for K ₀template has:

$\begin{array}{c}\left\{\begin{array}{c}{H}_j=\underset{s=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{t=0}{\overset{N-1}{\mathrm{\Σ}}}{K}_0\[s\]\[t\]C\[i-\frac{M}{2}+S\]\[j-\frac{N}{2}+t\],j=\frac{N}{2},\frac{N+1}{2},...,\mathrm{col}-1\\ H_{g0}=\max (H_{\frac{N}{2},}{H}_{\frac{N}{2}+1},...,H_{\mathrm{col}-1}),\frac{N}{2}\≤j\≤\mathrm{col}-1\end{array}\right.---\left(8\right)\end{array}$

Wherein M is the corresponding line number of template; N is columns corresponding to template; K ₀[s] [] t>=0; represent the gray-scale value of point; Accordingly for template K ₁, K ₂, K ₃there is H _g1, H _g2, H _g3; Ask for H _g=max (H _g0, H _g1, H _g2, H _g3), there is the position of central point of the capable laser stripe of i at a g place; By the method, two-dimensional digital image is carried out can completing by pixel detection line by line the extraction of laser stripe center line; Complete on the basis of laser stripe central line pick-up, adopt with spot center point coupling in the present invention (2) and rebuild identical method and carry out coupling and the reconstruction of laser stripe central point, obtaining the D coordinates value of laser stripe centerline points under world coordinate system;

2) B-spline Curve matching two space curves

The present invention adopts B-spline Curve matching two space laser striped curves, and B-spline curves piecewise function expression formula is:

$\left\{\begin{array}{cc}{c}_1:p=P_0\·{N_{10}}^3+P_1\·{N_{11}}^3+P_2\·{N_{12}}^3+P_3{N_{13}}^3& u\∈\[u_2,u_3\]\\ c_2:p=P_1\·{N_{20}}^3+P_2\·{N_{21}}^3+P_3\·{N_{22}}^3+P_4{N_{23}}^3& u\∈\[u_3,u_4\]\\ c_1:p=P_2\·{N_{30}}^3+P_3\·{N_{31}}^3+P_4\·{N_{32}}^3+P_5{N_{33}}^3& u\∈\[u_4,u_5\]\end{array}\right.---\left(9\right)$

Wherein P _i(i=0,1 ... 5) represent respectively control vertex; N _ij(i=1 ... 3, j=0,1 ... 4) represent basis function; Being provided with discrete point on the curve that two camera rebuilding go out is b ₁, b ₂,, b _n; Wherein front i point is positioned at c ₁in section, k-i point is positioned at c ₂in section, n-j point is positioned at c ₃in section, above-mentioned some substitution system of equations is obtained:

Making M is the matrix of coefficients on the left side, the vector forming that P is required control vertex, and the laser stripe centerline points that p is three-dimensional reconstruction, above-mentioned equation is abbreviated as:

M·P＝p (11)

The normal equation that can obtain thus matching is:

M'·M·P＝M'·p (12)

For near the fitting precision of curve raising intersection point, above-mentioned equation is introduced to weights; Equation after weighting is:

(M'·H'·M·P)＝(M'·H')·M·p (13)

Can ask for the equation of two curves by this weighted equation.Ask for respectively on this basis the cut arrow of two curves at tested point both direction, be designated as required method vector is:

The invention has the beneficial effects as follows that invented measuring method is that noncontact, flexibility are strong, real-time is high.Online high-level efficiency applicable to curved surface difference is measured, and its method is simple, and algorithm is easy to realize.

Accompanying drawing explanation:

Fig. 1 is Surface Method vector method for solving schematic diagram.Wherein, L ₁'-horizontal projection laser stripe, L ₂'-vertical projection laser stripe, P '-tested point, G ₁the-the first projection hot spot, G ₂the-the second projection hot spot, G ₃-tri-projection hot spots, G ₄the normal vector of-tetra-projection hot spots, S-fit Plane, m-fit Plane S, d-tested point P ' to the distance of fit Plane S, -curved surface the method vector of a P ', -curve L ₁' the tangent vector of a P ', -curve L ₂' in the tangent vector of a P '.

Fig. 2 is the projection pattern of invention.Wherein L ₁-horizontal projection line, L ₂-vertical projection line, P-pairwise orthogonal projection line intersection point, G ₁the-the first circular light spot, G ₂the-the second circular light spot, G ₃-tri-circular light spots, G ₄-tetra-circular light spots.

Fig. 3 is that the method vector based on two CCD camera measure system solves process flow diagram.

Embodiment

Combination technology scheme of the present invention and accompanying drawing, for better explanation method vector solution procedure, describe in detail it take aircraft skin as example.As follows by the idiographic flow shown in accompanying drawing 3: (1) utilize digital control system by laser projection device move to aircraft skin tested point P ' (x ', y ', z ') locate, guaranteeing on the basis that two laser stripe intersection points are tested point, accompanying drawing 2 patterns are projected on aircraft skin surface to be measured, and projection is four highlighted hot spot G ₁', G ₂', G ₃', G ₄' and two laser stripe L ₁', L ₂', meanwhile utilize the left and right high-speed camera acquired projections pattern image of binocular vision system.

(2) extraction of the spot center based on threshold value grey scale centre of gravity method

Select Canny operator in conjunction with threshold values grey scale centre of gravity method, spot center in the collected by camera image of left and right to be extracted, complete the location of spot center.Obtain the image coordinates (X of four spot center points in left image _i, Y _i) i=1,2,3,4 and the image coordinates of four spot center points of right image be (X _{i '}, Y _{i '}) i '=1,2,3,4.

(3) coupling of spot center point and reconstruction

Bring the image coordinates of the spot center point of left and right image into formula (3) and (4) D coordinates value of spot center point under world coordinate system that obtain matching:

G ₁′(x ₁,y ₁,z ₁)、G ₂′(x ₂,y ₂,z ₂)、G ₃′(x ₃,y ₃,z ₃)、G ₄′(x ₄,y ₄,z ₄)。

(4) vertex neighborhood curvature is judged

1) based on spot center discrete point least square fitting space plane

Using four spot center that reconstruct as space finite points, utilize least square fitting space plane S.Bring the three-dimensional coordinate of four spot center points into formula (6), obtaining plane equation is z=a ₀x+a ₁y+a ₂, the normal vector that obtains plane is

2) ask the distance of tested point P ' to fit Plane

To put P ' (x ', y ', z ') generation to the range formula (7) of space plane ask for tested point to the distance d of fit Plane and by this apart from comparing and obtain d > ε with set threshold epsilon.Now should choose two space curves and ask for method vector at the cross product of cutting arrow of tested point P ' (x ', y ', z ').

(5) solving of curved surface any point method vector

1) extraction of laser stripe centerline points, coupling and reconstruction

Adopt the laser stripe Spot detection method based on direction template, complete the extraction of laser stripe centerline points, as formula (8).Obtain the image coordinates (X of four spot center points in left image _i, Y _i) i=1,2 ... image coordinates (the X of four spot center points of n and right image _{i '}, Y _{i '}) i '=1,2 ... n.Coupling and the reconstruction of spot center line point are carried out in image coordinates substitution formula (3) and (4) of the left and right image extracting, and the D coordinates value that obtains spot center line point is (x _i, y _i, z _i) i=1,2 ... n.

2) utilize B-spline Curve matching based on spatial point discrete points data

By the D coordinates value (x of the laser stripe centerline points reconstructing _i, y _i, z _i) i=1,2 ... n substitution formula (10) and weighted equation (13), ask for the equation of two curves.Ask for respectively on this basis the tangent vector of two curves at tested point both direction, be designated as required method vector is:

Measuring method of the present invention is non-contact measurement, is taking into full account in the curvature situation of curved surface one vertex neighborhood, chooses different measurement scheme and ask for the measurement of free form surface any point method vector.Its method is simple, and flexibility is strong, real-time is high, algorithm is easy to realize, and has well improved method vector and ask for efficiency under the condition that meets measuring accuracy requirement.

Claims (1)

1. the free form surface method vector measurement method based on binocular vision, is characterized in that: in measuring method, by laser projection device to the projection pattern of free form surface projection by two orthogonal straight lines L ₁, L ₂form with four circular light spot G that are positioned on two lines; Two straight-line intersections are P, four circular light spot equal and opposite in directions and being distributed on same circumference; Utilize the image of binocular vision system acquired projections pattern; By the threshold determination condition based on distance, estimate the amount of curvature of some small neighbourhood scopes of curved surface, to choose different method vector measurement schemes: in the time of d≤ε, select the normal vector of fit Plane to approach curved surface tested point method vector; In the time of d > ε, utilize two space curves after matching to ask for the method vector at tested point place at the cross product of tested point place tangent vector; The concrete steps of measuring method are as follows:

(1) spot center based on threshold value grey scale centre of gravity method is extracted

The present invention adopts Canny operator, in conjunction with grey scale centre of gravity method, spot center is carried out to extracted with high accuracy, and in gray level image I (i, j), the grey scale centre of gravity of target S is:

$\left\{\begin{array}{c}{X}_k=\frac{\underset{(i,j)\∈S}{\mathrm{\Σ}}i\×W(i,j)}{\underset{(i,j)\∈S}{\mathrm{\Σ}}W(i,j)}\\ Y_k=\frac{\underset{(i,j)\∈S}{\mathrm{\Σ}}j\×W(i,j)}{\underset{(i,j)\∈}{\mathrm{\Σ}}W(i,j)}\end{array}\right.---\left(1\right)$

In formula, (X _k, Y _k) be the image coordinate of k spot center point; The weights of W (i, j) for setting; Consider the half-tone information situation between real background and target, the present invention adopts threshold value grey scale centre of gravity method, and its weights W (i, j) are defined as:

$\begin{array}{c}W(i,j)=\left\{\begin{array}{c}I(i,j)\\ 0\end{array}\right.\\ (I(i,j)>T)\\ (I(i,j)\≤T)\end{array}---\left(2\right)$

Wherein, T is the threshold value of distinguishing target and background; Grey scale centre of gravity is got W (i, j)=I (i, j);

(2) coupling of spot center point and reconstruction

After the extraction that completes spot center point, the spot center point on the image of left and right cameras collection is mated and rebuild; Matching process is as follows:

First adopt 8 normalization algorithms of improvement of Hartley proposition to calculate the fundamental matrix F of left and right cameras, then between the two-dimensional digital image gathering by left and right two high-speed cameras, polar curve restriction relation is carried out the first coupling of spot center point, supposes left image spot central point x _i' and right image spot central point x _i'' match, 2 spot center points meet limiting constraint, and limit equation of constraint can be expressed as follows:

$x_i^{\′T}F{x_{i^{\′}}}^{\′}=0---\left(3\right)$

Wherein, x _i' be the image coordinates of the image spot central point of left camera acquisition; x _i'' be and x _i' matching is gathered the image coordinates of image spot central point by right video camera; F is the fundamental matrix between two video cameras;

On this basis all spot center points that meet limiting constraint in the image of left and right are carried out to three-dimensional reconstruction to obtain the D coordinates value of spot center point under world coordinate system, reconstruction formula is as follows:

$\left\{\begin{array}{c}{x}_i=\frac{{\mathrm{zX}}_i^{\′}}{f_1}\\ y_i=\frac{{\mathrm{zY}}_i^{\′}}{f_1}\\ z_i=\frac{f_1(f_2{t}_y-{Y_{i^{\′}}}^{\′}{t}_z)}{Y_1(r_7{X}_i^{\′}+r_8{Y}_i^{\′}+r_9{f}_1)-f_2(r_4{X}_i^{\′}+r_5{Y}_i^{\′}+r_6{f}_1)}\end{array}\right.---\left(4\right)$

Wherein, x _i'=(X _i', Y _i'), X _i', Y _i' be respectively the image spot central point x of left camera acquisition _i' horizontal stroke, ordinate under image coordinates system; x _i''=(X _i'', Y _i''), X _i'', Y _i'' be respectively the image spot central point x of right camera acquisition _{i '}' horizontal stroke, ordinate under image coordinates system; (x _i, y _i, z _i) be by two coupling spot center point x _i', x _{i '}' rebuild the three-dimensional coordinate of free token point out; f ₁, f ₂be respectively the focal length of left and right cameras; for connecting the rotation matrix of left and right cameras relation, [t _xt _yt _z] be the translation matrix of right video camera with respect to left video camera;

(3) curvature is judged

1) least square fitting space plane

Take four spot center points reconstructing in the D coordinates value of world coordinate system as basis, utilize least square fitting space plane, step is as follows:

The general expression of plane equation is:

$\left\{\begin{array}{c}\mathrm{Ax}+\mathrm{By}+\mathrm{Cz}+D=0,(C\≠0)\\ z=-\frac{A}{C}x-\frac{B}{C}y-\frac{D}{C}\end{array}\right.---\left(5\right)$

The normal vector that wherein (A, B, C) is plane; D is the distance that initial point arrives plane; Note

$a_0=-\frac{A}{D},a_1=-\frac{B}{D},a_2=-\frac{C}{D};$ Za ₀x+a ₁y+a ₂;

Select least square method to utilize n point (n>=3): (x _i, y _i, z _i), i=0,1 ...,, the above-mentioned plane of n-1 matching, makes: $S=\underset{i=0}{\overset{n-1}{\mathrm{\Σ}}}{(a_{0}x+a_{1}y+a_2-z)}^2$ Minimum;

Wherein S is the quadratic sum that a little arrives the distance of straight line;

Make S obtain minimum value, should meet: k=0,1,2; That is:

$\left\{\begin{array}{c}\mathrm{\Σ}2(a_0{x}_i+a_1{y}_i+a_2-z_i)x_{i=0}\\ \mathrm{\Σ}2(a_1{x}_i+a_1{y}_i+a_2-z_i)y_i=0\\ \mathrm{\Σ}2(a_1{x}_i+a_1{y}_i+a_2-z_i)=0\end{array}\right.---\left(6\right)$

Rebuild the 3 d space coordinate (x of spot center by four _i, y _i, z _i), i=0,1,2,3 bring above-mentioned system of equations into tries to achieve a ₀, a ₁, a ₂;

The equation that is fit Plane is: z=a ₀x+a ₁y+a ₂; The normal vector of spatial fit plane is: 2) ask the distance of tested point P ' to fit Plane

Space a bit can be expressed as to the range formula of plane:

Wherein, S _planefor the equation of spatial fit plane; D is the distance that tested point arrives plane; P '=(x ', y ', z ') be the coordinate of tested point under world coordinate system; Q=(x _q, y _q, z _q) be any point in fit Plane; ε is set threshold value; In the time of d≤ε, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes little; In the time of d > ε, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes greatly;

(4) method vector solves

Based on the method vector measurement Scheme Choice criterion of distance threshold constraint, situation one: if the tested point P ' being positioned on curved surface meets d≤ε to the distance of spatial fit plane, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes little, now think the normal vector of plane be exactly the method vector of tested point on curved surface, $\stackrel{\→}{n}=(a_0{a}_1,-1);$

Situation two: if tested point P ' is to the distance d > ε of spatial fit plane on curved surface, think that tested point P ' small neighbourhood curved surface scope intrinsic curvature changes greatly, its Proximal surface may be other quadric surfaces such as sphere, parabola, saddle face, now selects two space curves that project on curved surface to carry out solving of method vector; Its step is as follows:

1) extraction of laser stripe centerline points, coupling and reconstruction

The present invention adopts the laser stripe center line detecting method based on direction template, respectively in level, vertical, left bank 45., right bank 45.In direction, arrange the template that big or small fixed-direction is variable, be designated as respectively K ₀, K ₁, K ₂, K ₃, the every a line of two-dimensional digital image is processed respectively by these four templates; With right _irow is treated to example, for K ₀template has:

$\begin{array}{c}\left\{\begin{array}{c}{H}_j=\underset{s=0}{\overset{M-1}{\mathrm{\Σ}}}\underset{t=0}{\overset{N-1}{\mathrm{\Σ}}}{K}_0\[s\]\[t\]C\[i-\frac{M}{2}+S\]\[j-\frac{N}{2}+t\],j=\frac{N}{2},\frac{N+1}{2},...,\mathrm{col}-1\\ H_{g0}=\max (H_{\frac{N}{2},}{H}_{\frac{N}{2}+1},...,H_{\mathrm{col}-1}),\frac{N}{2}\≤j\≤\mathrm{col}-1\end{array}\right.---\left(8\right)\end{array}$

Wherein M is the corresponding line number of template; N is columns corresponding to template; K ₀[s] [] t>=0; represent the gray-scale value of point; Accordingly for template K ₁, K ₂, K ₃there is H _g1, H _g2, H _g3; Ask for H _g=max (H _g0, H _g1, H _g2, H _g3), there is the position of central point of the capable laser stripe of i at a g place; By the method, two-dimensional digital image is carried out can completing by pixel detection line by line the extraction of laser stripe center line; Complete on the basis of laser stripe central line pick-up, adopt with spot center point coupling in the present invention (2) and rebuild identical method and carry out coupling and the reconstruction of laser stripe central point, obtaining the D coordinates value of laser stripe centerline points under world coordinate system;

2) B-spline Curve matching two space curves

The present invention adopts B-spline Curve matching two space laser striped curves, and B-spline curves piecewise function expression formula is:

$\left\{\begin{array}{cc}{c}_1:p=P_0\·{N_{10}}^3+P_1\·{N_{11}}^3+P_2\·{N_{12}}^3+P_3{N_{13}}^3& u\∈\[u_2,u_3\]\\ c_2:p=P_1\·{N_{20}}^3+P_2\·{N_{21}}^3+P_3\·{N_{22}}^3+P_4{N_{23}}^3& u\∈\[u_3,u_4\]\\ c_1:p=P_2\·{N_{30}}^3+P_3\·{N_{31}}^3+P_4\·{N_{32}}^3+P_5{N_{33}}^3& u\∈\[u_4,u_5\]\end{array}\right.---\left(9\right)$

Wherein P _i(i=0,1 ... 5) represent respectively control vertex; N _ij(i=1 ... 3, j=0,1 ... 4) represent basis function; Being provided with discrete point on the curve that two camera rebuilding go out is b ₁, b ₂..., b _n; Wherein front i point is positioned at c ₁in section, k-i point is positioned at c ₂in section, n-j point is positioned at c ₃in section, above-mentioned some substitution system of equations is obtained:

Making M is the matrix of coefficients on the left side, the vector forming that P is required control vertex, and the laser stripe centerline points that p is three-dimensional reconstruction, above-mentioned equation is abbreviated as:

The normal equation that MP=p (11) can obtain matching is thus:

M'·M·P＝M'·p (12)

For near the fitting precision of curve raising intersection point, above-mentioned equation is introduced to weights; Equation after weighting is:

(M'·H'·M·P)＝(M'·H')·M·p (13)

Can ask for the equation of two curves by this weighted equation.Ask for respectively on this basis the cut arrow of two curves at tested point both direction, be designated as required method vector is:

$\stackrel{\→}{n}=\frac{{\stackrel{\→}{P}}_n\×{\stackrel{\→}{P}}_n}{|{\stackrel{\→}{P}}_m\×{\stackrel{\→}{P}}_n|}.$