CN106595517A - Structured light measuring system calibration method based on projecting fringe geometric distribution characteristic - Google Patents

Abstract

The invention relates to the visual detection technology, and provides a calibration method of a structured light measuring system. According to a calibration model, the application range is wide, the measuring precision is high, and the calibration process is simple. According to the technical scheme, the structured light measuring system calibration method based on a projecting fringe geometric distribution characteristic includes: firstly obtaining coordinates of known spatial points in a camera coordinate system by employing an uncertain viewing angle calibration method, then performing system calibration by employing the camera coordinate system coordinates and image coordinates of the points and coding values thereof, and respectively establishing the relation between Z-direction coordinates and image information and the relation between XY direction coordinates and the image information. The method is mainly applied to occasions of visual detection.

Description

Projection striped geometric distribution feature structure light measurement system scaling method

Technical field

The present invention relates to vision detection technology, more particularly to projects striped geometric distribution feature structure light measurement system mark Determine method.

Background technology

Structured light three-dimensional vision e measurement technology, the noncontact with vision measurement, speed are fast, high degree of automation, flexible The advantages of good.Structured light three-dimensional vision is based on optic triangle method principle, by the various optical mode characteristic points for calculating collection image Offset information inverse go out the surface profile of testee.The optical mode that the projection of optical projection device determines so that structure light image Information is easy to extract, thus certainty of measurement is higher, is widely used in the on-line checking of various industrial products.

The precision of structured light measurement system depends on system calibrating precision.Existing structured light measurement system scaling method point For three kinds, the respectively photogrammetry based on matrixing, the triangulation and polynomial fitting method based on geometrical relationship. Photogrammetry is divided into pseudo- camera method, reverse camera method and optical plane method.The major defect of the method is the calibrated of projector Journey depends on camera calibration parameter, and so as to cause the diffusion of camera calibration error, advantage is the scaling method generally to being Without special constraint, equipment is installed and compares simple to operate with system calibrating process for the installation of system.Triangulation based on geometrical relationship Method is the mathematic(al) representation set up between 3D coordinates and a few parameter of system according to the geometrical relationship of system, used as demarcation With the mathematical model of measurement.The advantage of the method is that of avoiding the demarcation of projector, has the disadvantage that system installation accuracy is required higher, Model can cause precision low if excessively simplifying.Polynomial fitting method assumes that the 3D coordinates of determinand can be with which in video camera figure The polynomial repressentation of the encoded radio as at respective pixel, is determined by experiment polynomial parameter then, directly sets up shooting Mapping of 2 dimension coordinates of machine image to the space 3-dimensional coordinate of scene point.This method avoid the mark to video camera and projector It is fixed, but demarcate time-consuming longer and relatively costly.A kind of space reflection model that Lendray et al. is proposed is adopted in a large number, should Method is substantially a kind of interpolation method, has larger error when measuring the object outside calibration range.In sum, invent one Kind of caliberating device is simple, and calibration process is convenient, and the nominal time is fast and scaling method of high precision has very great meaning.

The content of the invention

To overcome the deficiencies in the prior art, it is contemplated that proposing a kind of scaling method of structured light measurement system, the mark Cover half type scope of application width, certainty of measurement are high, and calibration process is simple.For this purpose, the technical solution used in the present invention is, striped is projected Geometric distribution feature structure light measurement system scaling method, obtains camera coordinate system first with uncertain visual angle scaling method Under known spatial point coordinate, recycle these point camera coordinate system coordinate and image coordinate and its encoded radio system System is demarcated, and sets up the relation of relation and XY direction coordinate of the Z-direction coordinate with image information and image information respectively.

Comprising the concrete steps that for Z-direction is demarcated, the Z-direction numerical value of measuring system is by image coordinate (u, v) and corresponding volume Code value p determines that projector lens optical axis and ccd video camera camera lens optical axis have certain angle α and assume projector projects jointly The stripe order recognition direction for going out is parallel with the u direction of video camera, three planes h1, h2, h3 represent three it is parallel with camera imaging face Plane, plane h1, h2 and plane h2, the distance of h3 be identical, is Δ h, and plane h3 is with camera optical axis intersection point to projector Position A lines are followed successively by D, B with the focus of plane h2, h1, and plane h1, h2, h3 and projector optical axes crosspoint are followed successively by C, E, G, Encoded radio p on the same light that projector projects go out is identical, and the u in the same depth of video camera is with the change of p Rate of change meet relational expression：

Du/dp=kp+b (1)

Wherein du/dp is u with the rate of change of the change of p, and k is slope, and b is intercept, and due in the same depth of video camera On degree, u does not change with the change of v, so and having

Du/dv=0 (2)

Wherein du/dv is u with the rate of change of the change of v；It is integrated using formula (1) and formula (2)

U=∫ (kp+b) dp (3)

The relation function of the image coordinate (u, v) in the same depth of video camera and corresponding encoded radio p is obtained, its In：A₀It is the secondary term coefficient with regard to encoded radio p, B₀It is the Monomial coefficient with regard to encoded radio p, D₀It is constant term；

U=A₀p²+B₀p+D₀ (4)

In view of in camera coordinate system uov and projector coordinates system u'o'v', coordinate axess o'u' and ou has angle β Exist, need rotation transformation to be done to uov coordinate systems：

u₀=ucos β+vsin β (5)

Bring formula (4) into obtain

Ucos β+vsin β=A₀p²+B₀p+D₀

U=A₀p²/cosβ+B₀p/cosβ-vtanβ+D₀/cosβ (6)

As

U=A₁p²+B₁p+C₁v+D₁ (7)

Wherein A₁It is the secondary term coefficient with regard to encoded radio p, B₁It is the Monomial coefficient with regard to encoded radio p, C₁It is with regard to figure As the Monomial coefficient of coordinate v, D₁It is constant term；

(u, the v, p) of same camera depth is on a parabola, and A₁With projector and camera lens light The increase of the angle α and camera depth of axle and increase, using obtain image information combine method of least square to formula (7) not Know that parameter is calculated；

Δ ABC～Δ ADE Δ AFG are known by similar triangle theory, is obtained

Wherein p₀For the encoded radio on projector optical axis, l represents the length of point-to-point transmission, by striped knowable to geometric optics knowledge Periodic width is also linear with camera depth, i.e.,：

Wherein r₁For Monomial coefficient of the molecule item with regard to h, r in fraction₂For the constant term of denominator term in fraction, r₃To divide Monomial coefficient of the denominator term with regard to h, r in formula₄For the constant term of denominator term in fraction；

To the coefficient A in surface equation formula (7)₁Normalized is done, that is, eliminates the change of striped thickness different to video camera The impact of the coding difference of depth, obtains：

Wherein u/A₁And v/A₁It is the image coordinate after normalization, due to eliminating the change of striped thickness to encoding the shadow of difference Ring, so B₁/A₁As camera depth h linearly changes, constant term D₁/A₁With rule of the camera depth h in quadratic function Rule change, i.e.,：

B₁/A₁=s₁h+s₂

D₁/A₁=t₀h²+t₁h+t₂ (11)

Wherein s₁It is the Monomial coefficient of expression of first degree, s₂It is the constant term of expression of first degree, t₀It is quadratic secondary term coefficient, t₁It is quadratic Monomial coefficient, t₂It is quadratic constant term；

Bring formula (9) and formula (11) into formula (7) to obtain

Consider to eliminate the optical axis non-coplanar band in the horizontal plane of camera lens distortion and projector and camera lens The impact for coming, using second order error compensation model, wherein k₀～k₅, l₀～l₅It is error correction coefficient；

Therefore formula (12) is changed into

Wherein a₀, a₁It is the constant term and Monomial coefficient in the secondary term coefficient with regard to h respectively, b₀～b₇It is to close respectively Constant term in the secondary term coefficient of h, Monomial coefficient and secondary term coefficient, c₀～c₇It is the secondary term coefficient with regard to h respectively In constant term, Monomial coefficient and secondary term coefficient；

The coordinate Z of the N groups known spatial point of acquisition Z-direction under camera coordinate system_CiWith image corresponding informance (u_i,v_i, p_i) meet formula (14) condition, as

PX=Q (15)

Wherein X is coefficient matrix, is 18 × 1 column vector, and matrix of the form that P is for N × 18, Q are that form is N × 1 Column vector, wherein

X=[g₀ g₁ … g_i … g₁₇]^T

Instrument error function

Obtain unknown parameter in formula (17) using Levenburg-marquardt algorithms, thus by image information (u, v, P) the coordinate Z for obtaining Z-direction under camera coordinate system is solved equation with reference to simple cubic equation solution formula_C；

Demarcate comprising the concrete steps that for XY directions：

The XY direction values of system are by Z-direction numerical value under the image coordinate (u, v) and camera coordinate system of Jing distortion corrections Z_CIt is common to determine, using formula

In formula, s is scale factor, m₁₁～m₃₄It is polynomial parameters.When demarcating, sat in video camera using known spatial point Coordinate (X under mark system_C,Y_C,Z_C) and Jing distortion corrections image coordinate point (u, v) with reference to method of least square can calculate it is many Item formula parameter m₁₁～m₃₄, in measurement, using image coordinate (u, v) and Z-direction numerical value Z_CXY side is drawn by bringing multinomial into To the corresponding coordinate figure (X of difference_C,Y_C), draw measured object under camera coordinate system hence with image information (u, v, p) Three-dimensional information (X_C,Y_C,Z_C)。

Coordinate (the X under world coordinate system is obtained_W,Y_W,Z_W), sat using the video camera that Formula of Coordinate System Transformation (20) is obtained Coordinate Conversion under mark system is the coordinate under world coordinate system, and wherein R is spin matrix, and T is translation matrix；

During demarcation, target is placed in camera field of view, moving target mark, often moving a position needs projective structure light Striped shooting image, obtain coordinate of the characteristic point under camera coordinate system on target using uncertain visual angle scaling method, The image coordinate and its eigenvalue of characteristic point are obtained by image procossing, known quantity are brought into formula (17) and formula (19) by calculating Systematic parameter is obtained, during actual measurement, you can seat of the measured point under camera coordinate system is obtained by formula (18) and formula (19) Mark, then these coordinates under world coordinate system are obtained by formula (20).

The characteristics of of the invention and beneficial effect are：

The present invention is applied to the grating and two-value striped mode of delivery of vertical light strips.Built by the derivation of geometric model The relation of image characteristic point and its encoded radio and space coordinatess is found.Overcome traditional triangulation based on geometrical relationship The strict shortcoming of middle system restriction, cannot measure the outer object of calibration range in also solving the problems, such as polynomial fitting method.The mark Determine process simple and convenient, certainty of measurement is high, be suitable for measurement range big.

Description of the drawings：

Fig. 1 system geometric model schematic diagrams,

Fig. 2 feature point for calibration and actual spot of measurement comparison diagram,

Fig. 3 measurement effect figures.

Specific embodiment

The scaling method that the system is proposed does not need the auxiliary of precise guide rail, and calibration process is easy, and stated accuracy is high, therefore It is especially suitable for field calibration.

This scaling method is made up of two parts, is obtained under camera coordinate system first with uncertain visual angle scaling method The coordinate of known spatial point, recycles the camera coordinate system coordinate and image coordinate and its encoded radio of these points to carry out system mark It is fixed, the relation of relation and XY direction coordinate of the Z-direction coordinate with image information and image information is set up respectively.

The demarcation in 1Z directions

The Z-direction numerical value of measuring system is determined jointly by image coordinate (u, v) and corresponding encoded radio p.Due to projection Instrument camera lens optical axis and ccd video camera camera lens optical axis there is certain angle α and assume the stripe order recognition direction that goes out of projector projects with The u direction of video camera is parallel, is known by geometric optics relative theory, and the width of fringe that projector projects go out is with the increasing of projection distance Big linear increase tendency, thus the u in the same depth of video camera meets relational expression with the rate of change of the change of p：

Du/dp=kp+b (1)

Wherein du/dp is u with the rate of change of the change of p, and k is slope, and b is intercept.Again due in the same depth of video camera On degree, u does not change with the change of v, so and having

Du/dv=0 (2)

Wherein du/dv is u with the rate of change of the change of v.

It is integrated using formula (1) and formula (2)

U=∫ (kp+b) dp (3)

The relation function of the image coordinate (u, v) in the same depth of video camera and corresponding encoded radio p can be obtained, Wherein：A₀It is the secondary term coefficient with regard to encoded radio p, B₀It is the Monomial coefficient with regard to encoded radio p, D₀It is constant term.

U=A₀p²+B₀p+D₀ (4)

In view of in camera coordinate system uov and projector coordinates system u'o'v', coordinate axess o'u' and ou has small Angle β, it is therefore desirable to rotation transformation is done to uov coordinate systems

u₀=ucos β+vsin β (5)

Bring formula (4) into obtain

Ucos β+vsin β=A₀p²+B₀p+D₀

U=A₀p²/cosβ+B₀p/cosβ-vtanβ+D₀/cosβ (6)

As

U=A₁p²+B₁p+C₁v+D₁ (7)

Wherein A₁It is the secondary term coefficient with regard to encoded radio p, B₁It is the Monomial coefficient with regard to encoded radio p, C₁It is with regard to figure As the Monomial coefficient of coordinate v, D₁It is constant term.

Understand that (u, the v, p) of same camera depth is on a parabola, and A₁With projector and video camera mirror Head the angle α of optical axis and the increase of camera depth and increase.During demarcation, least square is combined using the image information for obtaining Method is calculated to the unknown parameter of formula (7).

Below exploring the Changing Pattern that parabola parameter changes with camera depth.

If Fig. 1 is system geometric model, the wherein optical axis included angle of projector and video camera is α, is gone out in projector projects Encoded radio p on same light is identical, such as C, and E, G have identical encoded radio.Three planes h1, h2, h3 represent three with The parallel plane in camera imaging face, plane h1, h2 and plane h2, the distance of h3 are identical, are Δ h.By similar triangle theory Know Δ ABC～Δ ADE～Δ AFG, can obtain

Wherein p₀For the encoded radio on projector optical axis, l represents the length of point-to-point transmission.As can be seen from Figure 1 it is same Coding difference is linear in the different corresponding length of camera depth and depth, and understands striped by geometric optics knowledge Periodic width is also linear with camera depth, i.e.,

Wherein r₁For Monomial coefficient of the molecule item with regard to h, r in fraction₂For the constant term of denominator term in fraction, r₃To divide Monomial coefficient of the denominator term with regard to h, r in formula₄For the constant term of denominator term in fraction.

To the coefficient A in surface equation formula (7)₁Normalized is done, that is, eliminates the change of striped thickness different to video camera The impact of the coding difference of depth, can obtain

Wherein u/A₁And v/A₁The image coordinate after normalization, below main consider B₁/A₁And D₁/A₁With video camera depth The Changing Pattern of degree h.Due to eliminating the change of striped thickness to encoding the impact of difference, so B₁/A₁As camera depth h is in Linear change, constant term D₁/A₁As rules of the camera depth h in quadratic function changes, i.e.,

B₁/A₁=s₁h+s₂

D₁/A₁=t₀h²+t₁h+t₂ (11)

Wherein s₁It is the Monomial coefficient of expression of first degree, s₂It is the constant term of expression of first degree, t₀It is quadratic secondary term coefficient, t₁It is quadratic Monomial coefficient, t₂It is quadratic constant term.

Bring formula (9) and formula (11) into formula (7) to obtain

Consider to eliminate the optical axis non-coplanar band in the horizontal plane of camera lens distortion and projector and camera lens The impact for coming, using second order error compensation model, wherein k₀～k₅, l₀～l₅It is error correction coefficient.

Therefore formula (12) is changed into

Wherein a₀, a₁It is the constant term and Monomial coefficient in the secondary term coefficient with regard to h respectively, b₀～b₇It is to close respectively Constant term in the secondary term coefficient of h, Monomial coefficient and secondary term coefficient, c₀～c₇It is the secondary term coefficient with regard to h respectively In constant term, Monomial coefficient and secondary term coefficient.

The coordinate Z of the N groups known spatial point of acquisition Z-direction under camera coordinate system_CiWith image corresponding informance (u_i,v_i, p_i) meet formula (14) condition, as

PX=Q (15)

Wherein X is coefficient matrix, is 18 × 1 column vector, and matrix of the form that P is for N × 18, Q are that form is N × 1 Column vector, wherein

X=[g₀ g₁ … g_i … g₁₇]^T

Instrument error function

Unknown parameter in formula (17) is obtained using Levenburg-marquardt algorithms, therefore image information can be passed through (u, v, p) solves equation the coordinate Z for obtaining Z-direction under camera coordinate system with reference to simple cubic equation solution formula_C。

The demarcation in 2XY directions

The XY direction values of system are by Z-direction numerical value under the image coordinate (u, v) and camera coordinate system of Jing distortion corrections Z_CIt is common to determine.Using formula

In formula, s is scale factor, m₁₁～m₃₄It is polynomial parameters.When demarcating, sat in video camera using known spatial point Coordinate (X under mark system_C,Y_C,Z_C) and Jing distortion corrections image coordinate point (u, v) with reference to method of least square can calculate it is many Item formula parameter m₁₁～m₃₄.In measurement, using image coordinate (u, v) and Z-direction numerical value Z_CXY side is drawn by bringing multinomial into To the corresponding coordinate figure (X of difference_C,Y_C), draw measured object under camera coordinate system hence with image information (u, v, p) Three-dimensional information (X_C,Y_C,Z_C)。

The coordinate under world coordinate system is obtained, using under the camera coordinate system that Formula of Coordinate System Transformation (20) is obtained Coordinate Conversion is the coordinate under world coordinate system, and wherein R is spin matrix, and T is translation matrix.

During demarcation, target is placed in camera field of view, moving target mark, often moving a position needs projective structure light Striped shooting image.Coordinate of the characteristic point under camera coordinate system on target is obtained using uncertain visual angle scaling method, The image coordinate and its eigenvalue of characteristic point are obtained by image procossing.Known quantity is brought into formula (17) and formula (19) by calculating Obtain systematic parameter.During actual measurement, you can obtain seat of the measured point under camera coordinate system by formula (18) and formula (19) Mark, then these coordinates under world coordinate system are obtained by formula (20).

Fig. 2 is the comparison diagram of the measured value with setting value of the characteristic point on target, and wherein Red Star represents measured value, blueness three It is angular to represent setting value, show that systematic measurement error shows that the present invention can be preferable in 0.1mm by analyzing experimental data Be applied in the demarcation of structured light measurement system.Fig. 3 is the design sketch of systematic survey face.

Claims (3)

1. a kind of projection striped geometric distribution feature structure light measurement system scaling method, is characterized in that, first with uncertain Visual angle scaling method obtains the coordinate of the known spatial point under camera coordinate system, recycles the camera coordinate system of these points to sit Mark and image coordinate and its encoded radio carry out system calibrating, set up relation and the XY directions of Z-direction coordinate and image information respectively The relation of coordinate and image information.

2. projection striped geometric distribution feature structure light measurement system scaling method as claimed in claim 1, is characterized in that, mark Determine comprising the concrete steps that for Z-direction, the Z-direction numerical value of measuring system is jointly true by image coordinate (u, v) and corresponding encoded radio p Determine, projector lens optical axis and ccd video camera camera lens optical axis have the stripe order recognition that certain angle α and hypothesis projector projects go out Direction is parallel with the u direction of video camera, and three planes h1, h2, h3 represent three planes parallel with camera imaging face, plane H1, h2 and plane h2, the distance of h3 are identical, are Δ h, plane h3 and camera optical axis intersection point to projector position A line with The focus of plane h2, h1 is followed successively by D, B, and plane h1, h2, h3 and projector optical axes crosspoint are followed successively by C, E, G, in projector projects The encoded radio p on same light for going out is identical, and the u in the same depth of video camera meets with the rate of change of the change of p Relational expression：

Du/dp=kp+b (1)

Wherein du/dp is u with the rate of change of the change of p, and k is slope, and b is intercept, and due to the u in the same depth of video camera Do not change with the change of v, so and having

Du/dv=0 (2)

Wherein du/dv is u with the rate of change of the change of v；It is integrated using formula (1) and formula (2)

U=∫ (kp+b) dp (3)

The relation function of the image coordinate (u, v) in the same depth of video camera and corresponding encoded radio p is obtained, wherein：A₀It is With regard to the secondary term coefficient of encoded radio p, B₀It is the Monomial coefficient with regard to encoded radio p, D₀It is constant term；

U=A₀p²+B₀p+D₀ (4)

In view of in camera coordinate system uov and projector coordinates system u'o'v', coordinate axess o'u' and ou has angle β and deposits Needing to do rotation transformation to uov coordinate systems：

u₀=ucos β+vsin β (5)

Bring formula (4) into obtain

U cos β+vsin β=A₀p²+B₀p+D₀

U=A₀p²/cosβ+B₀p/cosβ-vtanβ+D₀/cosβ (6)

As

U=A₁p²+B₁p+C₁v+D₁ (7)

Wherein A₁It is the secondary term coefficient with regard to encoded radio p, B₁It is the Monomial coefficient with regard to encoded radio p, C₁It is to sit with regard to image The Monomial coefficient of mark v, D₁It is constant term；

(u, the v, p) of same camera depth is on a parabola, and A₁With projector and the folder of camera lens optical axis The increase of angle α and camera depth and increase, using obtain image information combine unknown parameter of the method for least square to formula (7) Calculated；

Δ ABC～Δ ADE～Δ AFG is known by similar triangle theory, is obtained

$\frac{l\left(BC\right)}{L}=\frac{l\left(DE\right)}{L+\mathrm{\Δ}h}=\frac{l\left(FG\right)}{L+2\mathrm{\Δ}h}---\left(8\right)$

Wherein p₀For the encoded radio on projector optical axis, l represents the length of point-to-point transmission, by fringe period knowable to geometric optics knowledge Width is also linear with camera depth, i.e.,：

$A_1=\frac{r_{1}h+r_2}{r_{3}h+r_4}---\left(9\right)$

Wherein r₁For Monomial coefficient of the molecule item with regard to h, r in fraction₂For the constant term of denominator term in fraction, r₃For in fraction Monomial coefficient of the denominator term with regard to h, r₄For the constant term of denominator term in fraction；

To the coefficient A in surface equation formula (7)₁Normalized is done, that is, is eliminated striped thickness and is changed to video camera different depth The impact of coding difference, obtains：

$\frac{u}{A_1}=p^2+\frac{B_1}{A_1}p+C_1\frac{v}{A_1}+\frac{D_1}{A_1}---\left(10\right)$

Wherein u/A₁And v/A₁It is the image coordinate after normalization, due to eliminating the change of striped thickness to encoding the impact of difference, institute With B₁/A₁As camera depth h linearly changes, constant term D₁/A₁As rules of the camera depth h in quadratic function becomes Change, i.e.,：

B₁/A₁=s₁h+s₂

D₁/A₁=t₀h²+t₁h+t₂ (11)

Wherein s₁It is the Monomial coefficient of expression of first degree, s₂It is the constant term of expression of first degree, t₀It is quadratic secondary term coefficient, t₁It is two The Monomial coefficient of secondary formula, t₂It is quadratic constant term；

Bring formula (9) and formula (11) into formula (7) to obtain

$u=\frac{r_{1}h+r_2}{r_{3}h+r_4}(p^2+(s_{1}h+s_2)p+(t_0{h}^2+t_{1}h+t_2\left)\right)+C_{1}v---\left(12\right)$

The optical axis for considering to eliminate camera lens distortion and projector and camera lens non-coplanar in the horizontal plane brings Affect, using second order error compensation model, wherein k₀～k₅, l₀～l₅It is error correction coefficient；

$\left\{\begin{array}{c}u=k_0{u}_d^2+k_1{v}_d^2+k_2{u}_d{v}_d+k_3{u}_d+k_4{v}_d+k_5\\ v=l_0{u}_d^2+l_1{v}_d^2+l_2{u}_d{v}_d+l_3{u}_d+l_4{v}_d+l_5\end{array}\right.---\left(13\right)$

Therefore formula (12) is changed into

$\begin{array}{c}{h}^3+\left(a_0+a_{1}p\right)h^2+\left(b_0+b_{1}p+b_2{p}^2+b_3{u}_d^2+b_4{v}_d^2+b_5{u}_d{v}_d+b_6{u}_d+b_7{v}_d\right)h\\ +\left(c_0+c_{1}p+c_2{p}^2+c_3{u}_d^2+c_4{v}_d^2+c_5{u}_d{v}_d+c_6{u}_d+c_7{v}_d\right)=0\end{array}---\left(14\right)$

Wherein a₀, a₁It is the constant term and Monomial coefficient in the secondary term coefficient with regard to h respectively, b₀～b₇It is with regard to h respectively Constant term in secondary term coefficient, Monomial coefficient and secondary term coefficient, c₀～c₇In being the secondary term coefficient with regard to h respectively Constant term, Monomial coefficient and secondary term coefficient；

The coordinate Z of the N groups known spatial point of acquisition Z-direction under camera coordinate system_CiWith image corresponding informance (u_i,v_i,p_i) full Sufficient formula (14) condition, as

PX=Q (15)

Wherein X is coefficient matrix, is 18 × 1 column vector, and matrix of the form that P is for N × 18, Q are the row that form is N × 1 Vector, wherein

X=[g₀ g₁ … g_i … g₁₇]^T

$P=\left[\begin{array}{cccccccccccccccccc}{Z}_{C1}^2& p_1{Z}_{C1}^2& Z_{C1}& p_1{Z}_{C1}& p_1^2{Z}_{C1}& u_1^2{Z}_{C1}& v_1^2{Z}_{C1}& u_1{v}_1{Z}_{C1}& u_1{Z}_{C1}& v_1{Z}_{C1}& 1& p_1& p_1^2& u_1^2& v_1^2& u_1{v}_1& u_1& v_1\\ Z_{C2}^2& p_2{Z}_{C2}^2& Z_{C2}& p_2{Z}_{C2}& p_2^2{Z}_{C2}& u_2^2{Z}_{C2}& v_2^2{Z}_{C2}& u_2{v}_2{Z}_{C2}& u_2{Z}_{C2}& v_2{Z}_{C2}& 1& p_2& p_2^2& u_2^2& v_2^2& u_2{v}_2& u_2& v_2\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ Z_{Ci}^2& p_i{Z}_{Ci}^2& Z_{Ci}& p_i{Z}_{Ci}& p_i^2{Z}_{Ci}& u_i^2{Z}_{Ci}& v_i^2{Z}_{Ci}& u_i{v}_i{Z}_{Ci}& u_i{Z}_{Ci}& v_i{Z}_{Ci}& 1& p_i& p_i^2& u_i^2& v_i^2& u_i{v}_i& u_i& v_i\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}\\ Z_{CN}^2& p_N{Z}_{CN}^2& Z_{CN}& p_N{Z}_{CN}& p_N^2{Z}_{CN}& u_N^2{Z}_{CN}& v_N^2{Z}_{CN}& u_N{v}_N{Z}_{CN}& u_N{Z}_{CN}& v_N{Z}_{CN}& 1& p_N& p_N^2& u_N^2& v_N^2& u_N{v}_N& u_N& v_N\end{array}\right]$

$Q=-{\left[\begin{array}{cccccc}{Z}_{C1}^3& Z_{C2}^3& ...& {Z_{Ci}}^3& ...& {Z_{CN}}^3\end{array}\right]}^T---\left(16\right)$

Instrument error function

$\begin{array}{c}F=\mathrm{\Σ}\[\left(g_0+g_1{p}_i\right)Z_{Ci}^2+\left(g_2+g_3{p}_i+g_4{p_i}^2+g_5{u_i}^2+g_6{v_i}^2+g_7{u}_i{v}_i+g_8{u}_i+g_9{v}_i\right)Z_{Ci}\\ +\left(g_{10}+g_{11}{p}_i+g_{12}{p_i}^2+g_{13}{u_i}^2+g_{14}{v_i}^2+g_{15}{u}_i{v}_i+g_{16}{u}_i+g_{17}{v}_i\right)+Z_{Ci}^3{\]}^2\end{array}---\left(17\right)$

Unknown parameter in formula (17) is obtained using Levenburg-marquardt algorithms, therefore is tied by image information (u, v, p) Close simple cubic equation solution formula and solve equation the coordinate Z for obtaining Z-direction under camera coordinate system_C；

$\begin{array}{c}{Z}_{Ci}^3+\left(g_0+g_1{p}_i\right)Z_{Ci}^2+\left(g_2+g_3{p}_i+g_4{p_i}^2+g_5{u_i}^2+g_6{v_i}^2+g_7{u}_i{v}_i+g_8{u}_i+g_9{v}_i\right)Z_{Ci}\\ +\left(g_{10}+g_{11}{p}_i+g_{12}{p_i}^2+g_{13}{u_i}^2+g_{14}{v_i}^2+g_{15}{u}_i{v}_i+g_{16}{u}_i+g_{17}{v}_i\right)=0\end{array}---\left(18\right)$

Demarcate comprising the concrete steps that for XY directions：

The XY direction values of system are by Z-direction numerical value Z under the image coordinate (u, v) and camera coordinate system of Jing distortion corrections_CJointly It is determined that, using formula

$\left[\begin{array}{c}su\\ sv\\ s\end{array}\right]=\left[\begin{array}{cccc}{m}_{11}& m_{12}& m_{13}& m_{14}\\ m_{21}& m_{22}& m_{23}& m_{24}\\ m_{31}& m_{32}& m_{33}& m_{34}\end{array}\right]\left[\begin{array}{c}{X}_C\\ Y_C\\ Z_C\\ 1\end{array}\right]---\left(19\right)$

In formula, s is scale factor, m₁₁～m₃₄It is polynomial parameters.When demarcating, using known spatial point in camera coordinate system Under coordinate (X_C,Y_C,Z_C) and image coordinate point (u, v) of Jing distortion corrections can calculate multinomial with reference to method of least square Parameter m₁₁～m₃₄, in measurement, using image coordinate (u, v) and Z-direction numerical value Z_CXY directions point are drawn by bringing multinomial into Not corresponding coordinate figure (X_C,Y_C), measured object under camera coordinate system three has been drawn hence with image information (u, v, p) Dimension information (X_C,Y_C,Z_C)。

3. projection striped geometric distribution feature structure light measurement system scaling method as claimed in claim 1, is characterized in that, Obtain the coordinate (X under world coordinate system_W,Y_W,Z_W), using the seat under the camera coordinate system that Formula of Coordinate System Transformation (20) is obtained Mark is converted to the coordinate under world coordinate system, and wherein R is spin matrix, and T is translation matrix；

$\left[\begin{array}{c}{X}_w\\ Y_w\\ Z_w\end{array}\right]=R\left[\begin{array}{c}{X}_C\\ Y_C\\ Z_C\end{array}\right]+T---\left(20\right)$

During demarcation, target is placed in camera field of view, moving target mark, often moving a position needs projective structure striations And shooting image, coordinate of the characteristic point under camera coordinate system on target is obtained using uncertain visual angle scaling method, pass through Image procossing obtains the image coordinate and its eigenvalue of characteristic point, brings known quantity into formula (17) and formula (19) and is obtained by calculating Systematic parameter, during actual measurement, you can coordinate of the measured point under camera coordinate system is obtained by formula (18) and formula (19), then These coordinates under world coordinate system are obtained by formula (20).