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

Abstract

The invention relates to visual inspection technology, and aims to provide a calibration method for a structured light measurement system. The calibration model has wide application range, high measurement accuracy and simple calibration process. For this reason, the technical solution adopted by the present invention is that the calibration method of the projected fringe geometric distribution characteristic structured light measurement system first uses the uncertain viewing angle calibration method to obtain the coordinates of known spatial points in the camera coordinate system, and then uses the camera coordinates of these points The system coordinates, image coordinates and their coded values are used for system calibration, and the relationship between Z-direction coordinates and image information and the relationship between XY-direction coordinates and image information are respectively established. The invention is mainly applied to the occasion of visual detection.

Description

Calibration method for structured light measurement system with projected fringe geometric distribution characteristics

technical field

The invention relates to visual detection technology, in particular to a calibration method for a structured light measuring system with geometric distribution characteristics of projection fringes.

Background technique

Structured light three-dimensional visual measurement technology has the advantages of non-contact visual measurement, high speed, high degree of automation, and good flexibility. Structured light 3D vision is based on the principle of optical triangulation, and calculates the surface profile of the measured object by calculating the offset information of various light mode feature points in the collected image. The optical projector projects a certain light pattern, which makes the structured light image information easy to extract, so the measurement accuracy is high, and it is widely used in the online detection of various industrial products.

The accuracy of a structured light measurement system depends on the system calibration accuracy. The existing calibration methods for structured light measurement systems are divided into three types, namely photogrammetry based on matrix transformation, triangulation based on geometric relationship and polynomial fitting method. Photogrammetry is divided into pseudo camera method, reverse camera method and light plane method. The main disadvantage of this method is that the calibration process of the projector depends on the camera calibration parameters, resulting in the spread of camera calibration errors. The advantage is that this calibration method generally has no special restrictions on system installation, and the equipment installation and system calibration process are relatively simple to operate. The triangulation method based on the geometric relationship is to establish the mathematical expression between the 3D coordinates and a few parameters of the system according to the geometric relationship of the system, as a mathematical model for calibration and measurement. The advantage of this method is that it avoids the calibration of the projector, but the disadvantage is that the installation accuracy of the system is high, and if the model is too simplified, the accuracy will be low. The polynomial fitting method assumes that the 3D coordinates of the object to be measured can be represented by a polynomial of the coded value at the corresponding pixel in the camera image, and then the parameters of the polynomial are determined through experiments to directly establish the 2D coordinates of the camera image to the 3D spatial coordinates of the scene point mapping. This method avoids the calibration of cameras and projectors, but the calibration takes a long time and costs a lot. A spatial mapping model proposed by Lendray et al. is widely used. This method is essentially an interpolation method, and there is a large error when measuring objects outside the calibration range. In summary, it is of great significance to invent a calibration method with simple calibration device, convenient calibration process, fast calibration time and high precision.

Contents of the invention

In order to overcome the deficiencies of the prior art, the present invention aims to propose a calibration method for a structured light measurement system. The calibration model has a wide application range, high measurement accuracy, and a simple calibration process. For this reason, the technical solution adopted by the present invention is that the calibration method of the projected fringe geometric distribution characteristic structured light measurement system first uses the uncertain viewing angle calibration method to obtain the coordinates of known spatial points in the camera coordinate system, and then uses the camera coordinates of these points The system coordinates, image coordinates and their coded values are used for system calibration, and the relationship between Z-direction coordinates and image information and the relationship between XY-direction coordinates and image information are respectively established.

The specific steps for calibrating the Z direction are that the value of the Z direction of the measurement system is jointly determined by the image coordinates (u, v) and the corresponding code value p, the optical axis of the projector lens and the optical axis of the CCD camera lens have a certain angle α and assume that the projection The changing direction of the fringes projected by the instrument is parallel to the u direction of the camera. The three planes h1, h2, h3 represent three planes parallel to the imaging plane of the camera. The distances between the planes h1, h2 and the planes h2, h3 are the same, both are Δh, The intersection of plane h3 and the optical axis of the camera to the position A of the projector and the focal points of planes h2 and h1 are D and B in turn, and the intersection points of plane h1, h2 and h3 and the optical axis of the projector are C, E and G in turn. In the projector The encoded value p on the same projected ray is the same, and the rate of change of u at the same depth of the camera with the change of p conforms to the relational expression:

du/dp=kp+b (1)

Among them, du/dp is the change rate of u with the change of p, k is the slope, b is the intercept, and since u does not change with the change of v at the same depth of the camera, so there is

du/dv=0 (2)

Where du/dv is the rate of change of u with the change of v; use formula (1) and formula (2) to integrate

u＝∫(kp+b)dp (3)

Obtain the relationship function between the image coordinates (u, v) at the same depth of the camera and the corresponding coded value p, where: A ₀ is the quadratic coefficient of the coded value p, and B ₀ is the linear term of the coded value p Coefficient, D ₀ is a constant term;

u＝A ₀ p ² +B ₀ p+D ₀ (4)

Considering that in the camera coordinate system uov and the projector coordinate system u'o'v', there will be an angle β between the coordinate axis o'u' and ou, it is necessary to perform a rotation transformation on the uov coordinate system:

u ₀ ＝ucosβ+vsinβ (5)

Bring in (4) to get

ucosβ+vsinβ＝A ₀ p ² +B ₀ p+D ₀

u＝A ₀ p ² /cosβ+B ₀ p/cosβ-vtanβ+D ₀ /cosβ (6)

that is

u＝A ₁ p ² +B ₁ p+C ₁ v+D ₁ (7)

Wherein A ₁ is the quadratic term coefficient about the encoded value p, B ₁ is the first-order term coefficient about the encoded value p, C ₁ is the first-order term coefficient about the image coordinate v, and D ₁ is a constant term;

The (u,v,p) of the same camera depth is on a paraboloid, and A ₁ increases with the increase of the angle α between the projector and the optical axis of the camera lens and the depth of the camera. The unknown parameter of formula (7) is calculated by quadratic method;

Knowing ΔABC～ΔADEΔAFG from the principle of similar triangles, we get

Among them, p ₀ is the coding value on the optical axis of the projector, and l represents the length between two points. From the knowledge of geometric optics, we can know that the fringe period width is also linearly related to the depth of the camera, that is:

Where r ₁ is the first-order coefficient of the numerator item in the fraction with respect to h, r ₂ is the constant term of the denominator in the fraction, r ₃ is the first-order coefficient of the denominator in the fraction with respect to h, and r ₄ is the denominator in the fraction the constant term of the term;

The coefficient A ₁ in the surface equation (7) is normalized, that is, to eliminate the influence of the stripe thickness change on the encoding difference of different depths of the camera, and get:

Among them, u/A ₁ and v/A ₁ are the normalized image coordinates. Since the influence of stripe thickness changes on the encoding difference is eliminated, B ₁ /A ₁ changes linearly with the camera depth h, and the constant term D ₁ /A ₁ changes with the law of the quadratic function of the camera depth h, that is:

B ₁ /A ₁ =s ₁ h+s ₂

D ₁ /A ₁ =t ₀ h ² +t ₁ h+t ₂ (11)

Among them, s ₁ is the coefficient of the first term of the first-order formula, s ₂ is the constant term of the first-order formula, t ₀ is the coefficient of the second-order term of the second-order formula, t ₁ is the coefficient of the first-order term of the second-order formula, and t ₂ is the coefficient of the second-order term of the second-order formula. Constant term;

Substituting formula (9) and formula (11) into formula (7) can get

Considering the elimination of the camera lens distortion and the influence of the optical axis of the projector and the camera lens not being coplanar on the horizontal plane, a quadratic error compensation model is adopted, where k ₀ ~ k ₅ , l ₀ ~ l ₅ are error correction coefficients;

So formula (12) becomes

Among them, a ₀ and a ₁ are the constant term and the first-order coefficient in the quadratic coefficient of h respectively, and b ₀ to b ₇ are the constant term, the first-order coefficient and the quadratic term in the quadratic coefficient of h respectively Coefficients, c ₀ ~ c ₇ are the constant term, the first-order coefficient and the second-order coefficient in the quadratic coefficient of h, respectively;

The coordinates Z _Ci of the obtained N groups of known spatial points in the Z direction in the camera coordinate system and the corresponding image information (u _i , v _i , p _i ) satisfy the conditions of formula (14), that is,

PX=Q (15)

where X is the coefficient matrix and is a column vector of 18×1, P is a matrix of the form N×18, and Q is a column vector of the form N×1, where

X＝[g ₀ g ₁ ... g _i ... g ₁₇ ] ^T

construct error function

Use the Levenburg-marquardt algorithm to obtain the unknown parameters in the formula (17), so the coordinate Z _C in the Z direction under the camera coordinate system is obtained by combining the image information (u, v, p) with the unary cubic equation to solve the formula and solve the equation;

The specific steps to calibrate the XY direction are:

The XY direction value of the system is determined by the distortion-corrected image coordinates (u, v) and the Z direction value Z _C in the camera coordinate system, using the formula

In the formula, s is a scale factor, and m ₁₁ ~m ₃₄ are polynomial parameters. During calibration, the polynomial parameter m can be calculated by using the coordinates (X _C , Y _C , Z _C ) of the known space point in the camera coordinate system and the distortion-corrected image coordinate points (u, v) combined with the least square method ₁₁ ～m ₃₄ , when measuring, use the image coordinates (u,v) and the Z direction value Z _C to enter the polynomial to get the coordinate values (X _C , Y _C ) corresponding to the X and Y directions respectively, so using the image information ( u, v, p) to obtain the three-dimensional information (X _C , Y _C , Z _C ) of the measured object in the camera coordinate system.

To obtain the coordinates (X _W , Y _W , Z _W ) in the world coordinate system, use the coordinate conversion formula (20) to convert the coordinates in the camera coordinate system to the coordinates in the world coordinate system, where R is the rotation matrix, T is the translation matrix;

During calibration, the target is placed in the field of view of the camera, and the target is moved. Every time a position is moved, structured light stripes need to be projected and images are taken. The coordinates of the feature points on the target in the camera coordinate system are obtained by using the uncertain viewing angle calibration method. Through image processing Obtain the image coordinates of the feature points and their eigenvalues, and bring the known quantities into formula (17) and formula (19) to obtain the system parameters through calculation. In actual measurement, you can use formula (18) and formula (19) to obtain the The coordinates of the measurement points in the camera coordinate system, and then through the formula (20), the coordinates of these points in the world coordinate system can be obtained.

Features and beneficial effects of the present invention are:

The invention is suitable for grating and binary fringe projection in the form of vertical light stripes. The relationship between image feature points and their encoding values and space coordinates is established through the derivation of the geometric model. It overcomes the shortcomings of strict system constraints in the traditional triangulation method based on geometric relations, and also solves the problem that objects outside the calibration range cannot be measured in the polynomial fitting method. The calibration process is simple and convenient, the measurement accuracy is high, and the applicable measurement range is large.

Description of drawings:

Figure 1 Schematic diagram of the geometric model of the system,

Figure 2 The comparison chart of the calibration feature points and the actual measurement points,

Figure 3 Measurement effect diagram.

detailed description

The calibration method proposed by this system does not require the assistance of precision guide rails, the calibration process is simple, and the calibration accuracy is high, so it is very suitable for on-site calibration.

This calibration method is composed of two parts. Firstly, the coordinates of the known spatial points in the camera coordinate system are obtained by using the uncertain viewing angle calibration method, and then the system calibration is carried out by using the camera coordinate system coordinates and image coordinates of these points and their coded values. The relationship between the coordinates in the Z direction and the image information and the relationship between the coordinates in the XY direction and the image information.

1 Calibration in the Z direction

The Z-direction value of the measurement system is jointly determined by the image coordinates (u, v) and the corresponding coded value p. Since there is a certain angle α between the optical axis of the projector lens and the optical axis of the CCD camera lens, and it is assumed that the changing direction of the stripes projected by the projector is parallel to the u direction of the camera, it is known from the correlation principle of geometric optics that the width of the stripes projected by the projector increases with The increase of the projection distance shows a linear increase trend, so the rate of change of u at the same depth of the camera with the change of p conforms to the relational expression:

du/dp=kp+b (1)

Where du/dp is the rate of change of u as p changes, k is the slope, and b is the intercept. And because u does not change with the change of v at the same depth of the camera, so there is

du/dv=0 (2)

Where du/dv is the rate of change of u as v changes.

Integrate using formula (1) and formula (2)

u＝∫(kp+b)dp (3)

The relationship function between the image coordinates (u, v) at the same depth of the camera and the corresponding coded value p can be obtained, where: A ₀ is the quadratic coefficient of the coded value p, and B ₀ is the primary coefficient of the coded value p term coefficient, D ₀ is a constant term.

u＝A ₀ p ² +B ₀ p+D ₀ (4)

Considering that in the camera coordinate system uov and the projector coordinate system u'o'v', the coordinate axis o'u' and ou will have a small angle β, so it is necessary to perform a rotation transformation on the uov coordinate system

u ₀ ＝ucosβ+vsinβ (5)

Bring in (4) to get

ucosβ+vsinβ＝A ₀ p ² +B ₀ p+D ₀

u＝A ₀ p ² /cosβ+B ₀ p/cosβ-vtanβ+D ₀ /cosβ (6)

that is

u＝A ₁ p ² +B ₁ p+C ₁ v+D ₁ (7)

Among them, A ₁ is the quadratic term coefficient about the encoded value p, B ₁ is the first-order term coefficient about the encoded value p, C ₁ is the first-order term coefficient about the image coordinate v, and D ₁ is a constant term.

It can be seen that (u, v, p) of the same camera depth is on a paraboloid, and A ₁ increases with the angle α between the projector and the optical axis of the camera lens and the camera depth. During calibration, the unknown parameters of formula (7) can be calculated by using the acquired image information combined with the least square method.

Let's explore how the parameters of the paraboloid change with the depth of the camera.

Figure 1 shows the geometric model of the system, where the angle between the optical axis of the projector and the camera is α, and the coding value p on the same ray projected by the projector is the same, such as C, E, and G have the same coding value. The three planes h1, h2, h3 represent three planes parallel to the imaging plane of the camera, and the distances between the planes h1, h2 and the planes h2, h3 are the same, both are Δh. Knowing ΔABC～ΔADE～ΔAFG from the principle of similar triangles, we can get

Among them, p ₀ is the coded value on the optical axis of the projector, and l represents the length between two points. It can be seen from Figure 1 that the length and depth corresponding to the same encoding difference at different camera depths have a linear relationship, and from the knowledge of geometric optics, it can be known that the fringe period width also has a linear relationship with the camera depth, that is

Where r ₁ is the first-order coefficient of the numerator item in the fraction with respect to h, r ₂ is the constant term of the denominator in the fraction, r ₃ is the first-order coefficient of the denominator in the fraction with respect to h, and r ₄ is the denominator in the fraction The constant term of the term.

The coefficient A ₁ in the surface equation (7) is normalized, that is, to eliminate the influence of the variation of stripe thickness on the encoding difference of different depths of the camera, we can get

Among them, u/A ₁ and v/A ₁ are the normalized image coordinates. The following mainly considers the change law of B ₁ /A ₁ and D ₁ /A ₁ with the camera depth h. Since the influence of stripe thickness variation on the encoding difference is eliminated, B ₁ /A ₁ changes linearly with the camera depth h, and the constant term D ₁ /A ₁ changes with the law of the quadratic function of the camera depth h, namely

B ₁ /A ₁ =s ₁ h+s ₂

D ₁ /A ₁ =t ₀ h ² +t ₁ h+t ₂ (11)

Among them, s ₁ is the coefficient of the first term of the first-order formula, s ₂ is the constant term of the first-order formula, t ₀ is the coefficient of the second-order term of the second-order formula, t ₁ is the coefficient of the first-order term of the second-order formula, and t ₂ is the coefficient of the second-order term of the second-order formula. Constant term.

Substituting formula (9) and formula (11) into formula (7) can get

Considering the elimination of the camera lens distortion and the influence of the optical axis of the projector and the camera lens not being coplanar on the horizontal plane, a quadratic error compensation model is adopted, where k ₀ ~k ₅ and l ₀ ~l ₅ are error correction coefficients.

So formula (12) becomes

Among them, a ₀ and a ₁ are the constant term and the first-order coefficient in the quadratic coefficient of h respectively, and b ₀ to b ₇ are the constant term, the first-order coefficient and the quadratic term in the quadratic coefficient of h respectively The coefficients, c ₀ to c ₇ are the constant term, the first-order coefficient and the second-order coefficient in the quadratic coefficient of h, respectively.

The coordinates Z _Ci of the obtained N groups of known spatial points in the Z direction in the camera coordinate system and the corresponding image information (u _i , v _i , p _i ) satisfy the conditions of formula (14), that is,

PX=Q (15)

where X is the coefficient matrix and is a column vector of 18×1, P is a matrix of the form N×18, and Q is a column vector of the form N×1, where

X＝[g ₀ g ₁ ... g _i ... g ₁₇ ] ^T

construct error function

Use the Levenburg-marquardt algorithm to obtain the unknown parameters in formula (17), so the coordinate Z _C in the Z direction in the camera coordinate system can be obtained by solving the equation through the image information (u, v, p) combined with the unary cubic equation solution formula.

2. Calibration in XY direction

The XY direction values of the system are jointly determined by the distortion-corrected image coordinates (u, v) and the Z direction value Z _C in the camera coordinate system. use the formula

In the formula, s is a scale factor, and m ₁₁ ~m ₃₄ are polynomial parameters. During calibration, the polynomial parameter m can be calculated by using the coordinates (X _C , Y _C , Z _C ) of the known space point in the camera coordinate system and the distortion-corrected image coordinate points (u, v) combined with the least square method ₁₁ ~ m ₃₄ . When measuring, use the image coordinates (u, v) and the Z direction value Z _C to enter the polynomial to obtain the corresponding coordinate values (X _C , Y _C ) in the X and Y directions, so using the image information (u, v, p ) to obtain the three-dimensional information (X _C , Y _C , Z _C ) of the measured object in the camera coordinate system.

To obtain the coordinates in the world coordinate system, the coordinates in the camera coordinate system obtained by the coordinate conversion formula (20) can be converted into coordinates in the world coordinate system, where R is the rotation matrix and T is the translation matrix.

When calibrating, place the target in the field of view of the camera, move the target, and project structured light stripes and capture images for each position moved. The coordinates of the feature points on the target in the camera coordinate system are obtained by using the uncertain viewing angle calibration method, and the image coordinates and their feature values of the feature points are obtained by image processing. Bring known quantities into formula (17) and formula (19) to obtain system parameters through calculation. In actual measurement, the coordinates of the measured points in the camera coordinate system can be obtained through formula (18) and formula (19), and then the coordinates of these points in the world coordinate system can be obtained through formula (20).

Fig. 2 is the comparison diagram of the measured value and the set value of the feature point on the target, wherein the red star represents the measured value, and the blue triangle represents the set value, shows by analyzing the experimental data that the system measurement error is within 0.1mm, indicating that the present invention It can be better applied to the calibration of the structured light measurement system. Figure 3 is an effect diagram of the system measuring the 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).