CN113465544B - Stripe projection three-dimensional measurement nonlinear error correction method - Google Patents

Abstract

The invention discloses a non-linear error correction method for fringe projection three-dimensional measurement. Project N colored stripe patterns

to the surface of the object to be measured; Step S3: the camera collects the modulated color fringe image of the object to be measured; assuming ideally, the color fringes are expressed as In ( _x , y); under the influence of nonlinear non-color crosstalk, the color fringes are expressed as I′ _n (x, y); under the influence of nonlinear color crosstalk, the color stripes are expressed as I″ _n (x, y); Step S4: by setting the appropriate weighting coefficient α, calculate the red color under the influence of nonlinear color crosstalk Weighted stripes I″ _n,a (x,y) of channel stripes I″ _n,r (x,y) and blue channel stripes I″ _n,b (x,y); Step S5: adopt N-step phase shift algorithm Calculate the actual phase distribution φ″ _a (x,y) of the weighted fringe I″ _{n ,a} (x,y); since the 2nd harmonic amplitude of the weighted fringe I″ n,a (x,y) is zero, such that The nonlinear error Δφ″ _a (x, y) of the actual phase distribution φ″ _a (x, y) is greatly reduced.

Description

A nonlinear error correction method for fringe projection 3D measurement

technical field

The invention belongs to the technical field of three-dimensional measurement, and in particular relates to a nonlinear error correction method for fringe projection three-dimensional measurement.

Background technique

Fringe projection 3D measurement has the advantages of non-contact, high precision and fast speed, and has been widely used in various fields, such as industrial inspection, reverse engineering, virtual reality, etc. However, the gamma nonlinearity of the fringe projection system can distort the phase-shifted fringe image, and the phase distribution calculated from it has periodic errors, which in turn lead to 3D measurement errors.

Because the nonlinear error period of the N-step phase shift method is N times the corresponding fringe period, some scholars use the double N-step phase shift method to calculate two phases with π/N phase shift, and calculate the average phase to compensate for the nonlinearity However, this method needs to collect 2N fringe images and calculate the average phase of the two phases, which affects the measurement speed of the fringe projection system.

In addition, some scholars perform Hilbert transform on N-step phase-shift fringes to generate another group of phase-shift fringes, and calculate the average phase of the two groups of phase-shift fringes to correct nonlinear errors, but this method involves frequency domain operations, and the calculation The amount is too large, and the robustness is general.

In addition, some scholars correct nonlinear errors through pre-calibration processes, such as establishing a phase-error mapping table, estimating Gamma values, etc., but such methods require pre-calibration of the system and are less flexible.

In summary, how to correct the nonlinear error of the fringe projection system has important practical significance.

SUMMARY OF THE INVENTION

The present invention provides a nonlinear error correction method for fringe projection three-dimensional measurement, so as to solve the problems existing in the above-mentioned background technology.

In order to achieve the above purpose, the technical solution adopted by the present invention is: a method for correcting nonlinear errors of fringe projection three-dimensional measurement, which specifically includes the following steps:

Step S1: build a fringe projection three-dimensional measurement system, including a projector and a camera, the projector and the camera are triggered to start work synchronously, and the projector, the camera and the measured object form a triangulation relationship;

至被测物体表面，其中彩色条纹图案

的红色通道编码余弦条纹

蓝色通道编码正弦条纹

绿色通道不编码任何信息，直接置零；Step S2: The projector projects N color stripe patterns in sequence

to the surface of the measured object, in which the color stripe pattern

The red channel encodes the cosine fringe

Blue channel encoded sinusoidal stripes

The green channel does not encode any information and is directly set to zero;

Step S3: The camera collects the modulated color fringe image of the object to be measured; it is assumed that in an ideal situation, the color fringes are represented as I _n (x, y); under the influence of nonlinear non-color crosstalk, the color fringes are represented as I′ _n (x, y); under the influence of nonlinear color crosstalk, the color stripes are expressed as I″ _n (x, y);

Step S4: Calculate the weighted stripes of the red channel stripes I″ _n,r (x,y) and the blue channel stripes I″ _n,b (x,y) under the influence of nonlinear color crosstalk by setting an appropriate weighting coefficient α I″ _{n, a} (x, y);

Step S5: Calculate the actual phase distribution φ″ _a (x, y) of the weighted fringe I″ _{n,a (} x,y) by using the N-step phase shift algorithm; The amplitude of the second harmonic is zero, which greatly reduces the nonlinear error Δφ″ _a (x, y) of its actual phase distribution φ″ _a (x, y).

其红色通道编码的余弦条纹

蓝色通道编码的正弦条纹

分别表示为：Further, in the step S2, N color stripe patterns

its red channel encoded cosine fringes

Blue channel encoded sinusoidal stripes

They are respectively expressed as:

In the formula: n=0,1,2,...,N-1; (x ^p , y ^p ) represents the pixel coordinates of the projector; T represents the fringe period; δ _n =2πn/N represents the phase shift amount.

Further, ideally in the step S3, the color stripes I _n (x, y), the red channel stripes I _n,r (x, y) and the blue channel stripes I _n,b (x, y) respectively represent for:

I _n,r =A+B cos(φ+δ _n );

I _n,b =A+B sin(φ+δ _n );

where (x, y) represents the pixel coordinates of the camera; A(x, y), B(x, y) and φ(x, y) represent the average intensity, modulation intensity and ideal phase distribution, respectively.

Further, in the step S3, under the influence of nonlinear non-color crosstalk, the color stripes I' _n (x, y), the red channel stripes I' _n,r (x, y) and the blue channel stripes I' _n,b (x, y) are expressed as:

I′ _n,r =[A+B cos(φ+δ _n )] ^γ ;

I′ _n,b =[A+B sin(φ+δ _n )] ^γ ;

In the formula: γ represents the nonlinear Gamma value;

Further, the Fourier expansions of the red channel stripes I′ _n,r (x,y) and the blue channel stripes I′ _n,b (x,y) are respectively expressed as:

where a ₀ represents the DC component of the color stripe I′ _n (x, y); a _m represents the red channel stripe I′ _n,r (x,y) or the blue channel stripe I′ _n,b (x, The mth harmonic amplitude of y).

Further, in the step S3, the color stripes I″ _n (x, y) under the influence of nonlinear and color crosstalk, the red channel stripes I″ _n,r (x, y) and the blue channel stripes I″ _n,b (x,y) can be expressed as:

I″ _n,r =κ _rr I′ _n,r +κ _br I′ _n,b ;

I″ _n,b =κ _rb I′ _n,r +κ _bb I′ _n,b ;

where κ _rr , κ _br , κ _rb , κ _bb represent the color crosstalk coefficients of the red and blue channels; κ _rb , κ _br are much smaller than κ _rr , κ _bb .

Further, in the step S4, the weighted stripes I″ _n,a (x, y) of the red channel stripes I″ _n,r (x,y) and the blue channel stripes I″ _n,b (x,y) can be Expressed as:

I″ _n,a =I″ _n,r + αI″ _n,b =(κ _rr +ακ _rb )I′ _n,r +(κ _br +ακ _bb )I′ _n,b ;

Further, when η=κ _rr +ακ _rb =κ _br +ακ _bb , the Fourier expansion of the weighted fringes I″ _n,a (x,y) can be expressed as:

In the formula: 2ηa ₀ represents the DC component of the weighted fringe I″ _n,a (x,y); 2ηa′ _m =2ηa _m cos(mπ/4) represents the mth of the weighted fringe I″ _n,a (x,y) Subharmonic amplitude; φ _a =φ-π/4 represents the ideal phase distribution of the weighted fringes I″ _n,a (x,y).

Further, in the step S4, the calculation formula of the weighting coefficient α is as follows:

Further, in the step S5, the actual phase distribution φ" _a (x, y) of the weighted stripe I″ _{n, a} (x, y) is calculated by using the N-step phase shift algorithm, and its calculation formula is as follows:

In particular, taking the three-step phase shift method as an example, ignoring the m≥6 harmonics, the actual phase distribution φ″ _a (x, y) of the weighted fringes I″ _n,a (x,y), the calculation formula is as follows:

Further, in the step S5, the nonlinear error Δφ" _a (x, y) of the actual phase distribution φ " _a (x, y), taking the three-step phase shift method as an example, the calculation formula is as follows:

Substitute m=1, 2, 4, and 5 into a′ _m = a _m cos(mπ/4), we can get:

Further, the calculation formula of the nonlinear error Δφ″ _a (x, y) can be simplified as:

In the formula: the second harmonic amplitude a′ ₂ is eliminated, and the nonlinear error Δφ″ _a (x, y) is greatly reduced.

The beneficial effects of adopting the above technical solutions are:

1. The non-linear error correction method for fringe projection three-dimensional measurement provided by the present invention only needs to sequentially project N colored fringe patterns onto the surface of the object to be measured, and the measurement speed is fast.

2. The non-linear error correction method for fringe projection three-dimensional measurement provided by the present invention does not require an additional pre-calibration process and has high measurement flexibility.

3. The present invention provides a nonlinear error correction method for fringe projection three-dimensional measurement, which can greatly reduce the nonlinear error and has high measurement accuracy.

Description of drawings

Fig.1 Schematic diagram of nonlinear error correction of fringe projection 3D measurement;

(b)红色通道编码的余弦条纹

(c)蓝色通道编码的正弦条纹

Figure 2(a) Colored fringe pattern projected by the projector

(b) Cosine fringes encoded by the red channel

(c) Sine fringes encoded by the blue channel

Figure 3(a) Ideal red channel stripe I _n,r (x,y); (b) Red channel stripe I″ _n,r (x,y) under the influence of nonlinear color crosstalk; (c) Nonlinear Weighted fringes I″ _n,a (x,y) under the influence of color crosstalk; (d) red channel fringes I″ _n,r (x,y), blue channel fringes I″ _n,b (x,y) and Nonlinear errors of weighted fringes I″ _n,a (x,y) Δϕ″ _r (x,y), Δϕ″ _b (x,y) and Δϕ″ _a (x,y);

Figure 4(a) Object under test; (b) Color stripe I″ _n (x,y); (c) Red channel stripe I″ _n,r (x,y); (d) Blue channel stripe I″ _{n , b} (x, y); (e) weighted stripes I″ _{n, a} (x, y);

Figure 5 (a) The actual phase distribution φ″ _r (x, y) of the red channel stripe I″ _n,r (x,y); (b) The actual phase distribution of the blue channel stripe I″ _n,b (x,y) Phase distribution φ″ _b (x, y); (c) actual phase distribution φ″ _a (x, y) of weighted fringe I″ _n,a (x, y);

Detailed ways

Below with reference to the accompanying drawings, through the description of the embodiments, the specific embodiments of the present invention will be described in further detail, the purpose is to help those skilled in the art to have a more complete, accurate and in-depth understanding of the concept and technical solutions of the present invention, and contribute to its implementation.

As shown in FIGS. 1 to 5 , the present invention is a method for correcting nonlinear errors of fringe projection three-dimensional measurement, taking the three-step phase shift method as an example, and specifically includes the following steps:

Example 1:

Step S1: build a fringe projection three-dimensional measurement system, including a projector and a camera, the projector and the camera are triggered to start work synchronously, and the projector, the camera and the measured object form a triangulation relationship; Figure 1 shows the fringe projection three-dimensional measurement system. Schematic diagram of measurement nonlinear error correction;

至被测物体表面，其中彩色条纹图案

的红色通道编码余弦条纹

蓝色通道编码正弦条纹

绿色通道不编码任何信息，直接置零；图2(a)展示了彩色条纹图案

图2(b)展示了红色通道编码余弦条纹

图2(c)展示了蓝色通道编码正弦条纹

Step S2: The projector projects 3 color stripe patterns in sequence

to the surface of the measured object, in which the color stripe pattern

The red channel encodes the cosine fringe

Blue channel encoded sinusoidal stripes

The green channel does not encode any information and is set to zero directly; Figure 2(a) shows the color fringe pattern

Figure 2(b) shows the red channel encoded cosine fringes

Figure 2(c) shows the blue channel encoded sinusoidal fringes

Step S3: The camera collects the modulated color fringe image of the object to be measured; it is assumed that in an ideal situation, the color fringes are represented as I _n (x, y); under the influence of nonlinear non-color crosstalk, the color fringes are represented as I′ _n (x, y); under the influence of non-linear color crosstalk, the color stripes are expressed as I″ _n (x, y); Figure 3(a) shows the red channel stripes I n of the ideal color stripes I _n (x, y) _{, r} (x,y); Figure 3(b) shows the red channel stripe I″ _n,r (x,y) of the color stripe I″ _n (x,y) under the influence of nonlinear color crosstalk; by setting the red channel and the color crosstalk coefficient of the blue channel κ _rr =κ _bb =1.0, κ _rb =κ _br =0, we can obtain _{I′n(x,y)=I″n (} x,y);

Step S4: Calculate the weighted stripes of the red channel stripes I″ _n,r (x,y) and the blue channel stripes I″ _n,b (x,y) under the influence of nonlinear color crosstalk by setting the weighting coefficient α=1 I″ _n,a (x,y)=I″ _n,r (x,y)+I″ _n,b (x,y); Figure 3(c) shows the weighted fringe I under the influence of nonlinear color crosstalk " _n,a (x,y);

Step S5: Calculate the actual phase distribution φ″ _a (x, y) of the weighted fringe I″ _{n,a (} x,y) by using a three-step phase shift algorithm; The sub-harmonic amplitude is zero, which greatly reduces the nonlinear error Δφ″ _a (x, y) of its actual phase distribution φ″ _a (x, y); Figure 3(d) shows the red channel stripe I″ _n,r (x,y), non-linear errors Δφ″ _r (x _, y), Δφ″ _{b (} x, y) and Δφ″ _a (x, y). As can be seen from Figure 3(d), Δφ″ _a (x, y) is much smaller than Δφ″ _r (x, y), Δφ″ _b (x, y).

Example 2:

Step S1: build a fringe projection three-dimensional measurement system, including a projector and a camera, the projector and the camera are triggered to start work synchronously, and the projector, the camera and the measured object form a triangulation relationship; Figure 1 shows the fringe projection three-dimensional measurement system. Schematic diagram of measurement nonlinear error correction;

至被测物体表面；图4(a)展示了被测物体图像。Step S2: The projector projects 3 color stripe patterns in sequence

to the surface of the object to be measured; Figure 4(a) shows the image of the object to be measured.

Step S3: the camera collects the modulated color fringe image of the measured object; Figure 4(b) shows the collected color fringes I″ _n (x, y); Figure 4 (c) shows the red channel fringes I″ _{n, r} (x, y); Figure 4(d) shows the blue channel stripes I″ _{n, b} (x, y);

计算红色通道条纹I″_n,r(x,y)和蓝色通道条纹I″_n,b(x,y)的加权条纹I″_n,a(x,y)＝I″_n,r(x,y)+αI″_n,b(x,y)；图4(e)展示了加权条纹I″_n,a(x,y)。Step S4: by setting the weighting coefficient

Calculate the weighted fringes I″ _{n ,a} (x,y) = I″ _{n,r (} x ,y)+αI″ _n,b (x,y); Figure 4(e) shows the weighted fringes I″ _n,a (x,y).

Step S5: Using a three-step phase shift algorithm to calculate the red channel stripes I″ _n,r (x,y), the blue channel stripes I″ _n,b (x,y) and their weighted stripes I″ _n,a (x ,y) actual phase distributions φ″ _r (x,y), φ″ _b (x,y) and φ″ _a (x,y); Figure 5 shows the red channel fringes I″ _n,r (x,y ), the actual phase distributions of the blue channel stripes I″ _n,b (x,y) and the weighted stripes I″ _n,a (x,y) ϕ″ _r (x,y), ϕ″ _b (x,y) and φ″ _a (x,y). It can be seen from Figure 5 that the nonlinear error of φ″ _a (x, y) is much smaller than the nonlinear errors of φ″ _r (x, y) and φ″ _b (x, y).

The present invention has been exemplarily described above with reference to the accompanying drawings. Obviously, the specific implementation of the present invention is not limited by the above-mentioned manner, as long as various insubstantial improvements made by the method concept and technical solution of the present invention are adopted; or After improvement, it is within the protection scope of the present invention to directly apply the above-mentioned ideas and technical solutions of the present invention to other occasions.

Claims (8)

1. A stripe projection three-dimensional measurement nonlinear error correction method is characterized by comprising the following steps: the method specifically comprises the following steps:

step S1: the method comprises the following steps of constructing a fringe projection three-dimensional measurement system, wherein the fringe projection three-dimensional measurement system comprises a projector and a camera, the projector and the camera are triggered to start to work synchronously, and the projector, the camera and a measured object form a triangulation relation;

step S2: the projector sequentially projects N color stripe patterns

To the surface of the object to be measured, in which the colour stripe pattern

Red channel coded cosine stripes

Blue channel coded sinusoidal stripes

The green channel does not encode any information and is directly set to zero;

step S3: the camera collects the color stripe image modulated by the measured object; assuming ideal conditions, the color stripes are denoted as I_n(x, y); color stripes are denoted as I 'without the influence of nonlinear color crosstalk'_n(x, y); the color fringes are denoted as I ″, under the influence of nonlinear chromatic crosstalk_n(x,y)；

Step S4: calculating the red channel stripe I' under the influence of nonlinear colored crosstalk by setting a proper weighting coefficient alpha_n,r(x, y) and blue channel stripe I ″)_n,bWeighted stripe I ″ (x, y)_n,a(x,y)；

Step S5: calculating weighted stripe I' by adopting N-step phase shift algorithm_n,a(x, y) actual phase distribution φ ″)_a(x, y); because of the weighted stripe I ″)_n,aThe amplitude of the 2 nd harmonic of (x, y) is zero, so that its actual phase distribution phi ″, is_aNon-linearity error of (x, y) < delta phi_a(x, y) is greatly reduced.

2. The method for correcting the nonlinear error in the fringe projection three-dimensional measurement according to claim 1, wherein: the N color stripe patterns in the step S2

Cosine stripe of its red channel code

Blue channel coded sinusoidal stripes

Respectively expressed as:

in the formula: n-0, 1,2,. N, N-1; (x)^p,y^p) Pixel coordinates representing a projector; t represents a fringe period; delta_n2N/N represents the amount of phase shift.

3. The method for correcting the nonlinear error in the fringe projection three-dimensional measurement according to claim 1, wherein: in step S3, color stripe I is ideally selected_n(x, y) red channel stripe I thereof_n,r(x, y) and blue channel stripe I_n,b(x, y) are respectively expressed as:

I_n,r＝A+B cos(φ+δ_n)；

I_n,b＝A+B sin(φ+δ_n)；

in the formula: (x, y) represents pixel coordinates of the camera; a (x, y), B (x, y) and φ (x, y) represent the average intensity, modulation intensity and ideal phase distribution, respectively.

4. The method according to claim 3, wherein the method comprises the following steps: the non-linear color crosstalk influence lower color stripe I 'in the step S3'_n(x, y) its red channel stripe I'_n,r(x, y) and blue channel stripe I'_n,b(x, y) are respectively expressed as:

I′_n,r＝[A+B cos(φ+δ_n)]^γ；

I′_n,b＝[A+B sin(φ+δ_n)]^γ；

in the formula: gamma represents a nonlinear Gamma value;

further, a red channel stripe I'_n,r(x, y) and blue channel stripe I'_n,bThe fourier expansions of (x, y) are respectively expressed as:

in the formula: a is₀Denotes color stripe I'_nA direct current component of (x, y); a is_mRespectively represent red channel stripe I'_n,r(x, y) or blue channel stripe l'_n,bThe mth harmonic amplitude of (x, y).

5. The method according to claim 4, wherein the method comprises the following steps: color stripe I' under the influence of non-linearity and color crosstalk in the step S3_n(x, y) its red channel stripe I ″)_n,r(x, y) and blue channel stripe I ″)_n,b(x, y) may be represented as:

I″_n,r＝κ_rrI′_n,r+κ_brI′_n,b；

I″_n,b＝κ_rbI′_n,r+κ_bbI′_n,b；

in the formula kappa_rr,κ_br,κ_rb,κ_bbRepresenting color crosstalk coefficients of the red channel and the blue channel; kappa_rb,κ_brMuch less than kappa_rr,κ_bb。

6. The method according to claim 5, wherein the method comprises the following steps: the red channel stripe I ″' in step S4_n,r(x, y) and blue channel stripe I ″)_n,bWeighted stripe I ″ (x, y)_n,a(x, y) may be represented as:

I″_n,a＝I″_n,r+αI″_n,b＝(κ_rr+ακ_rb)I′_n,r+(κ_br+ακ_bb)I′_n,b；

further, when η ═ κ_rr+ακ_rb＝κ_br+ακ_bbTime, weighted stripe I ″)_n,aThe Fourier expansion of (x, y) can be expressed as:

in the formula: 2 eta a₀Denotes a weighted stripe I ″)_n,aA direct current component of (x, y); 2 η a'_m＝2ηa_mcos (m π/4) represents the weighted stripe I ″_n,a(x, y) th harmonic amplitude; phi is a_aPhi-pi/4 denotes a weighted stripe I ″_n,aIdeal phase distribution of (x, y).

7. The method according to claim 6, wherein the method comprises the following steps: in step S4, a weighting factor α is given, and the calculation formula is as follows:

8. the method according to claim 6, wherein the method comprises the following steps: in step S5, a weighted stripe I ″ is calculated by using an N-step phase shift algorithm_n,a(x, y) actual phase distribution φ ″)_a(x, y) which is calculated as follows:

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