CN113465544B - Stripe projection three-dimensional measurement nonlinear error correction method - Google Patents
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Abstract
The invention discloses a stripe projection three-dimensional measurement nonlinear error correction method, which comprises the following steps: step S1: a fringe projection three-dimensional measurement system is set up, and a triangulation relation is formed by a projector, a camera and a measured object; step S2: the projector sequentially projects N color stripe patterns
To the surface of the object to be measured; step S3: the camera collects the color stripe image modulated by the measured object; assuming ideal conditions, the color stripes are denoted as In(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 crosstalkn(x, y); step S4: calculating the red channel stripe I' under the influence of nonlinear colored crosstalk by setting a proper weighting coefficient alphan,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 algorithmn,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 ″, isaNon-linearity error of (x, y) < delta phia(x, y) is greatly reduced.
Description
Technical Field
The invention belongs to the technical field of three-dimensional measurement, and particularly relates to a stripe projection three-dimensional measurement nonlinear error correction method.
Background
The fringe projection three-dimensional measurement has the advantages of non-contact, high precision, high speed and the like, and is widely applied to various fields such as industrial detection, reverse engineering, virtual reality and the like. However, the Gamma nonlinearity of fringe projection systems distorts the phase-shifted fringe image, and the phase distribution calculated therefrom has a periodic error, which in turn leads to three-dimensional measurement errors.
Because the nonlinear error period of the N-step phase shift method is N times of the corresponding fringe period, part of scholars calculate two phases with pi/N phase shift by using the double N-step phase shift method and calculate the average phase to compensate the nonlinear error, but the method needs to acquire 2N fringe images and calculate the average phase of the two phases, thereby influencing the measurement speed of the fringe projection system.
In addition, some scholars generate another set of phase shift stripes by performing hilbert transform on the N-step phase shift stripes, and calculate the average phase of the two sets of phase shift stripes to correct the nonlinear error.
In addition, some scholars correct the non-linear error through a pre-calibration process, such as establishing a phase-error mapping table, estimating a Gamma value, and the like, but such methods need to calibrate the system in advance and have poor flexibility.
In summary, how to correct the non-linear error of the fringe projection system has important practical significance.
Disclosure of Invention
The invention provides a stripe projection three-dimensional measurement nonlinear error correction method, which aims to solve the problems in the background technology.
In order to achieve the purpose, the invention adopts the technical scheme that: a fringe projection three-dimensional measurement nonlinear error correction 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, whereinColor 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 In(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 crosstalkn(x,y)；
Step S4: calculating the red channel stripe I' under the influence of nonlinear colored crosstalk by setting a proper weighting coefficient alphan,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 algorithmn,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 ″, isaNon-linearity error of (x, y) < delta phia(x, y) is greatly reduced.
Further, in the step S2, N color stripe patterns
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,yp) Pixel coordinates representing a projector; t represents a fringe period; deltan2N/N represents the amount of phase shift.
Further, in step S3, the color stripe I is ideally selectedn(x, y) red channel stripe I thereofn,r(x, y) and blue channel stripe In,b(x, y) are respectively expressed as:
In,r＝A+B cos(φ+δn)；
In,b＝A+B sin(φ+δn)；
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.
Further, the color stripe I 'without the influence of the nonlinear 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) are respectively expressed as:
I′n,r＝[A+B cos(φ+δn)]γ；
I′n,b＝[A+B sin(φ+δn)]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 ismRespectively represent red channel stripe I'n,r(x, y) or blue channel stripe l'n,bThe mth harmonic amplitude of (x, y).
Further, the color stripe I ″ under the influence of the non-linear and color crosstalk in the step S3n(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＝κrrI′n,r+κbrI′n,b；
I″n,b＝κrbI′n,r+κbbI′n,b；
in the formula kapparr,κbr,κrb,κbbRepresenting color crosstalk coefficients of the red channel and the blue channel; kapparb,κbrMuch less than kapparr,κbb。
Further, in the step S4, the red channel stripe I ″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＝(κrr+ακrb)I′n,r+(κbr+ακbb)I′n,b；
further, when η ═ κrr+ακrb＝κbr+ακbbTime, 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＝2ηamcos (m π/4) represents the weighted stripe I ″n,a(x, y) th harmonic amplitude; phi is aaPhi-pi/4 denotes a weighted stripe I ″n,aIdeal phase distribution of (x, y).
Further, in step S4, a coefficient α is weighted, and the calculation formula is as follows:
further, in the step S5, a weighted stripe I ″ is calculated by using an N-step phase shift algorithmn,a(x, y) actual phase distribution φ ″)a(x, y) which is calculated as follows:
in particular, taking the three-step phase shift method as an example, neglecting m ≧ 6 th harmonic, weighted stripe I ″n,a(x, y) actual phase distribution φ ″)a(x, y) which is calculated as follows:
further, the actual phase distribution φ "in the step S5aNon-linearity error of (x, y) < delta phia(x, y), taking the three-step phase shift method as an example, the calculation formula is as follows:
substituting m ═ 1,2,4,5 into a'm＝amcos (m π/4), we can get:
further, nonlinear errorThe difference Δ φaThe formula for the calculation of (x, y) can be simplified as:
in the formula: eliminating the 2 nd harmonic amplitude a'2Greatly reduces the nonlinear error delta phi ″)a(x,y)。
The beneficial effect of adopting above technical scheme is:
1. the stripe projection three-dimensional measurement nonlinear error correction method provided by the invention only needs to sequentially project N color stripe patterns to the surface of a measured object, and the measurement speed is high.
2. The stripe projection three-dimensional measurement nonlinear error correction method provided by the invention does not need an additional pre-calibration process and has high measurement flexibility.
3. The stripe projection three-dimensional measurement nonlinear error correction method provided by the invention can greatly reduce nonlinear errors and has high measurement precision.
Drawings
FIG. 1 is a schematic diagram of the nonlinear error correction of fringe projection three-dimensional measurement;
FIG. 2(a) color fringe pattern projected by projector
(b) Red channel coded cosine stripes
(c) Blue channel coded sinusoidal stripes
FIG. 3(a) ideally shows the red channel stripe In,r(x, y); (b) red channel stripe I' under the influence of nonlinear chromatic crosstalkn,r(x, y); (c) weighted stripe I' under the influence of nonlinear colored crosstalkn,a(x, y); (d) red channel stripe I ″)n,r(x, y), blue channel stripe I ″)n,b(x, y) and weighted stripe I ″)n,aNon-linearity error of (x, y) < delta phir(x,y)、Δφ″b(x, y) and Δ φ ″)a(x,y)；
FIG. 4(a) an object under test; (b) color stripe In(x, y); (c) red channel stripe I ″)n,r(x, y); (d) blue channel stripe I ″)n,b(x, y); (e) weighted stripe I ″)n,a(x,y)；
FIG. 5(a) Red channel stripe I ″n,r(x, y) actual phase distribution φ ″)r(x, y); (b) blue channel stripe I ″)n,b(x, y) actual phase distribution φ ″)b(x, y); (c) weighted stripe I ″)n,a(x, y) actual phase distribution φ ″)a(x,y)；
Detailed Description
The following detailed description of the embodiments of the present invention will be given with reference to the accompanying drawings for a purpose of helping those skilled in the art to more fully, accurately and deeply understand the concept and technical solution of the present invention and to facilitate its implementation.
As shown in fig. 1 to 5, the present invention is a fringe projection three-dimensional measurement nonlinear error correction method, which takes a three-step phase shift method as an example, and specifically comprises the following steps:
example 1:
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; FIG. 1 shows a schematic diagram of the nonlinear error correction of fringe projection three-dimensional measurement;
step S2: the projector sequentially projects 3 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; FIG. 2(a) shows a color stripe pattern
FIG. 2(b) shows the red channel encoded cosine stripes
FIG. 2(c) shows the blue channel encoded sinusoidal stripes
Step S3: the camera collects the color stripe image modulated by the measured object; assuming ideal conditions, the color stripes are denoted as In(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 crosstalkn(x, y); FIG. 3(a) shows the color stripe I in the ideal casenRed channel stripe I of (x, y)n,r(x, y); FIG. 3(b) shows color stripe I ″' under the influence of nonlinear chromatic crosstalknRed channel stripe I ″ (x, y)n,r(x, y); by setting the color crosstalk coefficient k of the red and blue channelsrr＝κbb＝1.0，κrb＝κbrL 'can be obtained as'n(x,y)＝I″n(x,y)；
Step S4: calculating the red channel stripe I' under the influence of nonlinear colored crosstalk by setting the weighting coefficient alpha to 1n,r(x, y) and blue channel stripe I ″)n,bWeighted stripe I ″ (x, y)n,a(x,y)＝I″n,r(x,y)+I″n,b(x, y); FIG. 3(c) shows weighted fringes I' under the influence of nonlinear colored crosstalkn,a(x,y)；
Step S5: using three-step phase shift calculationMethod for calculating weighted stripe I ″)n,a(x, y) actual phase distribution φ ″)a(x, y); weighted stripe I ″)n,aThe amplitude of the 2 nd harmonic of (x, y) is zero, so that its actual phase distribution phi ″, isaNon-linearity error of (x, y) < delta phia(x, y) is greatly reduced; FIG. 3(d) shows the red channel stripe I ″n,r(x, y), blue channel stripe I ″)n,b(x, y) and weighted stripe I ″)n,aNon-linearity error of (x, y) < delta phir(x,y)、Δφ″b(x, y) and Δ φ ″)a(x, y). As can be seen in FIG. 3(d), Δ φ ″)a(x, y) is much less than Δ φr(x,y)、Δφ″b(x,y)。
Example 2:
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; FIG. 1 shows a schematic diagram of the nonlinear error correction of fringe projection three-dimensional measurement;
step S2: the projector sequentially projects 3 color stripe patterns
To the surface of the object to be measured; fig. 4(a) shows an image of the object to be measured.
Step S3: the camera collects the color stripe image modulated by the measured object; FIG. 4(b) shows the color stripe I ″, which is collectedn(x, y); FIG. 4(c) shows the red channel stripe I ″n,r(x, y); FIG. 4(d) shows a blue channel stripe I ″n,b(x,y)；
Step S4: by setting weighting coefficients
Calculate the Red channel stripe I ″)n,r(x, y) and blue channel stripe I ″)n,bWeighted stripe I ″ (x, y)n,a(x,y)＝I″n,r(x,y)+αI″n,b(x, y); FIG. 4(e) shows the weighted stripe I ″n,a(x,y)。
Step S5: by using threeThe step phase shift algorithm calculates the red channel stripe I ″' respectivelyn,r(x, y), blue channel stripe I ″)n,b(x, y) and their weighted stripes I ″)n,a(x, y) actual phase distribution φ ″)r(x,y)、φ″b(x, y) and φ ″)a(x, y); FIG. 5 shows a red channel stripe I ″n,r(x, y), blue channel stripe I ″)n,b(x, y) and weighted stripe I ″)n,a(x, y) actual phase distribution φ ″)r(x,y)、φ″b(x, y) and φ ″)a(x, y). As can be seen from FIG. 5, ", phiaThe non-linearity error of (x, y) is much less than phi ″)r(x,y)、φ″b(x, y) non-linearity error.
The present invention has been described in connection with the accompanying drawings, and it is to be understood that the invention is not limited to the specific embodiments described above, but is intended to cover various insubstantial modifications of the invention based on the principles and technical solutions of the invention; the present invention is not limited to the above embodiments, and can be modified in various ways.
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 In(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 crosstalkn(x,y)；
Step S4: calculating the red channel stripe I' under the influence of nonlinear colored crosstalk by setting a proper weighting coefficient alphan,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 algorithmn,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 ″, isaNon-linearity error of (x, y) < delta phia(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,yp) Pixel coordinates representing a projector; t represents a fringe period; deltan2N/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 selectedn(x, y) red channel stripe I thereofn,r(x, y) and blue channel stripe In,b(x, y) are respectively expressed as:
In,r＝A+B cos(φ+δn)；
In,b＝A+B sin(φ+δn)；
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+δn)]γ；
I′n,b＝[A+B sin(φ+δn)]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 ismRespectively 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 S3n(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＝κrrI′n,r+κbrI′n,b；
I″n,b＝κrbI′n,r+κbbI′n,b；
in the formula kapparr,κbr,κrb,κbbRepresenting color crosstalk coefficients of the red channel and the blue channel; kapparb,κbrMuch less than kapparr,κbb。
6. The method according to claim 5, wherein the method comprises the following steps: the red channel stripe I ″' in step S4n,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＝(κrr+ακrb)I′n,r+(κbr+ακbb)I′n,b；
further, when η ═ κrr+ακrb＝κbr+ακbbTime, 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＝2ηamcos (m π/4) represents the weighted stripe I ″n,a(x, y) th harmonic amplitude; phi is aaPhi-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 algorithmn,a(x, y) actual phase distribution φ ″)a(x, y) which is calculated as follows:
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