CN109141291A - A kind of fast phase unwrapping algorithm - Google Patents
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- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
- G01B11/25—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures by projecting a pattern, e.g. one or more lines, moiré fringes on the object
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Abstract
本发明公开了一种快速相位解包裹算法，由N步相移算法、制作Mask、求解条纹级次、相位解包裹四大关键部分组成。具体包括:(1)利用N步相移算法求解包裹相位；(2)利用N幅正弦条纹图制作Mask；(3)利用包裹相位和连通域标记算法求解条纹级次；(4)根据条纹级次进行相位解包裹获得用于三维重建的绝对相位。本发明提出的算法只需投影N幅正弦相移条纹图，就能进行相位求解与解包裹，其相位恢复效果与传统方法相当，但在计算速度上有极大优势，适合有快速三维测量需求的应用领域。
The invention discloses a fast phase unwrapping algorithm, which consists of four key parts: N-step phase shift algorithm, making Mask, solving fringe order and phase unwrapping. Specifically, it includes: (1) using the N-step phase shift algorithm to solve the wrapping phase; (2) using N sinusoidal fringe patterns to make a Mask; (3) using the wrapping phase and connected domain labeling algorithm to solve the fringe order; (4) according to the fringe level Phase unwrapping is performed twice to obtain the absolute phase for 3D reconstruction. The algorithm proposed by the invention only needs to project N sinusoidal phase-shift fringe patterns, and then the phase solution and unwrapping can be carried out. field of application.
Description
Technical field
The invention belongs to optical three-dimensional measurement technical fields, and in particular to a kind of fast phase unwrapping algorithm.
Background technique
Phase- un- wrapping is one of the key link of fringe projection three-dimensional measurement technology, how effectively and rapidly to carry out phase
Position unpacking is the emphasis research topic of this field researcher.By analyzing domestic and international present Research and developments
Research, Phase- un- wrapping technology includes time domain and airspace unwrapping algorithm at present.Airspace unpacks package method and is also easy to produce pixel error
Transmitting is easy failure when measuring complicated face shape, so time phase unpacks package method and more often uses.Time domain unpacking can be compared with
Benefit manages Surfaces of Unusual Shape, but there is the problems such as acquisition image width number is excessive, data volume is big and the processing time is long, and is mostly static survey
Amount.Therefore, the method for how carrying out Phase- un- wrapping with less projected fringe frame number, becomes the breach of this field.
The present invention proposes a kind of fast phase unwrapping algorithm, and the method need to only project N width sine phase shift bar graph, energy
Phase solution and unpacking are carried out, phase recovery effect is suitable with conventional method, but has great advantage in calculating speed, fits
Close the application field for having quick three-dimensional measurement demand.
Summary of the invention
The purpose of the present invention is to provide a kind of fast phase unwrapping algorithm, the method need to only project N width sine phase shift
Bar graph just can be carried out phase solution and unpacking, and phase recovery effect is suitable with conventional method, but has in calculating speed
Great advantage is suitble to the application field for having quick three-dimensional measurement demand.
To achieve the goals above, the invention adopts the following technical scheme: a kind of fast phase unwrapping algorithm, the party
Method includes the following steps: that the N width sine phase shift bar graph that computer generates successively is projected to measured object body surface with projector by (1)
Face is acquired every width projected image with camera；(2) phase shift algorithm is walked using N to collected N width sine phase shift bar graph
Solve wrapped phase；(3) Mask is made using N width sine streak figure；(4) it is asked using wrapped phase and connected component labeling algorithm
Solve fringe order；(5) absolute phase that Phase- un- wrapping acquisition is used for three-dimensional reconstruction is carried out according to fringe order.
Step 1: computer N width sine phase shift bar graph generated is successively projected to measured object body surface with projector
Face is acquired every width projected image with camera, obtains N width by the modulated bar graph of object under test, light distribution is such as
Under:
In formula (1), Ik(x, y) is the light intensity that pixel coordinate is (x, y) in the sinusoidal phase shift bar graph of camera acquisition, I'
(x, y) is average gray, and I " (x, y) is streak amplitude,For object wrapped phase to be asked,For phase shift size；
Step 2: N width sine phase shift bar graph collected to step 1 solves package phase using N step phase shift algorithm
Position, shown in method for solving such as formula (2):
Step 3: production Mask, N width sine phase shift bar graph collected to step 1 camera first are summed, are taken
Average gray is calculated using formula (3) in average value:
Then average gray figure done into binary image processing using formula (4), obtain for divide object phase range,
Eliminate the Mask of background；
Imask(x, y)=im2bw [I'(x, y)] (4)
Step 4: fringe order K is solved, be limited in by the wrapped phase that formula (2) arctan function solves [-
π, π], firstly, we press formula (5) respectively to wrapped phase and formula (6) carries out positive and negative binary conversion treatment twice, respectively obtain
Two opposite binarization resultsWith
Then, by the result after above-mentioned binaryzationWithRespectively with Mask convolution, knot after obtaining convolution
FruitWithAs shown in formula (7) and formula (8):
Then, fringe order is determined using connected component labeling algorithm；We use MATLAB image processing toolbox
Bwlabel function marks respectivelyWithThe connected domain of image, the function are substantially to mark two-dimentional two-value
Connected domain in image；The first step is first marked with bwlabel functionIt can be obtained by first initial connected domain
Mark value Kright(x, y), it corresponds to the right half part of each fringe order, left-half zero, as shown in formula (9):
Second step is equally marked with bwlabel functionIt can be obtained by second initial connected component labeling
Value Kleft(x, y), it corresponds to the left-half of each fringe order, right half part zero, as shown in formula (10):
Obtain the two initial markers values, so that it may using formula (11), by the two values, corresponding be added merges pixel-by-pixel,
Complete fringe order is calculated；
K (x, y)=Kright(x,y)+Kleft(x,y) (11)
Step 5: absolute phase solves, once acquiring fringe order K, the absolute phase Φ (x, y) of object can pass through
Formula (12) acquires:
The invention has the advantages that (1) present invention uses phase shift method, measurement result is rung smaller, strong robustness by environment shadow；
And as a result accurately error propagation directly will not be generated using wrapped phase solution fringe order；(2) present invention only needs N width sinusoidal
Phase shift bar graph just can be carried out phase solution and unpacking, and phase recovery effect is suitable with conventional method；(3) present invention meter
Calculation speed is fast, has potential application prospect and practical value in the quick of dynamic object, real-time three-dimensional measurement.
Detailed description of the invention
Fig. 1 is three-dimension measuring system schematic diagram of the invention.It is made of projector, camera, computer etc..Projector is successively
N width sine phase shift bar graph is projected, camera is shot in other direction by the modulated deforming stripe image of object.Projector and phase
The optical axis of machine intersects at the point of the O in plane, and projector and camera are sustained height, and the distance between they are d, they arrive reference
The distance of plane is L.The height calculation formula of testee are as follows:
Wherein: f is the phase shift fringe frequency in reference planes,It is corresponding for body surface image and reference planes image
The continuous phase potential difference of point.Parameter L, d and f are obtained by calibration.
Fig. 2 is execution flow chart of the invention.
Fig. 3 is in the embodiment of the present invention, with camera acquisition by the modulated sinusoidal phase shift stripe pattern of object, wherein scheming
3 (a) be bar graph I1, Fig. 3 (b) is bar graph I2, Fig. 3 (c) is bar graph I3。
Fig. 4 is the calculated result of step 2 and step 3 in the embodiment of the present invention, and wherein Fig. 4 (a) is what step 2 acquired
Wrapped phase, Fig. 4 (b) are the average gray figure that step 3 acquires, and Fig. 4 (c) is the Mask that step 3 acquires.
Fig. 5 is the calculated result of step 4 and step 5 in the embodiment of the present invention, wherein Fig. 5 (a) and Fig. 5 (b) is respectively
It is acquired for step 4WithFig. 5 (c) and Fig. 5 (d) is respectively the K that step 4 acquiresright(x,y)
And Kleft(x, y), Fig. 5 (e) are the fringe order that step 4 acquires, and Fig. 5 (f) is the object absolute phase that step 5 acquires.
Fig. 6 is the final measurement in the embodiment of the present invention.
Specific embodiment
It is readily appreciated that, technical solution according to the present invention, in the case where not changing connotation of the invention, this field
Those skilled in the art can imagine the present invention be used for three-dimensional measurement numerous embodiments.Therefore, embodiment party in detail below
Formula and attached drawing are only the exemplary illustrations to technical solution of the present invention, and are not to be construed as whole of the invention or are considered as pair
The limitation or restriction of technical solution of the present invention.Example of the invention is described in further detail below in conjunction with Detailed description of the invention, but
This example is not intended to restrict the invention, all using similar structure and its similar variation of the invention, should all be included in the present invention
Protection scope.
In conjunction with Fig. 2 execution flow chart, a kind of fast phase unwrapping algorithm of the present invention, steps are as follows:
Step 1: computer N width sine phase shift bar graph generated is successively projected to measured object body surface with projector
Face is acquired every width projected image with camera, obtains N width by the modulated bar graph of object under test, light distribution is such as
Under:
In formula (1), Ik(x, y) is the light intensity that pixel coordinate is (x, y) in the sinusoidal phase shift bar graph of camera acquisition,
In, I'(x, y) it is average gray, I " (x, y) is streak amplitude,For object wrapped phase to be asked,For phase shift size；
Step 2: N width sine phase shift bar graph collected to step 1 solves package phase using N step phase shift algorithm
Position, shown in method for solving such as formula (2):
Step 3: production Mask, N width sine phase shift bar graph collected to step 1 camera first are summed, are taken
Average gray is calculated using formula (3) in average value:
Then average gray figure done into binary image processing using formula (4), obtain for divide object phase range,
Eliminate the Mask of background；
Imask(x, y)=im2bw [I'(x, y)] (4)
Step 4: fringe order K is solved, be limited in by the wrapped phase that formula (2) arctan function solves [-
π, π], firstly, we press formula (5) respectively to wrapped phase and formula (6) carries out positive and negative binary conversion treatment twice, respectively obtain
Two opposite binarization resultsWith
Then, by the result after above-mentioned binaryzationWithRespectively with Mask convolution, knot after obtaining convolution
FruitWithAs shown in formula (7) and formula (8):
Then, fringe order is determined using connected component labeling algorithm；We use MATLAB image processing toolbox
Bwlabel function marks respectivelyWithThe connected domain of image, the function are substantially to mark two-dimentional two-value
Connected domain in image；The first step is first marked with bwlabel functionIt can be obtained by first initial connected domain
Mark value Kright(x, y), it corresponds to the right half part of each fringe order, left-half zero, as shown in formula (9):
Second step is equally marked with bwlabel functionIt can be obtained by second initial connected component labeling
Value Kleft(x, y), it corresponds to the left-half of each fringe order, right half part zero, as shown in formula (10):
Obtain the two initial markers values, so that it may using formula (11), by the two values, corresponding be added merges pixel-by-pixel,
Complete fringe order is calculated；
K (x, y)=Kright(x,y)+Kleft(x,y) (11)
Step 5: absolute phase solves, once acquiring fringe order K, the absolute phase Φ (x, y) of object can pass through
Formula (12) acquires:
Effect of the present invention can be further illustrated by following instance (as N=3):
Firstly, computer three width sine phase shift bar graph generated is successively projected to measured object body surface using projector
Face, camera are successively acquired by the modulated stripe pattern of object.Wherein, Fig. 3 (a) is bar graph I1, Fig. 3 (b) is bar graph I2,
Fig. 3 (c) is bar graph I3。
Then, it is calculated according to step 2 and step 3, obtains calculated result.Wherein, Fig. 4 (a) acquires for step 2
Wrapped phase, Fig. 4 (b) is the average gray figure that acquires of step 3, and Fig. 4 (c) is the Mask that step 3 acquires.
Finally, being calculated according to step 4 and step 5, calculated result is obtained.Wherein, Fig. 5 (a) and Fig. 5 (b) difference
It is acquired for step 4WithFig. 5 (c) and Fig. 5 (d) is respectively the K that step 4 acquiresright(x, y) and
Kleft(x, y), Fig. 5 (e) are the fringe order that step 4 acquires, and Fig. 5 (f) is the object absolute phase that step 5 acquires.
Fig. 6 is the final measurement in the embodiment of the present invention.
Claims (6)
1. a kind of fast phase unwrapping algorithm, it is characterised in that:
Wrapped phase is solved using N step phase shift algorithm；Mask is made using N width sine streak figure；Using wrapped phase be connected to
Field mark algorithm solves fringe order；The absolute phase that Phase- un- wrapping acquisition is used for three-dimensional reconstruction is carried out according to fringe order.
2. a kind of fast phase unwrapping algorithm according to claim 1, which is characterized in that absolute phase method for solving, phase
Machine is acquired through the modulated N width sine phase shift bar graph of object under test, and light distribution is as follows:
In formula (1), Ik(x, y) is the light intensity that pixel coordinate is (x, y) in the sinusoidal phase shift bar graph of camera acquisition, I'(x, y)
For average gray, I " (x, y) is streak amplitude,For object wrapped phase to be asked,For
Phase shift size.
3. a kind of fast phase unwrapping algorithm according to claim 2, which is characterized in that absolute phase method for solving, benefit
Wrapped phase is solved with N step phase shift algorithm, shown in method for solving such as formula (2):
4. a kind of fast phase unwrapping algorithm according to claim 3, which is characterized in that absolute phase method for solving, system
The process for making Mask is as follows:
N width sine phase shift bar graph collected to camera first is summed, and is averaged, is calculated using formula (3)
Average gray:
Then average gray figure is done into binary image processing using formula (4), obtained for dividing object phase range, eliminating
The Mask of background；
Imask(x, y)=im2bw [I'(x, y)] (4).
5. according to a kind of fast phase unwrapping algorithm of claim 3 or 4, which is characterized in that absolute phase method for solving,
The method for solving fringe order K is as follows:
[- π, π] is limited in by the wrapped phase that formula (2) arctan function solves, firstly, we are to wrapped phase point
Not An formula (5) and formula (6) carry out positive and negative binary conversion treatment twice, respectively obtain two opposite binarization resultsWith
Then, by the result after above-mentioned binaryzationWithRespectively with Mask convolution, result after obtaining convolutionWithAs shown in formula (7) and formula (8):
Then, fringe order is determined using connected component labeling algorithm；We use MATLAB image processing toolbox
Bwlabel function marks respectivelyWithThe connected domain of image, the function are substantially to mark two-dimentional two-value
Connected domain in image；The first step is first marked with bwlabel functionIt can be obtained by first initial connected domain
Mark value Kright(x, y), it corresponds to the right half part of each fringe order, left-half zero, as shown in formula (9):
Second step is equally marked with bwlabel functionIt can be obtained by second initial connected component labeling value
Kleft(x, y), it corresponds to the left-half of each fringe order, right half part zero, as shown in formula (10):
Obtain the two initial markers values, so that it may which corresponding be added merges pixel-by-pixel by the two values using formula (11), calculates
Obtain complete fringe order；
K (x, y)=Kright(x,y)+Kleft(x,y) (11)。
6. a kind of fast phase unwrapping algorithm according to claim 5, which is characterized in that absolute phase method for solving, root
The method for carrying out Phase- un- wrapping according to fringe order is as follows:
Once acquiring fringe order K, the absolute phase Φ (x, y) of object can be acquired by formula (12):
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| CN110440714A (en) * | 2019-09-05 | 2019-11-12 | 南昌航空大学 | A kind of phase unwrapping package method based on multifrequency and binary system striped |
| CN110686652A (en) * | 2019-09-16 | 2020-01-14 | 武汉科技大学 | A depth measurement method based on the combination of deep learning and structured light |
| CN111524173A (en) * | 2020-04-01 | 2020-08-11 | 中国科学技术大学 | Rapid large-range phase unwrapping method based on double reference planes |
| CN111947600A (en) * | 2020-07-24 | 2020-11-17 | 南京理工大学 | Robust Stereo Phase Unwrapping Method Based on Phase Order Cost Filtering |
| CN113048914A (en) * | 2021-04-19 | 2021-06-29 | 中国科学技术大学 | Phase unwrapping method and device |
| CN113155056A (en) * | 2021-02-08 | 2021-07-23 | 北京朗视仪器股份有限公司 | Rapid three-dimensional measurement method based on sinusoidal stripe and multi-gray-scale stripe projection |
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| CN113375600A (en) * | 2021-07-15 | 2021-09-10 | 河北工业大学 | A three-dimensional measurement method, device and electronic equipment |
| CN114234850A (en) * | 2021-12-20 | 2022-03-25 | 广东工业大学 | Three-dimensional measurement method for modulation order phase at cycle edge |
| CN115950378A (en) * | 2023-03-10 | 2023-04-11 | 南京信息工程大学 | Quick measuring method based on binary stripes |
| CN117073578A (en) * | 2023-05-31 | 2023-11-17 | 天津大学 | Active projection nonlinear gamma correction method for fringe projection profilometry |
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| CN111524173A (en) * | 2020-04-01 | 2020-08-11 | 中国科学技术大学 | Rapid large-range phase unwrapping method based on double reference planes |
| CN111947600A (en) * | 2020-07-24 | 2020-11-17 | 南京理工大学 | Robust Stereo Phase Unwrapping Method Based on Phase Order Cost Filtering |
| CN113155056A (en) * | 2021-02-08 | 2021-07-23 | 北京朗视仪器股份有限公司 | Rapid three-dimensional measurement method based on sinusoidal stripe and multi-gray-scale stripe projection |
| CN113048914A (en) * | 2021-04-19 | 2021-06-29 | 中国科学技术大学 | Phase unwrapping method and device |
| CN113048914B (en) * | 2021-04-19 | 2022-04-19 | 中国科学技术大学 | Phase unwrapping method and device |
| CN113358064A (en) * | 2021-06-09 | 2021-09-07 | 西安交通大学 | Phase unwrapping method and device for optical dynamic three-dimensional measurement |
| CN113375600A (en) * | 2021-07-15 | 2021-09-10 | 河北工业大学 | A three-dimensional measurement method, device and electronic equipment |
| CN114234850A (en) * | 2021-12-20 | 2022-03-25 | 广东工业大学 | Three-dimensional measurement method for modulation order phase at cycle edge |
| CN114234850B (en) * | 2021-12-20 | 2022-07-08 | 广东工业大学 | Three-dimensional measurement method for modulation order phase at cycle edge |
| CN115950378A (en) * | 2023-03-10 | 2023-04-11 | 南京信息工程大学 | Quick measuring method based on binary stripes |
| CN117073578A (en) * | 2023-05-31 | 2023-11-17 | 天津大学 | Active projection nonlinear gamma correction method for fringe projection profilometry |
| CN117073578B (en) * | 2023-05-31 | 2024-03-15 | 天津大学 | Active projection nonlinear Gamma correction method for fringe projection profilometry |
| CN119146888A (en) * | 2024-11-13 | 2024-12-17 | 浙江大学 | Flatness interference detection method for discontinuous surface of semiconductor sucker |
| CN119146888B (en) * | 2024-11-13 | 2025-02-25 | 浙江大学 | A method for interferometric detection of the flatness of a non-continuous surface of a semiconductor chuck |
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