CN107358584A - The filtering method of ESPI bar graphs based on adaptive Hilbert transform - Google Patents
The filtering method of ESPI bar graphs based on adaptive Hilbert transform Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 40
- 238000001914 filtration Methods 0.000 title claims abstract description 22
- 230000003044 adaptive effect Effects 0.000 title claims abstract description 15
- 238000001228 spectrum Methods 0.000 claims description 13
- 238000000354 decomposition reaction Methods 0.000 claims description 4
- 239000011159 matrix material Substances 0.000 claims description 4
- 230000009466 transformation Effects 0.000 claims description 4
- 238000009333 weeding Methods 0.000 claims description 4
- 238000004364 calculation method Methods 0.000 claims description 3
- 238000006243 chemical reaction Methods 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 3
- 238000000844 transformation Methods 0.000 claims description 3
- 230000003287 optical effect Effects 0.000 abstract description 3
- 238000005516 engineering process Methods 0.000 description 8
- 238000005305 interferometry Methods 0.000 description 5
- 238000006073 displacement reaction Methods 0.000 description 3
- 238000002474 experimental method Methods 0.000 description 2
- 238000005259 measurement Methods 0.000 description 2
- 238000012935 Averaging Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
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- 238000000605 extraction Methods 0.000 description 1
- 238000010587 phase diagram Methods 0.000 description 1
- 230000010363 phase shift Effects 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 238000005549 size reduction Methods 0.000 description 1
- 238000003860 storage Methods 0.000 description 1
- 230000001629 suppression Effects 0.000 description 1
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Classifications
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- G06T5/70—
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T5/00—Image enhancement or restoration
- G06T5/10—Image enhancement or restoration by non-spatial domain filtering
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20004—Adaptive image processing
Abstract
The filtering method of ESPI bar graphs of the invention based on adaptive Hilbert transform, belongs to optical image security field, and to realize the removal of speckle noise in ESPI bar graphs, method noise resisting ability proposed by the invention is stronger, and it is shorter to calculate the time.The technical solution adopted by the present invention is, based on the filtering method of adaptive Hilbert transform, step is to first pass through the density and stripe direction that calculate striped in stripe pattern, then carries out Hilbert transform, finally realizes the noise reduction of bar graph.Present invention is mainly applied to optical image security occasion.
Description
Technical field
The invention belongs to optical image security field, relates generally to a kind of filtering of electronic speckle interference fringe pattern newly side
Method.
Background technology
Electronic speckle pattern interferometry (Electronic speckle pattern interferometry ESPI) has
The ability of whole audience displacement measurement, high displacement sensitiveness and high s/n ratio, it is that a kind of effective non-contact whole audience of measuring strain is surveyed
Amount method.With the continuous development of computer technology, electronic technology and digital image variants technology, ESPI
Technology turns into holo-speckle measurement technology most one of technology of use value.Electronic speckle pattern interferometry is become by recording
The speckle field intensity signal of test specimen before and after shape, and using size reduction mode or add pattern to have the figure of speckle field information to two web
As being handled, so as to obtain the speckle interference fringe pattern for representing ohject displacement, deforming, or introduce phase shift method afterwards before being deformed and obtain
The phase diagram of deformation of body information must be characterized.[1-4]
Electronic speckle pattern interferometry is using CCD or TV video cameras and electronic memory record intensity signal, with digitized
In form deposit storage medium, but ESPI figure is with very strong granularity noise, while by experimental situation, experiment
The interference of the factors such as equipment, the observability and resolution ratio of striped are seriously reduced the quality of image, disturbed by strong influence
Computer realizes the automatic interpretation of speckle image, to the extraction of stripe fixed position and the expansion of phase brings challenge.Thus,
The filtering process of ESPI figure is become as one of committed step of electronic speckle pattern interferometry technology.[5-7]
Bibliography
[1] Tong Jingwei, Li Hongqi, photodynamics principle and measuring technology, Beijing：Science Press, 2009.
[2] Wang Renda, holographic and Speckle measurement, Beijing：China Machine Press, 2005:100~119.
[3]W.H.Peters,W.F.Ranson,Digital imaging techniques in experimental
stress analysis.Opt.Eng.1982,21:427~431.
[4]Michael E.Nixon.Experimental characterization and modeling of the
mechanical response of titanium for quasi-static and high strain rate
loads.University of Florida,2008.
[5]Q.Kemao,Windowed Fourier transform for fringe pattern analysis,
Appl.Opt.2004,43:2695~2702.
[6]Q.Kemao,Two-dimensional windowed Fourier transform for fringe
pattern analysis:principles,applications and implementations,Opt.Lasers Eng.,
2007,45:304~317.
[7]C.Li,C.Tang,H.Yan,et.al,Localized Fourier transform filter for
noise removal in electronic speckle pattern interferometry wrapped phase
patterns,Appl.Opt.2011,50:4903~4911.
The content of the invention
For overcome the deficiencies in the prior art, it is contemplated that the removal of speckle noise in ESPI bar graphs is realized, the present invention
The method noise resisting ability proposed is stronger, and it is shorter to calculate the time.The technical solution adopted by the present invention is, based on adaptive Xi Er
The filtering method of Bert conversion, step are to first pass through the density and stripe direction that calculate striped in stripe pattern, are then wished
You convert Bert, finally realize the noise reduction of bar graph.
Specific steps are refined as：
Step 1：It will be input to noisy ESPI bar graphs under matlab platforms, and carry out matrixing processing；
Step 2：The calculating of stripe direction and fringe density is carried out to image
Step 3：Hilbert transform is carried out to bar graph；
Step 4：Output image, obtain the image after denoising.
Hilbert is converted to high density electronic speckle interference fringe pattern filtering process：
1) set the high density ESPI bar graphs of input as：F (i, j), wherein i, j denotation coordinations position；
2) stripe direction in image is calculated with gradient method first, calculation formula is：
Above formula represents to be expressed as the deflection of (i, j) this point in image：Of(i, j), headed by the process of gradient method
Be selected on image select a size for：W × w window, wherein (i, j) this point is the center of window, (k, l) represents window
Interior any point, fx(k, l) and fy(k, l) is respectively partial derivative of this point along x directions and y directions, is calculated by above formula
Go out the direction of all pixels point in image；
3) Hilbert transform is carried out to image f (i, j) and obtains the frequency spectrum of image
Wherein Ψ represents the decomposition under partial fourier framework to image f, and p and q represent the position of local window respectively
With the frequency domain coordinates of the window；
Γ (ξ)=diag γp,q(ξ) is by the weight coefficient γ on frequency fields ξp,qThe diagonal matrix that (ξ) is formed, weighting system
Number γp,q(ξ) is defined as
Wherein, Gσ=exp (- (x/ σ)2/ 2), σ is that a scale parameter reflects texture frequency spectrum ξkWith ξ (xp) deviation as point xp
When surrounding is without obvious Directional texture, γ is made to all kp,k=1, the generation of false texture is avoided with this；
4) picture frequency that the image direction and step 3 obtained according to step 2 obtains, noise institute is weeded out using formula 3
Frequency spectrum；
5) carrying out Hilbert inverse transformations to weeding out the frequency spectrum after noise obtains last filtering image.
The features of the present invention and beneficial effect are：
Adaptive FILTERING BY HILBERT TRANSFORMATION method proposed by the present invention is small compared to conventional Fourier filtering method
Ripple filtering method, the parameter setting of this method are adaptive, save and calculate the time, the striped due to this method calculated in advance
Direction and density, the suppression of speckle noise is realized while the integrality that striped can be maximally maintained.
Brief description of the drawings：
Fig. 1 FILTERING BY HILBERT TRANSFORMATION flow charts.
The filter result comparison diagram of tri- kinds of methods of Fig. 2.
Embodiment
Step 1：It will be input to noisy ESPI bar graphs under matlab platforms, and carry out matrixing processing；
Step 2：The calculating of stripe direction and fringe density is carried out to image
Step 3：Hilbert transform is carried out to bar graph；
Step 4：Output image, obtain the image after denoising.
The present invention is further described with reference to the accompanying drawings and detailed description.
The principle of Xi Erbote conversion is introduced first, the principle combination ESPI stripeds then converted according to Xi Erbote
The method of the characteristics of figure construction filtering.
Adaptive H ilbert norms are defined as
Wherein, Ψ is represented in partial fourier framework { ψp,k}p,kUnder decomposition to v, p and k represent local window respectively
Position and the frequency domain coordinates of the window.Γ (ξ)=diagL=(p, k)γp,k(ξ) is by the weight coefficient γ on frequency fields ξp,k
The diagonal matrix that (ξ) is formed.Weight coefficient γp,k(ξ) is defined as
Wherein, Gσ=exp (- (x/ σ)2/ 2), σ is that a scale parameter reflects texture frequency spectrum ξ k and ξ (xp) deviation work as a little
xpWhen surrounding is without obvious Directional texture, γ is made to all kp,k=1, the generation of false texture is avoided with this.
The minimization problem of adaptive H ilbert norms is related to the frequency of bar graph and the estimation problem in direction, and profit
Weight coefficient γ is determined with the frequency and direction of estimationp,k(ξ), therefore adaptive H ilbert norms can effectively represent band
Directive image texture.And an evident characteristic is with directional, therefore with adaptive in electronic speckle interference fringe pattern
Answer Hilbert spaces and norm to describe stria be reasonable and appropriate.
Specifically：
Hilbert is converted to high density electronic speckle interference fringe pattern filtering process：
1. set the high density ESPI bar graphs of input as：F (i, j), wherein i, j denotation coordinations position；
2. calculating stripe direction in image with gradient method first, calculation formula is：
Above formula represents to be expressed as the deflection of (i, j) this point in image：Of(i,j).Headed by the process of gradient method
Be selected on image select a size for：W × w window, wherein (i, j) this point is the center of window, (k, l) represents window
Interior any point.The direction of all pixels point in image can be calculated by above formula.
3. couple image f (i, j) carries out Hilbert transform and obtains the frequency spectrum of image
Wherein Ψ represents the decomposition under partial fourier framework to image f, and p and q represent the position of local window respectively
With the frequency domain coordinates of the window.
Γ (ξ)=diag γp,q(ξ) is by the weight coefficient γ on frequency fields ξp,qThe diagonal matrix that (ξ) is formed.Weighting system
Number γp,q(ξ) is defined as
Wherein, Gσ=exp (- (x/ σ)2/ 2), σ is that a scale parameter reflects texture frequency spectrum ξkWith ξ (xp) deviation as point xp
When surrounding is without obvious Directional texture, γ is made to all kp,k=1, the generation of false texture is avoided with this.
4. the picture frequency that the image direction and step 3 that are obtained according to step 2 obtain, noise institute is weeded out using formula 3
Frequency spectrum；
5. the frequency spectrum after pair weeding out noise carries out Hilbert inverse transformations and obtains last filtering image.
For the validity of verification method, experimental results.Here we select conventional Fourier methods and small echo
Transform method method as a comparison.
Experiment one：Fig. 1 (a) is width simulation high density electronic speckle interference fringe pattern, and Fig. 1 (b)~(d) is respectively
The filter result of fourier methods, small wave converting method and adaptive Hilbert method proposed by the present invention.
In addition, table 1 gives signal to noise ratio (the Signal to Noise for calculating time and accordingly result of three kinds of methods
Ratio, SNR) and speckle index (Speckle Index, SI), wherein speckle index is used for weighing the slickness of filter result.
Speckle index SI is defined as
Wherein<Ik,l>For the window neighborhood averaging value of current point 3 × 3, standard deviation sigmak,lIt is defined as
Speckle index is smaller, and it is more smooth to represent filtering image.
Claims (3)
1. a kind of filtering method based on adaptive Hilbert transform, it is characterized in that, step is to first pass through calculating stripe pattern
The density and stripe direction of middle striped, then carry out Hilbert transform, finally realize the noise reduction of bar graph.
2. the filtering method as claimed in claim 1 based on adaptive Hilbert transform, it is characterized in that, specific steps refinement
For：
Step 1：It will be input to noisy ESPI bar graphs under matlab platforms, and carry out matrixing processing；
Step 2：The calculating of stripe direction and fringe density is carried out to image
Step 3：Hilbert transform is carried out to bar graph；
Step 4：Output image, obtain the image after denoising.
3. the filtering method as claimed in claim 1 based on adaptive Hilbert transform, it is characterized in that, Hilbert conversion
To high density electronic speckle interference fringe pattern filtering process：
1) set the high density ESPI bar graphs of input as：F (i, j), wherein i, j denotation coordinations position；
2) stripe direction in image is calculated with gradient method first, calculation formula is：
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Wherein, Gσ=exp (- (x/ σ)2/ 2), σ is that a scale parameter reflects texture frequency spectrum ξ k and ξ (xp) deviation as point xpAround
When not having obvious Directional texture, γ is made to all kp,k=1, the generation of false texture is avoided with this；
4) picture frequency that the image direction and step 3 obtained according to step 2 obtains, where weeding out noise using formula 3
Frequency spectrum；
5) carrying out Hilbert inverse transformations to weeding out the frequency spectrum after noise obtains last filtering image.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111768349A (en) * | 2020-06-09 | 2020-10-13 | 山东师范大学 | ESPI image noise reduction method and system based on deep learning |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3021110A1 (en) * | 2014-11-11 | 2016-05-18 | Paul Scherrer Institut | System for obtaining quantitative x-ray images using Hilbert transform on imaged fringes |
| CN106447619A (en) * | 2016-08-15 | 2017-02-22 | 天津大学 | Large change density fringe pattern filtering method based on generalized total variation |
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2017
- 2017-06-29 CN CN201710515645.2A patent/CN107358584A/en active Pending
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP3021110A1 (en) * | 2014-11-11 | 2016-05-18 | Paul Scherrer Institut | System for obtaining quantitative x-ray images using Hilbert transform on imaged fringes |
| CN106447619A (en) * | 2016-08-15 | 2017-02-22 | 天津大学 | Large change density fringe pattern filtering method based on generalized total variation |
Non-Patent Citations (2)
| Title |
|---|
| XIA CHEN ET AL.: "Variational image decomposition for estimation of fringe orientation and density from electronic speckle pattern interferometry fringe patterns with greatly variable density", 《OPTICS & LASERS IN ENGINEERING》 * |
| 朱新军: "基于变分图像分解的ESPI与FPP条纹分析新方法研究", 《万方学位论文》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111768349A (en) * | 2020-06-09 | 2020-10-13 | 山东师范大学 | ESPI image noise reduction method and system based on deep learning |
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Application publication date: 20171117 |