CN105043283A - Method for carrying out object deformation phase measurement by using optical flow field - Google Patents

Abstract

The present invention discloses a method for carrying out object deformation phase measurement by using an optical flow field. The method comprises the steps of (1) according to the basic assumption of the optical flow field theory, obtaining the two components u and v of a motion vector between two frames of successive images, (2) extracting the horizontal frequency fx0 and the vertical frequency fy0 of a first frame image fringe by a window Fourier transform method, and (3) using the two components u and v of the motion vector obtained in the step (1) and the horizontal frequency fx0 and the vertical frequency fy0 to calculate to obtain the change amount of a phase. According to the method, only two fringe images are used in a space domain to complete the extraction of the deformation phase, the operations of switching to a frequency domain and a phase unwrapping are not needed, the method is suitable for dynamic measurement, the effect of phase extraction is better in an area with intensive fringes, the disadvantage of large demodulation error when fringes are too dense in a present phase demodulation method, the process is simple and convenient, and the a new way is provided for optical interference dynamic measurement by the method.

Description

Optical flow field is utilized to carry out the method for deformation of body phase measurement

Technical field

The present invention relates to a kind of method utilizing optical flow field to carry out deformation of body phase measurement.

Background technology

Optical interferometry method occupies very consequence, as electronic speckle pattern interferometry, holographic interference, moiréinterferometry etc. because of the advantage of its uniqueness in the three-dimensional appearance and deformation measurement of object.Need the phase information demodulating every bit in bar graph just can realize deformation measurement in these methods.The method of demodulation phase is mainly divided into mensuration and the large class of space phase mensuration two time phase.Time phase mensuration, as temporal phase-shifting method (TemporalPhase-shiftingMethod, TPM) etc., there is displacement measurement precision high, advantages of simple structure and simple, but the bar graph that these class methods need is more, consuming time longer, be generally only applicable to static measurement; Space phase mensuration extracts phase place by spatially obtaining more information, as spatial phase-shifting method (SpatialPhase-shiftingMethod, and Fourier converter technique (FourierTransformMethod SPM), FTM) etc., the measurement to dynamic process phase place can be realized.But the former light path is comparatively complicated, and precision is lower; The processing procedure of the latter is more loaded down with trivial details, is difficult to the robotization realizing striped process.Meanwhile, above method does not all consider time-parameters for the measurement of displacement field, thus just cannot obtain satisfied result to the quantitative measurment of dynamic field.For this problem, have research worker to propose time series phase method (TimeSequencePhaseMethod, TSPM), time-parameters introduced in the middle of speckle interference, successfully extracted phase information, can adapt to large deformation, time become measure.But the method cannot provide determined value in displacement directivity, therefore can only be used in dull time-varying field.In addition, above method all needs to carry out Phase unwrapping operation, and this adds operand and the error of phase extraction undoubtedly.Meanwhile, owing to cannot judge the details of each striped in striped dense Region, therefore above method is all larger in the phase error of striped intensive place demodulation.

The 1950's, the researchists such as Gribson rebuild principle (StructureFromMotion based on motion structure, SFM) first time proposes the concept of light stream (opticalflow): in time dependent two-dimensional image sequence, the flowing that the three-dimensional scenic of motion produces due to the change of luminance patterns is light stream.Hereafter, Chinese scholars proposes different optical flow approach successively, and in precision, the many-side such as robustness and real-time all achieves important breakthrough.1997, studies in China personnel proposed optical flow field analytic approach to be introduced in the middle of Optical interfere mensuration, and for interference of light kinetic measurement provides new thinking, but it does not do deep discussion.2011, the people such as J.Vargas successfully extracted single image phase place by using the theoretical and SPT operator of optical flow field, but the method still needs the series of complex operations such as phase unwrapping, and were not suitable for and realize dynamic deformation measurement.

Summary of the invention

Object of the present invention is exactly to solve the problem, a kind of method utilizing optical flow field to carry out deformation of body phase measurement is provided, the extraction of distortion phase place only just need can be completed in the spatial domain with two width bar graphs, without the need to being transformed into frequency domain and Phase unwrapping operation, be applicable to kinetic measurement, and better in the effect of the more intensive extracted region phase place of striped, overcome the shortcoming that when striped is overstocked in existing phase demodulating method, demodulating error is larger completely.

To achieve these goals, the present invention adopts following technical scheme:

Utilize optical flow field to carry out the method for deformation of body phase measurement, comprise the following steps:

Step one: according to the basic assumption of optical flow field theory, obtains two component u and v of the motion vector between two frame consecutive images;

Step 2: the horizontal frequency f being extracted the first two field picture striped by window Fourier transform method _x0with longitudinal frequency f _y0;

Step 3: two component u and v of the motion vector utilizing described step one to obtain and described step 2 obtain the horizontal frequency f of striped _x0with longitudinal frequency f _y0calculate the knots modification of phase place.

The concrete grammar of described step one is: using formula:

U ⁿ⁺¹=u ⁿ-I _x[(I _xu ⁿ+ I _yv ⁿ+ I _t)]/(α ²+ I _x ²+ I _y ²) and

V ⁿ⁺¹=v ⁿ-I _y[(I _xu ⁿ+ I _yv ⁿ+ I _t)]/(α ²+ I _x ²+ I _y ²) iteration obtains,

Wherein, i _x, I _yand I _tbe respectively the partial derivative of image I for x, y, t, I is t pixel (x, y) place gray-scale value, u ⁿ⁺¹and v ⁿ⁺¹for the value of two component u and v of motion vector obtained after often (n+1)th iteration of image, the motion vector field namely between two width images; u ⁿand v ⁿfor the value of two component u and v of motion vector obtained after often n-th iteration of image; α is smoothing parameter.

The result of described step 2 is by formula try to achieve, (f _x0, f _y0) for making | SI (x, y, ξ, η) | get (ξ, the η) of maximal value, wherein, $SI(\mathrm{\μ},v;\mathrm{\ξ},\mathrm{\η})=\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}I(x,y)g(x-\mathrm{\μ},y-v)\exp (-j\mathrm{\ξ}x-j\mathrm{\η}y)dxdy,$ (ξ, η) is the space frequency domain coordinates that a bit (x, y) is corresponding, SI (μ, ν; ξ, η) be the result of I (x, y) corresponding frequency domain after window Fourier transform, I (x, y) is the two dimensional image of a width input; G (x, y) is window function, gets Gaussian function σ _xand σ _yfor the standard deviation of Gaussian distribution, its value decides the size of Gauss's window.

The concrete grammar of described step 3 is: by two of motion vector component u and v, the horizontal frequency f of striped _x0with longitudinal frequency f _y0bring formula into for point (x ₀, y ₀) knots modification of phase place within the Δ t time, try to achieve this variable of phase place of two frame consecutive images.

Beneficial effect of the present invention:

The present invention only just need can complete the extraction of distortion phase place in the spatial domain with two width bar graphs, without the need to being transformed into frequency domain and Phase unwrapping operation, be applicable to kinetic measurement, and it is better in the effect of the more intensive extracted region phase place of striped, overcome the shortcoming that when striped is overstocked in existing phase demodulating method, demodulating error is larger completely, process is simple, convenient, and the method is also for interference of light kinetic measurement provides new approach simultaneously.

Accompanying drawing explanation

Fig. 1 is original interference striped simulation drawing;

Fig. 2 (a) for additive phase is after striped simulation drawing, Fig. 2 (b) is additive phase after striped simulation drawing;

Fig. 3 is additive phase time estimate at x direction, y=127 place optical flow field cross-sectional view;

Fig. 4 is to additive phase the normalization analog result extracted;

Fig. 5 (a) is to additive phase the normalization notional result extracted, Fig. 5 (b) is to additive phase the normalization analog result extracted;

The initial bar graph that Fig. 6 (a) obtains for experiment, Fig. 6 (b) is the bar graph after additional π/7 phase place of experiment acquisition;

Fig. 7 is experimental result picture.

Embodiment

Below in conjunction with accompanying drawing and embodiment, the invention will be further described.

Utilize optical flow field to carry out the method for deformation of body phase measurement, comprise the following steps:

Step one: according to the basic assumption of optical flow field theory, obtains two component u and v of the motion vector between two frame consecutive images;

Step 2: the horizontal frequency f being extracted the first two field picture striped by window Fourier transform method _x0with longitudinal frequency f _y0;

Step 3: two component u and v of the motion vector utilizing described step one to obtain and described step 2 obtain the horizontal frequency f of striped _x0with longitudinal frequency f _y0calculate the knots modification of phase place.

The calculating of 1 motion vector

Being located at t pixel (x, y) place gray-scale value is I (x, y, t), and move to new position (x+ Δ x, y+ Δ y) at (t+ Δ t) this point of moment, gray-scale value is designated as I (x+ Δ x, y+ Δ y).According to image consistency hypothesis, namely image remains unchanged along movement locus brightness, meets $\frac{dI(x,y,t)}{dt}=0,$ Then

I(x，y，t)＝I(x+Δx，y+Δy，t+Δt)(1)

If u and v is respectively two components of this light stream vector along x and y direction, and i (x+ Δ x, y+ Δ y, t+ Δ t) Taylor's formula is launched, obtains:

$I(x+\mathrm{\Δ}x,y+\mathrm{\Δ}y,t+\mathrm{\Δ}t)=I(x,y,t)+\frac{\∂I}{\∂x}\mathrm{\Δ}x+\frac{\∂I}{\∂y}\mathrm{\Δ}y+\frac{\∂I}{\∂t}\mathrm{\Δ}t---\left(2\right)$

Formula (2) ignores the high-order term of more than second order, has

$\frac{\∂I}{\∂x}\mathrm{\Δ}x+\frac{\∂I}{\∂y}\mathrm{\Δ}y+\frac{\∂I}{\∂t}\mathrm{\Δ}t=0---\left(3\right)$

Due to Δ t → 0, formula (3) becomes

$\frac{\∂I}{\∂x}\frac{\mathrm{\Δ}x}{\mathrm{\Δ}t}+\frac{\∂I}{\∂y}\frac{\mathrm{\Δ}y}{\mathrm{\Δ}t}+\frac{\∂I}{\∂t}=0---\left(4\right)$

I _xu+I _yv+I _t＝0(5)

Wherein i _x, I _yand I _tbe respectively the partial derivative of image I for x, y, t, their value can be estimated to obtain by the first order difference of adjacent image target pixel points in image sequence.Formula (5) is the basic equation of light stream, owing to only having an equation, can only try to achieve light stream along the value I on gradient direction _x, I _yand I _t, and the solution of u, v is not exclusive, therefore need to add constraint condition ability solving speed vector.Light stream sports ground is calculated according to Horn-Schunck algorithm.

The basic thought of Horn-Schunck algorithm requires that when solving light stream light stream itself is level and smooth as much as possible.So-called level and smooth, be exactly in given neighborhood little as much as possible, namely

$\min \{{\[\frac{\∂u}{\∂x}\]}^2+{\[\frac{\∂u}{\∂y}\]}^2+{\[\frac{\∂v}{\∂x}\]}^2+{\[\frac{\∂v}{\∂y}\]}^2\}---\left(6\right)$

Composite type (5) and formula (6), the calculating of light stream (u, v) is summed up as the variational problem of formula (7) by Horn-Schunck algorithm.

$\min \{\∫\∫{\left(I_{x}u+I_{y}v+I_t\right)}^2+{\mathrm{\α}}^2\[{\left(\frac{\∂u}{\∂x}\right)}^2+{\left(\frac{\∂u}{\∂y}\right)}^2+{\left(\frac{\∂v}{\∂x}\right)}^2+{\left(\frac{\∂v}{\∂y}\right)}^2\]\}---\left(7\right)$

Corresponding Euler-Lagrange equation can be obtained, and utilize Gauss-Gauss-Seidel method to solve, obtain (the u of often (n+1) secondary iterative estimate on image ⁿ⁺¹, v ⁿ⁺¹) be:

u ⁿ⁺¹＝u ⁿ-I _x[(I _xu ⁿ+I _yv ⁿ+I _t)]/(α ²+I _x ²+I _y ²)(8)

v ⁿ⁺¹＝v ⁿ-I _y[(I _xu ⁿ+I _yv ⁿ+I _t)]/(α ²+I _x ²+I _y ²)(9)

U and v obtained according to formula (8) and (9) iteration is two components of the motion vector field between two two field pictures.

The calculating of 2 fringe frequency

For extracting fringe frequency, introduce following window Fourier computing:

$SI(\mathrm{\μ},v;\mathrm{\ξ},\mathrm{\η})=\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}\underset{-\mathrm{\∞}}{\overset{+\mathrm{\∞}}{\∫}}I(x,y)g(x-\mathrm{\μ},y-v)\exp (-j\mathrm{\ξ}x-j\mathrm{\η}y)dxdy---\left(10\right)$

In formula (10), (ξ, η) is the space frequency domain coordinates that a bit (x, y) is corresponding, SI (μ, ν; ξ, η) be the result of I (x, y) corresponding frequency domain after window Fourier transform.G (x, y) is window function, gets Gaussian function σ _xand σ _yfor the standard deviation of Gaussian distribution, its value decides the size of Gauss's window.

$(f_{x0},f_{y0})=\arg \underset{\mathrm{\ξ},\mathrm{\η}}{\max }\left(\right|SI\left(x,y,\mathrm{\ξ},\mathrm{\η}\right)\left|\right)---\left(11\right)$

Wherein (f _x0, f _y0) for making | SI (x, y, ξ, η) | get (ξ, the η) of maximal value, be also transverse direction and the longitudinal stripe frequency of every bit in interference fringe picture simultaneously.

Therefore fringe frequency f _x0and f _y0extracting method can be expressed as: first will by the fringe frequency (ξ of bar graph, η) uniform discrete in its span, then these values are brought into respectively | SI (x, y, ξ, η) |, wherein can make | SI (x, y, ξ, η) | get the point (f of maximal value _x0, f _y0) be the solution of formula (11), namely fringe frequency.

The calculating of 3 deformation of body phase places

Interference fringe picture generally can be expressed as:

Wherein a (x, y, t) is background light intensity, and b (x, y, t) is the amplitude of bar graph, for the phase information of bar graph.Function I (x, y, t) is done Taylor series expansion at point (x0, y0), and getting first approximation can obtain:

Usually think that a and b is constant.According to hypothesis and (1)-(5) formula of optical flow field theory, the basic equation of optical flow field (5) can be expressed as

Namely

Wherein for point (x ₀, y ₀) knots modification of phase place within the Δ t time.Due to wherein f _x0and f _y0represent point (x ₀, y ₀) the horizontal and vertical fringe frequency at place.Therefore formula (15) can be written as again

Abbreviation formula (16) can obtain

By the horizontal and vertical frequency f of striped that optical flow field motion vector u and v adopting the method for iteration to obtain according to formula (8) and formula (9) and formula (11) obtain _x0and f _y0bring the variable quantity that formula (17) can try to achieve the phase place of interference fringe picture into

This patent is theoretical based on optical flow field, proposes a kind of new method being demodulated deformation of body phase place by two spoke print images.First obtain the light stream vector field between two frame consecutive images according to optical flow field theory, then use the fringe frequency of initial pictures in binary image and this vector field to carry out the whole field deformation PHASE DISTRIBUTION calculating to obtain object.The present invention gives optical flow field phase calculation method, simulation and experiment checking has been carried out to it.Analog result and experimental result show, the extraction of motion vector field intuitively and distortion phase place can connect by this algorithm, deformation of body phase information can be demodulated, do not need Phase unwrapping computing, process is simple and convenient, and the distortion phase information extracted at the more intensive place of striped is more accurate.The method is that calculating object whole field deformation PHASE DISTRIBUTION and kinetic measurement provide new approach.

4 simulation and experiment result and analyses

4.1 analog results and analysis

According to formula (10), adopt Matlab Software Create one width interference fringe picture as original image, size is 256*256 pixel, and as shown in Figure 1, wherein a=0, b=1, PHASE DISTRIBUTION is

According to sampling thheorem, the maximum fringe frequency that piece image can be expressed is no more than 0.5, therefore is [-0.5,0.5] by the range set of frequency (ξ, η) uniform discrete, and the sampling interval gets Δ f=0.01.The σ of integration window _xand σ _yall get 10 pixel sizes.Extracting the fringe frequency (f of simulation drawing _x0, f _y0) after, then bar graph is added respectively stationary phase and distortion phase place.Why the size of selection distortion phase place is be because when in two width images, the distortion phase value of certain point is greater than π, this point there will be the jumping phenomenon of black and white strip, thus the value causing estimated motion vector u, v and last required phase place is zero.Therefore the span of the distortion phase place that can record in this method is [0, π].When distortion phase place time, the scope of its change is about (0, π/3), meets the condition restriction requirement of this method.Additive phase rear obtained bar graph is respectively shown in Fig. 2 (a) He Fig. 2 (b).

Use optical flow field theory respectively Fig. 1 and Fig. 2 (a) and Fig. 2 (b) to be carried out to the measurement of sports ground between two width figure, optical flow field iterations is 1000 times, and wherein Fig. 1 and Fig. 2 (a), namely addition of phase place rear estimated x direction light stream sports ground at y=127 place sectional view as shown in Figure 3.Make the time variation amount Δ t=1 between two width images, the phase place of adding finally is obtained according to formula (17), namely be out of shape phase information, its theoretical normalization Comparative result with simulating is as shown in Fig. 4, Fig. 5 (a), Fig. 5 (b).

Can be seen by Fig. 1, Fig. 2 (a) and Fig. 2 (b), the central authorities of all interference fringe pictures are a larger round spot, and more sparse the closer to core striped, and its fringe frequency is also lower.Due to less at striped more intensive place motion vector, therefore the size Ying Shiyou center of light stream sports ground estimated is between the two images to both sides monotone decreasing.But as shown in Figure 3, the optical flow field that this algorithm is estimated in fringe frequency lower can produce larger error, especially the sports ground estimated at Yuan Ban center place is 0, so the sports ground estimated between an a1 (x=80) and a2 (x=176) has larger fluctuating, and the sports ground estimated at x<80 and x>176 place is comparatively accurate.Due to the existence of above-mentioned error, therefore there will be one " hole " the same depression, as shown in Fig. 4 and Fig. 5 (b) in analog result in the central authorities of two simulation drawings.Through data analysis, fringe frequency absolute value corresponding to a1 and a2 place is 0.3, and the light stream sports ground namely estimated when the absolute value of fringe frequency is greater than 0.3 is ideal.Fringe frequency absolute value is greater than the phase place extracted at 0.3 place and is tending towards a plane in the diagram, namely additional phase place be a constant, this conforms to theoretical value.Meanwhile, the theory being greater than 0.3 place according to Fig. 5 (a) and Fig. 5 (b) at fringe frequency absolute value contrasts can find out with analog result, and the phase place of the method extraction is accurately.

4.2 Data Processing in Experiment result and analyses

Adopt Michelson interference to obtain interference fringe, gather initial pictures by CCD, image size is 512 × 512 pixels, as shown in Fig. 6 (a).With phase-shifter, interference fringe picture is added to the stationary phase of π/7, the bar graph of acquisition is as shown in Fig. 6 (b).Get Δ t=1, the experimental result obtained as shown in Figure 7.

As seen from Figure 7, owing to moving height between each pixel cannot being kept between image in the middle of experiment consistent and having the interference of noise factor, the sports ground error estimated at the sparse place of striped is larger, therefore there will be larger fluctuating at the periphery of concavity, and the data measured by region being greater than 0.3 at fringe frequency absolute value tend to be steady, namely additional phase place is tending towards a constant, therefore this result shows that this algorithm is feasible.Can be proved by simulation and experiment result, the phase place that the method obtains at the more intensive place of striped is more accurate, overcomes the defect that in existing phase demodulating method, the closeer error of striped is larger completely.In addition, if the image of process is several width continually varying images, the dynamic quantitative that the time variation amount Δ t time interval of getting between two two field pictures between every two two field pictures only need be made can to complete interference fringe picture phase differential extracts.

5 conclusions

This patent proposes the algorithm of phase differential between a kind of demodulation binary image based on optical flow field theory, the method obtains the sports ground between two width images according to the Horn-Schunck algorithm in optical flow field theory, extract initial pictures fringe frequency by window Fourier transform algorithm and calculate with sports ground, and then solving the variable quantity of phase place between two width images.This method only just need can complete the extraction of distortion phase place in the middle of spatial domain with two width bar graphs, eliminate and be transformed into frequency domain and Phase unwrapping operation, process is simple, convenient, all adapts to hologram fringe deformation field, electronic speckle fringe field.Simulation and experiment result shows that the calculating of this algorithm to the distortion phase place of variation range between [0, π] is accurately, and more accurate in the phase information of the more intensive extracted region of striped.In addition, as long as learn that the time interval in the video sequence between two two field pictures can complete the extraction of interference of light kinetic measurement distortion phase place.The method is that interference of light kinetic measurement provides new approach.

By reference to the accompanying drawings the specific embodiment of the present invention is described although above-mentioned; but not limiting the scope of the invention; one of ordinary skill in the art should be understood that; on the basis of technical scheme of the present invention, those skilled in the art do not need to pay various amendment or distortion that creative work can make still within protection scope of the present invention.

Claims (4)

1. utilize optical flow field to carry out the method for deformation of body phase measurement, it is characterized in that, comprise the following steps:

Step one: according to the basic assumption of optical flow field theory, obtains two component u and v of the motion vector between two frame consecutive images;

Step 2: the horizontal frequency f being extracted the first two field picture striped by window Fourier transform method _x0with longitudinal frequency f _y0;

Step 3: two component u and v of the motion vector utilizing described step one to obtain and described step 2 obtain the horizontal frequency f of striped _x0with longitudinal frequency f _y0calculate the knots modification of phase place.

2. utilize optical flow field to carry out the method for deformation of body phase measurement as claimed in claim 1, it is characterized in that, the concrete grammar of described step one is: using formula:

U ⁿ⁺¹=u ⁿ-I _x[(I _xu ⁿ+ I _yv ⁿ+ I _t)]/(α ²+ I _x ²+ I _y ²) and

V ⁿ⁺¹=v ⁿ-I _y[(I _xu ⁿ+ I _yv ⁿ+ I _t)]/(α ²+ I _x ²+ I _y ²) iteration obtains,

Wherein, i _x, I _yand I _tbe respectively the partial derivative of image I for x, y, t, I is t pixel (x, y) place gray-scale value, u ⁿ⁺¹and v ⁿ⁺¹for the value of two component u and v of motion vector obtained after often (n+1)th iteration of image, u ⁿand v ⁿfor the value of two component u and v of motion vector obtained after often n-th iteration of image, α is smoothing parameter.

3. utilize optical flow field to carry out the method for deformation of body phase measurement as claimed in claim 1, it is characterized in that, the result of described step 2 is by formula try to achieve, (f _x0, f _y0) for making | SI (x, y, ξ, η) | get (ξ, the η) of maximal value, wherein, $SI(\mathrm{\&mu;},v;\mathrm{\&xi;},\mathrm{\&eta;})=\underset{-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Integral;}}\underset{-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Integral;}}I(x,y)g(x-\mathrm{\&mu;},y-v)\exp (-j\mathrm{\&xi;}x-j\mathrm{\&eta;}y)dxdy,$ (ξ, η) is the space frequency domain coordinates that a bit (x, y) is corresponding, and I (x, y) is the two dimensional image of a width input, SI (μ, ν; ξ, η) be the result of I (x, y) corresponding frequency domain after window Fourier transform, g (x, y) is window function, gets Gaussian function σ _xand σ _yfor the standard deviation of Gaussian distribution, its value decides the size of Gauss's window.

4. utilize optical flow field to carry out the method for deformation of body phase measurement as claimed in claim 1, it is characterized in that, the concrete grammar of described step 3 is: by two of motion vector component u and v, the horizontal frequency f of striped _x0with longitudinal frequency f _y0bring formula into for point (x ₀, y ₀) knots modification of phase place within the Δ t time, try to achieve this variable of phase place of two frame consecutive images.