CN101655357B - Method for acquiring phase gradient correlated quality diagram for two-dimensional phase unwrapping - Google Patents

Abstract

The invention relates to a method for acquiring a phase gradient correlated quality diagram for two-dimensional phase unwrapping, comprising the following steps: firstly, respectively solving phase gradient diagrams of an x direction and a y direction of a wrapped phase diagram; then respectively carrying out correlated processing on each point of the phase gradient diagrams of the x direction and the y direction; selecting templates with same sizes by respectively taking a current processing point and a point with a special distance from the current processing point in the phase gradient diagrams as centers, and carrying out correlated computation on the two templates; and finally, solving the sum of correlated results corresponding to each point element in the phase gradient diagrams of the x direction and the y direction, and taking the sum as a quality value to obtain the phase gradient correlated quality diagram. The phase gradient correlated quality diagram can be directly led out from the wrapped phase diagram, can effectively distinguish low-quality areas with discontinuous actual phases, noises, sampling lacking, and the like in the wrapped phase diagram and can accurately unfold the wrapped phase diagram containing the low-quality areas.

Description

A kind of phase gradient correlated quality picture capturing method that is used for the two-dimensional phase expansion

Technical field

The present invention relates to image processing field, be used for being wrapped in [π, π) the wrapped phase figure in the principal value interval carries out the two-dimensional phase deployment algorithm of phase unwrapping, can be applicable to path trace method and minimum norm method equiphase method of deploying, be a kind of phase gradient correlated quality picture capturing method that is used for the two-dimensional phase expansion.

Background technology

Phase unwrapping is present in numerous research and applications that coherent wave is handled that relate to, as fields such as optical interference measuring surface form, interference synthetic aperture radar, medical magnetic resonance imaging and adaptive optics.In these fields, the continuous phase that distributes on the surface topography information of research object and the two dimensional surface has definite proportionate relationship, so the continuous phase that distributes on the available two dimensional surface comes the surface topography of description object.But during the phase place on obtaining two dimensional surface, the phase place of every bit calculate to be obtained by arctan function, is wrapped in that [π π) in the principal value interval, makes PHASE DISTRIBUTION in the two-dimensional phase bitmap present discontinuous step and distributes.Therefore, need expand into continuous actual phase to discontinuous wrapped phase, to reflect real testee surface topography.This process of being rebuild or being recovered the actual phase of continuous distribution on two dimensional surface by wrapped phase is called phase unwrapping.

Because discontinuous, noise of real profile and striped are owed factors such as sampling, it is generally comparatively difficult that the wrapped phase figure that various measurement means are obtained carries out phase unwrapping.In order to solve the difficult problem of phase unwrapping, more than two decades comes people to propose multiple phase developing method.Can be divided into two classes substantially: path trace method and minimum norm method.The path trace phase developing method by along certain path of integration to wrapped phase figure integration, rebuild real phase outline.In order to improve phase unwrapping result's reliability, path of integration determines to be guidance with quality figure in these class methods.Quality figure is a two-dimensional data array of describing each pixel data quality height of wrapped phase figure, and it is corresponding one by one on the pixel space position with corresponding wrapped phase figure., noise discontinuous in actual phase, the bigger zone of equiphase graded of owing to sample easily cause the phase unwrapping mistake, so the insecure zone of these phase unwrappings should be marked as the inferior quality zone.The less reliable zone of phase change then should be marked as the high-quality zone among the wrapped phase figure.When carrying out phase unwrapping, the high-quality zone is preferentially launched as preferential path of integration zone, and the inferior quality zone then obtains it by integration at last and launches phase place.Guide the method for path of integration by this quality figure, can guarantee that the phase unwrapping error is limited in the inferior quality zone, can effectively avoid the accumulation and the transmission of error.As another kind of phase developing method, the minimum norm method then solves the expansion phase face that its phase gradient and wrapped phase gradient are approached the most by the overall situation or local optimization methods.Actual phase is discontinuous in order to overcome, noise, the phase unwrapping mistake of owing to sample etc. and causing, the minimum norm method is given the certain weight of each pixel and is eliminated the influence of unreliable zone to the expansion result in the optimization aim function, and choosing of weight also is to instruct with the mass value.Those unreliable regional qualities that are prone to the phase unwrapping mistake are lower, give its lower weight; And higher weight is given in the high-quality zone.This dependence mass value determines that the weighting minimum norm method of weight has obtained good phase and launched the result.Therefore, quality figure has very crucial effect in phase unwrapping.

In the phase unwrapping process, common quality figure has (D.C.Ghiglia such as correlated quality diagram, degree of modulation quality figure, spurious correlation quality figure, maximum phase gradient quality figure and phase place derivative variance quality figure, M.Pritt.Two-dimensionalphase unwrapping:theory, algorithms, and software New York:Wiley-Intersciencepublication, 1998).

Correlated quality diagram is a kind of result of use preferable quality figure, but it only is applicable to interference of data of synthetic aperture radar, and this has significant limitation in practice.

Degree of modulation quality figure, it utilizes the degree of modulation of the striped that optical grating projection produces to weigh the quality of the wrapped phase quality of data.But it must carry out computing to primative streak figure, can't handle for wrapped phase figure.

Spurious correlation quality figure is the simulation to correlated quality diagram, and it has solved the limitation that correlogram can only be used for interference of data of synthetic aperture radar, has extensive applicability, and quality figure can obtain by following formula:

$\left|z_{m,n}\right|=\frac{\sqrt{{\left(\mathrm{\Σ}\cos {\mathrm{\ψ}}_{i,j}\right)}^2+{\left(\mathrm{\Σ}\sin {\mathrm{\ψ}}_{i,j}\right)}^2}}{k^2}---\left(1\right)$

Here (i is that (m n) is interior all pixels of k * k neighborhood at center with pixel j).ψ _{I, j}It is the phase data of wrapped phase figure.This phase place quality figure can calculate from any wrapped phase data plot.

The maximum phase gradient table is shown in maximum phase Grad in the k * k template of each pixel, and certain any maximum phase gradient is defined as follows:

$z_{m,n}=\max \left\{\max \right\{\left|{\mathrm{\Δ}}_{i,j}^x\right|\},\max \{\left|{\mathrm{\Δ}}_{i,j}^y\right|\left\}\right\}---\left(2\right)$

Here Δ _{I, j} ^xAnd Δ _{I, j} ^yBe the partial derivative of phase place in x and y direction, this formula represents to choose at first respectively the maximal value of partial derivative on x and the y direction, and then mutually relatively selects bigger that as the maximum phase gradient.

Phase place derivative variance function, its mass function is defined as follows:

$z_{m,n}=\frac{\sqrt{\mathrm{\Σ}{({\mathrm{\Δ}}_{i,j}^x-\stackrel{\‾}{{\mathrm{\Δ}}_{m,n}^x})}^2}+\sqrt{\mathrm{\Σ}{({\mathrm{\Δ}}_{i,j}^y-\stackrel{\‾}{{\mathrm{\Δ}}_{m,n}^y})}^2}}{k^2}---\left(3\right)$

Here (i is so that (m n) is the interior point of k * k template at center, Δ j) _{I, j} ^xAnd Δ _{I, j} ^yBe phase place in the x and y direction partial derivative, Δ _{M, n} ^xAnd Δ _{M, n} ^yBe the mean value of all pixels partial derivative in the x and y direction in k * k template.Existing studies show that, phase place derivative variation diagram are a kind of phase place quality figure comparatively reliably.

In the phase unwrapping of reality was used, can employed quality figure reflect the wrapped phase quality truly, determined to a great extent whether the phase unwrapping result is correct.Therefore, seek the reliable quality figure that can reflect the wrapped phase quality, significant for phase unwrapping.Existing quality figure mainly comprises correlated quality diagram, degree of modulation quality figure, spurious correlation quality figure, maximum phase gradient quality figure and phase place derivative variance quality figure etc.Correlated quality diagram and degree of modulation quality figure can't directly be obtained by wrapped phase figure, have bigger application limitation.Remaining several quality figure be owing to can directly directly obtain from wrapped phase figure, thereby more commonly used.For spurious correlation quality figure and maximum phase gradient quality figure, their error-prone ground with phase gradient greatly but sampling do not occur owing and muting reliable area identification is the inferior quality zone, therefore can not assess the phase diagram quality exactly sometimes, this will influence the phase unwrapping effect undoubtedly.Phase place derivative variance quality figure can overcome the drawback of spurious correlation quality figure and maximum phase gradient quality figure owing to utilized the interior phase gradient variance information of local, is considered to a kind of the most reliable at present quality figure.But also there is the defective of self in phase place derivative variance quality figure, its mass value is the phase gradient variance in the certain neighborhood of current pixel, this statistical property difference between the neighbor corresponding mass value that can weaken, cause discrimination variation, bring problem can for the phase unwrapping of some wrapped phase figure the wrapped phase quality.

Summary of the invention

The object of the invention is to overcome the deficiency of above-mentioned existing quality figure, and a kind of quality figure of energy correct response wrapped phase plot quality is provided, and this quality figure is used in can improve accuracy and the precision that two-dimensional phase launches in the phase-unwrapping algorithm.

Technical solution of the present invention is: a kind of phase gradient correlated quality picture capturing method that is used for the two-dimensional phase expansion may further comprise the steps:

1) (x y), obtains the phase gradient figure f of its x direction respectively, to utilize pending wrapped phase figure g _x(x, y)=g (x+1, y)-g (x, y) and the phase gradient figure f of y direction _y(x, y)=g (x, y+1)-(x, y), brief note is f to g respectively _xAnd f _yWherein the x direction refers to vertical direction, and the y direction refers to horizontal direction, 0＜x≤V, and 0＜y≤H, x, y is positive integer, and V, H are the image size on wrapped phase figure vertical direction and the horizontal direction;

2), from wrapped phase figure, appoint get a position (x, y), respectively to phase gradient figure f _xAnd f _yIn (x, y) locate element and carry out the processing of gradient correlativity:

$R_x(x,y,l,k)=\frac{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}[f_x(i,j)-u_{\mathrm{fx}1}][f_x(i+k,j+l)-u_{\mathrm{fx}2}]}{\sqrt{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_x(i,j)-u_{\mathrm{fx}1}]}^2\×\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_x(i+k,j+l)-u_{\mathrm{fx}2}]}^2}}$

$R_y(x,y,l,k)=\frac{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}[f_y(i,j)-u_{\mathrm{fy}1}][f_y(i+k,j+l)-u_{\mathrm{fy}2}]}{\sqrt{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_y(i,j)-u_{\mathrm{fy}1}]}^2\×\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_y(i+k,j+l)-u_{\mathrm{fy}2}]}^2}}$

M, N are respectively the size of neighborhood of pixels on x, the y direction in the formula, also are the template size that correlativity is handled, R _x(x, y, l, k) and R _y(l k) is the phase gradient related coefficient for x, y, among the expression phase gradient figure respectively with (x, y) and (x+l be that center, size are the related coefficient of two subgraphs of M * N y+k), l wherein, k is an integer, the span of l and k is respectively 0≤l≤M and 0≤k≤N, R _x(x, y, l, k) and R _y(l k) represents the phase gradient related coefficient of vertical direction and horizontal direction respectively for x, y; u _Fx1With u _Fx2Represent phase gradient figure f respectively _xIn with (x, y) and (x+l y+k) is the mean value of the M * n-quadrant interior element at center, u _Fy1With u _Fy2Represent phase gradient figure f respectively _yIn with (x, y) and (x+l y+k) is the mean value of the M * n-quadrant interior element at center;

3), obtain wrapped phase figure (x, y) locate the mass value of pixel correspondence:

$Q(x,y)=\frac{1}{2D}[R_x(x,y,l,k)+R_y(x,y,l,k)]$

Wherein (x y) represents that (x, the mass value of y) locating, D are (l, value number k) to Q;

4), change (x, value y), repeating step 2) and 3), the mass value of all pixel correspondences in obtaining wrapped phase figure obtains being used for the phase gradient correlated quality diagram of two-dimensional phase expansion.

As optimal way, step 2) in, template M * N that correlativity is handled is the square region of the odd number length of side, (l, value k) is (1,0), (0,1) or (1,1).

Beneficial effect of the present invention is as follows:

1) the present invention has overcome the problem that correlated quality diagram and degree of modulation quality figure can't directly draw from wrapped phase figure, can calculate applied range according to wrapped phase figure;

2) the phase gradient correlated quality diagram that obtains of the present invention has effectively been avoided the shortcoming of spurious correlation quality figure and maximum phase gradient quality figure, can be correctly with phase gradient greatly but sampling do not occur owing and muting reliable area identification is the high-quality zone;

3) the phase gradient correlated quality diagram that obtains of the present invention has overcome the defective of phase place derivative variance quality figure discrimination difference,, noise discontinuous for the actual phase among the wrapped phase figure, the differentiation effect of owing inferior quality zones such as sampling are fine, can be used for the correct expansion to wrapped phase figure effectively.

Description of drawings

Fig. 1 is the original image with complex outline of computer simulation.

Fig. 2 is the wrapped phase figure of Fig. 1 correspondence.

Fig. 3 is the phase unwrapping result who utilizes spurious correlation quality figure to obtain.

Fig. 4 is the 3-D display of Fig. 3.

Fig. 5 is the phase unwrapping result who utilizes maximum phase gradient quality figure to obtain.

Fig. 6 is the 3-D display of Fig. 5.

Fig. 7 is the phase unwrapping result who utilizes phase place derivative variance quality figure to obtain.

Fig. 8 is the 3-D display of Fig. 7.

The phase gradient correlated quality diagram of Fig. 2 that Fig. 9 obtains for the present invention.

The phase unwrapping result that Figure 10 utilizes the phase gradient correlated quality diagram to obtain for the present invention.

Figure 11 is the 3-D display of Figure 10.

Embodiment

The present invention obtains the phase gradient figure of wrapped phase figure x and y direction at first respectively; Respectively every bit on x and the y direction phase gradient figure is carried out relevant treatment then: the point of specific range is arranged is the center with current process points in the gradient map and with this point respectively, chooses the template of identical size, and these two templates are carried out correlation computations; At last the correlated results of every bit element correspondence among x and the y direction phase gradient figure is sued for peace as mass value.The quality figure of the present invention's structure can directly be derived by parcel figure, and good effect is arranged when phase unwrapping.

The present invention is further described below in conjunction with specific embodiments and the drawings, but do not limit protection scope of the present invention with this.

Fig. 1 be a computer simulation contain the discontinuous complex outline curved surface of actual phase, the image size is 256 * 256.Its corresponding wrapped phase figure as shown in Figure 2, this wrapped phase figure that treats phase unwrapping is owing to exist the actual phase non-continuous event, can be used for test mass figure to handle the ability of complex outline phase diagram.

Utilize quality guiding phase-unwrapping algorithm, adopt spurious correlation quality figure, maximum phase gradient quality figure and phase place derivative variance quality figure that Fig. 2 is carried out phase unwrapping, shown in Fig. 3,5 and 7, the 3-D display of their correspondences is respectively shown in Fig. 4,6 and 8 its result respectively.Result shown in these figure shows, utilizes these existing quality figure, all can't correctly launch the wrapped phase figure of this complex outline correspondence.

Utilize quality guiding phase-unwrapping algorithm, adopt the phase gradient correlated quality diagram that wrapped phase Fig. 2 is carried out phase unwrapping, quality figure obtains according to following steps:

1), (x y), obtains the phase gradient figure f of its x direction respectively to utilization pending wrapped phase figure g as shown in Figure 2 _x(x, y)=g (x+1, y)-g (x, y) and the phase gradient figure f of y direction _y(x, y)=g (x, y+1)-(x, y), brief note is f to g respectively _xAnd f _yWherein the x direction refers to vertical direction, and the y direction refers to horizontal direction,, 0＜x≤256,0＜y≤256, x, y is positive integer;

2), from wrapped phase figure, appoint get a position (x, y), respectively to phase gradient figure f _xAnd f _yIn (x, y) locate element and carry out the processing of gradient correlativity:

$R_x(x,y,l,k)=\frac{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}[f_x(i,j)-u_{\mathrm{fx}1}][f_x(i+k,j+l)-u_{\mathrm{fx}2}]}{\sqrt{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_x(i,j)-u_{\mathrm{fx}1}]}^2\×\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_x(i+k,j+l)-u_{\mathrm{fx}2}]}^2}}$

$R_y(x,y,l,k)=\frac{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}[f_y(i,j)-u_{\mathrm{fy}1}][f_y(i+k,j+l)-u_{\mathrm{fy}2}]}{\sqrt{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_y(i,j)-u_{\mathrm{fy}1}]}^2\×\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_y(i+k,j+l)-u_{\mathrm{fy}2}]}^2}}$

M, N are respectively the size of neighborhood of pixels on x, the y direction in the formula, also are the template size that correlativity is handled, R _x(x, y, l, k) and R _y(l k) is the phase gradient related coefficient for x, y, among the expression phase gradient figure respectively with (x, y) and (x+l be that center, size are the related coefficient of two subgraphs of M * N y+k), l wherein, k is an integer, the span of l and k is respectively 0≤l≤M and 0≤k≤N, R _x(x, y, l, k) and R _y(l k) represents the phase gradient related coefficient of vertical direction and horizontal direction respectively for x, y; u _Fx1With u _Fx2Represent phase gradient figure f respectively _xIn with (x, y) and (x+l y+k) is the mean value of the M * n-quadrant interior element at center, u _Fy1With u _Fy2Represent phase gradient figure f respectively _yIn with (x, y) and (x+l y+k) is the mean value of the M * n-quadrant interior element at center;

Here, M * N value is 3 * 3, and (l k) has two values, is respectively (1,0) and (0,1);

3) (x y) locates the mass value of pixel correspondence, to obtain wrapped phase figure

$Q(x,y)=\frac{1}{4}[R_x(x,y,1,0)+R_x(x,y,0,1)+R_y(x,y,\mathrm{1,0})+R_y(x,y,\mathrm{0,1});$

4), change (x, value y), repeating step 2) and 3), the mass value of all pixel correspondences in obtaining wrapped phase figure obtains being used for the phase gradient correlated quality diagram of two-dimensional phase expansion, obtains quality figure as shown in Figure 9.

Figure 10 is the expansion result who utilizes the phase gradient correlated quality diagram to obtain, and Figure 11 is its 3-D display, and it is correct to launch the result.As seen, the phase gradient correlated quality diagram that the present invention obtains has overcome the problem of other quality figure, has solved the difficult difficult problem of differentiating of the discontinuous place of phase place quality, and the quality figure that utilizes the present invention to obtain can correctly carry out the phase unwrapping of wrapped phase figure.

Claims (1)

1. one kind is used for the phase gradient correlated quality picture capturing method that two-dimensional phase launches, and it is characterized in that may further comprise the steps:

1) (x y), obtains the phase gradient figure f of its x direction respectively, to utilize pending wrapped phase figure g _x(x, y)=g (x+1, y)-g (x, y) and the phase gradient figure f of y direction _y(x, y)=g (x, y+1)-(x, y), brief note is f to g respectively _xAnd f _y, wherein the x direction refers to vertical direction, the y direction refers to horizontal direction, and 0＜x≤V, 0＜y≤H, x, y is positive integer, and V, H are the image size on wrapped phase figure vertical direction and the horizontal direction;

2), from wrapped phase figure, appoint get a position (x, y), respectively to phase gradient figure f _xAnd f _yIn (x, y) locate element and carry out the processing of gradient correlativity:

$R_x(x,y,l,k)=\frac{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}[f_x(i,j)-u_{\mathrm{fx}1}][f_x(i+k,j+l)-u_{\mathrm{fx}2}]}{\sqrt{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_x(i,j)-u_{\mathrm{fx}1}]}^2\×\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_x(i+k,j+l)-u_{\mathrm{fx}2}]}^2}}$

$R_y(x,y,l,k)=\frac{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}[f_y(i,j)-u_{\mathrm{fy}1}][f_y(i+k,j+l)-u_{\mathrm{fy}2}]}{\sqrt{\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_y(i,j)-u_{\mathrm{fy}1}]}^2\×\underset{i=x-M/2}{\overset{x+M/2}{\mathrm{\Σ}}}\underset{j=y-N/2}{\overset{y+N/2}{\mathrm{\Σ}}}{[f_y(i+k,j+l)-u_{\mathrm{fy}2}]}^2}}$

M, N are respectively the size of neighborhood of pixels on x, the y direction in the formula, also are the template size that correlativity is handled, R _x(x, y, l, k) and R _y(l k) is the phase gradient related coefficient for x, y, among the expression phase gradient figure respectively with (x, y) and (x+l be that center, size are the related coefficient of two subgraphs of M * N y+k), l wherein, k is an integer, the span of l and k is respectively 0≤l≤M and 0≤k≤N, R _x(x, y, l, k) and R _y(l k) represents the phase gradient related coefficient of vertical direction and horizontal direction respectively for x, y; u _Fx1With u _Fx2Represent phase gradient figure f respectively _xIn with (x, y) and (x+l y+k) is the mean value of the M * n-quadrant interior element at center, u _Fy1With u _Fy2Represent phase gradient figure f respectively _yIn with (x, y) and (x+l y+k) be the mean value of the M * n-quadrant interior element at center, and the template M * N of correlativity processing is the square region of the odd number length of side, (and l, value k) is (1,0), (0,1) or (1,1);

3), obtain wrapped phase figure (x, y) locate the mass value of pixel correspondence:

$Q(x,y)=\frac{1}{2D}[R_x(x,y,l,k)+R_y(x,y,l,k)]$

Wherein (x y) represents that (x, the mass value of y) locating, D are (l, value number k) to Q;

4), change (x, value y), repeating step 2) and 3), the mass value of all pixel correspondences in obtaining wrapped phase figure obtains being used for the phase gradient correlated quality diagram of two-dimensional phase expansion.

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