CN116823646A - Least square phase unwrapping method based on residual point correction for non-connected area - Google Patents
Least square phase unwrapping method based on residual point correction for non-connected area Download PDFInfo
- Publication number
- CN116823646A CN116823646A CN202310661873.6A CN202310661873A CN116823646A CN 116823646 A CN116823646 A CN 116823646A CN 202310661873 A CN202310661873 A CN 202310661873A CN 116823646 A CN116823646 A CN 116823646A
- Authority
- CN
- China
- Prior art keywords
- phase
- unwrapping
- residual
- sample block
- area
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 238000000034 method Methods 0.000 title claims abstract description 70
- 238000012937 correction Methods 0.000 title claims abstract description 49
- 238000010587 phase diagram Methods 0.000 claims abstract description 13
- 230000008439 repair process Effects 0.000 claims description 27
- 238000004364 calculation method Methods 0.000 claims description 9
- 230000008569 process Effects 0.000 claims description 6
- 238000005516 engineering process Methods 0.000 claims description 4
- 230000010287 polarization Effects 0.000 claims description 4
- 238000005305 interferometry Methods 0.000 claims description 3
- 238000010606 normalization Methods 0.000 claims description 3
- 238000012857 repacking Methods 0.000 claims description 3
- 230000000694 effects Effects 0.000 abstract description 10
- 230000003287 optical effect Effects 0.000 abstract description 5
- 238000001514 detection method Methods 0.000 abstract description 4
- 239000006187 pill Substances 0.000 abstract description 2
- 238000005070 sampling Methods 0.000 description 9
- 238000005259 measurement Methods 0.000 description 5
- 238000011084 recovery Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 3
- 238000012360 testing method Methods 0.000 description 3
- 230000008859 change Effects 0.000 description 2
- 238000004891 communication Methods 0.000 description 2
- 238000005457 optimization Methods 0.000 description 2
- 238000012545 processing Methods 0.000 description 2
- 230000001360 synchronised effect Effects 0.000 description 2
- 238000012935 Averaging Methods 0.000 description 1
- 238000003491 array Methods 0.000 description 1
- 230000005540 biological transmission Effects 0.000 description 1
- 230000000903 blocking effect Effects 0.000 description 1
- 238000001914 filtration Methods 0.000 description 1
- 238000009499 grossing Methods 0.000 description 1
- 230000010354 integration Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000009467 reduction Effects 0.000 description 1
- 230000001172 regenerating effect Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/30—Determination of transform parameters for the alignment of images, i.e. image registration
Landscapes
- Engineering & Computer Science (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Image Processing (AREA)
Abstract
The invention discloses a least square unwrapping method based on residual point correction for a non-connected area, which comprises the following steps: collecting four original interferograms of a measured sample containing non-connected areas; extracting an original parcel phase diagram by a four-step phase shifting method; adding a digital carrier frequency to obtain a reference phase diagram; repairing the non-connected region in the original parcel phase map by adopting a sample block matching method, comparing the non-connected region with a reference phase, and repeatedly iterating to obtain a final parcel phase map; obtaining an unwrapped phase map by adopting a least square unwrapped algorithm based on residual point correction; and obtaining correction coefficients and obtaining a final reconstructed phase map. The invention combines the advantages of sample block matching and residual error point correction, has good unwrapping effect on unwrapping phases of unconnected, high steepness and high noise, has high unwrapping phase precision, and has important significance in the fields of target pill detection, optical element surface type detection and the like.
Description
Technical Field
The invention belongs to the technical field of phase unwrapping in an optical phase-shifting interference technology, and particularly relates to a least square phase unwrapping method based on residual error point correction for a non-connected area.
Background
The phase is always focused in the field of optical measurement because of the fact that the phase contains various key information of the object, and the phase for measuring and solving the object at high speed, high efficiency and high precision is always the focused research direction of relevant researchers. In practical measurement solution, the measured object phase is often wrapped between (-pi, pi) due to the nature of the arctangent function, and various phase unwrapping algorithms are generated to obtain a high-precision object true phase.
Meanwhile, in practical measurement, due to the blocking of the supporting structure, the optical element with continuous surface is often divided into a plurality of divided areas, and the corresponding divided wrapping phases cannot represent the continuity of the original phases. If the previous method is used, then a high degree of error occurs between the different phase regions. Furthermore, the height error between these phase regions is more severe when taking multiple averaging measurements. In view of the above, the existing least square based unwrapping algorithm has poor effect on the processing of unconnected or steep wrapping phases, the unwrapping algorithm has low precision, and a new unwrapping method is needed to be improved.
Disclosure of Invention
The invention provides a least square unwrapping method based on residual point correction for an unconnected area, which aims at solving the problem that the traditional least square unwrapping method based on the least square unwrapping method has poor effect on the unconnected or large-gradient wrapped phase, has strong unwrapping capability on the unwrapped phase of the unconnected, high-gradient and large-noise wrapped phase, has high unwrapping phase precision, improves the application range of the traditional least square unwrapping method based on the least square unwrapping method, and has important significance in the fields of target pill detection, optical element surface detection and the like.
The technical scheme for realizing the purpose of the invention is as follows: a least squares unwrapping method based on residual point correction for non-connected areas, the method comprising:
step 1, a Fizeau reflection interferometry system is built, a polarization phase-shifting technology is combined to achieve four original interferograms of a measured sample with equal phase differences, and an original parcel phase diagram is calculated by a four-step phase-shifting method;
step 2, adding a digital carrier frequency to the original wrapped phase map, and reconstructing the interference map, carrying out phase unwrapping by adopting a least square unwrapping method based on residual error point correction, and obtaining a reference phase map by removing the digital carrier frequency;
step 3, performing image restoration on the non-connected region of the original wrapping phase by using a sample block matching algorithm to obtain a restoration phase;
step 4, comparing the repair phase with a reference phase diagram to obtain error points of the repair phase, and setting the area where the error points of the repair phase are located as a repair area of a next sample block matching algorithm;
step 5, repeating the iteration steps 3 and 4 until the absolute value of the difference between the repair phase and the reference phase in the nth iteration is smaller than a set value or the error point is not changed any more, and obtaining a final wrapping phase containing the information of the non-connected region;
and 6, carrying out phase unwrapping on the final wrapped phase by adopting a least square unwrapping method based on residual point correction to obtain a correction coefficient, and obtaining a reconstruction phase comprising the non-connected region according to the correction coefficient.
Preferably, the method for performing phase unwrapping by adopting the least square unwrapping method based on residual point correction specifically comprises the following steps:
step 2-1, setting an iteration minimum error epsilon and an iteration frequency upper limit N it Initial unwrapping phaseThe residual error of the initial unwrapped phase is delta 0 W { delta } is a wrap operator, W { delta } is 0 } =, Φ is the original parcel phase map;
step 2-2, calculating the wrapped phase derivativeResidual point R i,j ,
According to the residual difference point R i,j Value-over-wrap phase derivative of (2)Correcting;
the corrected wrap phase derivativeCarrying in and solving a noise-free poisson equation to obtain a solutionWrapping phase
Step 2-3 unwrapping phaseIs +.>Residual error delta between n Repacking, and solving a residual unwrapping error delta by using the unwrapping method in the step 2-2 pun ：
Residual error delta after unwrapping pun Superimposed on unwrapped phaseOn, unwrapped phase +.A more nearly true phase φ is obtained>
Step 2-4, according to the updated unwrapped phaseSolving for residual error delta pu(n+1) Calculating residual error delta pu(n+1) Is a repackaging result of (a):
step 2-5 repeating steps 2-3 and 2-4 to satisfy the condition |W { delta } pu(n+1) }-δ pun |<Epsilon, or number of iterations n>N it Stopping iteration to obtain final unwrapped phase
Preferably, a sample block matching algorithm is used for carrying out image restoration on the non-connected region of the original wrapping phase, and the specific method for obtaining the restoration phase is as follows:
step 3-1: finding out an area to be repaired of an input image, and calculating the priority values of all pixel points on the boundary of the area to be repaired;
step 3-2: comparing the priorities of the pixel points to find the pixel point P with the highest priority, and creating a sample block ψ to be repaired by taking the pixel P as the center p Searching in the unbroken area phi to find the best matching block ψ q ；
Step 3-3: the best matching block ψ to be searched q The gray value of the pixel point in the image sample block of the area to be repaired replaces the gray value of the corresponding pixel point in the image sample block of the area to be repaired, the image repair is completed, the repair phase is obtained, and the boundary of the area to be repaired, the related data item and the related confidence item parameters are updated for the image of which the one-time repair process is completed.
Preferably, the boundaryThe calculation of the priority value P (P) of any pixel P is as follows:
P(p)＝C(p)*D(p)
wherein, C (p) represents a confidence term, which is specifically expressed as:
d (p) represents a data item in the priority calculation, specifically expressed as:
|Ψ p i represents the number of pixel points in the broken sample block, alpha is a normalization factor, n p A unit vector representing the pixel point orthogonal to the boundary curve,the direction of the isotopy line representing the pixel point, ψ p To-be-repaired sample block centering on p, ψ p And n phi is the intersection of the sample block to be repaired and the unbroken sample block centered on p.
Preferably, a block of samples to be repaired ψ is created centered on pixel P p Finding the best matching block ψ by searching in the unbroken area q The specific method of (a) is as follows:
searching in an unbroken area by using a sample matching window, wherein in the searching process, a block with the closest defined color distance is the best matching block, and the color distance is defined as follows:
d(Ψ p ,Ψ q )＝∑ i ∑ j |Ψ p (i,j)-Ψ q (i,j)| 2
the sample block that satisfies the following condition is referred to as the optimal sample block:
wherein argmin () represents the value that the variable takes when the above formula assumes the minimum value, and wherein ψ is represented when the color distance is minimum q Corresponding areas in the unbroken area Φ.
Preferably, the correction coefficient k is specifically:
where phi is the original package phase diagram,for the final unwrapped phase.
Preferably, the reconstructed phase including the unconnected region is obtained based on the correction coefficient kThe method comprises the following steps:
compared with the prior art, the invention has the remarkable advantages that:
(1) According to the invention, the separated wrapped phase areas are connected through the iterative sample block matching algorithm, so that high-precision phases are obtained in the non-connected areas without any treatment on the wrapped phases, and even if the wrapped phases contain multiple speckle noise, the recovered phases are basically consistent with the actual phases, and the excellent anti-noise performance of the wrapped phases is verified.
(2) According to the invention, the residual points of the wrapping phase derivative model are identified, the wrapping phase derivative is corrected based on the value of the residual points, the interference of noise on the least square optimization function is reduced, and the influence of unwrapping errors at the residual points on the normal sampling points is avoided. The invention can realize the accurate unwrapping of wrapping phases with strong noise and large steepness, thereby obtaining high-precision object phase information.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
A least square unwrapping method based on residual point correction aiming at a non-connected area aims at solving the problem that the existing least square unwrapping algorithm is poor in wrapping phase processing capability of non-connected, high-gradient and high-noise. According to the method, the separated phase areas are connected through a sample block matching method, and the wrapped phase is not required to be processed in the non-connected areas, so that the phase with high precision can be obtained. Meanwhile, the correction capability of the existing least square algorithm correction model for the problem of phase dynamic range reduction caused by the smoothing effect in the traditional least square unwrapping algorithm is limited, residual points cannot be identified and distinguished in the correction process, and the reliability of the algorithm is affected. The least square unwrapping method based on the residual point correction reduces the influence of noise on the least square optimization function and avoids the influence of unwrapping errors at the residual points on the normal sampling points by carrying out residual point identification and correction on the differential model in the least square unwrapping algorithm.
The invention is described in further detail below with reference to the accompanying drawings.
With reference to fig. 1, the specific steps of the technical scheme for achieving the purpose of the invention are as follows:
step 1, a Fizeau type reflective interferometry system is built, and synchronous measurement of original interferograms of four measured samples with equal phase differences is achieved by combining a polarization phase shifting technology. The polarization camera consists of a plurality of groups of 2 x 2 micro-polarization arrays, the vibration transmission angles of the four linear polarizers are respectively 0 degree, 45 degree, 90 degree and 135 degree, additional phases of 0 degree, 90 degree, 180 degree and 270 degree are respectively introduced, and pixels containing the same additional phases are respectively combined into four interference patterns, so that synchronous acquisition of the four interference patterns is realized. And calculating phi from four phase difference interferograms by adopting a four-step phase shifting method.
Step 2, adding a digital carrier frequency T to the original wrapped phase diagram phi and reconstructing the interference diagram, adopting a least square unwrapping method based on residual error point correction to carry out phase unwrapping, and obtaining a reference phase diagram phi by removing the digital carrier frequency R 。
In a further embodiment, the specific method for adding the digital carrier frequency T to the original wrapped phase diagram Φ and regenerating the interference diagram is as follows:
the digital carrier frequency T is added to the wrapping phase Φ as follows:
Φ T (x,y)＝Φ(x,y)+T(x,y)
the digital carrier frequency T (x, y) can be written as:
T(x,y)＝αx+βy+γ
where α, β and γ are carrier frequency coefficients. By phi T Reconstructing interferogram I T
I T (x,y)＝cos(Φ T (x,y))
In a further embodiment, the method for phase unwrapping by using the least squares unwrapping method based on residual point correction specifically includes:
step 2-1, setting an iteration minimum error epsilon and an iteration frequency upper limit N it Initial unwrapping phaseThe residual error of the initial unwrapped phase is delta 0 W { delta } is a wrap operator, W { delta } is 0 }＝Φ；
Step 2-2, calculating the wrapped phase derivativeResidual point R i,j ,
According to the residual difference point R i,j Value-over-wrap phase derivative of (2)Correcting;
the corrected wrap phase derivativeCarrying in and solving a noise-free poisson equation to obtainTo obtain unwrapped phase ψ n ；
There is serious noise or undersampling in the real phase, and some sampling points may not meet the sampling condition. Points that exceed the sampling condition, which result in the integral around the closed path in the derivative plot of the wrapped phase being other than 0, are referred to as residual points (Residues) in the wrapped phase. At this time, the phase unwrapping result is related to the integral path, and when the integral path passes through the sampling point where the residual point is located, a correct unwrapping result cannot be obtained.
Adjacent pixel points around each sampling point in the phase diagram are connected in a certain sequence to form a minimum closed path, and the integral is obtained to detect residual points in the parcel phase diagram.The wrapping phase derivatives of four pixel points near the sampling point (i, j) are respectively represented, and then the residual point can be judged by the following formula
R is based on the nature of the wrapping operator i,j The values of (2) are only three cases, 2 pi, -2 pi and 0. If R is i,j =2pi, then there is a positive residual at sample point (i, j). If R is i,j -2pi, then there is a negative residual at sample point (i, j). Otherwise, if R i,j =0, then there is no residual. When no residual points exist on the entire mxn grid, the wrapped phases may be unwrapped by any method including linear integration. A wrapped phase derivative model corrected from residual points is as follows:
by putting the residueAnd setting the derivative value of the wrapping phase corresponding to the difference point to zero, so that noise or undersampled phase at the sampling point with residual error can be removed in the difference diagram, and the correction of the residual error point is realized. At this time, the wrapping phase phi and the real phase are minimized by a least square methodThe difference between the difference maps of (c) may be found as follows:
this can be equivalent to solving the discrete poisson equation in a grid:
wherein the method comprises the steps ofIs the input of the poisson equation after residual correction. The noiseless poisson equation in the formula is solved by a discrete cosine transform method, so that the reciprocal solution of phi in the DCT domain can be obtained. Finally, the unwrapped phase in the least square sense is obtained by inverse DCT transformation:
step 2-3 unwrapping phaseIs +.>There is an unwrapped residual error delta n But due to true phase->Unknown, the residual error delta is needed n Repacking, and solving a residual unwrapping error by using the unwrapping method in the step 2-2:
residual error delta after unwrapping pun Superimposed on unwrapped phaseOn top of that, unwrapped phases +.>
Step 2-4, unwrapping phase after updatingFor solving the residual error delta again pu(n+1) Calculating residual error delta pu(n+1) Is a repackaging result of (a):
step 2-5 repeating steps 2-3 and 2-4 to satisfy the condition |W { delta } pu(n+1) }-δ pun |<Epsilon, or number of iterations n>N it Stopping iteration to obtain final unwrapped phase
Obtaining a reference phase map phi by removing the digital carrier frequency R The method comprises the following steps:
wherein Ext {.cndot. } represents the interferogram extension algorithm, F s Representing positive first order sideband gaussian filtering, FT { · } and IFT { · } are the fourier transform and inverse fourier transform, respectively, PU { · } represents the phase unwrapping algorithm,is an unwrapped phase obtained by a least squares unwrapped method based on residual point correction.
Step 3, performing image restoration on the non-connected region of the original wrapping phase phi by using a sample block matching algorithm to obtain a restoration phaseThe method comprises the following specific steps:
step 3-1: finding the region to be repaired through the mask obtained in the interferogram analysis software and setting the region to be repaired asAnd if the boundary is judged to be empty, ending the whole sample matching algorithm flow.
And calculating the priority values of all the pixel points on the boundary of the area to be repaired through a priority calculation formula. The priority value determines the sequence of repairing the image blocks, so that the calculation of the priority value has great influence on the repairing effect. Boundary ofThe calculation of the priority value P (P) of any pixel is as follows:
P(p)＝C(p)*D(p)
where C (p) represents a confidence term, which may be expressed specifically as:
d (p) represents a data item in the priority calculation, and can be expressed specifically as:
the priority of the P point is determined by the data item and the confidence item, wherein the confidence item has the meaning of estimating the proportion of undamaged pixels in all sample blocks, |ψ p I represents the number of pixels in the broken sample block. The data item is a parameter for measuring the edge intensity of the pixel point, wherein alpha is a normalization factor, n p A unit vector representing the pixel point orthogonal to the boundary curve,indicates the maximum direction of the color change of the pixel point,/-, for example>Representing the direction of the isocenter of the pixel point, i.e. the orthogonal vector of the gradient vector of the point. The data item and the confidence coefficient item serve as two important indexes for calculating the priority, the data item guarantees that the algorithm preferentially repairs sample blocks with larger change of structural information of the edge of the area to be repaired, the confidence coefficient item guarantees that the algorithm preferentially repairs sample blocks with abundant known information of the edge of the area to be repaired, and the two parameters are balanced to repair images with better structural information and texture information.
Step 3-2: comparing the priorities of the pixel points to find the pixel point P with the highest priority, and creating a sample block ψ to be repaired by taking the pixel P as the center p Finding the best matching block ψ by searching in the unbroken area q . In performing image restoration, square blocks of pixels (sample blocks) are utilized, the size of the sample blocks being referred to as a sample matching window. The image restoration effect can be affected by selecting image restoration windows with different sizes, and a 9×9 sample matching window is adopted in the method. In the searching process, defining the block with the closest color distance as the most similar oneThe best match block, the color distance may be defined as:
d(Ψ p ,Ψ q )＝∑ i ∑ j |Ψ p (i,j)-Ψ q (i,j)| 2
the sample block that satisfies the following condition is referred to as the optimal sample block:
step 3-3: and replacing the gray value of the corresponding pixel point in the damaged image sample block with the gray value of the pixel point in the searched matching block, replacing the gray value of the corresponding pixel point in the damaged image sample block, and updating the boundary of the area to be repaired, related data items, confidence items and other parameters of the image subjected to one-time repair process.
Preferably, the sample matching window selected in the sample block matching is 9×9, for the following reasons:
the size of the window in which the sample block matches is related to the region to be repaired, the richness and roughness of the texture, etc. The large window size can reduce time loss, but because the data volume to be repaired is large, statistical errors easily occur in the calculation process, so that the repair points are inaccurate, and the subsequent image repair can be influenced. When the sample block matching window is smaller, the accuracy of repair will increase, but more time will be spent. However, if the window is too small, the repair effect is also affected and a large error is caused. In the actual test process, five different sample matching windows of 5×5,7×7,9×9, 11×11 and 13×13 are adopted to perform image recovery test, and the test result shows that the sample matching window of 9×9 has the best recovery effect and the least residual point. A 9 x 9 sample matching window is ultimately selected.
Step 4, repairing the phaseAnd reference phase phi R And comparing to obtain an error point of the repair phase. Setting the region where the phase error point is repaired to be the next sampleRepair area of the block matching algorithm.
Step 5, repeating the steps 3-3 and 3-4 until the phase is repaired in the nth iterationAnd reference phase phi R Satisfy->Or the error point is not changed any more, and the final wrapping phase phi containing the information of the non-connected area is obtained F 。
And 6, carrying out phase unwrapping on the final wrapped phase by adopting a least square unwrapping method based on residual point correction to obtain a correction coefficient, and obtaining a reconstruction phase comprising the non-connected region according to the correction coefficient.
The sample block matching algorithm copies the image information in the best matching block of the connected region into the disconnected region, but the phase information is not the real phase information of the corresponding region, so the sample block matching algorithm is used for repairing the final unwrapped phase obtained by performing image repairing on the disconnected wrapped phaseThere is an error with the true phase, but the error is smaller, both are in the same 2 pi interval. Can be used to solve the correction factor k:
where Φ is the original parcel phase map. The correction coefficient k and the original wrapping phase phi are combined to obtain a real reconstruction phaseObtaining a reconstruction phase including the unconnected region based on the correction factor k>The method comprises the following steps:
the invention can replace most of the existing unwrapping algorithm of the non-connected wrapping phase. The method connects the separated wrapping phase areas by means of a sample block matching algorithm to obtain high-precision phases in the non-communication areas, and the error points between the recovery phases of the noisy cross non-communication phases and the original phases are only 281, so that the recovery effect is remarkably improved. The least square unwrapping method based on residual point correction can replace most of the existing least square unwrapping algorithms. The method uses a wrapped phase derivative model to carry out residual correction, takes a Peaks function as an original phase, sets PV as 10, and when the standard deviation of added Gaussian noise is set as 1rad, the residual standard deviation between a recovered phase and the original phase is only 0.35rad, so that the recovery effect is obviously improved.
The technical features of the above-described embodiments may be arbitrarily combined. For brevity, all of the combinations of the technical features in the above embodiments are not described. However, as long as there is no contradiction between the combination of these technical features, it should be considered as the scope of the present description.
The above examples illustrate only a few embodiments of the invention, which are described in detail and are not to be construed as limiting the scope of the invention. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the invention, which are all within the scope of the invention. The scope of the invention is therefore intended to be covered by the appended claims.
Claims (7)
1. A least squares unwrapping method based on residual point correction for non-connected areas, the method comprising:
step 1, a Fizeau reflection interferometry system is built, a polarization phase-shifting technology is combined to achieve four original interferograms of a measured sample with equal phase differences, and an original parcel phase diagram is calculated by a four-step phase-shifting method;
step 2, adding a digital carrier frequency to the original wrapped phase map, and reconstructing the interference map, carrying out phase unwrapping by adopting a least square unwrapping method based on residual error point correction, and obtaining a reference phase map by removing the digital carrier frequency;
step 3, performing image restoration on the non-connected region of the original wrapping phase by using a sample block matching algorithm to obtain a restoration phase;
step 4, comparing the repair phase with a reference phase diagram to obtain error points of the repair phase, and setting the area where the error points of the repair phase are located as a repair area of a next sample block matching algorithm;
step 5, repeating the iteration steps 3 and 4 until the absolute value of the difference between the repair phase and the reference phase in the nth iteration is smaller than a set value or the error point is not changed any more, and obtaining a final wrapping phase containing the information of the non-connected region;
and 6, carrying out phase unwrapping on the final wrapped phase by adopting a least square unwrapping method based on residual point correction to obtain a correction coefficient, and obtaining a reconstruction phase comprising the non-connected region according to the correction coefficient.
2. The least squares phase unwrapping method based on residual point correction for the non-connected area according to claim 1, wherein the method for phase unwrapping by using the least squares unwrapping method based on residual point correction is specifically:
step 2-1, setting an iteration minimum error epsilon and an iteration frequency upper limit N it Initial unwrapping phaseThe residual error of the initial unwrapped phase is delta 0 W { delta } is a wrap operator, W { delta } is 0 } =, Φ is the original parcel phase map;
step 2-2, calculating the wrapped phase derivativeResidual pointsR i,j ,
According to the residual difference point R i,j Value-over-wrap phase derivative of (2)Correcting;
the corrected wrap phase derivativeBringing in and solving a noiseless poisson equation to obtain unwrapped phases +.>
Step 2-3 unwrapping phaseIs +.>Residual error delta between n Repacking, and solving a residual unwrapping error delta by using the unwrapping method in the step 2-2 pun ：
Residual error delta after unwrapping pun Superimposed on unwrapped phaseOn, unwrapped phase +.A more nearly true phase φ is obtained>
Step 2-4, according to the updated unwrapped phaseSolving for residual error delta pu(n+1) Calculating residual error delta pu(n+1) Is a repackaging result of (a):
step 2-5 repeating steps 2-3 and 2-4 to satisfy the condition |W { delta } pu(n+1) }-δ pun |<Epsilon, or number of iterations n>N it Stopping iteration to obtain final unwrapped phase
3. The least square phase unwrapping method based on residual point correction for non-connected areas according to claim 1, wherein the specific method for obtaining a repair phase by performing image repair on the non-connected areas of an original wrapped phase by using a sample block matching algorithm is as follows:
step 3-1: finding out an area to be repaired of an input image, and calculating the priority values of all pixel points on the boundary of the area to be repaired;
step 3-2: comparing the priorities of the pixel points to find the pixel point P with the highest priority, and creating a sample block ψ to be repaired by taking the pixel P as the center p Searching in the unbroken area phi to find the best matching block ψ q ；
Step 3-3: the best matching block ψ to be searched q The gray value of the pixel point in the image sample block of the area to be repaired replaces the gray value of the corresponding pixel point in the image sample block of the area to be repaired, the image repair is completed, the repair phase is obtained, and the boundary of the area to be repaired, the related data item and the related confidence item parameters are updated for the image of which the one-time repair process is completed.
4. The method of least squares phase unwrapping based on residual point correction for non-connected areas of claim 3, wherein the boundariesThe calculation of the priority value P (P) of any pixel P is as follows:
P(p)＝C(p)*D(p)
wherein, C (p) represents a confidence term, which is specifically expressed as:
d (p) represents a data item in the priority calculation, specifically expressed as:
|Ψ p i represents the number of pixel points in the broken sample block, alpha is a normalization factor, n p A unit vector representing the pixel point orthogonal to the boundary curve,the direction of the isotopy line representing the pixel point, ψ p To-be-repaired sample block centering on p, ψ p And n phi is the intersection of the sample block to be repaired and the unbroken sample block centered on p.
5. A least squares phase unwrapping method based on residual point correction for non-connected areas as in claim 3, characterized by creating a block of samples ψ to be repaired centered on pixel P p Finding the best matching block ψ by searching in the unbroken area q The specific method of (a) is as follows:
searching in an unbroken area by using a sample matching window, wherein in the searching process, a block with the closest defined color distance is the best matching block, and the color distance is defined as follows:
d(Ψ p ,Ψ q )＝∑ i ∑ j |Ψ p (i,j)-Ψ q (i,j)| 2
the sample block that satisfies the following condition is referred to as the optimal sample block:
wherein argmin () represents the value that the variable takes when the above formula assumes the minimum value, and wherein ψ is represented when the color distance is minimum q Corresponding areas in the unbroken area Φ.
6. The least squares phase unwrapping method based on residual point correction for non-connected areas according to claim 1, wherein the correction coefficient k is specifically:
where phi is the original package phase diagram,for the final unwrapped phase.
7. The least squares phase unwrapping method based on residual point correction for non-connected areas as set forth in claim 1, wherein a reconstructed phase including the non-connected areas is obtained from the correction coefficient kThe method comprises the following steps:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310661873.6A CN116823646A (en) | 2023-06-06 | 2023-06-06 | Least square phase unwrapping method based on residual point correction for non-connected area |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310661873.6A CN116823646A (en) | 2023-06-06 | 2023-06-06 | Least square phase unwrapping method based on residual point correction for non-connected area |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116823646A true CN116823646A (en) | 2023-09-29 |
Family
ID=88111974
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310661873.6A Pending CN116823646A (en) | 2023-06-06 | 2023-06-06 | Least square phase unwrapping method based on residual point correction for non-connected area |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116823646A (en) |
-
2023
- 2023-06-06 CN CN202310661873.6A patent/CN116823646A/en active Pending
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Zavorin et al. | Use of multiresolution wavelet feature pyramids for automatic registration of multisensor imagery | |
| CN104730519B (en) | A kind of high-precision phase position unwrapping method of employing error iterative compensation | |
| CN108955575B (en) | A method of corrugated is accurately restored based on single width interference fringe | |
| CN112097678B (en) | Multi-surface shape measurement method based on frequency blind estimation | |
| CN107490340B (en) | A kind of fast phase extracting method of the random phase-shift interference of three width | |
| CN108195408B (en) | Two-step phase extraction method, system and medium based on tilt phase shift error correction | |
| Zong et al. | Robust phase unwrapping algorithm for noisy and segmented phase measurements | |
| Wang et al. | Phase unwrapping based on adaptive image in-painting of fringe patterns in measuring gear tooth flanks by laser interferometry | |
| CN108170636B (en) | Method for recovering true phase from linear carrier frequency phase-shift interference pattern | |
| CN104614083B (en) | A kind of method of recovering phase shifting interference PHASE DISTRIBUTION and obtaining phase-shift phase between two width figure | |
| CN116823646A (en) | Least square phase unwrapping method based on residual point correction for non-connected area | |
| CN106441082A (en) | Phase recovery method and device | |
| CN116907379A (en) | Interference fringe wave surface iteration method and device | |
| CN112665529A (en) | Object three-dimensional shape measuring method based on stripe density area segmentation and correction | |
| CN117169886A (en) | High-efficiency phase unwrapping method based on unscented Kalman filtering | |
| CN115183697B (en) | Phase extraction method and system based on interference light intensity information | |
| CN115127683B (en) | Phase extraction method for parameter mismatch of dynamic interferometer interferogram | |
| CN107123097A (en) | A kind of imaging method of the calculation matrix based on optimization | |
| CN112097677B (en) | Rapid high-precision phase restoration method for anti-vibration interferometry | |
| Zhang | Random phase retrieval approach using Euclidean matrix norm of sum and difference map and fast least-squares algorithm | |
| Siddiolo et al. | A direction/orientation-based method for shape measurement by shadow moiré | |
| Zhang et al. | Automatic wavefront reconstruction on single interferogram with spatial carrier frequency using Fourier transform | |
| CN112330578A (en) | Image reconstruction method and system combining compressed sensing and cleaning algorithm | |
| Osherovich et al. | Phase retrieval combined with digital holography | |
| CN117078791B (en) | CT ring artifact correction method and device, electronic equipment and storage medium |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |