CN109712109A - A kind of optical imagery phase unwrapping winding method based on residual error convolutional neural networks - Google Patents
A kind of optical imagery phase unwrapping winding method based on residual error convolutional neural networks Download PDFInfo
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Abstract
The invention discloses a kind of optical imagery phase unwrapping winding method based on residual error convolutional neural networks.The present invention includes the following steps: step 1, generates the optical imagery that phase is not wound using Zernike multinomial；Step 2 carries out phase winding operation using the optical imagery not wound, obtains phase winding image；Step 3 utilizes convolutional neural networks training pattern；Step 4 utilizes trained model prediction.Present invention utilizes residual error convolutional neural networks, the specific aim of this method is very strong, mainly for the phase unwrapping in optical imagery around.There is very big application prospect in optical imagery research field.It compares and for traditional phase unwrapping winding method, has the advantages that solving speed is fast, it is high to solve accuracy rate.
Description
Technical field
The invention belongs to image phase unwrapping fields, especially for optical imagery, and in particular to one kind is rolled up based on residual error
The optical imagery phase unwrapping winding method of product neural network.
Background technique
The signal that many times optical imagery obtains is plural form, contains range value and phase value.But believe from plural number
When extracting true phase in number, phase value can be limited in the section of [- π, π], and the true phase outside the section is twined
In this section.This phenomenon is known as phase winding, and obtained phase is known as winding phase.It is obtained from winding phase true
Phase be known as phase unwrapping around.
Existing phase unwrapping winding method mainly has following three kinds.First method is based on Discrete Particle Swarm Optimization Algorithm
Branch tangential method.The residual error of entire image is first divided into several groups by this method；Discrete Particle Swarm Optimization Algorithm is used in every group
Positive-negative polarity residual error is matched；Well matched positive-negative polarity residual error in every group is connected with branch tangent line；Finally bypass these branches
Tangent line carries out phase unwrapping.Second of phase unwrapping method is the weighting minimum L based on direct solving methodpNorm method.It will be whole
The solution of a phase image twines phase gradient and winds the weighting L of difference between phase gradientpNorm is as optimization object function；It will
This objective function is converted to an equation group, and coefficient matrix is stored and expressed using sparsity structure；Finally using directly asking
Solution solve system of equation.Since to twine phase related for coefficient matrix and the solution of equation group, iterative manner is taken to obtain final
Disentanglement fruit.The third method is the region growth method based on mask.This method will using a kind of new mask extracting mode
Residual error is reasonably connected as the zero point in mask；Mask and phase derivative variance are bonded final Quality Map,
The point that connection residual error is passed through so is treated as the point of zero mass (namely quality is worst), can be detained to the end just by phase
Solution twines；Entire image is divided into multiple regions then according to Quality Map, individually carries out phase unwrapping in each region, wherein matter
It is average from multiple directions progress phase weighting to measure that worst region；Finally multiple regions are fused together.However it is above-mentioned
Method faces the disadvantage that solving speed is slow, solving precision is poor, robustness is insufficient.Therefore the invention proposes a kind of new based on volume
The optical imagery phase unwrapping winding method of product neural network.
Summary of the invention
It is more and more to be applied to phase in imaging signal present invention primarily contemplates the development with optical image technology
Information.How preferably to solve the problems, such as that the unwrapping of optical phase is to be worth inquiring into.The present invention is directed to by Zernike multinomial
The optical imagery of generation has carried out phase unwrapping around research.A kind of optical imagery phase based on residual error convolutional neural networks is provided
Unwrapping method.
The technical solution adopted by the present invention to solve the technical problems includes the following steps:
Step 1 generates the optical imagery that phase is not wound using Zernike multinomial
Aberration refers to the image defects in optical system.Aberration is divided into monochromatic aberraation of light and chromasia in geometric optics
Difference, the former includes spherical aberration, coma, astigmatism, the curvature of field and distortion, and the latter includes chromatism of position and ratio chromatism,；And in physical optics
Aberration is referred to as wave front aberration or wavefront aberration, is the waveform that the spherical wave of point light source sending is formed after optical system
The distance between ideal spherical face wave.Wave front aberration can pass through the geometric images such as Zernike polynomial period table or spherical aberration, coma
Difference is expressed.
Zernike introduced one group of complex function collection { V being defined on unit circle in 1934pq(x, y) }, { Vpq(x,
Y) } there is completeness and orthogonality, it is allowed to indicate to be defined on any quadractically integrable function in unit circle.It is defined
Are as follows: Vpq(x, y)=Vpq(ρ, θ)=Rpq(ρ)ejqθ
Wherein, ρ indicates the vector length of former point-to-point (x, y)；θ indicates vector ρ and the anticlockwise angle of x-axis；Rpq
(ρ) is real value radial polynomial:
Referred to as Zernike multinomial, Zernike multinomial meet orthogonality.Due to the polynomial Orthogonal Complete of Zernike
Property, so any image in unit circle can be indicated uniquely.Due to being observed in Zernike multinomial and optical detection
To the form of aberrational polynomial be consistent, thus common Zernike describes wavefront properties.
Therefore, the optical imagery that we are not wound using Zernike multinomial generation phase in the present invention.
Step 2 carries out phase winding operation using the optical imagery not wound, obtains phase winding image
By the way that after step 1, we have obtained the optical imagery similar with experiment that a batch is not wound.And then we are logical
It crosses following formula and obtains the difference of corresponding phase winding image and the two.
imgdiff=imgunwrap-imgwrap
Wherein, imgwrap、imgunwrapRespectively represent the optical imagery for not winding and winding；Angle (x) represents the phase of x
Position；imgdiffIt is the difference for the optical imagery for not winding and winding.
Step 3 utilizes convolutional neural networks training pattern
In computer vision, " grade " of feature is got higher with network depth is increased, studies have shown that the depth of network
An important factor for being the effect realized.However gradient disperse, explosion become the obstacle of the profound network of training, cause to train
It can not restrain.Although there is certain methods that can make up, if normalizing initializes, each layer input normalization allows to convergent net
The depth of network is promoted to original ten times.Although increasing the network number of plies but however, convergence, network start to deteriorate
Lead to bigger error.Then in 2015, He Kaiming, which proposes Resnet network, can allow network to increase with depth without moving back
Change.Resnet study is residual error function f (x)=H (x)-x.
In the present invention, the convolutional neural networks with residual error that we also use 25 layers have carried out related optical imagery solution and have twined
Around feature learning.In our algorithm, H (x) represents the feature of our the final optical imagery unwrapping algorithms to be learned.Its
The optical imagery being wound around is inputted, output is the optical imagery not wound.X represents our input, that is, the optics wound
Image.What f (x) was represented is the difference not wound between image and winding image that we learn.Why residual error net is selected
Network, reason have following two points.First is that residual error network in profound network both can with fast convergence it is also ensured that network not
Increase with depth and degenerates；Second is that being not random because not winding has certain regularity with the difference of winding image
Number.
Model of the invention uses the convolution kernel of 3*3,64 characteristic patterns of every layer of extraction.Activation primitive is Relu, activation
It is normalized later using Batch Normalization.It is finally solved using ADMM algorithm, specific loss function
Are as follows:
L (Y, y (x))=(Y-y (x))2
Wherein, Y represents the image that true optical imagery phase is not wound, and y (x) represents the optics that the present invention is predicted
The image that image phase is not wound.
Finally our network passes through the training of 50 epoch, and simulation result, which has substantially surmounted traditional image solution, to be twined
Around algorithm.
Step 4 utilizes trained model prediction
The network structure and parameter obtained present invention utilizes step 3 training result is saved.We utilize later
Above-mentioned preservation result has carried out the unwrapping of optics winding image.The prediction result accuracy of model and solving speed relative to
Traditional image unwrapping algorithm has very big improvement.
The method of the present invention has the advantage that and beneficial outcomes are as follows:
1, the invention proposes a kind of new optical imagery phase unwrapping around method.This process employs residual error convolution minds
Through network, the specific aim of this method is very strong, mainly for the phase unwrapping in optical imagery around.Have in optical imagery research field
Very big application prospect.
2, the phase unwrapping winding method proposed by the present invention based on residual error convolutional neural networks, compares and traditional phase
For unwrapping method, have the advantages that solving speed is fast, it is high to solve accuracy rate.
Detailed description of the invention
Fig. 1 (a), 1 (b), 1 (c) are the optical imagerys in example of the present invention.
The optical imagery that the phase that wherein Fig. 1 (a) generates for Zernike multinomial is not wound, Fig. 1 (b) is corresponding
The optical imagery of phase winding, Fig. 1 (c) are that phase does not wind image and winds the difference of image；
Fig. 2 is residual error convolutional neural networks structure chart of the invention；
Fig. 3 (a), 3 (b), 3 (c), 3 (d) are the optical phase winding image prediction knots in example of the present invention
Fruit.
Wherein Fig. 3 (a) is the optical imagery of phase winding, and Fig. 3 (b) is that the phase of prediction does not wind image and winding image
Difference, Fig. 3 (c) is the optical imagery that the phase of prediction is winding, and Fig. 3 (d) is the light that corresponding true phase is not wound
Learn image.
Specific embodiment
The present invention will be described in detail With reference to embodiment.
As shown in Figure 1-3, the present invention proposes the optical imagery phase unwrapping winding method based on residual error convolutional neural networks, press
Implement according to following steps.
Step 1 generates the optical imagery that phase is not wound using Zernike multinomial
Aberration refers to the image defects in optical system.Aberration is divided into monochromatic aberraation of light and chromasia in geometric optics
Difference, the former includes spherical aberration, coma, astigmatism, the curvature of field and distortion, and the latter includes chromatism of position and ratio chromatism,；And in physical optics
Aberration is referred to as wave front aberration or wavefront aberration, is the waveform that the spherical wave of point light source sending is formed after optical system
The distance between ideal spherical face wave.Wave front aberration can pass through the geometric images such as Zernike polynomial period table or spherical aberration, coma
Difference is expressed.
Zernike introduced one group of complex function collection { V being defined on unit circle in 1934pq(x, y) }, { Vpq(x,
Y) } there is completeness and orthogonality, it is allowed to indicate to be defined on any quadractically integrable function in unit circle.It is defined
Are as follows: Vpq(x, y)=Vpq(ρ, θ)=Rpq(ρ)ejqθ
Wherein, ρ indicates the vector length of former point-to-point (x, y)；θ indicates vector ρ and the anticlockwise angle of x-axis；Rpq
(ρ) is real value radial polynomial:
Referred to as Zernike multinomial, Zernike multinomial meet orthogonality.Due to the polynomial Orthogonal Complete of Zernike
Property, so any image in unit circle can be indicated uniquely.Due to being observed in Zernike multinomial and optical detection
To the form of aberrational polynomial be consistent, thus common Zernike describes wavefront properties.
Therefore, the optical imagery that we are not wound using Zernike multinomial generation phase in the present invention.
Step 2 carries out phase winding operation using the optical imagery not wound, obtains phase winding image
By the way that after step 1, we have obtained the optical imagery similar with experiment that a batch is not wound.And then we are logical
It crosses following formula and obtains the difference of corresponding phase winding image and the two.
imgdiff=imgunwrap-imgwrap
Wherein, imgwrap、imgunwrapRespectively represent the optical imagery for not winding and winding；Angle (x) represents the phase of x
Position；imgdiffIt is the difference for the optical imagery for not winding and winding.
Step 3 utilizes convolutional neural networks training pattern
In computer vision, " grade " of feature is got higher with network depth is increased, studies have shown that the depth of network
An important factor for being the effect realized.However gradient disperse, explosion become the obstacle of the profound network of training, cause to train
It can not restrain.Although there is certain methods that can make up, if normalizing initializes, each layer input normalization allows to convergent net
The depth of network is promoted to original ten times.Although increasing the network number of plies but however, convergence, network start to deteriorate
Lead to bigger error.Then in 2015, He Kaiming, which proposes Resnet network, can allow network to increase with depth without moving back
Change.Resnet study is residual error function f (x)=H (x)-x.
In the present invention, the convolutional neural networks with residual error that we also use 25 layers have carried out related optical imagery solution and have twined
Around feature learning.In our algorithm, H (x) represents the feature of our the final optical imagery unwrapping algorithms to be learned.Its
The optical imagery being wound around is inputted, output is the optical imagery not wound.X represents our input, that is, the optics wound
Image.What f (x) was represented is the difference not wound between image and winding image that we learn.Why residual error net is selected
Network, reason have following two points.First is that residual error network in profound network both can with fast convergence it is also ensured that network not
Increase with depth and degenerates；Second is that being not random because not winding has certain regularity with the difference of winding image
Number.
Regression model of the invention uses the convolution kernel of 3*3,64 characteristic patterns of every layer of extraction.Activation primitive is Relu,
It is normalized after activation using Batch Normalization.It is finally solved using ADMM algorithm, specific loss
Function are as follows:
L (Y, y (x))=(Y-y (x))2
Wherein, Y represents the image that true optical imagery phase is not wound, and y (x) represents the optics that the present invention is predicted
The image that image phase is not wound.
Finally our network passes through the training of 50 epoch, and simulation result, which has substantially surmounted traditional image solution, to be twined
Around algorithm.
Step 4 utilizes trained model prediction
The network structure and parameter obtained present invention utilizes step 3 training result is saved.We utilize later
Above-mentioned preservation result has carried out the unwrapping of optics winding image.The prediction result accuracy of model and solving speed relative to
Traditional image unwrapping algorithm has very big improvement.
Embodiment
Training set is similar to more by Zernike shown in Fig. 1 (a), 1 (b), 1 (c) in embodiment of the present invention
The optical imagery that item formula generates.Corresponding phase, which is generated, according to step 2 later winds image.Model training by step 3 it
Afterwards, it is tested using the parameter learnt.Shown in final testing result such as Fig. 3 (a), 3 (b), 3 (c), 3 (d).
Claims (1)
1. a kind of optical imagery phase unwrapping winding method based on residual error convolutional neural networks, it is characterised in that including walking as follows
It is rapid:
Step 1 generates the optical imagery that phase is not wound using Zernike multinomial；
Step 2 carries out phase winding operation using the optical imagery not wound, obtains phase winding image；
Step 3 utilizes convolutional neural networks training pattern；
Step 4 utilizes trained model prediction；
The step 1 is specific:
{Vpq(x, y) } it is one group of complex function collection being defined on unit circle, there is completeness and orthogonality；
{Vpq(x, y) } it can indicate any quadractically integrable function being defined in unit circle, is defined as:
Vpq(x, y)=Vpq(ρ, θ)=Rpq(ρ)ejqθ
Wherein, ρ indicates the vector length of former point-to-point (x, y)；θ indicates vector ρ and the anticlockwise angle of x-axis；Rpq(ρ) is
Real value radial polynomial:
Since the form of the aberrational polynomial observed in Zernike multinomial and optical detection is consistent, thus use
Zernike describes wavefront properties.
The step 2 is specific:
The optical imagery similar with experiment not wound by obtaining a batch after step 1, obtains corresponding phase by following formula
The difference of position winding image and the two.
imgdiff=imgunwrap-imgwrap
Wherein, imgwrap、imgunwrapRespectively represent the optical imagery for not winding and winding；Angle (x) represents the phase of x；
imgdiffIt is the difference for the optical imagery for not winding and winding.
The step 3 is specific:
3-1. carries out the feature learning in relation to optical imagery unwrapping using 25 layers of the convolutional neural networks with residual error, wherein residual
Difference function indicates are as follows: f (x)=H (x)-x；
Wherein, H (x) represents the feature of the optical imagery unwrapping algorithm finally to be learned.It inputs the optical imagery being wound around, defeated
It is the optical imagery not wound out；X represents input, that is, the optical imagery wound；What f (x) representative learnt does not wind figure
Difference between picture and winding image.
3-2. model uses the convolution kernel of 3*3,64 characteristic patterns of every layer of extraction.Activation primitive is Relu, is utilized after activation
Batch Normalization is normalized.
3-3. is solved using ADMM algorithm, specific loss function are as follows:
L (Y, y (x))=(Y-y (x))2
Wherein, Y represents the image that true optical imagery phase is not wound, and y (x) represents the optical imagery phase predicted and do not twine
Around image.
The step 4 is specific:
The network structure and parameter obtain to step 3 training result saves, and carries out optics winding figure using result is saved
The unwrapping of picture.
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| CN111325317A (en) * | 2020-01-21 | 2020-06-23 | 北京空间机电研究所 | Wavefront aberration determination method and device based on generation countermeasure network |
| CN111461224A (en) * | 2020-04-01 | 2020-07-28 | 西安交通大学 | Phase data unwrapping method based on residual self-coding neural network |
| CN111561877A (en) * | 2020-04-24 | 2020-08-21 | 西安交通大学 | Variable resolution phase unwrapping method based on point diffraction interferometer |
| CN111812647A (en) * | 2020-07-11 | 2020-10-23 | 桂林电子科技大学 | Phase unwrapping method for interferometric synthetic aperture radar |
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| CN113238227A (en) * | 2021-05-10 | 2021-08-10 | 电子科技大学 | Improved least square phase unwrapping method and system combined with deep learning |
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| WO2021003003A1 (en) * | 2019-07-02 | 2021-01-07 | Microsoft Technology Licensing, Llc | Phase depth imaging using machine-learned depth ambiguity dealiasing |
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| CN111461224B (en) * | 2020-04-01 | 2022-08-16 | 西安交通大学 | Phase data unwrapping method based on residual self-coding neural network |
| CN111561877A (en) * | 2020-04-24 | 2020-08-21 | 西安交通大学 | Variable resolution phase unwrapping method based on point diffraction interferometer |
| CN111561877B (en) * | 2020-04-24 | 2021-08-13 | 西安交通大学 | Variable resolution phase unwrapping method based on point diffraction interferometer |
| CN111812647A (en) * | 2020-07-11 | 2020-10-23 | 桂林电子科技大学 | Phase unwrapping method for interferometric synthetic aperture radar |
| CN112381172A (en) * | 2020-11-28 | 2021-02-19 | 桂林电子科技大学 | InSAR interference image phase unwrapping method based on U-net |
| CN113238227A (en) * | 2021-05-10 | 2021-08-10 | 电子科技大学 | Improved least square phase unwrapping method and system combined with deep learning |
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