CN112561931A - Class weighting SAR image segmentation method combining GMTRJ algorithm and EM algorithm - Google Patents

Class weighting SAR image segmentation method combining GMTRJ algorithm and EM algorithm Download PDF

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CN112561931A
CN112561931A CN202011473361.XA CN202011473361A CN112561931A CN 112561931 A CN112561931 A CN 112561931A CN 202011473361 A CN202011473361 A CN 202011473361A CN 112561931 A CN112561931 A CN 112561931A
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CN112561931B (en
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王玉
周国清
尤号田
石雪
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Guilin University of Technology
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Abstract

The invention provides a class weighting SAR image segmentation method combining a GMTRJ algorithm and an EM algorithm, and relates to the technical field of image processing. The method comprises the steps of firstly defining an SAR image to be segmented as one realization of a random field on an image domain D, and giving a weight to each category in the SAR image to form a weight set; then, defining a class-weighted SAR image by using the image to be segmented and the weight set, and defining the class-weighted SAR image as one implementation of a characteristic field on an image domain; then, dividing an image domain of the class-weighted SAR image into a plurality of sub-blocks by utilizing a rule division technology; establishing a class weighting SAR image segmentation model on the divided image domain; and finally, aiming at the established class-weighted SAR image segmentation model, setting iteration times, designing and solving all parameters in the class-weighted SAR image segmentation model by utilizing a GMTRJ algorithm in each iteration process, estimating a weight set by utilizing an EM algorithm, further determining the optimal solution of the class-weighted SAR image segmentation model, and completing the segmentation of the SAR image.

Description

Class weighting SAR image segmentation method combining GMTRJ algorithm and EM algorithm
Technical Field
The invention relates to the technical field of image processing, in particular to a class weighting SAR image segmentation method combining a GMTRJ algorithm and an EM algorithm.
Background
Statistical segmentation is a common method for SAR (Synthetic Aperture Radar) image segmentation. At present, most of statistical segmentation methods realize segmentation by constructing a segmentation model and solving parameters of the model.
The RJMCMC (Reversible Jump Markov Chain Monte Carlo) algorithm is a commonly used model parameter solving algorithm and is widely applied to the solution of segmentation model parameters. However, the RJMCMC algorithm has some potential problems in model parameter solution, for example, proper parameters are difficult to determine in each jump, and solution efficiency and solution quality are difficult to balance; that is, if the algorithm is fast converged, the obtained parameter solution is not the optimal solution, and the solving quality is difficult to ensure; if the acceptance rate is high and a better solution can be obtained, the time complexity is high, and the solving efficiency is difficult to ensure. GMTRJ (Generalized Multiple-Try Reversible Jump) is used as an improved algorithm of the RJMCMC algorithm, and the problem can be effectively solved; the algorithm utilizes a multiple trial strategy, ensures the solving efficiency, and determines more appropriate parameters by defining a weight function so as to improve the acceptance rate and further improve the solving quality. However, at present, the research and application of the algorithm in remote sensing image segmentation are still in the initial stage, and systematic research work is developed by domestic and foreign scholars in this respect.
Disclosure of Invention
The invention provides a class weighting SAR image segmentation method combining a GMTRJ algorithm and an EM algorithm to realize segmentation of an SAR image, aiming at the defects of the prior art.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows: a class weighting SAR image segmentation method combining a GMTRJ algorithm and an EM algorithm comprises the following steps:
step 1: inputting an SAR image to be segmented, and defining the SAR image as one realization of a random field on an image domain D;
inputting SAR image x to be segmented into { x ═ xdD ∈ D } is defined as the random field X ═ { X } in the image domain DdD e D), where D is the index of the pixel in the SAR image,xdis the intensity of pixel d, XdA random variable representing the intensity of pixel d;
step 2: giving each category of the SAR image a weight, wherein the weights corresponding to all the categories in the image form a weight set;
giving corresponding weight omega to the category marked with l in the SAR imagelDefining it as an analytical quantity; the weights of all classes in the SAR image form a set of weights, denoted as ω ═ ω { (ω ═ ω } ω { (ω })l1, …, k, where k is the total number of categories in the SAR image;
and step 3: defining a class-weighted SAR image by using an image to be segmented and a weight set, and defining the class-weighted SAR image as one implementation of a characteristic field on an image domain;
using x as { x ] of the image to be segmenteddD e D and set of weights ω { ω ═ D }lL ═ 1, …, k } defines a class-weighted SAR image, denoted y ═ { y { (y)dD ∈ D }, wherein,
Figure BDA0002836706410000021
for the class-weighted intensity of pixel d,/dIs the label of the class to which the pixel d belongs,
Figure BDA0002836706410000022
is the weight of the class to which the pixel d belongs; weighting SAR image y ═ ydD ∈ D } is defined as a feature field Y ═ { Y } in the image domain DdD ∈ D }; wherein the content of the first and second substances,
Figure BDA0002836706410000023
a random variable that is the class-weighted intensity of pixel d;
and 4, step 4: dividing an image domain of the class-weighted SAR image into a plurality of sub-blocks by using a rule division technology;
the image domain D is divided into m sub-blocks by using a regular division technique, i.e., D ═ Pi1, 1.., m }, wherein PiIs divided into ith sub-block, i is sub-block index, m is total number of divided sub-blocks, and P is sub-blockiThe number of rows or columns is an integer multiple of 2, allowing the smallest subblock to contain 2 × 2 pixel points; SAR imageEach homogeneous region of the image is formed by fitting one or more sub-blocks with the same reference number;
and 5: establishing a class weighting SAR image segmentation model on a divided image domain, wherein the specific method comprises the following steps:
firstly, defining a label field L ═ L on a regularly divided SAR image domaini1, 1.., m }, wherein L is LiRepresents a sub-block PiRandom variable of class label, LiE { 1.., k }; in the regularly divided SAR image domain, the characteristic field Y is defined as Y ═ YiI 1.. m }, wherein Y isi＝{Yd,d∈PiIs a sub-block PiA set of random variables with class-weighted intensities of d for all pixels within; each realization of the index field L ═ LiI 1.. m } is the segmentation result corresponding to the class-weighted SAR image y, liAs a sub-block PiClass label of, and sub-block PiAll pixels in the tile have class labels of li；
Step 5.1: setting the average value of the number m of the divided sub-blocks to be lambda on the divided SAR image domainmDefining a prior distribution of the number m of sub-blocks, as shown in the following equation:
Figure BDA0002836706410000024
wherein p (m) is a probability density function of the number m of sub-blocks;
step 5.2: on the divided SAR image domain, a label field model is defined by a potential energy function, and the following formula is shown:
Figure BDA0002836706410000025
wherein p (L | k, m) is the conditional probability density function of label field L under known k and m conditions, U (L) is a potential energy function, A is a constant, gamma is the space action parameter of the neighborhood sub-block, NPiAs a sub-block PiI' is the subblock PiNeighborhood sub-block P ofi′Index of (1), Li′For a neighborhood sub-block Pi′Random variables of the index of (1); if L isi＝Li′Then, delta (L)i,Li′) 1 is ═ 1; if L isi≠Li′Then, delta (L)i,Li′)＝0；
Step 5.3: defining a characteristic field model on the divided SAR image domain;
setting sub-block PiRandom variable Y of class weighting intensity corresponding to all pixels d in the imagedSatisfies the mean value of mulStandard deviation of σlAnd a set Y of random variables of class-weighted intensities corresponding to all sub-blocks in the SAR image domainiThe gaussian distributions are all independent, and then the characteristic field model is defined as shown in the following formula:
Figure BDA0002836706410000031
where p (Y | L, θ, k, m) is a conditional probability density function of the characteristic field Y given the known L, θ, k and m conditions, θ ═ θ { [ theta ]lWhere l is 1, …, k represents a parametric vector set of the characteristic field model, θl＝(μl,σl) A parameter vector denoted by reference character l;
step 5.4: establishing prior distribution of a characteristic field model parameter vector set;
setting mulAnd σlRespectively obey mean value of muμAnd muσStandard deviation of σμAnd σσAre independent of each other, the parameter vector theta of index llA priori distribution p (theta)l) As shown in the following equation:
Figure BDA0002836706410000032
wherein, p (mu)l) And p (σ)l) Are respectively mulAnd σlA priori distribution of;
at the same time, all the parameter vectors theta are setlThe prior distributions of (a) are all independent of each other,then the set of characteristic field model parameter vectors θ ═ θlThe prior distribution p (θ | k) of 1, …, k is shown as follows:
Figure BDA0002836706410000033
step 5.5: on the basis of the step 5.1 to the step 5.4, establishing a class weighting SAR image segmentation model;
according to Bayes' theorem, a class-weighted SAR image segmentation model is defined by combining the prior distribution of the number m of the sub-blocks in the step 5.1, the label field model in the step 5.2, the characteristic field model in the step 5.3 and the prior distribution of the parameter vector set of the characteristic field model in the step 5.4, and the following formula is shown:
Figure BDA0002836706410000041
wherein p (L, theta, m | X, omega, k) is a conditional probability density function of L, theta and m under known X, omega and k conditions; step 6: setting iteration times aiming at the established class-weighted SAR image segmentation model, designing and solving all parameters in the class-weighted SAR image segmentation model by utilizing a GMTRJ algorithm in each iteration process, estimating a weight set by utilizing an EM algorithm, and further determining the optimal solution of the class-weighted SAR image segmentation model;
step 6.1: sampling a characteristic field model parameter vector set by sampling parameter vectors in the characteristic field model parameter vector set by utilizing a GMTRJ algorithm;
randomly extracting a label l from {1, …, k }, wherein the corresponding characteristic field model parameter vector is thetalFinal candidate feature field model parameter vector θ for labelsl *Is the probability p (theta )*) From the set { theta }l (g)G is selected from 1, …, G, wherein thetal (g)Is the G-th candidate characteristic field model parameter vector, and G is the total number of candidate characteristic field model parameter vectors; the feature field model parameter vector corresponding to the label which is not extracted is unchanged; wherein, thetal (g)Obey meanIs thetalStandard deviation of σθ(ii) a gaussian distribution of; the original characteristic field model parameter vector set is theta ═ theta1,…,θl,…,θkThe set of candidate characteristic field model parameter vectors is theta*＝{θ1,…,θl *,…,θk}; changing the parameter vector set of the sampling characteristic field model from theta to theta*Acceptance rate of (a)p(θ,θ*) As shown in the following equation:
ap(θ,θ*)＝min{1,Rp}
wherein the content of the first and second substances,
Figure BDA0002836706410000042
wherein the content of the first and second substances,
Figure BDA0002836706410000043
wherein w (theta )*) And w (theta )(g)) Are all weight functions, and are respectively expressed as:
w(θ,θ*)＝p(Y|L,θ*,k,m)p(θ*|k)
w(θ,θ(g))＝p(Y|L,θ(g),k,m)p(θ(g)|k)
generating a random number from 0-1, determining the random number and the acceptance rate ap(θ,θ*) When the acceptance rate a isp(θ,θ*) When the number is larger than the random number, receiving the condition that the parameter vector set of the sampling characteristic field model is changed from theta to theta*Otherwise, abandoning the parameter vector set of the sampling characteristic field model at this time from theta to theta*The operation of (1);
step 6.2: on the basis of the step 6.1 of sampling the characteristic field model parameter vector set, sampling a label field by sampling a random variable of a label in the label field by using a GMTRJ algorithm;
from video domain D ═ PiRandomly extracting a sub-block P from the i 1iWith the corresponding labeled random variable Li(ii) a Candidate index random variable of sub-block
Figure BDA0002836706410000051
With probability p (L, L)*) From the collection
Figure BDA0002836706410000052
Is extracted from, wherein
Figure BDA0002836706410000053
Figure BDA0002836706410000054
And is
Figure BDA0002836706410000055
The random variable of the label to which the sub-block which is not extracted belongs is unchanged; then L ═ L1,…,Li,…,LmThe original label field is used as the label field,
Figure BDA0002836706410000056
is a candidate label field; obtaining the sampling label field from L to L*Acceptance rate of (a)l(L,L*) As shown in the following equation:
al(L,L*)＝min{1,Rl}
wherein the content of the first and second substances,
Figure BDA0002836706410000057
wherein the content of the first and second substances,
Figure BDA0002836706410000058
wherein, w (L, L)*) And w (L, L)(g)) Are all weight functions, and are respectively expressed as:
w(L,L*)＝p(L*|k,m)p(Y|L*,θ,k,m)
w(L,L(g))＝p(L(g)|k,m)p(Y|L(g),θ,k,m)
generating a random number from 0-1, determining the random number and the acceptance rate al(L,L*) When the acceptance rate a isl(L,L*) When the sampling number is larger than the random number, the sampling number field is changed from L to L*Otherwise, abandoning the sampling label field from L to L*The operation of (1);
step 6.3: on the basis of the sampling label field in the step 6.2, increasing or reducing the number of sampling sub-blocks by splitting or merging sub-blocks by utilizing a GMTRJ algorithm;
step 6.3.1: randomly extracting a sub-block P from the image domain D which is formed by fitting m sub-blocks after the sampling of the label field in the step 6.2iThe random variable of the corresponding label is Li；
Step 6.3.2: judging the extracted sub-block PiWhether the split can be performed; if P isiIs greater than 4 and the number of rows or columns is an integer multiple of 2, then step 6.3.3 is performed for the sub-block PiSplitting is carried out, and the number of sub blocks in an image domain is increased; otherwise, the sub-block P is not splitiIf the number of sub-blocks in the image domain is not changed, ending the splitting operation;
step 6.3.3: sub-block P capable of realizing splitting operation in image domain DiSplitting into two new sub-blocks Pi1And Pi2New subblock Pi1The random variable of the corresponding index is
Figure BDA0002836706410000061
New subblock Pi2Random variation of corresponding label
Figure BDA0002836706410000062
And is
Figure BDA0002836706410000063
Figure BDA0002836706410000064
Wherein, the sub-block Pi1Is from a collection
Figure BDA0002836706410000065
Has a mean probability of p (D, D)*) To obtain, corresponding to Pi2Is composed of corresponding sets
Figure BDA0002836706410000066
Has a mean probability of p (D, D)*) Obtaining; the non-split sub-blocks are not changed, and the random variables of the corresponding labels are also not changed; the number of sub-blocks in the video domain is increased by one, and the video domain D is { P ═ P1,...,Pi-1,Pi...,PmIs changed into
Figure BDA00028367064100000614
Label field L ═ L1,...,Li-1,Li...,LmIs changed into
Figure BDA0002836706410000067
m*Representing the number of sub-blocks after sampling; the number of sampling sub-blocks is changed from m to m*The acceptance rate of (c) is shown by the following formula:
as(m,m*)＝min{1,Rs}
wherein the content of the first and second substances,
Figure BDA0002836706410000068
wherein the content of the first and second substances,
Figure BDA0002836706410000069
wherein the content of the first and second substances,
Figure BDA00028367064100000610
w(D,D*) And w (D, D)(g)) Are all weight functions, and are respectively expressed as:
w(D,D*)＝p(L*|k,m*)p(Y|L*,θ,k,m*)p(m*)
w(D,D(g))＝p(L(g)|k,m(g))p(Y|L(g),θ,k,m(g))p(m(g))
wherein the content of the first and second substances,
Figure BDA00028367064100000611
Figure BDA00028367064100000612
is a sub-block
Figure BDA00028367064100000613
The corresponding label variable;
step 6.3.4: generating a random number from 0-1, determining the random number and the acceptance rate as(m,m*) When the acceptance rate a iss(m,m*) If the number of the sub-blocks is larger than the random number, the operation of sampling the number of the sub-blocks by splitting the sub-blocks is received, otherwise, the operation of sampling the number of the sub-blocks by splitting the sub-blocks is abandoned;
step 6.3.5: the sub-block number is reduced by combining a sub-block randomly extracted from the image domain D and any neighborhood sub-block into a new sub-block, which is a dual operation of splitting sub-blocks, so that the acceptance rate of sampling the sub-block number by combining sub-blocks is as follows:
am(m,m*)＝min{1,1/Rs}
generating a random number from 0-1, determining the random number and the acceptance rate am(m,m*) When the acceptance rate a ism(m,m*) If the number of the sub-blocks is larger than the random number, receiving the operation of sampling the image domain by merging the sub-blocks, otherwise giving up the operation of sampling the number of the sub-blocks by merging the sub-blocks;
step 6.4: on the basis of the number of the sampling sub-blocks in the step 6.3, estimating a weight set by using an EM (effective noise) algorithm;
setting the weight set estimation value of the nth iteration as omega*Then the expected value of this iteration Q (ω)*ω) is shown by the following equation:
Q(ω*,ω)＝E[log p(Y*|L*,θ*,k,m*)|ω]
wherein the content of the first and second substances,E[log p(Y*|L*,θ*,k,m*)|ω]is log p (Y)*|L*,θ*,k,m*) In the expectation that the position of the target is not changed,
Figure BDA0002836706410000071
Figure BDA0002836706410000072
for Q (omega)*ω) and setting the derivative to 0, ω '═ ω'l(ii) a 1, k, wherein,
Figure BDA0002836706410000073
wherein N isoThe total number of pixels with the label l;
then, to'lIs subjected to normalization processing to obtain
Figure BDA0002836706410000074
As shown in the following equation:
Figure BDA0002836706410000075
further, a set of weights is obtained
Figure BDA0002836706410000076
Step 6.5: repeatedly executing the step 6.1 to the step 6.4 according to the set iteration times to obtain a set of parameters L, theta, m and a weight set omega, wherein the segmentation result corresponding to the maximum p (L, theta, m | X, omega, k) in the set is the optimal solution of the class-weighted SAR image segmentation model;
and 7: and outputting the segmentation result of the SAR image.
Adopt the produced beneficial effect of above-mentioned technical scheme to lie in: according to the class-weighted SAR image segmentation method combining the GMTRJ algorithm and the EM algorithm, the GMTRJ method is adopted to solve the model parameters, and although the model parameters can be solved by the traditional RJMCMC algorithm, the appropriate parameters are difficult to determine in the solving process, and the solving efficiency and the solving quality are difficult to balance. GMTRJ is used as an improved algorithm of RJMCMC, a multiple trial strategy is adopted, more appropriate parameters can be determined through a weight function while solving efficiency is guaranteed, solving quality is improved, and SAR image segmentation precision is further improved.
Drawings
Fig. 1 is a flowchart of a class-weighted SAR image segmentation method combining a GMTRJ algorithm and an EM algorithm according to an embodiment of the present invention;
fig. 2 is an SAR image to be segmented according to an embodiment of the present invention;
fig. 3 is a segmentation result image of an SAR image to be segmented according to an embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the present invention is provided in connection with the accompanying drawings and examples. The following examples are intended to illustrate the invention but are not intended to limit the scope of the invention.
In this embodiment, a class-weighted SAR image segmentation method combining a GMTRJ algorithm and an EM algorithm, as shown in fig. 1, includes the following steps:
step 1: inputting an SAR image to be segmented, and defining the SAR image as one realization of a random field on an image domain D;
inputting SAR image x to be segmented into { x ═ xdD ∈ D } is defined as the random field X ═ { X } in the image domain DdD ∈ D }, where D is the pixel index in the SAR image, xdIs the intensity of pixel d, XdA random variable representing the intensity of pixel d;
step 2: giving each category of the SAR image a weight, wherein the weights corresponding to all the categories in the image form a weight set;
giving corresponding weight omega to the category marked with l in the SAR imagelDefining it as an analytical quantity; the weights of all classes in the SAR image form a set of weights, denoted as ω ═ ω { (ω ═ ω } ω { (ω })l1, …, k, where k is the total number of categories in the SAR image;
and step 3: defining a class-weighted SAR image by using an image to be segmented and a weight set, and defining the class-weighted SAR image as one implementation of a characteristic field on an image domain;
using x as { x ] of the image to be segmenteddD e D and set of weights ω { ω ═ D }lL ═ 1, …, k } defines a class-weighted SAR image, denoted y ═ { y { (y)dD ∈ D }, wherein,
Figure BDA0002836706410000081
for the class-weighted intensity of pixel d,/dIs the label of the class to which the pixel d belongs,
Figure BDA0002836706410000082
is the weight of the class to which the pixel d belongs; weighting SAR image y ═ ydD ∈ D } is defined as a feature field Y ═ { Y } in the image domain DdD ∈ D }; wherein the content of the first and second substances,
Figure BDA0002836706410000091
a random variable that is the class-weighted intensity of pixel d;
and 4, step 4: dividing an image domain of the class-weighted SAR image into a plurality of sub-blocks by using a rule division technology;
the image domain D is divided into m sub-blocks by using a regular division technique, i.e., D ═ Pi1, 1.., m }, wherein PiIs divided into ith sub-block, i is sub-block index, m is total number of divided sub-blocks, and P is sub-blockiThe number of rows or columns is an integer multiple of 2, allowing the smallest subblock to contain 2 × 2 pixel points; each homogeneous region of the SAR image is formed by fitting one or more sub-blocks with the same label;
and 5: establishing a class weighting SAR image segmentation model on a divided image domain, wherein the specific method comprises the following steps:
firstly, defining a label field L ═ L on a regularly divided SAR image domaini1, 1.., m }, wherein L is LiRepresents a sub-block PiRandom variable of class label, LiE { 1.., k }; in the regularly divided SAR image domain, the characteristic field Y is defined as Y ═ Yi,i＝1,...M }, wherein Y isi＝{Yd,d∈PiIs a sub-block PiA set of random variables with class-weighted intensities of d for all pixels within; each realization of the index field L ═ LiI 1.. m } is the segmentation result corresponding to the class-weighted SAR image y, liAs a sub-block PiClass label of, and sub-block PiAll pixels in the tile have class labels of li；
Step 5.1: setting the average value of the number m of the divided sub-blocks to be lambda on the divided SAR image domainmDefining a prior distribution of the number m of sub-blocks, as shown in the following equation:
Figure BDA0002836706410000092
wherein p (m) is a probability density function of the number m of sub-blocks;
step 5.2: on the divided SAR image domain, a label field model is defined by a potential energy function, and the following formula is shown:
Figure BDA0002836706410000093
wherein p (L | k, m) is the conditional probability density function of label field L under known k and m conditions, U (L) is a potential energy function, A is a constant, gamma is the space action parameter of the neighborhood sub-block, NPiAs a sub-block PiI' is the subblock PiNeighborhood sub-block P ofi′Index of (1), Li′For a neighborhood sub-block Pi′Random variables of the index of (1); if L isi＝Li′Then, delta (L)i,Li′) 1 is ═ 1; if L isi≠Li′Then, delta (L)i,Li′)＝0；
Step 5.3: defining a characteristic field model on the divided SAR image domain;
setting sub-block PiRandom variable Y of class weighting intensity corresponding to all pixels d in the imagedSatisfies the mean value of mulStandard deviation of σlAnd a set Y of random variables of class-weighted intensities corresponding to all sub-blocks in the SAR image domainiThe gaussian distributions are all independent, and then the characteristic field model is defined as shown in the following formula:
Figure BDA0002836706410000101
where p (Y | L, θ, k, m) is a conditional probability density function of the characteristic field Y given the known L, θ, k and m conditions, θ ═ θ { [ theta ]lWhere l is 1, …, k represents a parametric vector set of the characteristic field model, θl＝(μl,σl) A parameter vector denoted by reference character l;
step 5.4: establishing prior distribution of a characteristic field model parameter vector set;
setting mulAnd σlRespectively obey mean value of muμAnd muσStandard deviation of σμAnd σσAre independent of each other, the parameter vector theta of index llA priori distribution p (theta)l) As shown in the following equation:
Figure BDA0002836706410000102
wherein, p (mu)l) And p (σ)l) Are respectively mulAnd σlA priori distribution of;
at the same time, all the parameter vectors theta are setlAll the prior distributions are independent, and then a characteristic field model parameter vector set theta is { theta ═ theta { (theta) }lThe prior distribution p (θ | k) of 1, …, k is shown as follows:
Figure BDA0002836706410000103
step 5.5: on the basis of the step 5.1 to the step 5.4, establishing a class weighting SAR image segmentation model;
according to Bayes' theorem, a class-weighted SAR image segmentation model is defined by combining the prior distribution of the number m of the sub-blocks in the step 5.1, the label field model in the step 5.2, the characteristic field model in the step 5.3 and the prior distribution of the parameter vector set of the characteristic field model in the step 5.4, and the following formula is shown:
Figure BDA0002836706410000104
wherein p (L, theta, m | X, omega, k) is a conditional probability density function of L, theta and m under known X, omega and k conditions;
step 6: setting iteration times aiming at the established class-weighted SAR image segmentation model, designing and solving all parameters in the class-weighted SAR image segmentation model by utilizing a GMTRJ algorithm in each iteration process, estimating a weight set by utilizing an EM algorithm, and further determining the optimal solution of the class-weighted SAR image segmentation model;
step 6.1: sampling a characteristic field model parameter vector set by sampling parameter vectors in the characteristic field model parameter vector set by utilizing a GMTRJ algorithm;
randomly extracting a label l from {1, …, k }, wherein the corresponding characteristic field model parameter vector is thetalFinal candidate feature field model parameter vector θ for labelsl *Is the probability p (theta )*) From the set { theta }l (g)G is selected from 1, …, G, wherein thetal (g)Is the G-th candidate characteristic field model parameter vector, and G is the total number of candidate characteristic field model parameter vectors; the feature field model parameter vector corresponding to the label which is not extracted is unchanged; wherein, thetal (g)Obeying a mean value of thetalStandard deviation of σθ(ii) a gaussian distribution of; the original characteristic field model parameter vector set is theta ═ theta1,…,θl,…,θkThe set of candidate characteristic field model parameter vectors is theta*＝{θ1,…,θl *,…,θk}; changing the parameter vector set of the sampling characteristic field model from theta to theta*Acceptance rate of (a)p(θ,θ*) As shown in the following equation:
ap(θ,θ*)＝min{1,Rp}
wherein the content of the first and second substances,
Figure BDA0002836706410000111
wherein the content of the first and second substances,
Figure BDA0002836706410000112
wherein w (theta )*) And w (theta )(g)) Are all weight functions, and are respectively expressed as:
w(θ,θ*)＝p(Y|L,θ*,k,m)p(θ*|k)
w(θ,θ(g))＝p(Y|L,θ(g),k,m)p(θ(g)|k)
generating a random number from 0-1, determining the random number and the acceptance rate ap(θ,θ*) When the acceptance rate a isp(θ,θ*) When the number is larger than the random number, receiving the condition that the parameter vector set of the sampling characteristic field model is changed from theta to theta*Otherwise, abandoning the parameter vector set of the sampling characteristic field model at this time from theta to theta*The operation of (1);
step 6.2: on the basis of the step 6.1 of sampling the characteristic field model parameter vector set, sampling a label field by sampling a random variable of a label in the label field by using a GMTRJ algorithm;
from video domain D ═ PiRandomly extracting a sub-block P from the i 1iWith the corresponding labeled random variable Li(ii) a Candidate index random variable of sub-block
Figure BDA0002836706410000113
With probability p (L, L)*) From the collection
Figure BDA0002836706410000114
Is extracted from, wherein
Figure BDA0002836706410000115
Figure BDA0002836706410000116
And is
Figure BDA0002836706410000117
The random variable of the label to which the sub-block which is not extracted belongs is unchanged; then L ═ L1,…,Li,…,LmThe original label field is used as the label field,
Figure BDA0002836706410000118
is a candidate label field; obtaining the sampling label field from L to L*Acceptance rate of (a)l(L,L*) As shown in the following equation:
al(L,L*)＝min{1,Rl}
wherein the content of the first and second substances,
Figure BDA0002836706410000121
wherein the content of the first and second substances,
Figure BDA0002836706410000122
wherein, w (L, L)*) And w (L, L)(g)) Are all weight functions, and are respectively expressed as:
w(L,L*)＝p(L*|k,m)p(Y|L*,θ,k,m)
w(L,L(g))＝p(L(g)|k,m)p(Y|L(g),θ,k,m)
generating a random number from 0-1, determining the random number and the acceptance rate al(L,L*) When the acceptance rate a isl(L,L*) When the sampling number is larger than the random number, the sampling number field is changed from L to L*Otherwise, abandoning the sampling label field from L to L*The operation of (1);
step 6.3: on the basis of the sampling label field in the step 6.2, increasing or reducing the number of sampling sub-blocks by splitting or merging sub-blocks by utilizing a GMTRJ algorithm;
step 6.3.1: randomly extracting a sub-block P from the image domain D which is formed by fitting m sub-blocks after the sampling of the label field in the step 6.2iThe random variable of the corresponding label is Li；
Step 6.3.2: judging the extracted sub-block PiWhether the split can be performed; if P isiIs greater than 4 and the number of rows or columns is an integer multiple of 2, then step 6.3.3 is performed for the sub-block PiSplitting is carried out, and the number of sub blocks in an image domain is increased; otherwise, the sub-block P is not splitiIf the number of sub-blocks in the image domain is not changed, ending the splitting operation;
step 6.3.3: sub-block P capable of realizing splitting operation in image domain DiSplitting into two new sub-blocks Pi1And Pi2New subblock Pi1The random variable of the corresponding index is
Figure BDA0002836706410000123
New subblock Pi2Random variation of corresponding label
Figure BDA0002836706410000124
And is
Figure BDA0002836706410000125
Figure BDA0002836706410000126
Wherein, the sub-block Pi1Is from a collection
Figure BDA0002836706410000127
Has a mean probability of p (D, D)*) To obtain, corresponding to Pi2Is composed of corresponding sets
Figure BDA0002836706410000128
Has a mean probability of p (D, D)*) Obtaining; the non-split sub-blocks are not changed, and the random variables of the corresponding labels are also not changed; the number of sub-blocks in the video domain is increased by one, and the video domain D is { P ═ P1,...,Pi-1,Pi...,PmIs changed into
Figure BDA0002836706410000138
Label field L ═ L1,...,Li-1,Li...,LmIs changed into
Figure BDA0002836706410000131
m*Representing the number of sub-blocks after sampling; the number of sampling sub-blocks is changed from m to m*The acceptance rate of (c) is shown by the following formula:
as(m,m*)＝min{1,Rs}
wherein the content of the first and second substances,
Figure BDA0002836706410000132
wherein the content of the first and second substances,
Figure BDA0002836706410000133
wherein the content of the first and second substances,
Figure BDA0002836706410000134
w(D,D*) And w (D, D)(g)) Are all weight functions, and are respectively expressed as:
w(D,D*)＝p(L*|k,m*)p(Y|L*,θ,k,m*)p(m*)
w(D,D(g))＝p(L(g)|k,m(g))p(Y|L(g),θ,k,m(g))p(m(g))
wherein the content of the first and second substances,
Figure BDA0002836706410000135
Figure BDA0002836706410000136
is a sub-block
Figure BDA0002836706410000137
The corresponding label variable;
step 6.3.4: generating a random number from 0-1, determining the random number and the acceptance rate as(m,m*) When the acceptance rate a iss(m,m*) If the number of the sub-blocks is larger than the random number, the operation of sampling the number of the sub-blocks by splitting the sub-blocks is received, otherwise, the operation of sampling the number of the sub-blocks by splitting the sub-blocks is abandoned;
step 6.3.5: the sub-block number is reduced by combining a sub-block randomly extracted from the image domain D and any neighborhood sub-block into a new sub-block, which is a dual operation of splitting sub-blocks, so that the acceptance rate of sampling the sub-block number by combining sub-blocks is as follows:
am(m,m*)＝min{1,1/Rs}
generating a random number from 0-1, determining the random number and the acceptance rate am(m,m*) When the acceptance rate a ism(m,m*) If the number of the sub-blocks is larger than the random number, receiving the operation of sampling the image domain by merging the sub-blocks, otherwise giving up the operation of sampling the number of the sub-blocks by merging the sub-blocks;
step 6.4: on the basis of the number of the sampling sub-blocks in the step 6.3, estimating a weight set by using an EM (effective noise) algorithm;
setting the weight set estimation value of the nth iteration as omega*Then the expected value of this iteration Q (ω)*ω) is shown by the following equation:
Q(ω*,ω)＝E[log p(Y*|L*,θ*,k,m*)|ω]
wherein E [ log p (Y)*|L*,θ*,k,m*)|ω]Is log p (Y)*|L*,θ*,k,m*) In the expectation that the position of the target is not changed,
Figure BDA0002836706410000141
Figure BDA0002836706410000142
for Q (omega)*ω) and setting the derivativeTo 0, ω '═ ω'l(ii) a 1, k, wherein,
Figure BDA0002836706410000143
wherein N isoThe total number of pixels with the label l;
then, to'lIs subjected to normalization processing to obtain
Figure BDA0002836706410000144
As shown in the following equation:
Figure BDA0002836706410000145
further, a set of weights is obtained
Figure BDA0002836706410000146
Step 6.5: repeatedly executing the step 6.1 to the step 6.4 according to the set iteration times to obtain a set of parameters L, theta, m and a weight set omega, wherein the segmentation result corresponding to the maximum p (L, theta, m | X, omega, k) in the set is the optimal solution of the class-weighted SAR image segmentation model;
and 7: and outputting the segmentation result of the SAR image.
In this embodiment, for the SAR image to be segmented as shown in fig. 2, the segmentation result obtained after segmentation by the segmentation method of the present invention is shown in fig. 3, and it can be seen from the figure that the method of the present invention can accurately segment the SAR image.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; such modifications and substitutions do not depart from the spirit of the corresponding technical solutions and scope of the present invention as defined in the appended claims.

Claims (8)

1. A class weighting SAR image segmentation method combining GMTRJ algorithm and EM algorithm is characterized in that: the method comprises the following steps:
step 1: inputting an SAR image to be segmented, and defining the SAR image as one realization of a random field on an image domain D;
step 2: giving each category of the SAR image a weight, wherein the weights corresponding to all the categories in the image form a weight set;
and step 3: defining a class-weighted SAR image by using an image to be segmented and a weight set, and defining the class-weighted SAR image as one implementation of a characteristic field on an image domain;
and 4, step 4: dividing an image domain of the class-weighted SAR image into a plurality of sub-blocks by using a rule division technology;
and 5: establishing a class weighting SAR image segmentation model on the divided image domain;
step 6: setting iteration times aiming at the established class-weighted SAR image segmentation model, designing and solving all parameters in the class-weighted SAR image segmentation model by utilizing a GMTRJ algorithm in each iteration process, estimating a weight set by utilizing an EM algorithm, and further determining the optimal solution of the class-weighted SAR image segmentation model;
and 7: and outputting the segmentation result of the SAR image.
2. The method for segmenting the SAR image with the combination of the GMTRJ algorithm and the EM algorithm and the like weighted according to claim 1, wherein: the specific method of the step 1 comprises the following steps:
inputting SAR image x to be segmented into { x ═ xdD ∈ D } is defined as the random field X ═ { X } in the image domain DdD ∈ D }, where D is the pixel index in the SAR image, xdIs the intensity of pixel d, XdA random variable representing the intensity of pixel d.
3. The method for segmenting the SAR image with the combination of the GMTRJ algorithm and the EM algorithm and the weighted SAR image according to claim 2, wherein the image segmentation method comprises the following steps: the specific method of the step 2 comprises the following steps:
giving corresponding weight omega to the category marked with l in the SAR imagelDefining it as an analytical quantity; the weights of all classes in the SAR image form a set of weights, denoted as ω ═ ω { (ω ═ ω } ω { (ω })lAnd l is 1, …, k, where k is the total number of categories in the SAR image.
4. The method for segmenting the SAR image with the combination of the GMTRJ algorithm and the EM algorithm and the weighted SAR image according to claim 3, wherein the image segmentation method comprises the following steps: the specific method of the step 3 comprises the following steps:
using x as { x ] of the image to be segmenteddD e D and set of weights ω { ω ═ D }lL ═ 1, …, k } defines a class-weighted SAR image, denoted y ═ { y { (y)dD ∈ D }, wherein,
Figure FDA0002836706400000011
for the class-weighted intensity of pixel d,/dIs the label of the class to which the pixel d belongs,
Figure FDA0002836706400000012
is the weight of the class to which the pixel d belongs; weighting SAR image y ═ ydD ∈ D } is defined as a feature field Y ═ { Y } in the image domain DdD ∈ D }; wherein the content of the first and second substances,
Figure FDA0002836706400000021
a random variable of class-weighted intensity for pixel d.
5. The GMTRJ algorithm and EM algorithm combined weighted SAR image segmentation method according to claim 4, wherein: the specific method of the step 4 comprises the following steps:
the image domain D is divided into m sub-blocks by using a regular division technique, i.e., D ═ Pi1, 1.., m }, wherein PiIs divided into ith sub-block, i is sub-block index, m is total number of divided sub-blocks, and P is sub-blockiThe number of rows or columns is an integer multiple of 2, allowing the smallest subblock to contain 2 × 2 pixel points; SAR imageEach homogenous region of (a) is fitted with one or more sub-blocks having the same reference number.
6. The method for segmenting the SAR image with the combination of the GMTRJ algorithm and the EM algorithm and the weighted SAR image according to claim 5, wherein the image segmentation method comprises the following steps: the specific method of the step 5 comprises the following steps:
firstly, defining a label field L ═ L on a regularly divided SAR image domaini1, 1.., m }, wherein L is LiRepresents a sub-block PiRandom variable of class label, LiE { 1.., k }; in the regularly divided SAR image domain, the characteristic field Y is defined as Y ═ YiI 1.. m }, wherein Y isi＝{Yd,d∈PiIs a sub-block PiA set of random variables with class-weighted intensities of d for all pixels within; each realization of the index field L ═ LiI 1.. m } is the segmentation result corresponding to the class-weighted SAR image y, liAs a sub-block PiClass label of, and sub-block PiAll pixels in the tile have class labels of li；
Step 5.1: setting the average value of the number m of the divided sub-blocks to be lambda on the divided SAR image domainmDefining a prior distribution of the number m of sub-blocks, as shown in the following equation:
Figure FDA0002836706400000022
wherein p (m) is a probability density function of the number m of sub-blocks;
step 5.2: on the divided SAR image domain, a label field model is defined by a potential energy function, and the following formula is shown:
Figure FDA0002836706400000023
wherein p (L | k, m) is the conditional probability density function of label field L under known k and m conditions, U (L) is a potential energy function, A is a constant, gamma is the space action parameter of the neighborhood sub-block, NPiAs a sub-block PiI' is the subblock PiNeighborhood sub-block P ofi′Index of (1), Li′For a neighborhood sub-block Pi′Random variables of the index of (1); if L isi＝Li′Then, delta (L)i,Li′) 1 is ═ 1; if L isi≠Li′Then, delta (L)i,Li′)＝0；
Step 5.3: defining a characteristic field model on the divided SAR image domain;
setting sub-block PiRandom variable Y of class weighting intensity corresponding to all pixels d in the imagedSatisfies the mean value of mulStandard deviation of σlAnd a set Y of random variables of class-weighted intensities corresponding to all sub-blocks in the SAR image domainiThe gaussian distributions are all independent, and then the characteristic field model is defined as shown in the following formula:
Figure FDA0002836706400000031
where p (Y | L, θ, k, m) is a conditional probability density function of the characteristic field Y given the known L, θ, k and m conditions, θ ═ θ { [ theta ]lWhere l is 1, …, k represents a parametric vector set of the characteristic field model, θl＝(μl,σl) A parameter vector denoted by reference character l;
step 5.4: establishing prior distribution of a characteristic field model parameter vector set;
setting mulAnd σlRespectively obey mean value of muμAnd muσStandard deviation of σμAnd σσAre independent of each other, the parameter vector theta of index llA priori distribution p (theta)l) As shown in the following equation:
Figure FDA0002836706400000032
wherein, p (mu)l) And p (σ)l) Are respectively mulAnd σlA priori distribution of;
at the same time, all the parameter vectors theta are setlAll the prior distributions are independent, and then a characteristic field model parameter vector set theta is { theta ═ theta { (theta) }lThe prior distribution p (θ | k) of 1, …, k is shown as follows:
Figure FDA0002836706400000033
step 5.5: on the basis of the step 5.1 to the step 5.4, establishing a class weighting SAR image segmentation model;
according to Bayes' theorem, a class-weighted SAR image segmentation model is defined by combining the prior distribution of the number m of the sub-blocks in the step 5.1, the label field model in the step 5.2, the characteristic field model in the step 5.3 and the prior distribution of the parameter vector set of the characteristic field model in the step 5.4, and the following formula is shown:
Figure FDA0002836706400000034
where p (L, θ, m | X, ω, k) is the conditional probability density function of L, θ and m under known X, ω and k conditions.
7. The GMTRJ and EM combined weight-like SAR image segmentation method according to claim 6, wherein: the specific method of the step 6 comprises the following steps:
step 6.1: sampling a characteristic field model parameter vector set by sampling parameter vectors in the characteristic field model parameter vector set by utilizing a GMTRJ algorithm;
randomly extracting a label l from {1, …, k }, wherein the corresponding characteristic field model parameter vector is thetalFinal candidate feature field model parameter vector θ for labelsl *Is the probability p (theta )*) From the set { theta }l (g)G is selected from 1, …, G, wherein thetal (g)Is the G-th candidate feature field model parameter vector, and G is the sum of the candidate feature field model parameter vectorsCounting; the feature field model parameter vector corresponding to the label which is not extracted is unchanged; wherein, thetal (g)Obeying a mean value of thetalStandard deviation of σθ(ii) a gaussian distribution of; the original characteristic field model parameter vector set is theta ═ theta1,…,θl,…,θkThe set of candidate characteristic field model parameter vectors is theta*＝{θ1,…,θl *,…,θk}; changing the parameter vector set of the sampling characteristic field model from theta to theta*Acceptance rate of (a)p(θ,θ*) As shown in the following equation:
ap(θ,θ*)＝min{1,Rp}
wherein the content of the first and second substances,
Figure FDA0002836706400000041
wherein the content of the first and second substances,
Figure FDA0002836706400000042
wherein w (theta )*) And w (theta )(g)) Are all weight functions, and are respectively expressed as:
w(θ,θ*)＝p(Y|L,θ*,k,m)p(θ*|k)
w(θ,θ(g))＝p(Y|L,θ(g),k,m)p(θ(g)|k)
generating a random number from 0-1, determining the random number and the acceptance rate ap(θ,θ*) When the acceptance rate a isp(θ,θ*) When the number is larger than the random number, receiving the condition that the parameter vector set of the sampling characteristic field model is changed from theta to theta*Otherwise, abandoning the parameter vector set of the sampling characteristic field model at this time from theta to theta*The operation of (1);
step 6.2: on the basis of the step 6.1 of sampling the characteristic field model parameter vector set, sampling a label field by sampling a random variable of a label in the label field by using a GMTRJ algorithm;
from video domain D ═ PiRandomly extracting a sub-block P from the i 1iWith the corresponding labeled random variable Li(ii) a Candidate index random variable of sub-block
Figure FDA0002836706400000043
With probability p (L, L)*) From the collection
Figure FDA0002836706400000044
Is extracted from, wherein
Figure FDA0002836706400000045
Figure FDA0002836706400000046
And is
Figure FDA0002836706400000047
The random variable of the label to which the sub-block which is not extracted belongs is unchanged; then L ═ L1,…,Li,…,LmThe original label field is used as the label field,
Figure FDA0002836706400000048
is a candidate label field; obtaining the sampling label field from L to L*Acceptance rate of (a)l(L,L*) As shown in the following equation:
al(L,L*)＝min{1,Rl}
wherein the content of the first and second substances,
Figure FDA0002836706400000051
wherein the content of the first and second substances,
Figure FDA0002836706400000052
wherein, w (L, L)*) And w (L, L)(g)) Are all weight functions, and are respectively expressed as:
w(L,L*)＝p(L*|k,m)p(Y|L*,θ,k,m)
w(L,L(g))＝p(L(g)|k,m)p(Y|L(g),θ,k,m)
generating a random number from 0-1, determining the random number and the acceptance rate al(L,L*) When the acceptance rate a isl(L,L*) When the sampling number is larger than the random number, the sampling number field is changed from L to L*Otherwise, abandoning the sampling label field from L to L*The operation of (1);
step 6.3: on the basis of the sampling label field in the step 6.2, increasing or reducing the number of sampling sub-blocks by splitting or merging sub-blocks by utilizing a GMTRJ algorithm;
step 6.4: on the basis of the number of the sampling sub-blocks in the step 6.3, estimating a weight set by using an EM (effective noise) algorithm;
setting the weight set estimation value of the nth iteration as omega*Then the expected value of this iteration Q (ω)*ω) is shown by the following equation:
Q(ω*,ω)＝E[log p(Y*|L*,θ*,k,m*)|ω]
wherein E [ log p (Y)*|L*,θ*,k,m*)|ω]Is log p (Y)*|L*,θ*,k,m*) In the expectation that the position of the target is not changed,
Figure FDA0002836706400000053
Figure FDA0002836706400000054
for Q (omega)*ω) and setting the derivative to 0, ω '═ ω'l(ii) a 1, k, wherein,
Figure FDA0002836706400000055
wherein N isoThe total number of pixels with the label l;
then, to'lIs subjected to normalization processing to obtain
Figure FDA0002836706400000061
As shown in the following equation:
Figure FDA0002836706400000062
further, a set of weights is obtained
Figure FDA0002836706400000063
Step 6.5: and (4) repeatedly executing the steps 6.1 to 6.4 according to the set iteration times to obtain a set of the parameters L, theta, m and the weight set omega, wherein the segmentation result corresponding to the maximum p (L, theta, m | X, omega, k) in the set is the optimal solution of the class-weighted SAR image segmentation model.
8. The method for segmenting the SAR image with the combination of the GMTRJ algorithm and the EM algorithm according to claim 7, wherein: the specific method of the step 6.3 comprises the following steps:
step 6.3.1: randomly extracting a sub-block P from the image domain D which is formed by fitting m sub-blocks after the sampling of the label field in the step 6.2iThe random variable of the corresponding label is Li；
Step 6.3.2: judging the extracted sub-block PiWhether the split can be performed; if P isiIs greater than 4 and the number of rows or columns is an integer multiple of 2, then step 6.3.3 is performed for the sub-block PiSplitting is carried out, and the number of sub blocks in an image domain is increased; otherwise, the sub-block P is not splitiIf the number of sub-blocks in the image domain is not changed, ending the splitting operation;
step 6.3.3: sub-block P capable of realizing splitting operation in image domain DiSplitting into two new sub-blocks Pi1And Pi2New subblock Pi1The random variable of the corresponding index is
Figure FDA0002836706400000064
New subblock Pi2Random variation of corresponding label
Figure FDA0002836706400000065
And is
Figure FDA0002836706400000066
Figure FDA0002836706400000067
Wherein, the sub-block Pi1Is from a collection
Figure FDA0002836706400000068
Has a mean probability of p (D, D)*) To obtain, corresponding to Pi2Is composed of corresponding sets
Figure FDA0002836706400000069
Has a mean probability of p (D, D)*) Obtaining; the non-split sub-blocks are not changed, and the random variables of the corresponding labels are also not changed; the number of sub-blocks in the video domain is increased by one, and the video domain D is { P ═ P1,...,Pi-1,Pi...,PmIs changed into
Figure FDA00028367064000000612
Label field L ═ L1,...,Li-1,Li...,LmIs changed into
Figure FDA00028367064000000610
m*Representing the number of sub-blocks after sampling; the number of sampling sub-blocks is changed from m to m*The acceptance rate of (c) is shown by the following formula:
as(m,m*)＝min{1,Rs}
wherein the content of the first and second substances,
Figure FDA00028367064000000611
wherein the content of the first and second substances,
Figure FDA0002836706400000071
wherein the content of the first and second substances,
Figure FDA0002836706400000072
w(D,D*) And w (D, D)(g)) Are all weight functions, and are respectively expressed as:
w(D,D*)＝p(L*|k,m*)p(Y|L*,θ,k,m*)p(m*)
w(D,D(g))＝p(L(g)|k,m(g))p(Y|L(g),θ,k,m(g))p(m(g))
wherein the content of the first and second substances,
Figure FDA0002836706400000073
Figure FDA0002836706400000074
is a sub-block
Figure FDA0002836706400000075
The corresponding label variable;
step 6.3.4: generating a random number from 0-1, determining the random number and the acceptance rate as(m,m*) When the acceptance rate a iss(m,m*) If the number of the sub-blocks is larger than the random number, the operation of sampling the number of the sub-blocks by splitting the sub-blocks is received, otherwise, the operation of sampling the number of the sub-blocks by splitting the sub-blocks is abandoned;
step 6.3.5: the sub-block number is reduced by combining a sub-block randomly extracted from the image domain D and any neighborhood sub-block into a new sub-block, which is a dual operation of splitting sub-blocks, so that the acceptance rate of sampling the sub-block number by combining sub-blocks is as follows:
am(m,m*)＝min{1,1/Rs}
generating a random number from 0-1, determining the random number and the acceptance rate am(m,m*) When the acceptance rate a ism(m,m*) And if the number of the sub-blocks is larger than the random number, receiving the operation of sampling the image domain by merging the sub-blocks, otherwise, giving up the operation of sampling the number of the sub-blocks by merging the sub-blocks.
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