CN105787935B - A kind of fuzzy clustering SAR image segmentation method based on Gamma distributions - Google Patents
A kind of fuzzy clustering SAR image segmentation method based on Gamma distributions Download PDFInfo
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Abstract
The present invention provides a kind of fuzzy clustering SAR image segmentation method based on Gamma distributions, including：Using the gray value of each pixel of SAR image to be split as sample point, FCM object function of the structure with Gamma distribution functions；Determine the solution formula of each parameter in FCM object functions；SAR image fuzzy clustering to be split is carried out using the FCM object functions with Gamma distribution functions, the gray value for obtaining each pixel of SAR image to be split belongs to the other fuzzy membership matrix of various regions species；Anti fuzzy method is carried out by maximum membership grade principle to above-mentioned fuzzy membership matrix, realizes that SAR image is split.The non-similarity that the present invention describes pixel to cluster using the negative logarithm of Gamma distribution probability density functions is estimated, influence of the noise in SAR image to segmentation result is further overcome by Accurate Curve-fitting SAR image distribution characteristics, so as to improve segmentation precision, fitting and the segmentation precision of SAR image are effectively increased.
Description
Technical Field
The invention belongs to the field of image processing, and particularly relates to a fuzzy clustering SAR image segmentation method based on Gamma distribution.
Background
Synthetic Aperture Radar (SAR) image segmentation is a key technology in SAR image processing, and the accuracy of segmentation directly affects subsequent interpretation processing, so that the method has important significance for the research of the SAR image segmentation technology. However, it is difficult to obtain a high-precision segmentation result because the imaging principle of SAR is contrary to human vision, and the high resolution brings more clear details and is influenced by many factors such as intrinsic speckle noise caused by the imaging process.
At present, an image segmentation method based on an SAR mainly comprises the following steps: threshold methods, statistical methods and clustering methods. The principle of the threshold-based method is simple, but a reasonable threshold is difficult to find and the method can only carry out SAR image segmentation of limited classes; the method based on statistics can model noise, has better noise immunity, but is difficult to solve; the method based on clustering has the biggest characteristic of easy modeling and solving, but cannot be used for noise modeling, so the method is sensitive to noise. Among the above methods, the clustering method, especially the Fuzzy clustering method, is most widely applied due to the characteristics of simple principle, good algorithm stability, fast convergence speed, etc., such as the most commonly used SAR image segmentation method based on Fuzzy C-means (FCM), but because the method uses Euclidean distance to define the non-similarity measure and does not consider the neighborhood pixel effect, the method is sensitive to the speckle noise and abnormal values in the SAR image, and therefore, a large amount of noise exists in the segmentation result of the SAR image based on the traditional FCM. In order to overcome the problem that the segmentation method is sensitive to noise, a fuzzy clustering high-resolution remote sensing image segmentation algorithm based on a hidden Markov Gaussian random field model, namely Zhao Ching, li Yu, zhao Quanhua, etc. (Zhao Ching, li Yu, zhao Ching. Hidden Markov Gaussian random field model: electronics and informatics, 2014,36 (11): 2730-2736) is combined with a statistical method and the characteristics of a clustering method, a neighborhood relationship between a characteristic field and a label field is established by using the hidden Markov random field and a Gaussian regression model, and SAR image segmentation is realized by an FCM method, so that the problems of inaccurate segmentation and multiple mistaken pixels in a classical method are effectively solved. However, the method considers that the distribution of the SAR image is gaussian distribution and does not conform to the characteristics of the SAR image obeying Gamma distribution, and the segmentation problem of all SAR images cannot be solved.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a fuzzy clustering SAR image segmentation method based on Gamma distribution.
The technical scheme of the invention is as follows:
a fuzzy clustering SAR image segmentation method based on Gamma distribution comprises the following steps:
step 1: reading an SAR image to be segmented;
step 2: taking the gray value of each pixel of the SAR image to be segmented as a sample point, constructing an FCM target function with a Gamma distribution function, wherein the target function takes overcoming the influence of noise in the SAR image on the segmentation result as a target, and takes the negative logarithm of the Gamma distribution function as the non-similarity measure of the target function according to the characteristic that the SAR image gray distribution obeys the Gamma distribution; the prior probability in the FCM objective function is determined by defining the potential energy function of the label field. The FCM target function parameters comprise fuzzy factors, fuzzy membership functions, prior probability, shape parameters and scale parameters in Gamma distribution functions;
and step 3: determining a solving formula of each parameter in the FCM objective function;
and 4, step 4: fuzzy clustering is carried out on the SAR image to be segmented by using an FCM target function with a Gamma distribution function, and a fuzzy membership matrix of gray values of all pixels of the SAR image to be segmented belonging to all terrain categories is obtained;
and 5: and performing defuzzification on the fuzzy membership matrix according to a maximum membership principle to realize SAR image segmentation.
The specific steps of the step 3 are as follows:
step 3.1: determining a prior probability formula in the FCM objective function;
step 3.1.1: defining a potential energy function: when the gray value of the neighborhood pixel and the gray value of the central pixel belong to the same ground object class, the potential energy is 0, otherwise, the potential energy is 1;
step 3.1.2: defining prior probability in an FCM target function according to the potential energy function and carrying out normalization processing;
step 3.2: determining a numerical solution formula of the fuzzy membership degree: adding a Lagrange multiplier into the FCM target function, then solving a partial derivative of a fuzzy membership function in the FCM target function, making the first derivative equal to 0 to obtain a fuzzy membership function with a Lagrange coefficient, and then eliminating the Lagrange coefficient;
step 3.3: determining numerical solution formulas of shape parameters and scale parameters in the Gamma distribution function:
determining a numerical solution formula of the shape parameter: carrying out equivalent infinitesimal replacement on the shape parameters;
determining a numerical solution formula of the scale parameter: let the first order partial derivative of the FCM objective function to the shape parameter equal zero.
The specific steps of the step 4 are as follows:
step 4.1: setting the number of clustering centers, initializing a fuzzy membership matrix, fuzzy factors and iteration stop conditions; the number of the clustering centers is the number of ground object types in the SAR image to be segmented, and the fuzzy factor represents the chaos degree of the SAR image segmentation result;
step 4.2: randomly initializing an FCM objective function value, a scale parameter and a shape parameter of a Gamma distribution function;
step 4.3: calculating prior probability for restricting clustering scale in FCM objective function;
step 4.4: estimating new shape parameters and scale parameters to obtain a non-similarity measure;
step 4.5: calculating the fuzzy membership degree of the gray value of each pixel belonging to each ground object class according to the prior probability and the non-similarity measure in the FCM target function;
step 4.6: calculating a current FCM objective function value according to the fuzzy membership, the non-similarity measure and the prior probability;
step 4.7: if the difference between the current FCM objective function value and the FCM objective function value calculated last time is larger than a set threshold value, taking the current fuzzy membership degree as an initial fuzzy membership degree, and returning to the step 4.3; if the difference between the current FCM objective function value and the FCM objective function value calculated in the previous time is smaller than a set threshold, stopping iteration;
step 4.8: and the current fuzzy membership matrix is the optimal fuzzy membership matrix of each pixel gray value of the SAR image to be segmented.
Has the beneficial effects that:
the invention provides a fuzzy clustering SAR image segmentation method based on Gamma distribution by utilizing the characteristics of Gamma distribution for accurately describing the SAR image intensity distribution and combining with an FCM method. The method utilizes the negative logarithm of the Gamma distribution probability density function to describe the non-similarity measure from the pixel point to the cluster, and further overcomes the influence of noise in the SAR on the segmentation result through accurately fitting the SAR image distribution characteristics, thereby improving the segmentation precision and effectively improving the fitting and segmentation precision of the SAR image. The SAR image automatic interpretation method is good in stability and high in convergence speed, and provides a new idea for automatic interpretation of the SAR image.
Drawings
FIG. 1 is a flowchart of a fuzzy clustering SAR image segmentation method based on Gamma distribution according to an embodiment of the present invention;
FIG. 2 is a flowchart illustrating step 3 of the present invention;
FIG. 3 is a flowchart of step 4 in an embodiment of the present invention;
FIG. 4 is a simulation image in the embodiment of the present invention, wherein (a) is a template, (b) is a simulation image, and (c) is a real SAR image, ice melt and water are sequentially provided from light to dark;
FIG. 5 is a graph of a simulation image segmentation experiment using the method of the present invention, the conventional FCM method, and the FCM method based on the Gaussian regression model according to the present invention, wherein (a) is the segmentation result of the standard FCM method, (b) is the segmentation result of the FCM method based on the Gaussian regression model, and (c) is the segmentation result of the FCM method according to the present invention;
fig. 6 is a segmentation experiment of a real SAR image by applying the method of the present invention, the conventional FCM method, and the FCM method based on the gaussian regression model in the embodiment of the present invention, wherein (a) is a segmentation result of the standard FCM method, (b) is a segmentation result of the FCM method based on the gaussian regression model, and (c) is a segmentation result of the method of the present invention;
FIG. 7 is a graph of the fitting effect of a Gaussian regression model and a corresponding histogram of the segmentation results of a real SAR image in accordance with an embodiment of the present invention;
fig. 8 is a diagram illustrating the fitting effect of the Gamma distribution function and the corresponding histogram of the real SAR image segmentation result according to the embodiment of the present invention.
Detailed Description
The following detailed description of embodiments of the invention refers to the accompanying drawings.
A fuzzy clustering SAR image segmentation method based on Gamma distribution is disclosed, as shown in figure 1, and comprises the following steps:
step 1: reading an SAR image to be segmented;
in this embodiment, a SAR image domain X = { X } to be segmented is defined 1 ,…,x i ,…,x N In which x i Is the gray scale measure of the ith pixel, i is the pixel index, N is the total number of pixels, X is 128X 128 pixels, and the total number of pixels N =16384.
Step 2: taking the gray value of each pixel of the SAR image to be segmented as a sample point, constructing an FCM target function with a Gamma distribution function, wherein the target function takes the effect of noise in the SAR image on the segmentation result of the SAR image as a target, and takes the negative logarithm of the Gamma distribution function as the non-similarity measure of the target function according to the characteristic that the gray distribution of the SAR image obeys the Gamma distribution; the prior probability in the FCM objective function is determined by defining the potential energy function of the label field. The FCM target function parameters comprise fuzzy factors, fuzzy membership functions, prior probability, shape parameters in Gamma distribution and scale parameters;
the FCM objective function determines the prior probability in the objective function by defining the potential energy function of the label field to consider the influence of the neighborhood relationship of the pixels on the segmentation result.
The FCM objective function with the Gamma distribution function is defined as follows:
wherein c is the number of clustering centers, u ij Is a fuzzy membership function, represents the membership degree of the gray value of the ith pixel belonging to the j ground object class, and satisfies that u is more than or equal to 0 ij Constraint less than or equal to 1, lambda is fuzzy factor, representing disorder degree of SAR image segmentation result, pi ij The variable-prior probability for constraining the clustering scale is a c × N matrix, pi ij Is the posterior probability.
In this embodiment, the following function is defined as the measure of dissimilarity of the FCM objective function:
wherein alpha is j ，β j As a describing parameter of the Gamma distribution function, alpha j As a shape parameter, β j Is a scale parameter.
And 3, step 3: determining a solving mode of each parameter in the FCM target function;
as shown in fig. 2, the specific steps are as follows:
step 3.1: determining a prior probability formula in the FCM objective function;
step 3.1.1: defining a potential energy function V c : when the gray value of the neighborhood pixel and the gray value of the central pixel belong to the same ground object class, the potential energy is 0, otherwise, the potential energy is 1;
in this embodiment, the neighborhood pixel relationship is defined in the label field, and the potential energy function formula is defined as follows:
in the present embodiment, let L = { L = 1 ,l 2 ,…,l N Is the index field of X,/ i E {1,2, \8230;, j, \8230;, c } is the label of the ground object class to which the gray value of the ith pixel belongs, and if the gray value is classified into 3 classes, l i Is equal to {1,2,3}, and a potential energy function is defined in a 3 multiplied by 3 window, l iˊ Reference numeral, l, indicating the ground object class to which the gray value of the neighborhood pixel belongs i Is the mark of the ground object class to which the gray value of the central pixel belongs, when the gray value of the adjacent pixel and the gray value of the central pixel have the same mark of the ground object class, the stable state is reached, the potential energy is 0, otherwise, the potential energy is 1, wherein V c ∈{0,1,2,…,8}。
Step 3.1.2: defining a prior probability pi in an FCM objective function from a potential energy function ij Carrying out normalization processing;
normalized pi ij The formula is as follows:
where μ is a parameter in the energy function, when implemented μ =0.5;
step 3.2: determining a numerical solution formula of the fuzzy membership function: adding a Lagrange multiplier into the FCM target function, then solving a partial derivative of a fuzzy membership function in the FCM target function, enabling an first derivative to be equal to 0, obtaining a fuzzy membership function with the Lagrange multiplier, and then eliminating the Lagrange multiplier;
in this embodiment, in order to solve the FCM objective function J, it is necessary to derive the fuzzy membership function u in the equation (1) ij A measure of non-similarity d ij ；u ij Representing the membership degree of the gray value of the ith pixel to the jth ground feature class, and meeting the following conditions;
in this embodiment, in order to obtain the fuzzy membership function, a lagrange multiplier m needs to be added to the FCM objective function to obtain the following FCM objective function:
then, the fuzzy membership function in the FCM target function is subjected to partial derivative calculation, the first derivative of the fuzzy membership function is equal to 0, and a fuzzy membership function u containing m is obtained ij ：
Substituting the step (8) into the formula (5), and eliminating a Lagrange multiplier m to obtain the following fuzzy membership function:
step 3.3: determining numerical solution formulas of shape parameters and scale parameters in the Gamma distribution function;
in this embodiment, the first-order partial derivative of the FCM objective function to the shape parameter is made equal to zero, and the scale parameter β is determined j The numerical solution of (c) is as follows:
simplified to obtain the following beta j The numerical solution formula of (c):
determining the shape parameter alpha by performing an equivalent infinitesimal substitution of the shape parameter j A numerical solution formula of (c);
in the present embodiment, the factor Γ (α) j ) For α in the FCM objective function j Since it is difficult to differentiate, gamma (alpha) is first aligned j ) Equivalent infinitesimal substitutions are made, namely:
substituting the formula (12) into the formula (2) results in the presence of no gamma (. Alpha.) ( j ) Approximate Gamma distribution type dissimilarity measure formula of (2):
substituting the formula (13) into the formula (1), and making the first-order partial derivative of the FCM objective function to the shape parameter equal to zero, thereby solving the shape parameter and solving the formula alpha j ；
In this embodiment, the specific process is as follows:
and 4, step 4: carrying out fuzzy clustering on the SAR image to be segmented by using an FCM target function with a Gamma distribution function to obtain a fuzzy membership matrix of gray values of pixels of the SAR image to be segmented belonging to various ground object classes;
as shown in fig. 3, the specific steps are as follows:
step 4.1: setting the number c of clustering centers and initializing a fuzzy membership matrix u ij A fuzzy factor lambda and an iteration stop condition e; the number of clustering centers, namely the number of ground object types in the SAR image to be segmented, is expressed by fuzzy factorsThe chaos degree of the SAR image segmentation result;
in the embodiment, the number c =3 of the ground object types of the simulated SAR image to be segmented, and the number c =3 of the ground object types of the real SAR image to be segmented; initial fuzzy membership matrix u ij Randomly generating, wherein the fuzzy factor lambda is obtained from experience to be about 2.3; the iteration stop conditions are as follows: minimum value e of difference between two FCM objective functions in iterative process<0.02；
Step 4.2: randomly initializing FCM objective function value J 0 The scale parameter beta of the Gamma distribution function j 0 And a shape parameter alpha j 0 ；
Step 4.3: calculating prior probability pi of constraint cluster scale in FCM objective function by using formula (4) ij 0 ；
μ in equation (4) is a parameter in the potential energy function, μ =0.5;
step 4.4: estimating a new shape parameter beta j 1 And a scale parameter alpha j 1 Further, the non-similarity measure is obtained;
step 4.5: calculating fuzzy membership u of gray value of each pixel belonging to each ground object class according to prior probability and non-similarity measure in FCM target function ij 1 ；
Step 4.6: calculating the current FCM objective function value J according to the fuzzy membership, the non-similarity measure and the prior probability 1 ；
Step 4.7: if the difference between the current FCM objective function value and the FCM objective function value calculated last time is larger than a set threshold, taking the current fuzzy membership degree as an initial fuzzy membership degree, and returning to the step 3.3; if the difference between the current FCM objective function value and the FCM objective function value calculated in the previous time is smaller than a set threshold, stopping iteration;
in the present embodiment, | J is set 1 -J 0 |>, e, will make J 1 ＝J 0 ，β j 1＝β j 0 ，α j 1 ＝α j 0 Repeating the step 4.3 to 4.7; if J 1 -J 0 And e is less than or equal to the absolute value, and iteration is stopped.
Step 4.8: and the current fuzzy membership matrix is the optimal fuzzy membership matrix of each pixel gray value of the SAR image to be segmented.
And 5: and performing defuzzification on the fuzzy membership matrix according to a maximum membership principle to realize SAR image segmentation. Maximum membership principle: and comparing fuzzy membership values corresponding to the pixels to be divided in the SAR image in the fuzzy membership matrix, and determining the surface feature class corresponding to the maximum membership value as the surface feature class of the current pixel.
Z j ＝arg i {max{U ij }} j＝1,...,N；i＝1,...,m (16)
Wherein Z is j A belonging object class representing a gradation value of the jth pixel, and is represented by Z = { Z = 1 ,Z 2 ,…,Z N And expressing the segmentation result of the SAR image.
The invention can realize simulation by using MATLAB7.12.0 software programming on a Core (TM) i5-34703.20GHz, memory 4GB and Windows 7 flagship version system as a CPU.
In this embodiment, a real SAR image including 3 surface feature types and a generated surface feature type simulated SAR image having 3 Gamma distributions are designed as a simulation image, where Gamma distribution parameters of the simulated SAR image are known. Table 1 lists the Gamma distribution parameters of each feature type in the simulated SAR image in this embodiment.
TABLE 1 simulation SAR image Gamma distribution parameter
Fig. 4 is a simulation image, in which (a) is a template, (b) is a simulation image, and (c) is a real SAR image, and ice, ice melt and water are sequentially formed from light to dark.
Fig. 5 is a segmentation experiment of a simulated SAR image by applying the method of the present invention, the conventional FCM method, and the FCM method based on the gaussian regression model in this embodiment, where (a) is a segmentation result of the standard FCM method, (b) is a segmentation result of the FCM method based on the gaussian regression model, and (c) is a segmentation result of the SAR image by the method of the present invention. It can be seen that the FCM segmentation result is the worst, and the segmentation result of the present invention (fig. 5 (c)) is significantly better than the FCM segmentation result based on the gaussian regression model distribution.
Fig. 6 is a segmentation experiment of a real SAR image by applying the method of the present invention, the conventional FCM method, and the FCM method based on the gaussian regression model in this embodiment, where (a) is a segmentation result of the standard FCM method, (b) is a segmentation result of the FCM method based on the gaussian regression model, and (c) is a segmentation result of the method of the present invention. It can be seen that the noise of the segmentation result of the method is greatly reduced, and the segmentation effect is greatly improved.
Table 2 shows the quantitative evaluation of the segmentation result of the simulated image by the method of the present invention and the FCM method based on the gaussian regression model, using the template image as a standard in the present embodiment. Because the standard FCM segmentation effect contains a large amount of noise and is poor in segmentation effect, the accuracy index of the standard FCM is not considered during accuracy evaluation, and only the latter two methods are quantitatively evaluated. It can be seen that the overall segmentation accuracy of the FCM method based on the Gaussian regression model is 61.1%, while the overall segmentation accuracy of the segmentation method of the invention reaches 99.1%, compared with the comparison method, the segmentation accuracy of the invention is improved by 38%, the segmentation effect is good, and the segmentation accuracy is improved remarkably.
TABLE 2 quantitative evaluation of the FCM method based on the Gaussian regression model and the segmentation results of the method of the invention
Fig. 7 is a graph showing the effect of fitting the gaussian regression model to the corresponding histogram of the segmentation result of the real SAR image in the present embodiment, in which discrete points represent the histograms of four feature types in the segmentation result of fig. 6 (b), and a black curve represents the gaussian regression fit model of the four feature types. It can be seen that the gaussian regression model does not fit its corresponding histogram accurately.
Fig. 8 is a graph showing the effect of fitting the Gamma distribution function to the corresponding histogram of the segmentation result of the real SAR image in the present embodiment, where discrete points represent the histograms of four surface feature classes in the segmentation result of fig. 6 (c), and a black curve represents the Gamma distribution fitting model of four classes. Therefore, the Gamma distribution function used in the invention can accurately fit the SAR image distribution characteristics, thereby verifying the rationality of the FCM method for modeling the SAR image model by using the Gamma distribution function.
The above description is only the most basic embodiment of the present invention, but the scope of the present invention is not limited thereto, and any alternative that can be understood by those skilled in the art within the technical scope of the present invention shall be covered by the present invention, such as classification processing, feature extraction, etc. of other remote sensing data types based on the method of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (3)
1. A fuzzy clustering SAR image segmentation method based on Gamma distribution comprises the following steps:
step 1: reading an SAR image to be segmented;
step 2: taking the gray value of each pixel of the SAR image to be segmented as a sample point, constructing an FCM target function, taking the target function as a target for overcoming the influence of noise in the SAR image on the segmentation result, and determining the prior probability in the FCM target function by defining a potential energy function of a label field; the FCM target function parameters comprise fuzzy factors, fuzzy membership functions, prior probability, shape parameters and scale parameters in a Gamma distribution function;
and step 3: determining a solving formula of each parameter in the FCM objective function;
and 4, step 4: fuzzy clustering is carried out on the SAR image to be segmented by utilizing the FCM target function, and a fuzzy membership matrix of gray values of all pixels of the SAR image to be segmented, which belong to all terrain categories, is obtained;
and 5: defuzzification is carried out on the fuzzy membership matrix according to a maximum membership principle, and SAR image segmentation is realized;
it is characterized in that the preparation method is characterized in that,
the FCM target function in the step 2 is an FCM target function with a Gamma distribution function, and according to the characteristic that the gray level distribution of the SAR image obeys the Gamma distribution, the negative logarithm of the Gamma distribution function is used as the non-similarity measure of the target function;
the following function is defined as the measure of dissimilarity of the FCM objective function:
wherein alpha is j 、β j Is a description parameter of the Gamma distribution function, x i Is a measure of the gray level of the ith pixel, α j As a shape parameter, β j Is a scale parameter;
and 4, when fuzzy clustering is carried out on the SAR image to be segmented by using the FCM target function, the number of clustering centers, namely the number of surface feature types in the SAR image to be segmented is set.
2. The method for segmenting the fuzzy clustering SAR image based on the Gamma distribution according to the claim 1, wherein the step 3 comprises the following steps:
step 3.1: determining a prior probability formula in the FCM objective function;
step 3.1.1: defining a potential energy function: when the gray value of the neighborhood pixel and the gray value of the central pixel belong to the same ground object category, the potential energy is 0, otherwise, the potential energy is 1;
step 3.1.2: defining prior probability in an FCM target function according to the potential energy function and carrying out normalization processing;
step 3.2: determining a numerical solution formula of the fuzzy membership degree: adding a Lagrange multiplier into the FCM target function, then solving a partial derivative of a fuzzy membership function in the FCM target function, making the first derivative equal to 0 to obtain a fuzzy membership function with the Lagrange multiplier, and then eliminating the Lagrange multiplier;
step 3.3: determining numerical solution formulas of shape parameters and scale parameters in the Gamma distribution function:
determining a numerical solution formula of the shape parameter: carrying out equivalent infinitesimal replacement on the shape parameters;
determining a numerical solution formula of the scale parameter: let the first order partial derivative of the FCM objective function to the shape parameter equal zero.
3. The fuzzy clustering SAR image segmentation method based on Gamma distribution according to the claim 1, wherein the specific steps of the step 4 are as follows:
step 4.1: setting initial fuzzy membership, fuzzy factors and iteration stop conditions; the fuzzy factor represents the chaos degree of the SAR image segmentation result;
and 4.2: randomly initializing an FCM objective function value, a scale parameter and a shape parameter of a Gamma distribution function;
step 4.3: calculating prior probability for restricting clustering scale in FCM objective function;
step 4.4: estimating new shape parameters and scale parameters to obtain a non-similarity measure;
step 4.5: calculating fuzzy membership degree of gray value of each pixel belonging to each ground object category according to prior probability and non-similarity measure in FCM target function;
step 4.6: calculating a current FCM objective function value according to the fuzzy membership, the non-similarity measure and the prior probability;
step 4.7: if the difference between the current FCM objective function value and the FCM objective function value calculated last time is larger than a set threshold, taking the current fuzzy membership degree as an initial fuzzy membership degree, and returning to the step 4.3; if the difference between the current FCM objective function value and the FCM objective function value calculated last time is smaller than a set threshold value, stopping iteration;
step 4.8: and the current fuzzy membership matrix is the optimal fuzzy membership matrix of each pixel gray value of the SAR image to be segmented.
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