CN109272515B - Unsupervised SAR image segmentation method based on high-order multi-scale CRF - Google Patents

Unsupervised SAR image segmentation method based on high-order multi-scale CRF Download PDF

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CN109272515B
CN109272515B CN201810943117.1A CN201810943117A CN109272515B CN 109272515 B CN109272515 B CN 109272515B CN 201810943117 A CN201810943117 A CN 201810943117A CN 109272515 B CN109272515 B CN 109272515B
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CN109272515A (en
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张鹏
江银银
李明
宋婉莹
谭啸峰
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Xidian University
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Abstract

The invention discloses a high-order multi-scale conditional random field CRF unsupervised synthetic aperture radar SAR image segmentation method. The method comprises the following implementation steps: performing wavelet transformation on an input Synthetic Aperture Radar (SAR) image; calculating histogram features; calculating a semivariance feature; forming a feature vector; calculating the conditional probability of the local class; initially segmenting a Synthetic Aperture Radar (SAR) image; calculating the edge probability of each pixel point; calculating the combined posterior marginal probability of each pixel point; calculating the posterior marginal probability of each pixel point; estimating parameters; and (5) segmenting the SAR image. According to the method, the model parameters are solved through the relevant parameter iteration and the characteristic parameter iteration, the characteristics of the image are fully utilized, and the requirement on the quantity of training data is greatly reduced.

Description

Unsupervised SAR image segmentation method based on high-order multi-scale CRF
Technical Field
The invention belongs to the technical field of image processing, and further relates to an unsupervised Synthetic Aperture Radar (SAR) image segmentation method based on a high-order multi-scale Conditional Random Field (CRF) in the technical field of radar image processing. The method can be used for segmenting the SAR image.
Background
Synthetic aperture radar SAR is a high resolution imaging radar. The synthetic aperture radar SAR image interpretation technology is required to be used for support in civil and military, the synthetic aperture radar SAR image segmentation is an important link of the synthetic aperture radar SAR image interpretation technology, and the synthetic aperture radar SAR image segmentation can provide integral structure information of the synthetic aperture radar SAR image, so that the application of the synthetic aperture radar SAR system in many fields, such as geological exploration, environment monitoring and the like, is promoted. The random field model is regarded as an important means for processing the segmentation problem of the synthetic aperture radar SAR image, and has the advantage that the spatial correlation among pixels can be considered in the image classification process.
The patent technology 'SAR image segmentation method based on wavelet pooling convolutional neural network' (application number: 201510512535.1, grant publication number: CN105139395B) owned by the university of Sigan electronic technology discloses a method for segmenting images by utilizing wavelet pooling convolutional neural network. The patent technology constructs a wavelet pooling layer and forms a wavelet pooled convolutional neural network, and then selects an image block to input into the wavelet pooled convolutional neural network for training. And inputting all the image blocks into a trained network for testing to obtain a first class mark of the SAR image. And then performing superpixel segmentation on the SAR image, and fusing the result with the first class mark of the SAR image to obtain a second class mark of the SAR image. And obtaining a third class mark of the SAR image according to the Markov random field model, and fusing the third class mark with the super-pixel segmentation result to obtain a fourth class mark of the SAR image. And according to the SAR image gradient map, fusing the second class mark and the fourth class mark of the SAR image to obtain a final segmentation result. The method has the disadvantages that the convolutional neural network needs enough training data to learn network parameters and is not suitable for the condition that only one synthetic aperture radar SAR image exists.
The patent document "SAR image segmentation method based on K-S distance merging cost" (application number: 201710242604.0, application publication number: CN107146230A) applied by the university of sienna electronics technology proposes an image segmentation method using K-S distance merging cost. The method comprises the steps of calculating proportional edge intensity mapping according to pixel values of an original SAR image, and carrying out watershed transformation on the proportional edge intensity mapping to obtain an initial segmentation result. An empirical distribution function of the pixel values of each region in the initial segmentation result is calculated. And then calculating the K-S distance of any two adjacent area sums in the initial segmentation result. And then calculating the value of the combined cost function. And finally, determining a final image segmentation result according to the value of the merging cost function. The method has the disadvantages that the method ignores the scattering statistical characteristics of the synthetic aperture radar SAR image, so that the accuracy of the segmentation result is not high.
Disclosure of Invention
The invention aims to provide an unsupervised SAR image segmentation method based on a high-order multi-scale conditional random field aiming at the defects of the prior art.
The specific idea for realizing the purpose of the invention is as follows: firstly, feature extraction is carried out on a synthetic aperture radar SAR image to be segmented, and then the synthetic aperture radar SAR image is initially segmented by utilizing a normalized logic model NLRM. And then, calculating the posterior marginal probability of the primarily segmented synthetic aperture radar SAR image step by step. And estimating the model parameters of the SAR image by using a logarithmic cumulant MoLC method, a related parameter iteration method and a characteristic parameter iteration method. And obtaining a segmentation result of the image after the posterior marginal probability is maximized, and then carrying out multiple iterations. And in each iteration, the current segmentation result is used as the basis of the next iteration segmentation, so that the segmentation result after multiple iterations approaches the optimal segmentation of the synthetic aperture radar image SAR.
The steps of the invention comprise:
(1) inputting a Synthetic Aperture Radar (SAR) image;
(2) performing wavelet transformation on the input synthetic aperture radar SAR image to obtain a multi-scale synthetic aperture radar SAR image;
(3) calculating the histogram feature of the high-order multi-scale conditional random field CRF:
(3a) sliding a window with the radius of 7 pixel points at intervals in the multi-scale synthetic aperture radar SAR image, performing sliding window operation on the multi-scale synthetic aperture radar SAR image, and respectively calculating the histogram characteristics of all pixel values in each sliding window;
(3b) the histogram features of all pixel values in each sliding window in the multi-scale synthetic aperture radar SAR image form the histogram features of a high-order multi-scale conditional random field CRF;
(4) calculating the half-variance characteristics of the high-order multi-scale conditional random field CRF:
(4a) sliding a window with the radius of 7 pixel points by taking one pixel point as an interval in the multi-scale synthetic aperture radar SAR image, and performing sliding window operation on the multi-scale synthetic aperture radar SAR image;
(4b) the east-west half-variance of all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000021
wherein the content of the first and second substances,
Figure GDA0002523167490000031
denotes the east-west half-variance, n, of all pixel values within the m-th sliding windowmRepresenting the total number of all pixels in the mth sliding window, ∑ representing the summation operation, i representing the sequence number of the pixel row in the mth sliding window, j representing the sequence number of the pixel column in the mth sliding window, yi,jExpressing the pixel value of the ith row and jth column pixel point in the mth sliding window;
(4c) the north-south half-variance of all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000032
wherein the content of the first and second substances,
Figure GDA0002523167490000033
representing the half-variance of the north-south direction of all pixel values within the mth sliding window;
(4d) the half-variance in the northeast-southwest direction for all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000034
wherein the content of the first and second substances,
Figure GDA0002523167490000035
representing the half-square of the northeast-southwest direction of all pixel values within the mth sliding windowA difference;
(4e) the half-variance in the northwest-southeast direction of all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000036
wherein the content of the first and second substances,
Figure GDA0002523167490000037
represents the half-variance of the northwest-southeast direction of all pixel values within the mth sliding window;
(4f) forming the half variance characteristics of the sliding window by the half variances of all pixel values in each sliding window in the east-west direction, the south-north direction, the north-east-west-south direction and the north-west-south direction;
(4g) forming the half variance characteristics of all pixel values in each sliding window in the multi-scale synthetic aperture radar SAR image into the half variance characteristics of a high-order multi-scale conditional random field CRF;
(5) and (3) forming a feature vector of the high-order multi-scale conditional random field CRF:
(5a) forming local feature vectors of the high-order multi-scale conditional random field CRF by all histogram features, half-variance features and numbers 1 of the high-order multi-scale conditional random field CRF;
(5b) calculating the edge strength between each pixel point of the multi-scale synthetic aperture radar SAR image in each scale and each pixel point in the neighborhood system of the multi-scale synthetic aperture radar SAR image by using an exponential weighted average ratio operator;
(5c) forming a feature vector of the high-order multi-scale conditional random field CRF by using the local feature vector and the edge strength of the high-order multi-scale conditional random field CRF;
(6) calculating the local class conditional probability of the high-order multi-scale conditional random field CRF by using the following nominal logistic regression model NLRM:
Figure GDA0002523167490000041
wherein, PsIndicating the synthetic pore sizeLocal class conditional probability, w, of high-order multi-scale conditional random field CRF of s-th pixel point in radar SAR imagelThe method comprises the steps of representing characteristic parameters of the ith category in a multi-scale synthetic aperture radar SAR image, wherein an initial value is a unit vector, T represents transposition operation, d represents the serial number of the category in the multi-scale synthetic aperture radar SAR image, and L represents the total number of the category in the multi-scale synthetic aperture radar SAR image;
(7) initially segmenting a Synthetic Aperture Radar (SAR) image:
initially segmenting the SAR image by utilizing a method of maximizing the local class conditional probability;
(8) calculating the edge probability of each pixel:
calculating the edge probability of each pixel point high-order multi-scale conditional random field CRF in the current segmented synthetic aperture radar SAR image by using a mean field estimation method;
(9) calculating the combined posterior marginal probability of each pixel point:
calculating the joint posterior marginal probability of each pixel point high-order multi-scale conditional random field CRF in the current segmented synthetic aperture radar SAR image by using the marginal probability of each pixel point by adopting a bottom-up recursion method;
(10) calculating the posterior marginal probability of each pixel point:
calculating the posterior marginal probability of each pixel point of the currently segmented synthetic aperture radar SAR image in a high-order multi-scale conditional random field CRF by using a top-down recursion method and the combined posterior marginal probability of each pixel point;
(11) estimating model parameters of a high-order multi-scale conditional random field CRF:
(11a) forming model parameters of a high-order multi-scale conditional random field CRF by using generalized Gamma Gamma parameters, horizontal related parameters, vertical related parameters, inter-scale related parameters and characteristic parameters of the high-order multi-scale conditional random field CRF of the segmented multi-scale synthetic aperture radar SAR image;
(11b) calculating posterior marginal probability of each pixel point in the synthetic aperture radar SAR according to model parameters of a current high-order multi-scale conditional random field CRF, and inputting the posterior marginal probability of all the pixel points and an original synthetic aperture radar SAR image into a Gibbs sampler to obtain 2 sampling images;
(11c) calculating the generalized Gamma parameter of each sampling image by adopting a logarithmic cumulant MoLC method;
(11d) calculating the related parameters of each sampling image by adopting a related parameter iteration method;
(11e) calculating the characteristic parameters of each sampling image by adopting a characteristic parameter iteration method;
(11f) respectively averaging the model parameters of the high-order multi-scale conditional random field CRF obtained by the two sampling images to obtain the model parameters of the high-order multi-scale conditional random field CRF;
(11g) judging whether the current model parameters are converged, if so, executing the step (11 h); otherwise, adding 1 to the iteration number of the current parameter estimation, and executing the step (11 b):
the convergence refers to that the difference between the parameters obtained by the current iteration and the parameters obtained by the last iteration is less than 10-3；
(11h) Obtaining model parameters based on the high-order multi-scale conditional random field CRF;
(12) segmenting the SAR image:
calculating the category corresponding to the maximum value of the posterior marginal probability of each pixel point of the multi-scale synthetic aperture radar SAR image in each scale by using the model parameters of the current high-order multi-scale conditional random field CRF, and taking the category as the category of the pixel point to obtain the current segmentation result of the synthetic aperture radar SAR image;
(13) judging whether the result of the current SAR is stable, if so, executing the step (14); otherwise, adding 1 to the current iteration number and then executing the step (6):
the stability means that the segmentation result of the image obtained by the iteration is not obviously different from the segmentation result of the previous iteration;
(14) and (5) finishing the segmentation:
and finishing the segmentation of the SAR image to obtain a high-order multi-scale conditional random field CRF unsupervised SAR image segmentation result.
Compared with the prior art, the invention has the following advantages:
firstly, the invention adopts the Gibbs sampler to generate two sampling images, thereby overcoming the problem that the prior art can not train due to insufficient quantity of synthetic aperture radar SAR images when the environmental conditions for acquiring the synthetic aperture radar SAR images are severe. According to the method, the model parameters of the high-order multi-scale synthetic aperture radar SAR image are obtained through iteration by utilizing a relevant parameter method estimation method and a characteristic parameter iteration method, and the requirement on the quantity of training data is greatly reduced.
Secondly, the invention integrates the scattering statistics of the synthetic aperture radar SAR image into the posterior marginal probability of the high-order multi-scale conditional random field CRF, thereby overcoming the problem of low precision in the prior art, so that the invention utilizes the scattering statistics of the synthetic aperture radar SAR image to construct the unitary potential energy of the generalized conditional random field GCRF, and finally obtains the posterior marginal probability of the high-order multi-scale conditional random field CRF through one-step derivation, fully utilizes the self characteristics of the synthetic aperture radar SAR image, and improves the precision.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a simulation diagram of a synthetic aperture radar SAR image combined by three homogeneous areas by using the method of the present invention;
FIG. 3 is a simulation diagram of synthetic aperture radar SAR images of a river channel respectively by adopting the method of the invention and the generalized conditional random field CRF method;
FIG. 4 is a simulation result diagram of an airport synthetic aperture radar SAR image by using the method of the present invention and the generalized conditional random field CRF method.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The steps of the present invention will be further described with reference to fig. 1.
Step 1, inputting a synthetic aperture radar SAR image.
And 2, performing wavelet transformation on the input synthetic aperture radar SAR image to obtain a multi-scale synthetic aperture radar SAR image.
And 3, calculating the histogram characteristics of the high-order multi-scale conditional random field CRF.
And sliding the multi-scale synthetic aperture radar SAR image by taking one pixel point as an interval in the multi-scale synthetic aperture radar SAR image by using a window with the radius of 7 pixel points, and respectively calculating the histogram characteristics of all pixel values in each sliding window.
The specific steps for calculating the histogram features of all pixel values in each sliding window are as follows:
step 1, calculating the average value of all pixel values in each sliding window according to the following formula:
Figure GDA0002523167490000061
wherein, mumRepresenting the mean of all pixel values within the mth sliding window.
Step 2, calculating the variance of all pixel values in each sliding window according to the following formula:
Figure GDA0002523167490000071
wherein the content of the first and second substances,
Figure GDA0002523167490000072
representing the variance of all pixel values within the mth sliding window.
And 3, calculating skewness of all pixel values in each sliding window according to the following formula:
Figure GDA0002523167490000073
wherein phimRepresenting the skewness of all pixel values within the mth sliding window.
And 4, calculating the peak states of all pixel values in each sliding window according to the following formula:
Figure GDA0002523167490000074
wherein, KmRepresenting the peak state of all pixel values within the mth sliding window.
And 5, calculating the entropy of all pixel values in each sliding window according to the following formula:
Figure GDA0002523167490000075
wherein, TmRepresenting the entropy of all pixel values within the mth sliding window.
And 6, forming the histogram characteristics of each sliding window by the mean value, the variance, the skewness, the kurtosis and the entropy of all pixel values in each sliding window.
And (3) in the multi-scale synthetic aperture radar SAR image, the histogram features of all pixel values in each sliding window form the histogram features of a high-order multi-scale conditional random field CRF.
And 4, calculating the half-variance characteristics of the high-order multi-scale conditional random field CRF.
And sliding the window of which the radius is 7 pixel points by taking one pixel point as an interval in the multi-scale synthetic aperture radar SAR image, and performing sliding window operation on the multi-scale synthetic aperture radar SAR image.
The east-west half-variance of all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000076
wherein the content of the first and second substances,
Figure GDA0002523167490000077
denotes the east-west half-variance, n, of all pixel values within the m-th sliding windowmRepresenting the total number of all pixels in the mth sliding window, ∑ representing the summation operation, i representing the sequence number of the pixel row in the mth sliding window, j representing the sequence number of the pixel column in the mth sliding window, yi,jAnd the pixel value of the ith row and the jth column of pixel points in the mth sliding window is represented.
The north-south half-variance of all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000081
wherein the content of the first and second substances,
Figure GDA0002523167490000082
representing the half-variance in the north-south direction of all pixel values within the mth sliding window.
The half-variance in the northeast-southwest direction for all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000083
wherein the content of the first and second substances,
Figure GDA0002523167490000084
representing the half-variance in the northeast-southwest direction of all pixel values within the mth sliding window.
The half-variance in the northwest-southeast direction of all pixel values within each sliding window is calculated as follows:
Figure GDA0002523167490000085
wherein the content of the first and second substances,
Figure GDA0002523167490000086
representing the half-variance in the northwest-southeast direction of all pixel values within the mth sliding window.
And forming the half variance characteristics of the sliding window by the half variance of all pixel values in each sliding window in the east-west direction, the half variance of the south-north direction, the half variance of the north-east-south direction and the half variance of the north-west-south direction.
And in the multi-scale synthetic aperture radar SAR image, the half variance characteristics of all pixel values in each sliding window form the half variance characteristics of a high-order multi-scale conditional random field CRF.
And 5, forming a feature vector of the high-order multi-scale conditional random field CRF.
And (4) forming a local feature vector of the high-order multi-scale conditional random field CRF by all histogram features, half-variance features and the number 1 of the high-order multi-scale conditional random field CRF.
And calculating the edge strength between each pixel point of the multi-scale synthetic aperture radar SAR image in each scale and each pixel point in the adjacent domain system by using an exponential weighted average ratio operator.
The formula of the exponential weighted average ratio operator is as follows:
Figure GDA0002523167490000087
wherein the content of the first and second substances,
Figure GDA0002523167490000088
the method is characterized in that the method represents the edge strength between the s-th pixel point of the multi-scale synthetic aperture radar SAR image in the nth scale and the t-th pixel point of the multi-scale synthetic aperture radar SAR image in a neighborhood system, the value range of n is {0,1,2}, exp (·) represents exponential operation with a natural constant as a base,
Figure GDA0002523167490000089
representing the pixel value of the s-th pixel point of the multi-scale synthetic aperture radar SAR image in the nth scale,
Figure GDA0002523167490000091
and expressing the pixel value of the t-th pixel point of the multi-scale synthetic aperture radar SAR image in the nth scale.
And forming the feature vector of the high-order multi-scale conditional random field CRF by using the local feature vector and the edge strength of the high-order multi-scale conditional random field CRF.
Step 6, calculating the local class conditional probability of the high-order multi-scale conditional random field CRF by using the following nominal logistic regression model NLRM:
Figure GDA0002523167490000092
wherein, PsLocal class conditional probability, w, of high-order multi-scale conditional random field CRF (random field) representing s-th pixel point in SAR (synthetic aperture radar) imagelAnd (3) representing characteristic parameters of the ith category in the multi-scale synthetic aperture radar SAR image, wherein the initial value is a unit vector, the parameter values are updated by using a characteristic parameter iteration method in the step (11e), T represents transposition operation, d represents the serial number of the categories in the multi-scale synthetic aperture radar SAR image, and L represents the total number of the categories in the multi-scale synthetic aperture radar SAR image.
And 7, initially segmenting the SAR image.
And initially segmenting the SAR image by utilizing a method for maximizing the local class conditional probability.
And 8, calculating the edge probability of each pixel point.
And calculating the edge probability of each pixel point high-order multi-scale conditional random field CRF in the current segmented synthetic aperture radar SAR image by using a mean field estimation method.
The mean field estimation method comprises the following specific steps:
step 1, taking the local class conditional probability as an initial value of local mean field energy of the segmented synthetic aperture radar SAR image.
Step 2, calculating local radical energy between each pixel point in the segmented multi-scale synthetic aperture radar SAR image and each pixel point in the neighborhood system according to the following formula:
Figure GDA0002523167490000093
wherein Q is{s,t}Representing the local radical energy between the s-th pixel point in the segmented multi-scale synthetic aperture radar SAR image and the t-th pixel point in the neighborhood system, αHRepresenting the horizontal correlation parameter between the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image and the t-th pixel point in the horizontal neighborhood systemThe initial value of the parameter is 1, the parameter value is updated by using a relevant parameter iteration method in step (11d),
Figure GDA0002523167490000101
expressing a constant, and when the segmented multi-scale synthetic aperture radar SAR image is in the category of the s pixel point in the n scale
Figure GDA0002523167490000102
And the category of the t-th pixel point in the neighborhood system
Figure GDA0002523167490000103
When the phase of the mixture is the same as the phase of the mixture,
Figure GDA0002523167490000104
when the label of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n scale
Figure GDA0002523167490000105
Label of t-th pixel point in its neighborhood system
Figure GDA0002523167490000106
At a different time,
Figure GDA0002523167490000107
Figure GDA0002523167490000108
representing an arbitrary symbol, ∈ belonging to the symbol, NHHorizontal neighborhood system representing the s-th pixel in segmented multi-scale synthetic aperture radar SAR image, αVRepresenting a vertical correlation parameter between an s-th pixel point in the segmented multi-scale synthetic aperture radar SAR image and a t-th pixel point in a vertical neighborhood system, wherein the initial value of the parameter is 1, and updating the parameter value N in step (11d) by using a correlation parameter iteration methodVAnd (4) representing the vertical neighborhood system of the s-th pixel point in the segmented multi-scale synthetic aperture radar SAR image.
And 3, calculating the local mean field energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000109
wherein the content of the first and second substances,
Figure GDA00025231674900001010
representing the local mean value field energy, N, of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the N-th scalesThe method comprises the steps of representing a neighborhood system of an s-th pixel point in a segmented multi-scale synthetic aperture radar SAR image, k representing the number of classes in the neighborhood system, L representing the total number of the segmented multi-scale synthetic aperture radar SAR image classes, L representing the number of the segmented multi-scale synthetic aperture radar SAR image classes, and elRepresenting the class of the s-th pixel point in the segmented multi-scale synthetic aperture radar SAR image, ekRepresents the category of the t-th pixel point in the neighborhood system,
Figure GDA00025231674900001011
the local mean field energy of the t-th pixel point in the nth scale of the neighborhood system is represented,
Figure GDA00025231674900001012
and values are taken in a synthetic aperture radar SAR image category set according to category numbers.
And 4, executing the step 3 twice to obtain local mean field energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale, and taking the local mean field energy as an estimated value of the prior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale.
And 5, calculating the inter-scale potential energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000111
wherein the content of the first and second substances,
Figure GDA0002523167490000112
expressing the inter-scale potential energy of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale and the s pixel point of the n +1 scale, η expressing the inter-scale related parameters of the segmented multi-scale synthetic aperture radar SAR image, the initial value of the parameter is 1, updating the parameter value by using a related parameter iteration method in the step (11d),
Figure GDA0002523167490000113
and representing the category of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) -th scale.
And 6, calculating the conditional prior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000114
wherein the content of the first and second substances,
Figure GDA0002523167490000115
and expressing the conditional prior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale.
And 7, calculating unitary potential energy of the conditional random field CRF model of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000116
wherein the content of the first and second substances,
Figure GDA0002523167490000117
conditional random field C for expressing s pixel point of segmented multi-scale synthetic aperture radar SAR image in n scaleThe unitary potential of the RF model, log, represents the base 10 logarithmic operation.
And 8, calculating the scattering statistics of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000121
wherein the content of the first and second substances,
Figure GDA0002523167490000122
representing scattering statistics of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale, βlA shape parameter representing a generalized Gamma Gamma distribution model, the parameter value being calculated by the logarithmic cumulant MoLC method in step (11c), λlIndex shape parameters representing a Gamma distribution model, the parameter values of which are calculated by the logarithmic cumulant MoLC method in step (11c),
Figure GDA0002523167490000123
representing the intensity of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n scale, αlAnd (3) a scale parameter representing a generalized Gamma distribution model, wherein the parameter value is calculated by a logarithm cumulant MoLC method in the step (11c), and (DEG) represents a Gamma function.
And 9, calculating unitary potential energy of the generalized conditional random field GCRF model of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000124
wherein the content of the first and second substances,
Figure GDA0002523167490000125
and representing unary potential energy of the generalized conditional random field GCRF model of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale.
And step 10, sliding a window with the radius of 7 pixel points at intervals in the segmented synthetic aperture radar SAR image, and performing one-time window sliding operation on the segmented multi-scale synthetic aperture radar SAR image.
And 11, calculating the probability of each category in each sliding window according to the following formula:
Figure GDA0002523167490000126
wherein the content of the first and second substances,
Figure GDA0002523167490000127
is shown as
Figure GDA0002523167490000128
The probability of the ith class within the sliding window,
Figure GDA0002523167490000129
is shown as
Figure GDA00025231674900001210
The number of the ith class in a sliding window,
Figure GDA00025231674900001211
is shown as
Figure GDA00025231674900001212
Single radical C in a sliding window1A single group represents a group consisting of a single pixel.
And 12, calculating the probability of each category adjacent to other categories in each sliding window according to the following formula:
Figure GDA0002523167490000131
wherein the content of the first and second substances,
Figure GDA0002523167490000132
is shown as
Figure GDA0002523167490000133
Probability that the ith category is adjacent to the first category in each sliding window, pi represents the product operation, tau represents the type of a binary group, the binary group represents a group formed by two adjacent pixel points,
Figure GDA0002523167490000134
is shown as
Figure GDA0002523167490000135
A left binary group C formed by the first category and the second category in the sliding window2(1) The left binary group represents the binary group left adjacent to the l-th class,
Figure GDA0002523167490000136
is shown as
Figure GDA0002523167490000137
Right binary group C formed by the first category and the second category in the sliding window2(2) Right binary radical denotes the binary radical which is right-adjacent to the l-th class,
Figure GDA0002523167490000138
is shown as
Figure GDA0002523167490000139
The lower binary group C formed by the first category and the second category in the sliding window2(3) The lower binary group represents the binary group next to the first class,
Figure GDA00025231674900001310
is shown as
Figure GDA00025231674900001311
The upper binary group C formed by the first class and the second class in the sliding window2(4) Right binary radical denotes the binary radical which is right-adjacent to the l-th class,
Figure GDA00025231674900001312
is shown as
Figure GDA00025231674900001313
The total number of left binary clusters of the ith class within the individual sliding window,
Figure GDA00025231674900001314
is shown as
Figure GDA00025231674900001315
The total number of the first category of right binary radicals in each sliding window,
Figure GDA00025231674900001316
is shown as
Figure GDA00025231674900001317
The total number of binary groups under the ith class in each sliding window,
Figure GDA00025231674900001318
is shown as
Figure GDA00025231674900001319
Total number of binary groups on the l-th class within each sliding window.
And step 13, calculating the high-order potential energy of each pixel point in each sliding window according to the following formula:
Figure GDA00025231674900001320
wherein the content of the first and second substances,
Figure GDA00025231674900001321
is shown as
Figure GDA00025231674900001322
The high-order potential energy of the s-th pixel point in each sliding window.
And 14, calculating the mean field energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA00025231674900001323
wherein the content of the first and second substances,
Figure GDA00025231674900001324
and representing the mean field energy of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale.
And step 15, calculating the edge probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000141
wherein the content of the first and second substances,
Figure GDA0002523167490000142
and representing the marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale.
And 9, calculating the joint posterior marginal probability of each pixel point.
And calculating the joint posterior marginal probability of the high-order multi-scale conditional random field CRF of each pixel point in the current segmented synthetic aperture radar SAR image by adopting a bottom-to-top recursion method and utilizing the marginal probability of each pixel point.
The bottom-up recursion method comprises the following specific steps:
step 1, taking the edge probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in the 0 th scale as the local posterior edge probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in the 0 th scale.
Step 2, calculating the local posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000143
wherein the content of the first and second substances,
Figure GDA0002523167490000144
the local posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale is represented,
Figure GDA0002523167490000145
representing the descendant of the s-th pixel in the multi-scale synthetic aperture radar SAR image, representing the s-th pixel point of the multi-scale synthetic aperture radar SAR image in the scale lower than the n-th scale,
Figure GDA0002523167490000146
representing the category of the c generation in the filial generation of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image,
Figure GDA0002523167490000147
representing the posterior marginal probability of the c generation in the s pixel point descendant of the segmented multi-scale synthetic aperture radar SAR image,
Figure GDA0002523167490000148
representing the conditional prior marginal probability of the c generation in the s pixel point descendant of the segmented multi-scale synthetic aperture radar SAR image,
Figure GDA0002523167490000149
and expressing the prior edge probability of the c generation in the s pixel point descendant of the segmented multi-scale synthetic aperture radar SAR image.
And 3, executing the step 2 twice to obtain the local posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale.
And 4, calculating the joint posterior marginal probability of each pixel point and the parent pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000151
wherein the content of the first and second substances,
Figure GDA0002523167490000152
expressing the combined posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale and the parent pixel point thereof, wherein the parent represents the s-th pixel point of the multi-scale synthetic aperture radar image SAR in the nth scale,
Figure GDA0002523167490000153
represents a parent of the s-th pixel in the multi-scale synthetic aperture radar SAR image,
Figure GDA0002523167490000154
representing the nth of the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) th scale
Figure GDA0002523167490000155
The prior edge probability of an individual pixel point,
Figure GDA0002523167490000156
representing the nth of the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) th scale
Figure GDA0002523167490000157
A category of individual pixels.
And step 10, calculating the posterior marginal probability of each pixel point.
And calculating the posterior marginal probability of the high-order multi-scale conditional random field CRF of each pixel point of the currently segmented synthetic aperture radar SAR image by adopting a top-down recursion method and utilizing the combined posterior marginal probability of each pixel point.
The top-down recursion method comprises the following specific steps:
step 1, setting an initial value of posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in the 2 nd scale as the local posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in the 2 nd scale.
Step 2, calculating the posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure GDA0002523167490000158
wherein the content of the first and second substances,
Figure GDA0002523167490000159
representing the posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale,
Figure GDA00025231674900001510
representing the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) th scale
Figure GDA00025231674900001511
Posterior marginal probability of each pixel point.
And 3, executing the step 2 twice to obtain the posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in all scales.
Step 11, estimating model parameters of the high-order multi-scale conditional random field CRF:
(11.1) forming model parameters of the high-order multi-scale conditional random field CRF by using generalized Gamma Gamma parameters, horizontal related parameters, vertical related parameters, inter-scale related parameters and characteristic parameters of the high-order multi-scale conditional random field CRF of the segmented multi-scale synthetic aperture radar SAR image.
(11.2) calculating the posterior marginal probability of each pixel point in the synthetic aperture radar SAR according to the model parameters of the current high-order multi-scale conditional random field CRF, and inputting the posterior marginal probabilities of all the pixel points and the original synthetic aperture radar SAR image into a Gibbs sampler to obtain 2 sampling images.
And (11.3) calculating the generalized Gamma parameters of each sampling image by adopting a logarithmic cumulant MoLC method.
The log cumulant MoLC method comprises the following specific steps:
and 1, performing Mellin transform on a probability density function of generalized Gamma distribution to obtain a first second characteristic function of the generalized Gamma distribution.
Step 2, calculating a second class characteristic function of the generalized Gamma distribution according to the following formula:
ξ(ω)＝lnγ(ω)
where ξ (ω) is the second class of characteristic function of the generalized Gamma distribution, ω is the argument of the probability density function of the generalized Gamma distribution, and γ (ω) is the first second class of characteristic function of the generalized Gamma distribution.
And 3, calculating first-order logarithmic cumulant, second-order logarithmic cumulant and third-order logarithmic cumulant of a second class characteristic function of generalized Gamma distribution according to the following formula:
Figure GDA0002523167490000161
and 4, establishing a first moment model of parameter estimation according to the following formula:
Figure GDA0002523167490000162
wherein ψ (0, λ)l) The parameter k 'representing the multi-gamma poly gamma function is 0, and x' is lambdalCase of (a), ns'Representing the number of pixel points of the segmented multi-scale synthetic aperture radar SAR,
Figure GDA0002523167490000163
and (3) representing the intensity of each sampled image at the S 'th pixel point, and S' representing the set of all pixel points in each sampled image.
And 5, establishing a second moment model for parameter estimation according to the following formula:
Figure GDA0002523167490000171
wherein ψ (1, λ)l) The parameter k 'representing the multi-gamma poly gamma function is 1, and x' is lambdalThe situation of (c)1The first-order log cumulant of the second class of characteristic functions representing the generalized Gamma distribution.
And 6, establishing a third moment model for parameter estimation according to the following formula:
Figure GDA0002523167490000172
wherein ψ (2, λ)l) The parameter k 'representing the multi-gamma poly gamma function is 2, and the parameter x' is lambdalThe situation of time.
7, solving α parameters of generalized Gamma distribution according to the first moment, the second moment and the third moment model formulas of parameter estimationl，βlAnd λl。
And (11.4) calculating the correlation parameter of each sampling image by adopting a correlation parameter iteration method.
The specific steps of the related parameter iteration method are as follows:
step 1, calculating the potential energy of each sampling image according to the following formula:
Figure GDA0002523167490000173
wherein, WqThe potential energy of the qth sampling image is shown, the value range of q is {1,2},
Figure GDA0002523167490000174
representing the univariate potential energy of the generalized conditional random field CRF of the s' th pixel point of the q-th sampling image in the nth scale,
Figure GDA0002523167490000175
represents the qth sampleThe image is at
Figure GDA0002523167490000176
The high-order potential energy of the s' -th pixel point in each sliding window,
Figure GDA0002523167490000177
the mean field energy of the s ' -th pixel point in the nth scale of the q-th sampling image is represented, and t ' represents the neighborhood system N of the s ' -th pixel point in the q-th sampling images′One pixel in (b).
And 2, calculating the posterior marginal probability of each pixel point in the synthetic aperture radar SAR by using the current horizontal related parameters, vertical related parameters and inter-scale related parameters, and inputting the posterior marginal probability of all the pixel points and the original synthetic aperture radar SAR image into a Gibbs sampler to obtain the sampling image of the iteration.
And 3, calculating the horizontal related parameters of each sampling image in the iteration according to the following formula:
Figure GDA0002523167490000181
wherein the content of the first and second substances,
Figure GDA0002523167490000182
representing the horizontal correlation parameter of the q-th sampled image in the current iteration,
Figure GDA0002523167490000183
representing the horizontal related parameters of the q-th sampling image in the last iteration of the current iteration, N representing the total number of pixel points of each sampling image, a representing the number of times of the current iteration,
Figure GDA0002523167490000184
which means that the operation of finding the gradient is performed,
Figure GDA0002523167490000185
representing the q-th sampled image,
Figure GDA0002523167490000186
representing the sampled image of this iteration.
And 4, calculating the vertical correlation parameter of each sampling image in the iteration according to the following formula:
Figure GDA0002523167490000187
wherein the content of the first and second substances,
Figure GDA0002523167490000188
the vertical correlation parameter of the q-th sampling image in the current iteration is shown,
Figure GDA0002523167490000189
and the vertical correlation parameters of the q-th sampling image in the last iteration of the current iteration are shown.
And 5, calculating the inter-scale related parameters of each sampling image in the iteration according to the following formula:
Figure GDA00025231674900001810
wherein, ηqRepresents the inter-scale correlation parameter of the q-th sampling image in the current iteration, η'qAnd representing the inter-scale related parameters of the q-th sampling image in the last iteration of the current iteration.
Step 6, judging whether the current horizontal related parameters, the vertical related parameters and the inter-scale related parameters are converged, if so, executing the step 7; otherwise, adding 1 to the current iteration number and then executing the step 2:
the convergence refers to that the difference between the parameters obtained by the current iteration and the parameters obtained by the last iteration is less than 10-3。
And 7, obtaining a horizontal related parameter, a vertical related parameter and an inter-scale related parameter of each sampling image.
And (11.5) calculating the characteristic parameters of each sampling image by adopting a characteristic parameter iteration method.
The characteristic parameter iteration method comprises the following specific steps:
step 1, calculating the posterior marginal probability of each pixel point in the synthetic aperture radar SAR and the original synthetic aperture radar SAR image according to the current characteristic parameters, and inputting the posterior marginal probability and the original synthetic aperture radar SAR image into a Gibbs sampler to obtain a sampling image of the iteration.
Step 2, calculating the deviation value of the characteristic parameter of each category of each sampling image in the iteration according to the following formula:
Figure GDA0002523167490000191
wherein the content of the first and second substances,
Figure GDA0002523167490000192
the deviation value of the characteristic parameter of the ith category of the qth sampling image in the current iteration is shown,
Figure GDA0002523167490000193
and indicating the deviation value of the characteristic parameter of the ith category of the qth sampling image in the last iteration of the current iteration.
And 3, calculating the characteristic parameters of each category of each sampling image in the iteration according to the following formula:
Figure GDA0002523167490000194
wherein the content of the first and second substances,
Figure GDA0002523167490000195
and the characteristic parameters of the ith category of the qth sampling image in the iteration are shown.
Step 4, judging whether the characteristic parameters of each category of each current sampling image are converged, if so, executing step 5; otherwise, the step 1 is executed after the current iteration number is added with 1: the convergence refers to that the difference between the parameters obtained by the current iteration and the parameters obtained by the last iteration is less than 10-3。
And 5, obtaining the characteristic parameters of each sampling image.
And (11.6) respectively averaging the model parameters of the high-order multi-scale conditional random field CRF obtained by the two sampling images to obtain the model parameters of the high-order multi-scale conditional random field CRF.
(11.7) judging whether the current model parameters are converged, if so, executing the step (11.8); otherwise, after adding 1 to the current iteration number, returning to the step (11.2):
the convergence refers to that the difference between the parameters obtained by the current iteration and the parameters obtained by the last iteration is less than 10-3。
And (11.8) obtaining model parameters of the high-order multi-scale conditional random field CRF.
And step 12, segmenting the SAR image.
And calculating the category corresponding to the maximum value of the posterior marginal probability of each pixel point of the multi-scale synthetic aperture radar SAR image in each scale by using the model parameters of the current high-order multi-scale conditional random field CRF, and taking the category as the category of the pixel point to obtain the current segmentation result of the synthetic aperture radar SAR image.
Step 13, judging whether the result of the current SAR is stable, if so, executing step 14; otherwise, after adding 1 to the current iteration number, executing step 6:
the stability means that the segmentation result of the image obtained by the current iteration has no obvious difference from the segmentation result of the previous iteration.
And step 14, finishing the segmentation.
And finishing the segmentation of the SAR image to obtain a high-order multi-scale conditional random field CRF unsupervised SAR image segmentation result.
The effect of the present invention will be further described with reference to simulation experiments.
1. Simulation experiment conditions are as follows:
the hardware test platform of the simulation experiment of the invention is as follows: the processor is a CPU intel Core i7-7700, the main frequency is 4.2GHz, and the internal memory is 16 GB; the software platform is as follows: windows 10 family version, 64-bit operating system, MATLAB R2016 a.
2. Simulation content and simulation result analysis:
the simulation experiment 1 is to simulate the synthetic aperture radar SAR image combined by three homogeneous areas by adopting the method, and is shown in figure 2. The simulation experiment 2 is to respectively simulate the synthetic aperture radar SAR image of the river channel by adopting the method of the invention and the generalized conditional random field CRF method in the prior art, as shown in FIG. 3. The simulation experiment 3 is to simulate the synthetic aperture radar SAR image of the airport by adopting the method of the invention and the generalized conditional random field CRF method in the prior art, as shown in FIG. 4.
Simulation experiment 1:
fig. 2(a) shows the original image input in the simulation experiment 1 of the present invention. The figure is a simulated image generated from the pafvullan area near munich, germany using ESAR L-band HV data from the aerospace center, germany. And manually selecting three types of uniform areas from the simulated image, and then putting the areas into a preset ground truth to obtain the synthetic aperture radar SAR image formed by combining the three types of uniform areas. Fig. 2(b) is a reference diagram of the original image after segmentation. FIG. 2(c) is a graph of the simulation results of the segmentation of FIG. 2(a) using the method of the present invention. In the simulation experiment, in a related parameter iteration method, the iteration times of convergence of horizontal related parameters, vertical related parameters and inter-scale related parameters of a sampled image are 4 times. In the feature parameter iteration, the number of iterations for which the feature parameter converges is 2. In the iteration of the model parameters of the whole high-order multi-scale synthetic aperture radar SAR image, the iteration times of model parameter convergence are 6 times. And the iteration times of the whole SAR image segmentation are 10 times.
As can be seen from fig. 2(a), the original image has strong noise, and comparing the simulation result of the method of the present invention, fig. 2(c), with the reference image of the original image after segmentation, it can be seen that the noise interference has less influence on the method of the present invention, and comparing the three homogeneous regions segmented in the simulation result of the method of the present invention, fig. 2(c), with the reference image 2(b), it can be seen that the simulation result of the method of the present invention has strong region consistency, less erroneous segmentation, and clear boundary positioning.
Simulation experiment 2:
fig. 3(a) is an original image input by simulation experiment 2 of the present invention, which is a synthetic aperture radar SAR image of a river channel generated from L-band data of a river channel acquired by a jet propulsion laboratory in the united states. FIG. 3(b) is a graph of simulation results of a prior art generalized conditional random field CRF method for segmenting FIG. 3 (a). FIG. 3(c) is a graph of the simulation results of the segmentation of FIG. 3(a) using the method of the present invention. In the simulation experiment, in a related parameter iteration method, the iteration times of convergence of horizontal related parameters, vertical related parameters and inter-scale related parameters of a sampled image are 4 times. In the feature parameter iteration, the number of iterations for which the feature parameter converges is 2. In the iteration of the model parameters of the whole high-order multi-scale synthetic aperture radar SAR image, the iteration times of model parameter convergence are 6 times. And the iteration times of the whole SAR image segmentation are 10 times.
As can be seen from the original image 3(a), the image mainly comprises three areas, namely farmland, land and river channel, and the simulation result of the method of the invention, namely a graph 3(c), is compared with the simulation result of the generalized conditional random field CRF method in the prior art, namely a graph 3(b), so that the simulation result of the method of the invention is obviously superior to the boundary positioning of the river channel and the farmland to the conventional generalized conditional random field CRF method, and more detailed information is reserved.
Simulation experiment 3:
fig. 4(a) is an original image input by the simulation experiment 3 of the present invention, which is an airport synthetic aperture radar SAR image generated from domestic airborne radar data. FIG. 4(b) is a graph of simulation results of the segmentation of FIG. 4(a) using a prior art generalized conditional random field CRF method. FIG. 4(c) is a graph showing the results of a simulation in which the method of the present invention is used to segment FIG. 4 (a). In the simulation experiment, in a related parameter iteration method, the iteration times of convergence of horizontal related parameters, vertical related parameters and inter-scale related parameters of a sampled image are 4 times. In the feature parameter iteration, the number of iterations for which the feature parameter converges is 2. In the iteration of the model parameters of the whole high-order multi-scale synthetic aperture radar SAR image, the iteration times of model parameter convergence are 6 times. And the iteration times of the whole SAR image segmentation are 10 times.
It can be seen from the original image 4(a) that the image mainly contains airport runways and urban areas, and comparing the simulation result of the method of the present invention, fig. 4(c), with the simulation result of the generalized conditional random field CRF method of the prior art, it can be seen that the airport runway boundary in the simulation result of the method of the present invention is accurately located, the number of false segmentation is small, and the urban areas contain more detailed information.

Claims (9)

1. An unsupervised synthetic aperture radar SAR image segmentation method based on a high-order multi-scale conditional random field CRF is characterized in that a nominal logistic regression model NLRM is used for calculating the local class conditional probability of the high-order multi-scale conditional random field; calculating the related parameters of the high-order multi-scale conditional random field CRF by using a related parameter iteration method; calculating the characteristic parameters of the high-order multi-scale conditional random field CRF by using a characteristic parameter iteration method, wherein the method comprises the following steps:
(1) inputting a Synthetic Aperture Radar (SAR) image;
(2) performing wavelet transformation on the input synthetic aperture radar SAR image to obtain a multi-scale synthetic aperture radar SAR image;
(3) calculating the histogram feature of the high-order multi-scale conditional random field CRF:
(3a) sliding a window with the radius of 7 pixel points at intervals in the multi-scale synthetic aperture radar SAR image, performing sliding window operation on the multi-scale synthetic aperture radar SAR image, and respectively calculating the histogram characteristics of all pixel values in each sliding window;
(3b) the histogram features of all pixel values in each sliding window in the multi-scale synthetic aperture radar SAR image form the histogram features of a high-order multi-scale conditional random field CRF;
(4) calculating the half-variance characteristics of the high-order multi-scale conditional random field CRF:
(4a) sliding a window with the radius of 7 pixel points by taking one pixel point as an interval in the multi-scale synthetic aperture radar SAR image, and performing sliding window operation on the multi-scale synthetic aperture radar SAR image;
(4b) the east-west half-variance of all pixel values within each sliding window is calculated as follows:
Figure FDA0002523167480000011
wherein the content of the first and second substances,
Figure FDA0002523167480000012
denotes the east-west half-variance, n, of all pixel values within the m-th sliding windowmRepresenting the total number of all pixels in the mth sliding window, ∑ representing the summation operation, i representing the sequence number of the pixel row in the mth sliding window, j representing the sequence number of the pixel column in the mth sliding window, yi,jExpressing the pixel value of the ith row and jth column pixel point in the mth sliding window;
(4c) the north-south half-variance of all pixel values within each sliding window is calculated as follows:
Figure FDA0002523167480000013
wherein the content of the first and second substances,
Figure FDA0002523167480000021
representing the half-variance of the north-south direction of all pixel values within the mth sliding window;
(4d) the half-variance in the northeast-southwest direction for all pixel values within each sliding window is calculated as follows:
Figure FDA0002523167480000022
wherein the content of the first and second substances,
Figure FDA0002523167480000023
represents the half-variance of the northeast-southwest direction of all pixel values within the mth sliding window;
(4e) the half-variance in the northwest-southeast direction of all pixel values within each sliding window is calculated as follows:
Figure FDA0002523167480000024
wherein the content of the first and second substances,
Figure FDA0002523167480000025
represents the half-variance of the northwest-southeast direction of all pixel values within the mth sliding window;
(4f) forming the half variance characteristics of the sliding window by the half variances of all pixel values in each sliding window in the east-west direction, the south-north direction, the north-east-west-south direction and the north-west-south direction;
(4g) forming the half variance characteristics of all pixel values in each sliding window in the multi-scale synthetic aperture radar SAR image into the half variance characteristics of a high-order multi-scale conditional random field CRF;
(5) and (3) forming a feature vector of the high-order multi-scale conditional random field CRF:
(5a) forming local feature vectors of the high-order multi-scale conditional random field CRF by all histogram features, half-variance features and numbers 1 of the high-order multi-scale conditional random field CRF;
(5b) calculating the edge strength between each pixel point of the multi-scale synthetic aperture radar SAR image in each scale and each pixel point in the neighborhood system of the multi-scale synthetic aperture radar SAR image by using an exponential weighted average ratio operator;
(5c) forming a feature vector of the high-order multi-scale conditional random field CRF by using the local feature vector and the edge strength of the high-order multi-scale conditional random field CRF;
(6) calculating the local class conditional probability of the high-order multi-scale conditional random field CRF by using the following nominal logistic regression model NLRM:
Figure FDA0002523167480000026
wherein, PsLocal class conditional probability, w, of high-order multi-scale conditional random field CRF (random field) representing s-th pixel point in SAR (synthetic aperture radar) imagelExpress a plurality ofThe initial value of the characteristic parameter of the ith category in the SAR image is a unit vector, T represents transposition operation, d represents the serial number of the category in the SAR image, and L represents the total number of the categories in the SAR image;
(7) initially segmenting a Synthetic Aperture Radar (SAR) image:
initially segmenting the SAR image by utilizing a method of maximizing the local class conditional probability;
(8) calculating the edge probability of each pixel:
calculating the edge probability of each pixel point high-order multi-scale conditional random field CRF in the current segmented synthetic aperture radar SAR image by using a mean field estimation method;
(9) calculating the combined posterior marginal probability of each pixel point:
calculating the joint posterior marginal probability of each pixel point high-order multi-scale conditional random field CRF in the current segmented synthetic aperture radar SAR image by using the marginal probability of each pixel point by adopting a bottom-up recursion method;
(10) calculating the posterior marginal probability of each pixel point:
calculating the posterior marginal probability of each pixel point of the currently segmented synthetic aperture radar SAR image in a high-order multi-scale conditional random field CRF by using a top-down recursion method and the combined posterior marginal probability of each pixel point;
(11) estimating model parameters of a high-order multi-scale conditional random field CRF:
(11a) forming model parameters of a high-order multi-scale conditional random field CRF by using generalized Gamma Gamma parameters, horizontal related parameters, vertical related parameters, inter-scale related parameters and characteristic parameters of the high-order multi-scale conditional random field CRF of the segmented multi-scale synthetic aperture radar SAR image;
(11b) calculating posterior marginal probability of each pixel point in the synthetic aperture radar SAR according to model parameters of a current high-order multi-scale conditional random field CRF, and inputting the posterior marginal probability of all the pixel points and an original synthetic aperture radar SAR image into a Gibbs sampler to obtain 2 sampling images;
(11c) calculating a generalized Gamma parameter of each sampling image by adopting a logarithmic accumulation quantity MoLC method;
(11d) calculating the related parameters of each sampling image by adopting a related parameter iteration method;
(11e) calculating the characteristic parameters of each sampling image by adopting a characteristic parameter iteration method;
(11f) respectively averaging the model parameters of the high-order multi-scale conditional random field CRF obtained by the two sampling images to obtain the model parameters of the high-order multi-scale conditional random field CRF;
(11g) judging whether the current model parameters are converged, if so, executing the step (11 h); otherwise, adding 1 to the iteration number of the current parameter estimation, and executing the step (11 b):
the convergence refers to that the difference between the parameters obtained by the current iteration and the parameters obtained by the last iteration is less than 10-3；
(11h) Obtaining model parameters of a high-order multi-scale conditional random field CRF;
(12) segmenting the SAR image:
calculating the category corresponding to the maximum value of the posterior marginal probability of each pixel point of the multi-scale synthetic aperture radar SAR image in each scale by using the model parameters of the current high-order multi-scale conditional random field CRF, and taking the category as the category of the pixel point to obtain the current segmentation result of the synthetic aperture radar SAR image;
(13) judging whether the result of the current SAR is stable, if so, executing the step (14); otherwise, adding 1 to the current iteration number and then executing the step (6):
the stability means that the segmentation result of the image obtained by the iteration is not obviously different from the segmentation result of the previous iteration;
(14) and (5) finishing the segmentation:
and finishing the segmentation of the SAR image to obtain a high-order multi-scale conditional random field CRF unsupervised SAR image segmentation result.
2. The method for segmenting the SAR image based on the CRF unsupervised SAR of claim 1, wherein the specific steps for calculating the histogram features of all the pixel values in each sliding window in step (3a) are as follows:
first, the mean of all pixel values within each sliding window is calculated according to the following formula:
Figure FDA0002523167480000041
wherein, mumRepresents the mean of all pixel values within the mth sliding window;
secondly, calculating the variance of all pixel values in each sliding window according to the following formula:
Figure FDA0002523167480000042
wherein the content of the first and second substances,
Figure FDA0002523167480000043
represents the variance of all pixel values within the mth sliding window;
thirdly, calculating the skewness of all pixel values in each sliding window according to the following formula:
Figure FDA0002523167480000044
wherein phimRepresenting skewness of all pixel values within the mth sliding window;
fourthly, calculating the peak state of all pixel values in each sliding window according to the following formula:
Figure FDA0002523167480000051
wherein, KmRepresenting the kurtosis of all pixel values within the mth sliding window;
fifthly, calculating the entropy of all pixel values in each sliding window according to the following formula:
Figure FDA0002523167480000052
wherein, TmRepresenting the entropy of all pixel values within the mth sliding window;
and sixthly, forming the histogram characteristics of the sliding window by the mean value, the variance, the skewness, the kurtosis and the entropy of all the pixel values in each sliding window.
3. The method for unsupervised segmentation of Synthetic Aperture Radar (SAR) images based on high-order multi-scale Conditional Random Field (CRF) according to claim 1, wherein the formula of the exponentially weighted average ratio operator in step (5b) is as follows:
Figure FDA0002523167480000053
wherein the content of the first and second substances,
Figure FDA0002523167480000054
the method is characterized in that the method represents the edge strength between the s-th pixel point of the multi-scale synthetic aperture radar SAR image in the nth scale and the t-th pixel point of the multi-scale synthetic aperture radar SAR image in a neighborhood system, the value range of n is {0,1,2}, exp (·) represents exponential operation with a natural constant as a base,
Figure FDA0002523167480000055
representing the pixel value of the s-th pixel point of the multi-scale synthetic aperture radar SAR image in the nth scale,
Figure FDA0002523167480000056
and expressing the pixel value of the t-th pixel point of the multi-scale synthetic aperture radar SAR image in the nth scale.
4. The method for unsupervised segmentation of Synthetic Aperture Radar (SAR) images based on high-order multi-scale Conditional Random Field (CRF) according to claim 1, wherein the mean field estimation method in step (8) comprises the following specific steps:
step one, taking the local class conditional probability as an initial value of local mean field energy of a segmented synthetic aperture radar SAR image;
secondly, calculating local radical energy between each pixel point in the segmented multi-scale synthetic aperture radar SAR image and each pixel point in the neighborhood system according to the following formula:
Figure FDA0002523167480000061
wherein Q is{s,t}Representing the local radical energy between the s-th pixel point in the segmented multi-scale synthetic aperture radar SAR image and the t-th pixel point in the neighborhood system, αHThe horizontal correlation parameter between the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image and the t-th pixel point in the horizontal neighborhood system is represented, the initial value of the parameter is 1,
Figure FDA0002523167480000062
expressing a constant, and when the segmented multi-scale synthetic aperture radar SAR image is in the category of the s pixel point in the n scale
Figure FDA0002523167480000063
And the category of the t-th pixel point in the neighborhood system
Figure FDA0002523167480000064
When the phase of the mixture is the same as the phase of the mixture,
Figure FDA0002523167480000065
when the label of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n scale
Figure FDA0002523167480000066
Label of t-th pixel point in its neighborhood system
Figure FDA0002523167480000067
At a different time,
Figure FDA0002523167480000068
Figure FDA0002523167480000069
representing an arbitrary symbol, ∈ belonging to the symbol, NHHorizontal neighborhood system representing the s-th pixel in segmented multi-scale synthetic aperture radar SAR image, αVRepresenting a vertical correlation parameter between an s-th pixel point in a segmented multi-scale synthetic aperture radar SAR image and a t-th pixel point in a vertical neighborhood system, wherein the initial value of the parameter is 1, NVA vertical neighborhood system for expressing the s-th pixel point in the segmented multi-scale synthetic aperture radar SAR image;
thirdly, calculating the local mean field energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA00025231674800000610
wherein the content of the first and second substances,
Figure FDA00025231674800000611
representing the local mean value field energy, N, of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the N-th scalesThe method comprises the steps of representing a neighborhood system of an s-th pixel point in a segmented multi-scale synthetic aperture radar SAR image, k representing the number of classes in the neighborhood system, L representing the total number of the segmented multi-scale synthetic aperture radar SAR image classes, L representing the number of the segmented multi-scale synthetic aperture radar SAR image classes, and elRepresenting the class of the s-th pixel point in the segmented multi-scale synthetic aperture radar SAR image, ekRepresents the category of the t-th pixel point in the neighborhood system,
Figure FDA0002523167480000071
the local mean field energy of the t-th pixel point in the nth scale of the neighborhood system is represented,
Figure FDA0002523167480000072
values are taken in a synthetic aperture radar SAR image category set according to category numbers;
fourthly, executing the third step twice to obtain local mean value field energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale, and taking the local mean value field energy as an estimated value of prior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale;
fifthly, calculating the inter-scale potential energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000073
wherein the content of the first and second substances,
Figure FDA0002523167480000074
representing the inter-scale potential energy of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale and the s-th pixel point of the n +1 th scale, η representing the inter-scale related parameters of the segmented multi-scale synthetic aperture radar SAR image, the initial value of the parameters is 1,
Figure FDA0002523167480000075
representing the category of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) scale;
sixthly, calculating the conditional prior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000076
wherein the content of the first and second substances,
Figure FDA0002523167480000077
expressing the conditional prior marginal probability of an s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in an n-th scale;
and seventhly, calculating unitary potential energy of the conditional random field CRF model of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000078
wherein f iss nExpressing unary potential energy of a conditional random field CRF model of an s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in an n-th scale, and log expressing logarithmic operation with 10 as a base;
and eighthly, calculating the scattering statistics of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000081
wherein the content of the first and second substances,
Figure FDA0002523167480000082
representing scattering statistics of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale, βlShape parameter, λ, representing a generalized Gamma Gamma distribution modellIndex shape parameters representing a Gamma distribution model,
Figure FDA0002523167480000083
representing the intensity of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n scale, αlScale parameters representing a generalized Gamma distribution model, (. cndot.) representing a Gamma function;
and ninthly, calculating unitary potential energy of the generalized conditional random field GCRF model of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000084
wherein the content of the first and second substances,
Figure FDA0002523167480000085
representing unary potential energy of a generalized conditional random field GCRF model of an s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale;
tenthly, sliding a window with the radius of 7 pixel points at intervals in the segmented synthetic aperture radar SAR image, and performing one-time window sliding operation on the segmented multi-scale synthetic aperture radar SAR image;
the tenth step, calculate the probability of each class in each sliding window according to the following equation:
Figure FDA0002523167480000086
wherein the content of the first and second substances,
Figure FDA0002523167480000087
is shown as
Figure FDA00025231674800000817
The probability of the ith class within the sliding window,
Figure FDA0002523167480000088
is shown as
Figure FDA0002523167480000089
The number of the ith class in a sliding window,
Figure FDA00025231674800000810
is shown as
Figure FDA00025231674800000811
Single radical C in a sliding window1The total number of (c);
the twelfth step, according to the following formula, calculates the probability of each category adjacent to other categories in each sliding window:
Figure FDA00025231674800000812
wherein the content of the first and second substances,
Figure FDA00025231674800000813
is shown as
Figure FDA00025231674800000814
Probability that the ith class is adjacent to the first class in the sliding window, pi represents the product operation, tau represents the type of the binary group,
Figure FDA00025231674800000815
is shown as
Figure FDA00025231674800000816
A left binary group C formed by the first category and the second category in the sliding window2(1) The total number of (a) and (b),
Figure FDA0002523167480000091
is shown as
Figure FDA0002523167480000092
Right binary group C formed by the first category and the second category in the sliding window2(2) The total number of (a) and (b),
Figure FDA0002523167480000093
is shown as
Figure FDA0002523167480000094
The lower binary group C formed by the first category and the second category in the sliding window2(3) The total number of (a) and (b),
Figure FDA0002523167480000095
is shown as
Figure FDA0002523167480000096
The upper binary group C formed by the first class and the second class in the sliding window2(4) The total number of (a) and (b),
Figure FDA0002523167480000097
is shown as
Figure FDA0002523167480000098
The total number of left binary clusters of the ith class within the individual sliding window,
Figure FDA0002523167480000099
is shown as
Figure FDA00025231674800000910
The total number of the first category of right binary radicals in each sliding window,
Figure FDA00025231674800000911
is shown as
Figure FDA00025231674800000912
The total number of binary groups under the ith class in each sliding window,
Figure FDA00025231674800000913
is shown as
Figure FDA00025231674800000914
The total number of binary groups in the first category within each sliding window;
step thirteen, calculating the high-order potential energy of each pixel point in each sliding window according to the following formula:
Figure FDA00025231674800000915
wherein the content of the first and second substances,
Figure FDA00025231674800000916
is shown as
Figure FDA00025231674800000917
The high-order potential energy of the s-th pixel point in each sliding window;
fourthly, calculating the mean field energy of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA00025231674800000918
wherein the content of the first and second substances,
Figure FDA00025231674800000919
representing the mean field energy of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale;
fifthly, calculating the edge probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA00025231674800000920
wherein the content of the first and second substances,
Figure FDA00025231674800000921
and representing the marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale.
5. The unsupervised synthetic aperture radar SAR image segmentation method based on the high-order multi-scale conditional random field CRF as claimed in claim 1, wherein the bottom-up recursion method in step (9) specifically comprises the following steps:
step one, taking the edge probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in the 0 th scale as the local posterior edge probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in the 0 th scale;
secondly, calculating the local posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000101
wherein the content of the first and second substances,
Figure FDA0002523167480000102
the local posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale is represented,
Figure FDA0002523167480000103
representing the descendant of the s-th pixel in the multi-scale synthetic aperture radar SAR image, representing the s-th pixel point of the multi-scale synthetic aperture radar SAR image in the scale lower than the n-th scale,
Figure FDA0002523167480000104
representing the category of the c generation in the filial generation of the s pixel point of the segmented multi-scale synthetic aperture radar SAR image,
Figure FDA0002523167480000105
representing the posterior marginal probability of the c generation in the s pixel point descendant of the segmented multi-scale synthetic aperture radar SAR image,
Figure FDA0002523167480000106
representing the offspring of the s th pixel point of the segmented multi-scale synthetic aperture radar SAR imageThe conditional a priori edge probabilities of the c-th generation,
Figure FDA0002523167480000107
representing the prior marginal probability of the c generation in the s pixel point descendant of the segmented multi-scale synthetic aperture radar SAR image;
thirdly, the second step is executed twice to obtain the local posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale;
fourthly, calculating the combined posterior marginal probability of each pixel point and the parent pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000108
wherein the content of the first and second substances,
Figure FDA0002523167480000109
expressing the combined posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the nth scale and the parent pixel point thereof, wherein the parent represents the s-th pixel point of the multi-scale synthetic aperture radar image SAR in the nth scale,
Figure FDA00025231674800001013
represents a parent of the s-th pixel in the multi-scale synthetic aperture radar SAR image,
Figure FDA00025231674800001010
representing the nth of the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) th scale
Figure FDA00025231674800001011
The prior edge probability of an individual pixel point,
Figure FDA00025231674800001012
representing the nth of the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) th scale
Figure FDA0002523167480000111
A category of individual pixels.
6. The method for unsupervised segmentation of Synthetic Aperture Radar (SAR) images based on high-order multi-scale Conditional Random Fields (CRF) according to claim 1, wherein the top-down recursive method in step (10) comprises the following steps:
firstly, setting an initial value of posterior marginal probability of each pixel point of a segmented multi-scale synthetic aperture radar SAR image in a 2 nd scale as a local posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in the 2 nd scale;
secondly, calculating the posterior marginal probability of each pixel point of the segmented multi-scale synthetic aperture radar SAR image in each scale according to the following formula:
Figure FDA0002523167480000112
wherein the content of the first and second substances,
Figure FDA0002523167480000113
representing the posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in the n-th scale,
Figure FDA0002523167480000114
representing the segmented multi-scale synthetic aperture radar SAR image in the (n + 1) th scale
Figure FDA0002523167480000115
Posterior marginal probability of each pixel point;
and thirdly, executing the second step twice to obtain the posterior marginal probability of the s-th pixel point of the segmented multi-scale synthetic aperture radar SAR image in all scales.
7. The method for segmenting the SAR image based on the high-order multi-scale conditional random field CRF unsupervised basis as claimed in claim 1, wherein the log-cumulative MoLC method in the step (11c) comprises the following steps:
firstly, performing Mellin transform on a probability density function of generalized Gamma distribution to obtain a first second type characteristic function of the generalized Gamma distribution;
secondly, calculating a second class characteristic function of the generalized Gamma distribution according to the following formula:
ξ(ω)＝lnγ(ω)
where ξ (ω) is the second class of characteristic function of the generalized Gamma distribution, ω is the argument of the probability density function of the generalized Gamma distribution, and γ (ω) is the first second class of characteristic function of the generalized Gamma distribution;
thirdly, calculating first-order logarithmic cumulant, second-order logarithmic cumulant and third-order logarithmic cumulant of a second-class characteristic function of generalized Gamma distribution according to the following formula:
Figure FDA0002523167480000121
fourthly, establishing a first moment model of parameter estimation according to the following formula:
Figure FDA0002523167480000122
wherein ψ (0, λ)l) The parameter k 'representing the multi-gamma poly gamma function is 0, and x' is lambdalCase of (a), ns'Representing the number of pixel points of the segmented multi-scale synthetic aperture radar SAR,
Figure FDA0002523167480000123
expressing the intensity of each sampled image at the S 'th pixel point, and S' expressing all the pixel points in each sampled imageA set of (a);
fifthly, establishing a second moment model of parameter estimation according to the following formula:
Figure FDA0002523167480000124
wherein ψ (1, λ)l) The parameter k 'representing the multi-gamma poly gamma function is 1, and x' is lambdalThe situation of (c)1A first order logarithmic cumulant of a second class of characteristic functions representing a generalized Gamma distribution;
sixthly, establishing a third moment model for parameter estimation according to the following formula:
Figure FDA0002523167480000125
wherein ψ (2, λ)l) The parameter k 'representing the multi-gamma poly gamma function is 2, and the parameter x' is lambdalThe situation of time;
seventhly, solving α generalized Gamma distributed parameters according to the first moment, the second moment and the third moment model formulas of the parameter estimationl，βlAnd λl。
8. The method for segmenting the SAR image based on the CRF unsupervised SAR of claim 1, wherein the step (11d) is implemented by the following steps of the iterative method of the relevant parameters:
firstly, calculating the potential energy of each sampling image according to the following formula:
Figure FDA0002523167480000131
wherein, WqThe potential energy of the qth sampling image is shown, the value range of q is {1,2},
Figure FDA0002523167480000132
representing the q-th sampled image at the nth scaleThe uniary potential energy of the generalized conditional random field CRF of the middle s' th pixel point,
Figure FDA0002523167480000133
indicating that the q-th sampled image is in the second
Figure FDA0002523167480000134
The high-order potential energy of the s' -th pixel point in each sliding window,
Figure FDA0002523167480000135
the mean field energy of the s ' -th pixel point in the nth scale of the q-th sampling image is represented, and t ' represents the neighborhood system N of the s ' -th pixel point in the q-th sampling images′One pixel of (1);
secondly, calculating the posterior marginal probability of each pixel point in the synthetic aperture radar SAR by using the current horizontal related parameters, vertical related parameters and inter-scale related parameters, and inputting the posterior marginal probability of all the pixel points and the original synthetic aperture radar SAR image into a Gibbs sampler to obtain a sampling image of the iteration;
thirdly, calculating the horizontal related parameters of each sampling image in the iteration according to the following formula:
Figure FDA0002523167480000136
wherein the content of the first and second substances,
Figure FDA0002523167480000137
representing the horizontal correlation parameter of the q-th sampled image in the current iteration,
Figure FDA0002523167480000138
representing the horizontal related parameters of the q-th sampling image in the last iteration of the current iteration, N representing the total number of pixel points of each sampling image, a representing the number of times of the current iteration, ▽ representing gradient solving operation,
Figure FDA0002523167480000139
representing the q-th sampled image,
Figure FDA00025231674800001310
representing a sampled image of the iteration;
fourthly, calculating the vertical correlation parameter of each sampling image in the iteration according to the following formula:
Figure FDA00025231674800001311
wherein the content of the first and second substances,
Figure FDA00025231674800001312
the vertical correlation parameter of the q-th sampling image in the current iteration is shown,
Figure FDA00025231674800001313
representing the vertical correlation parameter of the q sampling image in the last iteration of the current iteration;
fifthly, calculating the inter-scale related parameters of each sampling image in the iteration according to the following formula:
Figure FDA00025231674800001314
wherein, ηqRepresents the inter-scale correlation parameter of the q-th sampling image in the current iteration, η'qRepresenting the inter-scale related parameters of the q sampling image in the last iteration of the current iteration;
sixthly, judging whether the current horizontal related parameters, the vertical related parameters and the inter-scale related parameters are converged, if so, executing the seventh step; otherwise, the second step is executed after adding 1 to the current iteration number:
the convergence refers to that the difference between the parameters obtained by the current iteration and the parameters obtained by the last iteration is less than 10-3；
And seventhly, obtaining the horizontal related parameters, the vertical related parameters and the inter-scale related parameters of each sampling image.
9. The method for segmenting the SAR image based on the high-order multi-scale conditional random field CRF unsupervised basis as claimed in claim 1, wherein the specific steps of the characteristic parameter iteration method in the step (11e) are as follows:
calculating the posterior marginal probability of each pixel point in the synthetic aperture radar SAR and an original synthetic aperture radar SAR image according to the current characteristic parameters, and inputting the posterior marginal probability and the original synthetic aperture radar SAR image into a Gibbs sampler to obtain a sampling image of the iteration;
secondly, calculating the deviation value of the characteristic parameter of each category of each sampling image in the iteration according to the following formula:
Figure FDA0002523167480000141
wherein the content of the first and second substances,
Figure FDA0002523167480000142
the deviation value of the characteristic parameter of the ith category of the qth sampling image in the current iteration is shown,
Figure FDA0002523167480000143
representing the deviation value of the characteristic parameter of the ith category of the qth sampling image in the last iteration of the current iteration;
thirdly, calculating the characteristic parameters of each category of each sampling image in the iteration according to the following formula:
Figure FDA0002523167480000144
wherein the content of the first and second substances,
Figure FDA0002523167480000145
the characteristic parameters of the ith category of the qth sampling image in the iteration are represented;
step four, judging whether the characteristic parameters of each category of each current sampling image are converged, if so, executing the step five; otherwise, the first step is executed after adding 1 to the current iteration number: the convergence refers to that the difference between the parameters obtained by the current iteration and the parameters obtained by the last iteration is less than 10-3；
And fifthly, obtaining the characteristic parameters of each sampling image.
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