CN107862701A - Remote sensing image segmentation method based on markov random file and mixed kernel function - Google Patents
Remote sensing image segmentation method based on markov random file and mixed kernel function Download PDFInfo
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Abstract
Remote sensing image segmentation method based on markov random file and mixed kernel function, belongs to Remote Sensing Image Segmentation and identification technology field, it is characterised in that mainly solves the problems, such as that the region consistency of segmentation result in the prior art and detailed information can not meet simultaneously.Realize that step is：1. input space resolution ratio is 0.3 meter of remote sensing SAR image；2. according to the administrative division map of remote sensing SAR image, remote sensing SAR image is divided into structural region subspace and homogenous region subspace；2. pair homogenous region subspace is split using the markov random file based on gaussian radial basis function；3. pair structural region subspace is split using the markov random file based on thresholding Ridgelet kernel functions；4. the segmentation result of homogenous region subspace and the segmentation result of structural region subspace are merged, the segmentation result of remote sensing SAR image is obtained.The present invention realizes the good segmentation effect of remote sensing SAR image, available for Remote Sensing Image Segmentation.
Description
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to a remote sensing image segmentation method which can be used for image classification, identification and detection.
Background
At present, remote sensing image segmentation technology has achieved some research results, and various segmentation methods are proposed. The classic remote sensing image processing method comprises a threshold value-based method, a clustering method and the like. The method designs various characteristics suitable for remote sensing images based on gray level information of pixels, such as gray level co-occurrence matrix characteristics, gabor characteristics, SIFT characteristics, half-difference characteristics and the like. Extracting the characteristics of each pixel point, and obtaining the segmentation result of the image by using a clustering method for the extracted characteristics, such as K-means clustering, hierarchical clustering, AP clustering, fuzzy C-means and other clustering methods. The methods only simply use the values of the pixels of the remote sensing images and do not consider the characteristics of the remote sensing images, so that wrong segmentation is inevitable. In order to improve the segmentation effect of the remote sensing image, some researchers have proposed a level set method, a Markov Random Field (MRF) method, a conditional random field method, a polynomial hidden model and other methods for remote sensing image segmentation. The methods mainly comprise a feature model and a spatial context model. The characteristic model is used for describing the statistical characteristics of the amplitude and texture of the remote sensing image, and the context model is used for describing the spatial context relationship of the remote sensing image.
The markov random field method is a basic probabilistic graphical model in which context information of an image is captured by comparing relationships between a central pixel class label and surrounding pixel class labels, and weights of surrounding pixels to the central pixel are considered to be the same. The single spatial relationship is difficult to describe the mixed structure of the remote sensing images, for example, the spatial context of a homogeneous region is different from that of a heterogeneous region, especially the spatial context of remote sensing images of urban areas, including buildings with smaller dimensions and large open spaces, etc., is quite different. In homogeneous regions, the weight of the central pixel to the surrounding pixels is isotropic. In the heterogeneous region, there is a strong correlation between the peripheral pixels and the central pixel along the direction of the boundary, and the correlation rapidly decays in the direction perpendicular to the boundary. Because different spatial structure characteristics of the remote sensing image are not considered, the region consistency and detail information retention in the segmentation result cannot be simultaneously met, and subsequent classification, identification and detection of the remote sensing image are influenced.
Disclosure of Invention
The invention aims to provide a remote sensing image segmentation method based on a Markov random field and a mixed kernel function aiming at the defects of the existing method so as to improve the effect of remote sensing image segmentation.
The technical idea of the invention is as follows: the method comprises the following steps of taking an urban remote sensing SAR image with set spatial resolution as an object, improving a general Markov random field model, and improving the segmentation effect of the remote sensing image, namely dividing the remote sensing SAR image into a homogeneous region subspace and a structural region subspace by utilizing a region map of the remote sensing SAR image, segmenting the homogeneous region subspace by adopting a Markov random field based on a Gaussian radial basis function, segmenting the structural region subspace by adopting a Markov random field based on a thresholding Ridgelet kernel function, combining the segmentation result of the homogeneous region subspace and the segmentation result of the structural region subspace to obtain the segmentation result of the remote sensing SAR image, and sequentially realizing the following steps in a computer:
step (1), inputting: an urban remote sensing SAR image with set spatial resolution, referred to as a remote sensing image for short, is divided into a structural region subspace and a homogeneous region subspace according to a region map of the remote sensing image, wherein the structural region subspace is obtained by mapping a sketch region formed on the basis of sketch lines of the remote sensing image with a set geometric window constructed on the remote sensing image, the homogeneous region subspace is an irreducible sketch region in the remote sensing image,
and step (2), the computer is initialized,
setting: the class mark sequence number of the homogeneous region subspace of the remote sensing SAR image is R, R =1,2,.. Multidot.r, R is the total class mark number of the homogeneous region subspace in the remote sensing SAR image, the class mark sequence number of the structural region subspace of the remote sensing SAR image is W, W =1,2,.. Multidot.w, W is the total class mark number of the structural region subspace in the remote sensing SAR image, one class mark sequence number is preset for each pixel in the remote sensing SAR image,
and (3) segmenting all pixels in the subspace of the homogeneous region by adopting a Markov random field based on a Gaussian radial basis kernel function, wherein the steps are as follows:
step (3.1) setting: by the symbol y s Denotes each pixel in the homogeneous region subspace, with the subscript s being the pixel number, s =1,2 s Total number of (2), N s Is y s Neighborhood pixel y as center t T is the neighborhood pixel y t N, t =1,2 s ，
And (3) calculating: center pixel y s And each domain pixel y t Gaussian radial basis kernel function between:
wherein, c s ＝(cx s ,cy s ) Is y s Coordinates of (c) t ＝(cx t ,cy t ) Is y t Is determined by the coordinate of (a) in the space,
k(y s ,y t ) Denotes y s And y t The correlation between them, called y s And y t Have an isotropic spatial context relationship therebetween,
σ 1 for the scale parameter, take σ 1 ＝3，
And (3.2) setting:
center pixel y s Class label set of X s ，Superscript r as central pixel y s Class label x of s The serial number of (a) is included,
X t is the central pixel y s Class label x of s Neighborhood class label x as center t The set of (a) or (b),
and (3) calculating: calculating the appearance and center class mark in the neighborhood according to the following formulaSame neighborhood classmarkPrior probability of (2)
Wherein:in order to be a function of the first indicator,
an arrow = > indicates correspondence, an ≠ indicates no correspondence,
neighborhood class labelPrior probability of (2)Numerically equal to the central classmarkA priori probability of
In step (3.3), when the central pixel of the subspace of the homogeneous region follows the Nakagami distribution, the central pixel y s The likelihood probability of (a) is,
wherein: r =1, 2.. RTM., R.. RTM.,
Γ(α r ) Is a function of the Gamma function and is,
μ r is composed ofm r For counting, m, by setting a class index for each pixel from initialization r Indicating the total number of pixels labeled with the r-th class index,
α r is a measurement of the visual significance of a remote sensing target marked by a class mark number r in a remote sensing SAR image, is a dimensionless numerical value and is in an interval [0,1 ]]The medium value is selected from the group consisting of,
α r calculated from the formula:
ψ 1 (α r )＝d(log(Γ(α r )))/dα r ，
step (3.4), obtaining a certain central pixel y according to the results of the step (3.2) to the step (3.3) s Class labelThe posterior probability of (a) is:
obtaining a pixel y in a homogeneous region subspace in the remote sensing SAR image according to the maximum posterior probability s Class labelComprises the following steps:
step (3.5), repeating the step (3.2) -the step (3.4) to obtain the class label of each pixel in the homogeneous region subspaceThereby obtaining the partition result of the subspace of the homogeneous region,
step (4), a structural region subspace is segmented by a Markov random field based on a thresholding Ridgelet kernel function,
step (4.1), the following symbols are defined:
the pixel of the structural region subspace is y a A =1, 2., n., Q is the pixel y a Total number of (2), V a Is y a Neighborhood pixel y as center b B is the neighborhood pixel y b Serial number of (a), b =1,2 a ，
Since the structural region subspace contains the boundary, the central pixel y, in the remote sensing SAR image a And its neighborhood pixel y b Has anisotropic spatial context, and thus thresholded Ridgelet kernel function h (y) a ,y b ) To indicate that the user is not in a normal position,
wherein: (cx) a ,cy a ) Is y a (cx), (cx) of b ,cy b ) Is y b Is determined by the coordinate of (a) in the space,
σ 2 is a scale parameter and σ 2 ＝1，
d is a translation parameter and d =0,
theta is the direction of the sketch points on the sketch line segment obtained from the remote sensing SAR image sketch, is a direction function and is a known value,
order to
Then the process of the first step is carried out,
and (4.2) setting:
center pixel y a The corresponding class label set is X a ，Wherein W =1, 2.. Times.w.. Times.w.w is the center pixel y a Corresponding class label x a The serial number of (a) is included,
center pixel y a Is adjacent to the pixel y b Class label x of b Is set as X b ，
Calculating the occurrence and center class labels in the neighborhoodSame neighborhood classmarkPrior probability of (2)
Wherein the content of the first and second substances,in the form of a second indication function,
an arrow = > indicates correspondence, ≠ > indicates no correspondence,
neighborhood class labelA priori probability ofNumerically equal to the center class labelA priori probability of
Step (4.3), pixel y of the structural region subspace a Obeying the Nakagami distribution, y a The likelihood probability of (c) is:
wherein: w =1, 2., W,
Γ(α w ) Is a function of the Gamma function and is,
μ w is composed ofm w Is obtained by counting according to the class mark number w set for each pixel during initialization, m w The total number of pixels labeled with the w-th class index,
α w is a measure of the visual saliency of a remote sensing target marked by a class mark number w in a remote sensing SAR image, is a dimensionless numerical value and is in an interval [0,1 ]]The medium value is selected from the group consisting of,
α w calculated from the formula:
ψ 1 (α w )＝d(log(Γ(α w )))/dα w ，
step (4.4), obtaining a pixel y in the subspace of the structural region according to the results of the step (4.2) to the step (4.3) a Class label ofThe posterior probability of (a) is:
obtaining a pixel y in a subspace of a structural region in the remote sensing SAR image according to the maximum posterior probability a Class label ofComprises the following steps:
and (4.5) repeating the steps (4.2) to (4.4) to obtain the class label of each pixel in the subspace of the structural regionThereby obtaining the segmentation result of the subspace of the structural region,
step (5), merging the partition result of the subspace of the homogeneous region and the partition result of the subspace of the structural region, namely { x s |s∈M}∪{x a |a∈Q}。
Compared with the prior art, the invention has the following advantages:
firstly, the invention combines the information of the pixel space of the remote sensing SAR image with the regional map to segment the remote sensing SAR image, thereby effectively completing the task of segmenting the remote sensing SAR image.
Secondly, the invention constructs different kernel functions for the regions with different characteristics, captures the spatial context of the regions with different characteristics in the remote sensing image, not only improves the region consistency of the segmentation result, but also effectively retains the detail information of the image.
Drawings
FIG. 1 is a flow chart of the present invention for implementing remote sensing SAR image segmentation;
fig. 2 is a result diagram of division of a subspace of a remote sensing SAR image in the present invention, fig. 2 (a) is a remote sensing SAR image with a spatial resolution of 0.3 m, and fig. 2 (b) is a sketch of the remote sensing SAR image; fig. 2 (c) is a regional diagram of the remote sensing SAR image;
FIG. 3 is a schematic diagram of various kernel functions in the present invention, where FIG. 3 (a) is a 3-dimensional schematic diagram of a Gaussian radial basis kernel function, and FIG. 3 (b) is a 3-dimensional schematic diagram of a Ridgelet kernel function;
fig. 4 is a diagram showing a result of segmenting a remote sensing SAR image with a spatial resolution of 0.3 m by using the method of the present invention and the conventional method, fig. 4 (a) is a diagram showing a remote sensing SAR image with a spatial resolution of 0.3 m, fig. 4 (b) is a diagram showing a segmentation result of a markov random field model, fig. 4 (c) is a diagram showing a segmentation result of a high order markov random field model, and fig. 4 (d) is a diagram showing a segmentation result of the present invention.
Detailed Description
Referring to fig. 1, a remote sensing SAR image with a set spatial resolution is input, and the remote sensing SAR image is divided into a homogeneous region subspace and a structural region subspace according to a regional diagram of the remote sensing SAR image; a homogeneous region subspace is segmented by adopting a Markov random field based on a Gaussian radial basis kernel function; partitioning the structural region subspace by adopting a Markov random field based on a thresholding Ridgelet kernel function; combining the partition result of the subspace of the homogeneous region and the partition result of the subspace of the structural region to obtain the partition result of the remote sensing SAR image, and sequentially realizing the following steps in a computer:
step (1), inputting: the method comprises the following steps of dividing an urban remote sensing SAR image with set spatial resolution into a structural region subspace and a homogeneous region subspace according to a region map of the remote sensing image, wherein the structural region subspace is obtained by mapping a sketch region formed on the basis of sketch lines of the remote sensing image with a set geometric window constructed on the remote sensing image, and the homogeneous region subspace is an irreducible sketch region in the remote sensing image, and comprises the following steps:
step (1.1), obtaining a sketch map of the Remote Sensing SAR image according to a sketch model provided in an article Local maximum genetic region search for SAR specific reproduction with sketch-based geographic kernel function published in IEEE Transactions on Geoscience and Remote Sensing journal by Wujie and Liu Fang et al in 2014, wherein the sketch map consists of sketch line segments and gives a direction theta of sketch points on the sketch line segments;
step (1.2), constructing a geometric structure window with the size of 5 multiplied by 5 for the sketch lines in the sketch to obtain a structure area;
step (1.3), taking the part of the sketch except the structural area as a non-sketch area;
and (1.4) mapping an non-sketch region and a structural region in the sketch map onto the remote sensing SAR image, and dividing the remote sensing SAR image into a homogeneous region subspace and a structural region subspace, wherein as shown in FIG. 2, FIG. 2 (a) is an original remote sensing SAR image, FIG. 2 (b) is a sketch map of the remote sensing SAR image, FIG. 2 (c) is a region map of the remote sensing SAR image, in the region map, a white part is a structural region subspace, and a black part is a homogeneous region subspace.
Step (2), the computer is initialized,
setting: the class mark sequence number of the subspace of the homogeneous region of the remote sensing SAR image is R, R =1,2, a.
And (3) segmenting all pixels in the subspace of the homogeneous region by adopting a Markov random field based on a Gaussian radial basis kernel function, wherein the steps are as follows:
step (3.1) setting: by the symbol y s Denotes each pixel in the homogeneous region subspace, subscript s being the pixel number, s =1,2 s Total number of (2), N s Is y s Centered neighborhood pixel y t T is the neighborhood pixel y t N, t =1,2 s ，
And (3) calculating: center pixel y s And each domain pixel y t Gaussian radial basis kernel function between:
wherein, c s ＝(cx s ,cy s ) Is y s Coordinates of (c) t ＝(cx t ,cy t ) Is y t Is determined by the coordinate of (a) in the space,
k(y s ,y t ) Denotes y s And y t The correlation between them, called y s And y t Have an isotropic spatial context relationship therebetween,
σ 1 for the scale parameter, take σ 1 ＝3，
And (3.2) setting:
center pixel y s Is X s ，Superscript r as centre pixel y s Class label x of s The serial number of (a) is included,
X t is the central pixel y s Class label x of s Neighborhood class label x as center t The set of (a) and (b),
computing: calculating the appearance and center class mark in the neighborhood according to the following formulaSame neighborhood classmarkPrior probability of (2)
Wherein:in order to be a function of the first indicator,
an arrow = > indicates correspondence, an ≠ indicates no correspondence,
neighborhood class labelA priori probability ofNumerically equal to the central classmarkA priori probability ofIn step (3.3), when the central pixel of the subspace of the homogeneous region follows the Nakagami distribution, the central pixel y s The probability of likelihood of (a) is,
wherein: r =1, 2.., R.,. R.,
Γ(α r ) Is a function of the Gamma function and is,
μ r is composed ofm r For counting, m, by setting a class index for each pixel from initialization r Indicating the total number of pixels labeled with the r-th class designation,
α r is a measure of the visual significance of a remote sensing target marked by a class mark serial number r in a remote sensing SAR image, is a dimensionless numerical value and is in an interval [0,1 ]]The medium value is selected from the group consisting of,
α r calculated from the formula:
ψ 1 (α r )＝d(log(Γ(α r )))/dα r ，
step (3.4), obtaining a certain central pixel y according to the results of the step (3.2) to the step (3.3) s Class labelThe posterior probability of (a) is:
obtaining a pixel y in a homogeneous region subspace in the remote sensing SAR image according to the maximum posterior probability s Class label ofComprises the following steps:
step (3.5), repeating the step (3.2) -the step (3.4) to obtain the class label of each pixel in the homogeneous region subspaceThereby obtaining the partition result of the subspace of the homogeneous region,
step (4), a structural region subspace is segmented by a Markov random field based on a thresholding Ridgelet kernel function,
step (4.1), the following symbols are defined:
the pixel of the structural area subspace is y a A =1,2, n, Q is the pixel y a Total number of (B), V a Is y a Centered neighborhood pixel y b B is the neighborhood pixel y b Serial number of (a), b =1,2 a ，
Since the structural region subspace contains the boundary, the central pixel y, in the remote sensing SAR image a And its neighborhood pixel y b Has anisotropic spatial context, and thus thresholded Ridgelet kernel function h (y) a ,y b ) To indicate that the position of the movable member,
wherein: (cx) a ,cy a ) Is y a (cx), (cx) b ,cy b ) Is y b Is determined by the coordinate of (a) in the space,
σ 2 is a scale parameter and σ 2 ＝1，
d is a translation parameter and d =0,
theta is the direction of the sketch points on the sketch line segment obtained from the remote sensing SAR image sketch, is a direction function and is a known value,
order to
Then the process of the first step is carried out,
and (4.2) setting:
center pixel y a The corresponding class label set is X a ，Wherein W =1,2, W is the central pixel y a Corresponding class label x a The serial number of (a) is included,
center pixel y a Is adjacent to the pixel y b Class label x of b Is set as X b ，
Computing occurrence and center class labels within a neighborhoodSame neighborhood classmarkPrior probability of (2)
Wherein the content of the first and second substances,in the form of a second indication function,
the arrow = > indicates correspondence, the not ≠ > indicates no correspondence,
neighborhood class labelA priori probability ofNumerically equal to the center class labelPrior probability of (2)
Step (4.3), pixel y of the structural region subspace a Obeying the Nakagami distribution, y a The likelihood probability of (c) is:
wherein: w =1, 2., W,
Γ(α w ) Is a function of the Gamma function and is,
μ w is composed ofm w Is obtained by counting according to the class mark number w set for each pixel during initialization, m w Is the total number of pixels labeled with the w-th class serial number,
α w is a measure of the visual saliency of a remote sensing target marked by a class mark number w in a remote sensing SAR image, is a dimensionless numerical value and is in an interval [0,1 ]]The medium value is selected from the group consisting of,
α w calculated from the formula:
ψ 1 (α w )＝d(log(Γ(α w )))/dα w ，
step (4.4), obtaining a pixel y in the subspace of the structural region according to the results of the step (4.2) to the step (4.3) a Class labelThe posterior probability of (a) is:
obtaining a pixel y in a subspace of a structural region in the remote sensing SAR image according to the maximum posterior probability a Class labelComprises the following steps:
and (4.5) repeating the steps (4.2) to (4.4) to obtain the class label of each pixel in the subspace of the structural regionThereby obtaining the segmentation result of the subspace of the structural region,
step (5), merging the partition result of the subspace of the homogeneous region and the partition result of the subspace of the structural region, namely { x s |s∈M}∪{x a |a∈Q}。
The advantages of the invention are further illustrated by the following remote sensing SAR images.
1. Simulation conditions
The remote sensing image used by the simulation of the invention is as follows: and the spatial resolution is 0.3 m.
2. Simulation content and results
Simulation content: the remote sensing image with the resolution of 0.3 m is segmented by the method and the conventional Markov random field model and the high-order Markov random field model, and the result is shown in FIG. 4, wherein FIG. 4 (a) is an original remote sensing SAR image with the resolution of 0.3 m, FIG. 4 (b) is a segmentation result of the Markov random field model, FIG. 4 (c) is a segmentation result of the high-order Markov random field model, and FIG. 4 (d) is a segmentation result of the method.
And (3) simulation results: as can be seen from FIG. 4, the Markov random field model keeps the image boundary and detail information well, but causes the over-segmentation phenomenon, and the region consistency is poor; the region consistency of the segmentation result based on the high-order Markov random field is good, but the detail information of the remote sensing SAR image is lost, because the high-order Markov random field can not capture the heterogeneous structure of the image; according to the method, the remote sensing SAR image is divided into different region subspaces through the region map, different kernel functions are designed for the different region subspaces, the kernel functions are embedded into the Markov random field model, and the segmentation result of the remote sensing SAR image is obtained, and not only is the segmentation result good in region consistency, but also the detail information of the image is reserved.
In conclusion, the invention simultaneously realizes the region consistency and detail information maintenance in the remote sensing SAR image segmentation, and obtains the good segmentation effect of the remote sensing SAR image.
Claims (1)
1. The remote sensing image segmentation method based on the Markov random field and the mixed kernel function is characterized by being sequentially realized in a computer according to the following steps:
step (1), inputting: an urban remote sensing SAR image with set spatial resolution, referred to as a remote sensing image for short, is divided into a structural region subspace and a homogeneous region subspace according to a region map of the remote sensing image, wherein the structural region subspace is obtained by mapping a sketch region formed on the basis of sketch lines of the remote sensing image with a set geometric window constructed on the remote sensing image, the homogeneous region subspace is an irreducible sketch region in the remote sensing image,
and step (2), the computer is initialized,
setting: the class mark sequence number of the homogeneous region subspace of the remote sensing SAR image is R, R =1,2,.. Multidot.r, R is the total class mark number of the homogeneous region subspace in the remote sensing SAR image, the class mark sequence number of the structural region subspace of the remote sensing SAR image is W, W =1,2,.. Multidot.w, W is the total class mark number of the structural region subspace in the remote sensing SAR image, one class mark sequence number is preset for each pixel in the remote sensing SAR image,
and (3) segmenting all pixels in the homogeneous region subspace by adopting a Markov random field based on a Gaussian radial basis kernel function, wherein the steps are as follows:
step (3.1) setting: by the symbol y s Denotes each pixel in the homogeneous region subspace, with the subscript s being the pixel number, s =1,2 s Total number of (2), N s Is y s Neighborhood pixel y as center t T is the neighborhood pixel y t N, t =1,2 s ，
And (3) calculating: center pixel y s And each domain pixel y t Gaussian radial basis kernel function between:
wherein, c s ＝(cx s ,cy s ) Is y s Coordinates of (c) t ＝(cx t ,cy t ) Is y t The coordinates of (a) are calculated,
k(y s ,y t ) Denotes y s And y t The correlation between them, called y s And y t Have an isotropic spatial context relationship therebetween,
σ 1 taking σ as a scale parameter 1 ＝3，
And (3.2) setting:
center pixel y s Is X s ，Superscript r as centre pixel y s Class label x of s The serial number of (a) is included,
X t is the central pixel y s Class label x of s Neighborhood class label x as center t The set of (a) and (b),
and (3) calculating: calculating the appearance and center class mark in the neighborhood according to the following formulaSame neighborhood classmarkA priori probability of
Wherein:in order to be a function of the first indication,
an arrow = > indicates correspondence, an ≠ indicates no correspondence,
neighborhood class labelPrior probability of (2)Numerically equal to the central classmarkA priori probability of
In step (3.3), when the central pixel of the subspace of the homogeneous region follows the Nakagami distribution, the central pixel y s The likelihood probability of (a) is,
wherein: r =1, 2.., R.,. R.,
Γ(α r ) Is a function of the Gamma function and is,
μ r is composed ofm r For counting, m, by setting a class index for each pixel from initialization r Indicating the total number of pixels labeled with the r-th class index,
α r is a measure of the visual significance of a remote sensing target marked by a class mark serial number r in a remote sensing SAR image, is a dimensionless numerical value and is in an interval [0,1 ]]The medium value is selected from the group consisting of,
α r calculated from the following formula:
ψ 1 (α r )＝d(log(Γ(α r )))/dα r ，
step (3.4), obtaining a certain central pixel y according to the results of the step (3.2) to the step (3.3) s Class labelThe posterior probability of (a) is:
obtaining a pixel y in a homogeneous region subspace in the remote sensing SAR image according to the maximum posterior probability s Class labelComprises the following steps:
and (3.5) repeating the steps (3.2) to (3.4) to obtain the class label of each pixel in the subspace of the homogeneous regionThereby obtaining the partition result of the subspace of the homogeneous region,
step (4), a structural region subspace is segmented by a Markov random field based on a thresholding Ridgelet kernel function,
step (4.1), the following symbols are defined:
the pixel of the structural region subspace is y a A =1, 2., n., Q is the pixel y a Total number of (B), V a Is y a Neighborhood pixel y as center b B is the neighborhood pixel y b Serial number of (a), b =1,2 a ，
Since the structural region subspace contains the boundary, the central pixel y, in the remote sensing SAR image a And its neighborhood pixel y b Has anisotropic spatial context, and therefore thresholded Ridgelet kernel function h (y) a ,y b ) To indicate that the position of the movable member,
wherein: (cx) a ,cy a ) Is y a (cx), (cx) of b ,cy b ) Is y b The coordinates of (a) are calculated,
σ 2 is a scale parameter and σ 2 ＝1，
d is a translation parameter and d =0,
theta is the direction of the pixel points on the sketch line segment obtained from the remote sensing SAR image sketch, is a direction function, is a known value,
order to
Then the process of the first step is carried out,
and (4.2) setting:
center pixel y a The corresponding class label set is X a ，Wherein W =1, 2.. Times.w.. Times.w.w is the center pixel y a Corresponding classmark x a The serial number of (a) is included,
center pixel y a Is adjacent to the pixel y b Class label x of b Is X b ，
Computing occurrence and center class labels within a neighborhoodSame neighborhood classmarkPrior probability of (2)
Wherein, the first and the second end of the pipe are connected with each other,in the form of a second indication function,
the arrow = > indicates correspondence, the not ≠ > indicates no correspondence,
neighborhood class labelPrior probability of (2)Numerically equal to the central classmarkPrior probability of (2)
Step (4.3), pixel y of the structural region subspace a Obeying the Nakagami distribution, y a The likelihood probability of (c) is:
wherein: w =1, 2., W,
Γ(α w ) Is a function of the Gamma function and is,
μ w is composed ofm w Is obtained by counting according to the class mark number w set for each pixel during initialization, m w The total number of pixels labeled with the w-th class index,
α w is a measurement of the visual significance of a remote sensing target marked by a class mark number w in a remote sensing SAR image, is a dimensionless numerical value and is in an interval [0,1 ]]The medium value is selected from the group consisting of,
α w calculated from the following formula:
ψ 1 (α w )＝d(log(Γ(α w )))/dα w ，
step (4.4), obtaining a pixel y in the subspace of the structural region according to the results of the step (4.2) to the step (4.3) a Class labelThe posterior probability of (a) is:
obtaining a pixel y in a subspace of a structural region in the remote sensing SAR image according to the maximum posterior probability a Class label ofComprises the following steps:
and (4.5) repeating the steps (4.2) to (4.4) to obtain the class label of each pixel in the subspace of the structural regionThereby obtaining the segmentation result of the subspace of the structural region,
step (5), merging the partition result of the subspace of the homogeneous region and the partition result of the subspace of the structural region, namely { x s |s∈M}∪{x a |a∈Q}。
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