CN113657394A - Remote sensing image segmentation method based on Markov random field and evidence theory - Google Patents

Remote sensing image segmentation method based on Markov random field and evidence theory Download PDF

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CN113657394A
CN113657394A CN202110938948.1A CN202110938948A CN113657394A CN 113657394 A CN113657394 A CN 113657394A CN 202110938948 A CN202110938948 A CN 202110938948A CN 113657394 A CN113657394 A CN 113657394A
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dispute
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袁鹏
顾行发
黄祥志
王珂
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Jiangsu Tianhui Spatial Information Research Institute Co ltd
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Abstract

The invention discloses a remote sensing image segmentation method based on a Markov random field and an evidence theory, fuzzy C mean clustering FCM is respectively carried out on an original remote sensing image, a first marked image and a second marked image, various membership degrees of pixel points contained in a dispute image are calculated through each clustering center of the original remote sensing image, and a fundamental probability assignment m of a single proposition or a composite proposition of the dispute pixel points in the four images of the original remote sensing image, the first marked image and the second marked image and the dispute image is determined according to a fundamental probability assignment obtaining method. The method can perform fusion segmentation on the segmentation results of the two methods, namely the traditional MRF segmentation and the fuzzy Markov random Field Model (FMRF), by using a D-S evidence theory, so as to realize accurate segmentation of the image.

Description

Remote sensing image segmentation method based on Markov random field and evidence theory
Technical Field
The invention relates to the technical field of remote sensing image segmentation, in particular to a remote sensing image segmentation method based on a Markov random field and an evidence theory.
Background
The Markov random field model is used as a prior model and has been widely applied in the field of image segmentation, and practices prove that the model is favorable for improving the image segmentation effect. However, due to the influence of the environment and the sensor, the remote sensing image has the characteristics of large gray scale change, complex texture, fuzzy boundary and the like, and the segmentation effect of the classical markov random field model in the remote sensing image segmentation is not ideal. In the traditional MRF segmentation, the MRF is considered as hard segmentation in the iterative process, and a fuzzy Markov random field model is soft segmentation, but because the MRF has different attention degrees to details, some pixel points are classified into different classes when the MRF is used for segmenting the same remote sensing image respectively, so that the uncertainty of partial information is caused.
In view of the above situation, there is a need for a remote sensing image segmentation method based on a markov random field and an evidence theory, which can perform fusion segmentation on the segmentation results of the two methods, namely, the traditional MRF segmentation and the fuzzy markov random Field Model (FMRF), by using a D-S evidence theory, so that finally, the dispute points are reasonably classified, and further, the accurate segmentation of the image is realized.
Disclosure of Invention
The invention aims to provide a remote sensing image segmentation method based on a Markov random field and an evidence theory so as to solve the problems in the background technology.
In order to solve the technical problems, the invention provides the following technical scheme: a remote sensing image segmentation method based on a Markov random field and an evidence theory is characterized by comprising the following steps:
s1, segmenting the original remote sensing image by adopting the traditional MRF segmentation to obtain a first marked image, and segmenting the original remote sensing image by adopting the fuzzy MRF segmentation to obtain a second marked image;
s2, comparing the first marked image with the second marked image, respectively extracting dispute pixel points and non-dispute pixel points in the two marked images, and generating a dispute image;
s3, fuzzy C-means clustering FCM is conducted on the original remote sensing image and the two labeled images including the first labeled image and the second labeled image respectively, various membership degrees of pixel points included in the dispute image are calculated through each clustering center of the original remote sensing image, and the assignment m of the basic probability of single propositions or composite propositions of the pixel points corresponding to the dispute pixel points in the four images including the original remote sensing image, the first labeled image and the second labeled image and the dispute image is determined according to a basic probability assignment obtaining method;
s4, fusing basic probability assignment m of single propositions or composite propositions of corresponding pixel points of dispute pixel points in the four images, namely the original remote sensing image, the first marked image and the second marked image and the dispute image, by using a Dempster criterion in an evidence theory, carrying out segmentation judgment, selecting a maximum m value corresponding to the corresponding pixel point of each dispute pixel point, and attributing the corresponding pixel point of the dispute pixel point to a corresponding category according to the maximum m value to obtain a final fusion segmentation result.
Both traditional MRF and fuzzy MRF differ in detail concerns: in the implementation process of the traditional MRF method, each pixel is endowed with a hard label which belongs to hard judgment and easily causes information loss, and in the implementation process of the fuzzy MRF method, each pixel is endowed with the membership degree of each label which belongs to soft segmentation but possibly causes excessive segmentation, and the two are combined, so that the image segmentation effect can be effectively improved.
Further, the method for generating a dispute image in S2 includes the following steps:
s2.1, comparing a first marker image obtained by traditional MRF segmentation with a second marker image obtained by fuzzy MRF segmentation;
s2.2, taking pixel points with different segmentation results in the two images as dispute pixel points, and respectively extracting the dispute pixel points in the two images;
and S2.3, representing the gray value of the dispute pixel point by adopting the average value of the gray values of the neighborhood of the pixel point corresponding to the original remote sensing image of the dispute pixel point, and representing the gray value of the non-dispute pixel point by using the original gray value to generate a dispute image.
Further, the fuzzy C mean clustering in the S3 is recorded as FCM, the FCM obtains the membership degree of each sample point in all class centers by optimizing a target function, and determines the membership degree of the sample points in all class centers so as to automatically classify the sample data; assigning a membership function belonging to each class to each sample, classifying the samples by the magnitude of the membership value,
fuzzy c-means clustering mainly has three key parameters, the cluster number, the center of each cluster and the class corresponding to the closest cluster center of each sample point, the fuzzy c-means clustering obtains the cluster center by minimizing an objective function, the objective function is the sum of Euclidean distances from each sample point to each class, namely the square sum of errors,
the fuzzy C-means clustering method in the S3 comprises the following steps:
s3-1, initializing parameters, setting a fuzzy weighting index m to be 2, initializing a clustering result by using a random number with a value from 1 to C, and initializing a clustering center by using the mean value of each class, wherein C is the clustering number;
s3-2, solving the membership degree according to a membership degree solving formula
Figure BDA0003214220830000031
M is a fuzzy weighting index, C is a clustering center number, CjDenotes the jth cluster center, xiRepresenting the gray value, u, of the ith sample, i.e. the ith dispute pixelijRepresents a sample xiTo the clustering center cjDegree of membership, i.e. xiBelong to cjThe degree of membership representing the degree to which each sample point belongs to each class, x for a single sampleiThe sum of the membership degrees of each class is 1;
s3-3, updating the cluster centers according to the cluster center solving formula, namely, respectively evaluating all the cluster centers through the cluster center formula, and replacing the corresponding cluster centers with the values of the newly obtained cluster centersThe original value, the cluster center formula is
Figure BDA0003214220830000032
N is the number of samples;
s3-4, obtaining an objective function, and judging whether the objective function is converged, wherein the objective function is
Figure BDA0003214220830000033
Wherein, the | | xi-cj||2Representing data xiAnd cjThe similarity measure is Euclidean norm, also called Euclidean distance;
when the target function is not converged, acquiring the updated clustering center in S3-3, and returning to S3-2 until the target function is converged;
s3-5, when the objective function is converged, acquiring the membership degree of all classes corresponding to each sample point in all sample points in the current state, judging the membership degree of all classes corresponding to each sample point, and judging which class the sample point belongs to if the membership degree of each class of each sample point is the maximum.
Further, the method for obtaining the basic probability assignment in S3 includes the following steps:
s3.1, carrying out fuzzy C-means clustering on the image to obtain the membership mu of each pixel A to the kth classk，
S3.2, determining the basic probability assignment of each pixel A to each class label according to two conditions: single proposition and composite proposition, setting xi as a certain threshold value, muk1、μk2The membership degrees of the pixel point A to the k1 th and k2 th categories respectively;
s3.3, if μk1-μk2Determining the fuzzy clustering result as a single proposition if | ≧ xi, and directly obtaining the basic probability assignment m (A) of the single proposition by using the membershipk1)＝μk1，m(Ak2)＝μk2；
S3.4, | μk1-μk2If | is less than xi, determining the fuzzy clustering result as a composite proposition, and determining the basic probability assignment by adopting the composite proposition, then determining the basic probability assignmentBasic probability assignment for double-compound propositions
Figure BDA0003214220830000041
Further, the method for determining the membership degree of each type of the pixel points included in the dispute image in S3 is as follows:
carrying out fuzzy C-means clustering on the original image to obtain a clustering center CjAccording to the membership degree formula, the gray value x of the dispute pixel point in the dispute image is calculatediAnd a cluster center cjSubstituting the value into a membership degree formula to obtain various membership degrees of pixel points contained in the dispute image.
Further, the method for obtaining the final fusion segmentation result in S4 includes the following steps:
s4.1, obtaining two label images of an original remote sensing image, a first label image and a second label image and a four image of a dispute image, wherein each pixel of the four images corresponds to a basic probability assignment m of each label,
s4.2, calculating the combined basic probability assignment of each label of the dispute pixel point by using a Dempster combination rule, wherein the Dempster combination rule is as follows:
Figure BDA0003214220830000042
A. b, C, D and E represent different propositions, m1(B) Basic probability assignment of B propositions, m, representing original image2(C) Basic probability assignment of C proposition, m, representing first label image3(D) Basic probability assignment of D proposition, m, representing second label image4(E) A base probability assignment representing an E proposition of the dispute image, m (A) a combined base probability assignment representing an A proposition, k being a normalization constant;
and S4.3, comparing the combined basic probability assignment of each label of the dispute pixel point obtained in the step S4.2, screening out the label corresponding to the maximum combined basic probability assignment, and classifying the dispute pixel point as the label.
Compared with the prior art, the invention has the following beneficial effects: the method can perform fusion segmentation on the segmentation results of the two methods, namely the traditional MRF segmentation and the fuzzy Markov random Field Model (FMRF), by using a D-S evidence theory, so that the dispute points are classified reasonably finally, and the accurate segmentation of the image is further realized.
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The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:
FIG. 1 is a schematic flow chart of a remote sensing image segmentation method based on a Markov random field and evidence theory according to the present invention;
FIG. 2 is a schematic structural diagram of a basic probability assignment obtaining method in a remote sensing image segmentation method S3 based on a Markov random field and an evidence theory according to the present invention;
FIG. 3 is a schematic structural diagram of a segmentation reference data of an original image of a remote sensing image segmentation method based on a Markov random field and an evidence theory according to the present invention;
FIG. 4 is a schematic structural diagram of a segmentation result obtained by traditional MRF segmentation of a remote sensing image segmentation method based on a Markov random field and an evidence theory according to the present invention;
FIG. 5 is a schematic structural diagram of a segmentation result obtained by Fuzzy MRF (FMRF) segmentation of a remote sensing image segmentation method based on a Markov random field and an evidence theory according to the invention;
FIG. 6 is a schematic structural diagram of a segmentation result obtained by Dempster criterion (DS) in the evidence theory of the remote sensing image segmentation method based on the Markov random field and the evidence theory.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-6, the present invention provides the following technical solutions: a remote sensing image segmentation method based on a Markov random field and an evidence theory is characterized by comprising the following steps:
s1, segmenting the original remote sensing image by adopting the traditional MRF segmentation to obtain a first marked image, and segmenting the original remote sensing image by adopting the fuzzy MRF segmentation to obtain a second marked image;
s2, comparing the first marked image with the second marked image, respectively extracting dispute pixel points and non-dispute pixel points in the two marked images, and generating a dispute image;
s3, fuzzy C-means clustering FCM is conducted on the original remote sensing image and the two labeled images including the first labeled image and the second labeled image respectively, various membership degrees of pixel points included in the dispute image are calculated through each clustering center of the original remote sensing image, and the assignment m of the basic probability of single propositions or composite propositions of the pixel points corresponding to the dispute pixel points in the four images including the original remote sensing image, the first labeled image and the second labeled image and the dispute image is determined according to a basic probability assignment obtaining method;
s4, fusing basic probability assignment m of single propositions or composite propositions of corresponding pixel points of dispute pixel points in the four images, namely the original remote sensing image, the first marked image and the second marked image and the dispute image, by using a Dempster criterion in an evidence theory, carrying out segmentation judgment, selecting a maximum m value corresponding to the corresponding pixel point of each dispute pixel point, and attributing the corresponding pixel point of the dispute pixel point to a corresponding category according to the maximum m value to obtain a final fusion segmentation result.
The conventional MRF segmentation method in S1 of the present invention includes the following steps:
acquiring an image to be segmented with pixels of NxM, segmenting the image into L regions, representing a pixel set of the image to be segmented by using S { (i, j) |1 ≦ i ≦ N,1 ≦ j ≦ M }, wherein (i, j) represents the position of a pixel point of the image to be segmented,
conventional MRF split packetThe method comprises an MRF model, wherein an image to be segmented is described by two random fields, and one random field is a label field X ═ XsI S belongs to S, and the local correlation of the pixels is described by prior distribution; another random field is the observation field Y ═ Ys| S ∈ S }, describing the distribution of the observed data by a conditional distribution function,
let Ω ═ x1,x2,...,xMN) Is the set of all possible segmentations, let δ ═ { δ (S) | S ∈ S } be the set of general neighborhood systems defined on S, which satisfy the following characteristics:
(1)
Figure BDA0003214220830000061
(2)
Figure BDA0003214220830000069
(3)
Figure BDA0003214220830000062
the position r belongs to the neighborhood of S called delta (S), the neighborhood set of S called delta (S), and different neighborhood structures exist in S, when the subset
Figure BDA0003214220830000063
Each pair of different positions in (a) is always adjacent, say c is a radical, common neighborhood types are four neighbors and eight neighbors, a label field X is called MRF with respect to δ, if and only if the following properties are satisfied:
①P(X＝x)＞0,
Figure BDA0003214220830000064
②
Figure BDA0003214220830000065
from the property @, the correlation between pixel labels depends on the neighborhood system defined on S;
estimating optimal labels from observation field Y
Figure BDA0003214220830000066
MRF method adopts maximum posterior probability MAP estimation to complete the segmentation of the image to be segmented, and converts the image segmentation problem into the solution of the maximum posterior probability problem, namely
Figure BDA0003214220830000067
According to bayes rule: pX|Y(x|y)＝PX(x)PY|X(y|x)/PY(y) the PY(y) is a constant, PX|Y(x | y) depends on PX(x)PY|XThe magnitude of the (y | x) value, MRF being equivalent to the Gibbs random field GRF, an MRF can be represented by a Gibbs distribution as PX(x)＝Z-1[exp(-U1(x)/T)]Wherein T is a constant, and the ratio of the T,
Figure BDA0003214220830000068
in order to be a normalization constant, the method comprises the following steps of,
Figure BDA0003214220830000071
to define a prior energy function over the set in δ, C is the set of radicals, Vc(x) Is defined as a potential energy function on a radical, said potential energy function being defined as
Figure BDA0003214220830000072
t represents a neighborhood pixel point with the pixel point s as a center point, xtNumber of labels, x, representing neighborhood pixelssThe label value of the pixel point is represented, wherein beta is larger than 0 and is a parameter defined on the space neighborhood potential group;
for the observation field model, the gray attribute of the image is described by a Gaussian function, and each index x is assumeds(xsE {1, 2.., L }) pixel gray-scale values are subject to a mean of
Figure BDA0003214220830000073
Standard deviation of
Figure BDA0003214220830000074
Gauss ofDistribution, its expression:
Figure BDA0003214220830000075
given a label field x, the likelihood energy function can be expressed as follows:
Figure BDA0003214220830000076
for expression
Figure BDA0003214220830000077
Taking logarithm on two sides to obtain
Figure BDA0003214220830000078
The best label field will be estimated finally
Figure BDA0003214220830000079
Is converted into a label field problem corresponding to the minimum global energy U (x, y), namely
Figure BDA00032142208300000710
The fuzzy MRF segmentation method is based on image segmentation of a Markov random field and fuzzy C-means clustering (FCM), and is realized by introducing the Markov random field on the basis of the FCM method and improving a target function. Each pixel in an image with N pixels is classified into a corresponding class (C-class), and the criterion of least square sum of errors of the samples and the mean of the classes is generally adopted. The FCM algorithm also utilizes this clustering concept. And is associated with fuzzy membership degree by searching clustering center VkAnd membership value muk(i, j) applying an objective function
Figure BDA00032142208300000711
Taking the minimum value. So as to realize the optimal clustering of the images and achieve the optimal segmentation. In the objective function formula, X (i, j) is the gray value of the image at the pixel point (i, j), μk(i, j) is the degree of membership, V, of the pixel point (i, j) belonging to the kth classkIs as followsAnd in order to simplify the problem, m is 2, and | | · | |, which is a certain distance measure, a standard Euclidean distance is adopted.
A priori probability is introduced into an objective function based on a Markov random field and a fuzzy C-means clustering method, the priori probability of a certain mark on a point (i, j) is P (i, j), and a neighborhood N of the point (i, j)(i,j)The denial of acceptance for this tag is (1-P (i, j)), abbreviated as denial. The prior probability is provided by the Gibbs model, and the neighborhood probability is introduced, so the rejection degree contains spatial information. The prior probability and the improved objective function are respectively as follows:
Figure BDA0003214220830000081
Figure BDA0003214220830000082
where β > 0 is a parameter defining a potential group in a neighborhood relationship, ni(l) Is a neighborhood NiThe number of nodes marked as l can be obtained according to the Lagrange extremum method:
Figure BDA0003214220830000083
the algorithm comprises the following specific steps:
(1) and (5) initially segmenting the image and providing initial parameter estimation for the algorithm.
(2) Calculating the prior probability P of each pixel point of the image belonging to various types according to the prior probability expression by using the hard segmentation resultk(i, j). In which β assumes a fixed value of 0.5.
(3) Updating the membership matrix mukj。
(4) Updating the clustering center Vk。
(5) And defuzzification is carried out according to the maximum membership principle, and the soft segmentation result is converted into a hard segmentation result.
(6) And (5) judging whether convergence occurs or not, if not, turning to the step (2), and otherwise, outputting a segmentation result.
Both traditional MRF and fuzzy MRF differ in detail concerns: in the implementation process of the traditional MRF method, each pixel is endowed with a hard label which belongs to hard judgment and easily causes information loss, and in the implementation process of the fuzzy MRF method, each pixel is endowed with the membership degree of each label which belongs to soft segmentation but possibly causes excessive segmentation, and the two are combined, so that the image segmentation effect can be effectively improved.
The method for generating the dispute image in the S2 includes the following steps:
s2.1, comparing a first marker image obtained by traditional MRF segmentation with a second marker image obtained by fuzzy MRF segmentation;
s2.2, taking pixel points with different segmentation results in the two images as dispute pixel points, and respectively extracting the dispute pixel points in the two images;
and S2.3, representing the gray value of the dispute pixel point by adopting the average value of the gray values of the neighborhood of the pixel point corresponding to the original remote sensing image of the dispute pixel point, and representing the gray value of the non-dispute pixel point by using the original gray value to generate a dispute image.
The fuzzy C-means clustering in S3 comprises the following steps:
the fuzzy C mean value cluster is marked as FCM, the FCM obtains the membership degree of each sample point in all class centers by optimizing a target function, and determines the membership degree of the sample points in all class centers so as to automatically classify the sample data; assigning a membership function belonging to each class to each sample, classifying the samples according to the membership value, wherein the class number is a class number,
fuzzy c-means clustering mainly comprises three key parameters, wherein a fixed number of clusters and a centroid of each cluster belong to a class corresponding to the closest centroid, the fuzzy c-means clustering obtains a clustering center by minimizing an objective function, and the objective function is the sum of Euclidean distances from each point to each class, namely the square sum of errors;
the clustering process is the process of minimizing the target function, the error value of the target function is gradually reduced through repeated iterative operation, when the target function is converged, the final clustering result can be obtained, and the expression of the target function is
Figure BDA0003214220830000091
Wherein m is the number of clusters, N is the number of samples, C is the number of cluster centers, CjRepresenting the jth cluster center, the same dimension as the sample feature, xiDenotes the ith sample, uijRepresents a sample xiTo the clustering center cjDegree of membership, i.e. xiBelong to cjProbability of, | | xi-cj||2Representing data xiAnd cjThe measure of similarity, which is the euclidean norm, also known as euclidean distance,
the degree of membership represents the degree to which each sample point belongs to each class, for a single sample xiThe sum of the membership degrees of each class is 1, the class with the largest membership degree of each sample point is judged to belong to which class, the closer to 1, the higher the membership degree is, and otherwise, the lower the membership degree is, and the formula of the membership degree is used for judging the class with which the sample point belongs
Figure BDA0003214220830000092
The clustering center ci of each group is calculated to minimize the objective function (since the objective function is related to euclidean distance, when the objective function is minimized, euclidean distance is shortest and similarity is highest), which ensures the clustering principle of highest similarity in the group and lowest similarity among the groups. The cluster center is formulated as
Figure BDA0003214220830000093
The method for acquiring the basic probability assignment in the S3 comprises the following steps:
s3.1, carrying out fuzzy C-means clustering on the image to obtain the membership mu of each pixel A to the kth classk，
S3.2, determining the basic probability assignment of each pixel A to each class label according to two conditions: single proposition and composite proposition, setting xi as a certain threshold value, muk1、μk2The membership degrees of the pixel point A to the k1 th and k2 th categories respectively;
s3.3, if μk1-μk2Determining the fuzzy clustering result as single if | ≧ xiProposition, directly obtaining the basic probability assignment m (A) of single proposition by using membership degreek1)＝μk1，m(Ak2)＝μk2；
S3.4, | μk1-μk2If | is less than xi, determining the fuzzy clustering result as a composite proposition, and determining the basic probability assignment by adopting the composite proposition, and then assigning the basic probability of the double composite proposition
Figure BDA0003214220830000101
In this embodiment, if an image is divided into 4 labels, the pixel points s are clustered by the fuzzy C-means to obtain the label 1 with the membership degree of mu1And 2 has a degree of membership of mu2And the membership degree of the label 3 is mu3And 4 has a degree of membership of mu4The threshold xi takes the value of 0.1, if mu1-μ2If | ≧ 0.1, determining the fuzzy clustering result as a single proposition, and directly obtaining the basic probability assignment m(s) of the single proposition by using the membership degree1)＝μ1，m(s2)＝μ2(ii) a If μ1-μ2If the absolute value is less than 0.1, determining the fuzzy clustering result as a composite proposition, and assigning the basic probability of the double composite proposition
Figure BDA0003214220830000102
The method for determining the membership degree of the pixel points included in the dispute image in the step S3 is as follows:
carrying out fuzzy C-means clustering on the original image to obtain a clustering center CjAccording to the membership degree formula, the gray value x of the dispute pixel point in the dispute image is calculatediAnd a cluster center cjSubstituting the value into a membership degree formula to obtain various membership degrees of pixel points contained in the dispute image.
The method for obtaining the final fusion segmentation result in S4 includes the following steps:
s4.1, obtaining two label images of an original remote sensing image, a first label image and a second label image and a four image of a dispute image, wherein each pixel of the four images corresponds to a basic probability assignment m of each label,
s4.2, calculating the combined basic probability assignment of each label of the dispute pixel point by using a Dempster combination rule, wherein the Dempster combination rule is as follows:
Figure BDA0003214220830000103
A. b, C, D and E represent different propositions, m1(B) Basic probability assignment of B propositions, m, representing original image2(C) Basic probability assignment of C proposition, m, representing first label image3(D) Basic probability assignment of D proposition, m, representing second label image4(E) A base probability assignment representing an E proposition of the dispute image, m (A) a combined base probability assignment representing an A proposition, k being a normalization constant;
and S4.3, comparing the combined basic probability assignment of each label of the dispute pixel point obtained in the step S4.2, screening out the label corresponding to the maximum combined basic probability assignment, and classifying the dispute pixel point as the label.
In order to verify the segmentation performance of the fusion segmentation algorithm based on the evidence theory on the remote sensing image, a real remote sensing image is selected for experiment. A building image in a Mercded Land Use Dataset scene classification Dataset is selected for verification through an experiment, the Mercded Land Use Dataset is a 21-class Land Use image Dataset used for research, each class comprises 100 images, the images are manually extracted from large images of a USGU national map urban area image set, and the images are used for urban areas all over the country. The pixel resolution of this published data set is about 0.3m, the size of each image is 256x256 pixels, the image categories are type a vegetation, type B ground, type C rooftop, type D rooftop,
fig. 3 to 6 show the segmentation reference data of the original image and the segmentation results obtained from the conventional MRF segmentation, the fuzzy MRF segmentation (FMRF), and the Dempster criterion (DS) in the evidence theory, respectively, from which it can be found that the three algorithms have better segmentation on the D-class rooftop, both the user precision and the producer precision reach over 90%, for the B-class ground, the MRF algorithm has better producer precision than the FMRF algorithm, but has poorer user precision, and the DS fusion segmentation algorithm fuses the respective advantages of the two algorithms, the DS fusion segmentation algorithm has higher user precision than the MRF segmentation algorithm, the user precision is improved by 0.89%, and the producer precision is improved by 16.05% compared with the FMRF algorithm. For the class c roof, the spectral information of the nearby roof is very similar to that of the ground, so that the class c roof and the ground are difficult to distinguish in the segmentation process, the MRF algorithm and the DS fusion segmentation algorithm have the condition of missing points, and the FMRF algorithm has the condition of wrong points. For A-type vegetation, the DS fusion segmentation algorithm also has the advantage of fusing two algorithms, and compared with the MRF algorithm, the precision of a producer is improved by 0.05%, and compared with the FMRF algorithm, the precision of a user is improved by 26.01%.
It is noted that, herein, relational terms such as first and second, and the like may be used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A remote sensing image segmentation method based on a Markov random field and an evidence theory is characterized by comprising the following steps:
s1, segmenting the original remote sensing image by adopting the traditional MRF segmentation to obtain a first marked image, and segmenting the original remote sensing image by adopting the fuzzy MRF segmentation to obtain a second marked image;
s2, comparing the first marked image with the second marked image, respectively extracting dispute pixel points and non-dispute pixel points in the two marked images, and generating a dispute image;
s3, fuzzy C-means clustering FCM is conducted on the original remote sensing image and the two labeled images including the first labeled image and the second labeled image respectively, various membership degrees of pixel points included in the dispute image are calculated through each clustering center of the original remote sensing image, and the assignment m of the basic probability of single propositions or composite propositions of the pixel points corresponding to the dispute pixel points in the four images including the original remote sensing image, the first labeled image and the second labeled image and the dispute image is determined according to a basic probability assignment obtaining method;
s4, fusing basic probability assignment m of single propositions or composite propositions of corresponding pixel points of dispute pixel points in the four images, namely the original remote sensing image, the first marked image and the second marked image and the dispute image, by using a Dempster criterion in an evidence theory, carrying out segmentation judgment, selecting a maximum m value corresponding to the corresponding pixel point of each dispute pixel point, and attributing the corresponding pixel point of the dispute pixel point to a corresponding category according to the maximum m value to obtain a final fusion segmentation result.
2. The method for segmenting the remote sensing image based on the Markov random field and the evidence theory as claimed in claim 1, wherein: the method for generating the dispute image in the S2 includes the following steps:
s2.1, comparing a first marker image obtained by traditional MRF segmentation with a second marker image obtained by fuzzy MRF segmentation;
s2.2, taking pixel points with different segmentation results in the two images as dispute pixel points, and respectively extracting the dispute pixel points in the two images;
and S2.3, representing the gray value of the dispute pixel point by adopting the average value of the gray values of the neighborhood of the pixel point corresponding to the original remote sensing image of the dispute pixel point, and representing the gray value of the non-dispute pixel point by using the original gray value to generate a dispute image.
3. The method for segmenting the remote sensing image based on the Markov random field and the evidence theory as claimed in claim 1, wherein: the fuzzy C mean clustering in the S3 is recorded as FCM, the FCM obtains the membership degree of each sample point in all class centers by optimizing a target function, and determines the membership degree of the sample points in all class centers so as to automatically classify the sample data; assigning a membership function belonging to each class to each sample, classifying the samples by the magnitude of the membership value,
fuzzy c-means clustering mainly has three key parameters, the cluster number, the center of each cluster and the class corresponding to the closest cluster center of each sample point, the fuzzy c-means clustering obtains the cluster center by minimizing an objective function, the objective function is the sum of Euclidean distances from each sample point to each class, namely the square sum of errors,
the fuzzy C-means clustering method in the S3 comprises the following steps:
s3-1, initializing parameters, setting a fuzzy weighting index m to be 2, initializing a clustering result by using a random number with a value from 1 to C, and initializing a clustering center by using the mean value of each class, wherein C is the clustering number;
s3-2, solving the membership degree according to a membership degree solving formula
Figure FDA0003214220820000021
M is a fuzzy weighting index, C is a clustering center number, CjDenotes the jth cluster center, xiRepresenting the gray value, u, of the ith sample, i.e. the ith dispute pixelijRepresents a sample xiTo the clustering center cjDegree of membership, i.e. xiBelong to cjThe degree of membership representing the degree to which each sample point belongs to each class, x for a single sampleiThe sum of the membership degrees of each class is 1;
s3-3, calculating the cluster centerUpdating the cluster centers by formula, namely evaluating all cluster centers by a cluster center formula respectively, and replacing the original values of the corresponding cluster centers with the values of the newly obtained cluster centers, wherein the cluster center formula is
Figure FDA0003214220820000022
N is the number of samples;
s3-4, obtaining an objective function, and judging whether the objective function is converged, wherein the objective function is
Figure FDA0003214220820000023
Wherein, the | | xi-cj||2Representing data xiAnd cjThe similarity measure is Euclidean norm, also called Euclidean distance;
when the target function is not converged, acquiring the updated clustering center in S3-3, and returning to S3-2 until the target function is converged;
s3-5, when the objective function is converged, acquiring the membership degree of all classes corresponding to each sample point in all sample points in the current state, judging the membership degree of all classes corresponding to each sample point, and judging which class the sample point belongs to if the membership degree of each class of each sample point is the maximum.
4. The method for segmenting the remote sensing image based on the Markov random field and the evidence theory as claimed in claim 1, wherein the method for obtaining the basic probability assignment in S3 comprises the following steps:
s3.1, carrying out fuzzy C-means clustering on the image to obtain the membership mu of each pixel A to the kth classk；
S3.2, determining the basic probability assignment of each pixel A to each class label according to two conditions: single proposition and composite proposition, setting xi as a certain threshold value, muk1、μk2The membership degrees of the pixel point A to the k1 th and k2 th categories respectively;
s3.3, if μk1-μk2Determining the fuzzy clustering result as a single life if | ≧ xiThe subject directly obtains the basic probability assignment m (A) of a single proposition by using the membership degreek1)＝μk1，m(Ak2)＝μk2；
S3.4, | μk1-μk2If | is less than xi, determining the fuzzy clustering result as a composite proposition, and determining the basic probability assignment by adopting the composite proposition, and then assigning the basic probability of the double composite proposition
Figure FDA0003214220820000031
5. The method for segmenting the remote sensing image based on the Markov random field and the evidence theory as claimed in claim 3, wherein the method for calculating the membership degree of the pixel points included in the dispute image in the step S3 is as follows:
carrying out fuzzy C-means clustering on the original image to obtain a clustering center CjAccording to the membership degree formula, the gray value x of the dispute pixel point in the dispute image is calculatediAnd a cluster center cjSubstituting the value into a membership degree formula to obtain various membership degrees of pixel points contained in the dispute image.
6. The method for segmenting the remote sensing image based on the Markov random field and the evidence theory as claimed in claim 4, wherein: the method for obtaining the final fusion segmentation result in S4 includes the following steps:
s4.1, obtaining two label images of an original remote sensing image, a first label image and a second label image and a four image of a dispute image, wherein each pixel of the four images corresponds to a basic probability assignment m of each label,
s4.2, calculating the combined basic probability assignment of each label of the dispute pixel point by using a Dempster combination rule, wherein the Dempster combination rule is as follows:
Figure FDA0003214220820000032
A. b, C, D and E represent different propositions, m1(B) Basic probability assignment of B propositions, m, representing original image2(C) Basic probability assignment of C proposition, m, representing first label image3(D) Basic probability assignment of D proposition, m, representing second label image4(E) A base probability assignment representing an E proposition of the dispute image, m (A) a combined base probability assignment representing an A proposition, k being a normalization constant;
and S4.3, comparing the combined basic probability assignment of each label of the dispute pixel point obtained in the step S4.2, screening out the label corresponding to the maximum combined basic probability assignment, and classifying the dispute pixel point as the label.
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