CN107895373B - Image segmentation method based on local region consistency manifold constraint MRF model - Google Patents

Image segmentation method based on local region consistency manifold constraint MRF model Download PDF

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CN107895373B
CN107895373B CN201711123155.4A CN201711123155A CN107895373B CN 107895373 B CN107895373 B CN 107895373B CN 201711123155 A CN201711123155 A CN 201711123155A CN 107895373 B CN107895373 B CN 107895373B
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CN107895373A (en
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徐胜军
宋丽君
熊福力
刘光辉
孟月波
王慧琴
史亚
胡高珍
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Xian University of Architecture and Technology
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Abstract

The invention discloses an image segmentation method based on a local region consistency manifold constraint MRF model, which is based on a PairwiseMRF model, an image segmentation model based on the local region MRF model is constructed on an expansion neighborhood of an MRF node, and the prior distribution of a local region effectively avoids the interference of noise or texture mutation; meanwhile, based on manifold learning theory, a manifold regular term under a probability framework is established, the prior of the complex local space geometric structure of the natural image is effectively described by utilizing the probability distribution of the local area, and the local space geometric structure described by the manifold learning is introduced into the local area MRF segmentation model. Experiments prove that compared with the prior method, the method disclosed by the invention not only avoids the over-smoothing punishment of local area prior, but also effectively keeps the local geometric structure information of image segmentation.

Description

Image segmentation method based on local region consistency manifold constraint MRF model
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to an image segmentation method.
Background
An image segmentation method based on a Markov Random Field (MRF) model is widely applied, and the segmentation method is based on local spatial correlation of image information, uses a two-dimensional Random Field model to describe feature information of an image, and enhances the correlation of structure information by the MRF-based image segmentation model, so that the speed and the precision of natural image segmentation are greatly improved, but for natural images with abundant statistical characteristics, the currently common point-to-point interaction structure-based MRF (pairwise MRF) model cannot sufficiently describe complex statistical information and prior knowledge of the natural images, and therefore, in the image segmentation problem, the point-to-point MRF-based image processing algorithm often has wrong segmentation in the regions or edges of the images.
The complex natural image usually has a high-dimensional non-gaussian statistical characteristic, and the prior knowledge of the image needs to be accurately constructed to model the dependency relationship of the image structure in an extended neighborhood. A brain MR image segmentation algorithm [ J ] automatic science report based on an image slice Markov random field, 2014(08): 1754-. Zhufeng et al [ Zhufeng, Luo Li Min, Song Yun Qing et al. ] image segmentation [ J ] based on adaptive spatial neighborhood information Gaussian mixture model computer research and development, 2011,48(11): 2000) plus 2007 ] establishes weighted distribution of neighborhood information through the median probability of pixels in a local region, can effectively suppress noise and maintain edges, but the median probability still cannot completely reflect the characteristic spatial relationship of the local region.
Although the conventional local area MRF-based method adopts a distance measurement mode, such as euclidean distance, K-L divergence, etc., to introduce spatial information of local areas of an image and to serve as a constraint on consistency of the local areas, in the euclidean space, a sample point which represents a short distance in the space is not necessarily the closest distance in the space where an object itself is located. Therefore, the local region MRF method using the distance measurement cannot effectively describe the global consistency characteristics of the complex high-dimensional data, resulting in the erroneous segmentation of the complex natural image.
Disclosure of Invention
The invention aims to provide an image segmentation method based on a local region consistency manifold constraint MRF model, which aims to solve the problem that the conventional region MRF image segmentation model based on the Euclidean space distance measurement technology cannot describe the global consistency characteristic of complex high-dimensional data; the invention can effectively improve the image segmentation effect.
In order to achieve the purpose, the invention adopts the following technical scheme:
the image segmentation method based on the local region consistency manifold constraint MRF model comprises the following steps:
step 1: inputting a natural image X to be segmented as X ═ X1,x2,…xN}；
Step 2: initializing parameters: segmentation class number K, local region prior Potts model parameter beta, Lagrange multiplier lambda and Gibbs sampling algorithm initial temperature T0；
And step 3: constructing a nearest neighbor graph G which represents the local geometric structure of the image data manifold, wherein V is a vertex set, E is an edge set, and W is a weight matrix of the graph G;
and 4, step 4: searching low-dimensional representation of manifold through graph embedding, projecting sample data in high-dimensional space complex distribution to low-dimensional space, establishing a dimension reduction mapping relation in a local area by utilizing the homomorphism of the manifold in the local area of an image and a Euclidean space, establishing a geometric structure relation representing the manifold in the low-dimensional space, and establishing a manifold regular term under a probability frame;
and 5: based on a pairwise MRF model, modeling the dependency relationship of an image structure on an expansion neighborhood, expressing more complex image region characteristics, and establishing a region-based MRF energy segmentation model; introducing a consistent manifold constraint term of a local area of the image by utilizing a Lagrange multiplier method to obtain a consistent manifold constraint MRF image segmentation model of the local area;
step 6: method for estimating GMM parameter of local region consistency manifold constraint MRF image segmentation model provided by the invention by adopting expectation maximization algorithm
Figure BDA0001467825490000021
And 7, optimizing the consistent manifold constraint MRF segmentation model of the local area by adopting a Gibbs sampling algorithm, and outputting an image segmentation result.
Further, step 2 specifically includes:
2a) let Ω ═ {1,2, …, K } denote the pixel node label space, and the segmentation class number K is determined manually;
2b) the prior Potts model parameter beta of the local region belongs to [0.1,5], and the Lagrangian multiplier lambda of the manifold consistency region constraint term of the local region belongs to [10,100 ];
2c) initial temperature T of Gibbs sampling algorithm0＝4.0。
Further, step 3 specifically includes:
given image observation sample set X ═ X1,x2,…xNConstructing a nearest neighbor graph G (V, E, W) representing a local geometric structure of an image data manifold in a sample space set X based on manifold learning theory, wherein V is a vertex set, E is an edge set, and W is a weight matrix of the graph G;
Figure BDA0001467825490000031
in the formula, Nk(xs) Is a sample point xsK neighbor set of (1), if xs∈Nk(xr) Or xr∈Nk(xs) Then sample point xsAnd xrIs two adjacent sample points with weight wsrAccording to the thermal kernel function representation method weight wsrThe definition is as follows:
Figure BDA0001467825490000032
wherein t is 5, which is a thermonuclear parameter.
Further, step 4 specifically includes:
4a) under the probabilistic framework, let the observation sample set X ═ { X1,x2,…xNThe corresponding implicit variable set is Y ═ Y1,y2,…yNIn which y iss∈{1,2,…K, wherein K is the total number of the segmentation categories;
4b) let the smooth insert fk(x) Is a conditional probability distribution p (y ═ k | x), i.e.:
Figure BDA0001467825490000035
4c) based on a spectrogram theory, utilizing Laplacian feature mapping, establishing a nearest neighbor graph describing the local geometric structure of the image based on the step 3, and then searching for low-dimensional representation of the manifold through graph embedding; local information measure S of the established conditional probability distribution p (y ═ k | x)kThe definition is as follows:
Figure BDA0001467825490000033
in the formula:
Figure BDA0001467825490000034
D(p(k|xs),p(k|xr))2representing two adjacent nodes xs,xrConditional probability distribution p (y) ofs|xs) And p (y)r|xr) The distance of (c).
Further, step 5 specifically includes the following steps:
5a) based on a pairwise MRF model, more complex image region characteristics are expressed by utilizing the dependency relationship of an image structure on an expansion neighborhood, and the established region-based MRF energy segmentation model is shown as the following formula:
Figure BDA0001467825490000041
Figure BDA0001467825490000042
in the formula: eDataRepresenting the likelihood energy term of the MRF model in the local region, p (x)s|ys,Θ)Indicates a given condition (y)sΘ) time node xsTheta is a parameter of the conditional likelihood distribution, deltasA set of neighborhood nodes representing a node s; eSmoothThe prior smoothing energy term of the MRF model is obtained, and beta is a prior parameter of the MRF; w is ar(ys,yr) As a weight function of the center node s and the neighborhood nodes r, a standard normal distribution function is described as follows:
Figure BDA0001467825490000043
in the formula:
Figure BDA0001467825490000044
representing a local area deltasA set of labels of neighborhood nodes with equal label values of the central node s is neutralized; i S (yr) I represents the set S (y)r) A potential of (d);
5b) based on the MRF global energy segmentation model of the established local region model, introducing a consistent manifold constraint term of the local region of the image by utilizing a Lagrange multiplier method to obtain the MRF image segmentation model of the consistent manifold constraint of the local region as shown in the following formula:
Figure BDA0001467825490000045
Figure BDA0001467825490000046
6. the image segmentation method based on the local region consistency manifold constraint MRF model according to claim 1, wherein the step 6 specifically comprises:
6a) initializing and estimating GMM parameters by adopting K-means algorithm
Figure BDA0001467825490000051
6b) Iterative estimation of GMM parameters using EM algorithm
Figure BDA0001467825490000052
The estimation formula is as follows:
Figure BDA0001467825490000053
Figure BDA0001467825490000054
Figure BDA0001467825490000055
wherein, | δsAnd | is the number of neighborhood nodes of the central node s.
And 7, optimizing the consistent manifold constraint MRF segmentation model of the local region by adopting a Gibbs sampling algorithm, and estimating an image segmentation result based on a Maximum A Posteriori (MAP) criterion. Further, step 7 specifically includes:
7a) setting the maximum iteration number t of the Gibbs sampling algorithmmaxInitial temperature T04.0, annealing speed 0.95;
7b) sampling a consistent manifold constraint MRF segmentation model of a local area by adopting a Gibbs sampling algorithm, wherein a node y corresponding to a central pixelsBased on maximum a posteriori criteria (MAP):
Figure BDA0001467825490000056
accept a new tag k according to the following probability:
Figure BDA0001467825490000057
in the formula (I), the compound is shown in the specification,
Figure BDA0001467825490000058
for estimated optimal label, ELocal(k) Local region energy given a central pixel label of k;
7c) calculating pointsGlobal energy of cut model
Figure BDA0001467825490000059
If it is not
Figure BDA00014678254900000510
Or a maximum number of iterations t is reachedmaxThen, then
Figure BDA00014678254900000511
Outputting a segmentation result; otherwise, the temperature T is reduced to 0.95T(t)Returning to step 7b) and continuing the iteration.
Compared with the prior art, the invention has the advantages that:
based on a Pairwise MRF model, an image segmentation model based on a local region MRF model is constructed in an extended neighborhood of an MRF node, and the prior distribution of a local region effectively avoids the interference of noise or texture mutation; meanwhile, based on manifold learning theory, manifold regular terms under a probability framework are established, the local area probability distribution is utilized to effectively describe the prior of the complex local space geometric structure of the natural image, and the local space geometric structure described by the manifold learning is introduced into the local area MRF segmentation model.
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FIG. 1 is a flow chart of the present invention;
FIG. 2 shows experimental results of an embodiment of the present invention; wherein FIG. 2(a) is a beach, mountain, and windsurf artwork; FIG. 2(b) shows the results of the beach, mountain, and windsurfing based on Pairwise MRF segmentation model; FIG. 2(c) shows the results of the segmentation of beach, mountain, and windsurfing based on the Local Space Adaptive MRF (LSAMLF) model; FIG. 2(d) shows the segmentation results of beacon, mountain, and windsurfing models proposed by the present invention.
Detailed Description
The present invention is further described in detail below with reference to the attached drawings so that those skilled in the art can implement the invention by referring to the description text.
Referring to fig. 1, an image segmentation method based on a local region consistency manifold constraint MRF model according to the present invention includes the following steps:
step 1: inputting a natural image X to be segmented as X ═ X1,x2,…xs…xN}，xsRepresenting a pixel;
step 2: initializing parameters: segmentation class number K, local region prior Potts model parameter beta, Lagrange multiplier lambda and Gibbs sampling algorithm initial temperature T0；
2a) Let Ω ═ {1,2, …, K } denote the pixel node label space, and the segmentation class number K is determined manually.
2b) In the embodiment of the invention, the prior Potts model parameter beta of the local region belongs to [0.1,5], and the Lagrangian multiplier lambda belongs to [10,100] of the constraint term of the manifold consistency region of the local region.
2c) Initial temperature T of Gibbs sampling algorithm in the embodiment of the invention0＝4.0。
And step 3: creating nearest neighbor graph describing local geometry of image
Given image observation sample set X ═ X1,x2,…xNBased on manifold learning theory, constructing nearest neighbor graph G (V, E, W) representing local geometric structure of image data manifold in sample space set X, wherein V is vertex set, E is edge set, W is weight matrix of graph G,
Figure BDA0001467825490000071
in the formula, Nk(xs) Is a sample point xsK neighbor set of (1), if xs∈Nk(xr) Or xr∈Nk(xs) Then sample point xsAnd xrIs two adjacent sample points with weight wsrAccording to the thermal kernel function representation method weight wsrThe definition is as follows:
Figure BDA0001467825490000072
wherein t is 5-20, which is a thermonuclear parameter.
And 4, step 4: establishing a manifold regular term under a probability framework:
4a) under the probabilistic framework, let the observation sample set X ═ { X1,x2,…xNThe corresponding implicit variable set is Y ═ Y1,y2,…yNIn which y issE {1,2, … K }, where K is the total number of segmentation classes.
4b) Let the smooth insert fk(x) Is a conditional probability distribution p (y ═ k | x), i.e.:
Figure BDA0001467825490000073
according to the manifold assumption that points close to each other in the manifold are most likely to belong to the same class, the conditional probability distributions p (y) of the two sample pointss|xs) And p (y)r|xr) It is also approximate, that is, in the implicit geometry of the marginal probability distribution p (X) of the observation sample set X, the conditional probability distribution p (y | ·) is smooth along the geodesic line.
4c) And (3) establishing a nearest neighbor graph describing the local geometric structure of the image based on the spectrogram theory by utilizing Laplacian feature mapping and then searching for a low-dimensional representation of the manifold through graph embedding. Thus, the sample data is projected to a low-dimensional space in a complex distribution of a high-dimensional space, a dimensionality reduction mapping relation is established locally by utilizing the homomorphism of the manifold in a local and Euclidean space, and a geometric structure relation expressing the manifold is established in the low-dimensional space. Local information measure S of the established conditional probability distribution p (y ═ k | x)kThe definition is as follows:
Figure BDA0001467825490000074
in the formula:
Figure BDA0001467825490000075
D(p(k|xs),p(k|xr))2representing two adjacent nodes xs,xrConditional probability distribution p (y) ofs|xs) And p (y)r|xr) The distance of (c).
Due to local information measure SkIs calculated along the shortest distance on the manifold and is therefore based on the local information measure SkThe measure of (a) more accurately reflects the prior information of the spatial distribution of the data.
And 5: establishing a local region consistency manifold constraint MRF segmentation model
5a) Based on a pairwise MRF model, more complex image region characteristics are expressed by utilizing the dependency relationship of an image structure on an expansion neighborhood, and the established region-based MRF energy segmentation model is shown as the following formula:
Figure BDA0001467825490000081
Figure BDA0001467825490000082
in the formula: eDataRepresenting the likelihood energy term of the MRF model in the local region, p (x)s|ysΘ) represents a given condition (y)sΘ) time node xsTheta is a parameter of the conditional likelihood distribution, deltasA set of neighborhood nodes representing a node s; eSmoothIs the prior smoothing energy term of the MRF model, and beta is the prior parameter of the MRF. w is ar(ys，yr) As a weight function of the center node s and the neighborhood nodes r, a standard normal distribution function is described as follows:
Figure BDA0001467825490000083
in the formula:
Figure BDA0001467825490000084
representing a local area deltasA set of labels of neighborhood nodes equal to the label value of the central node s; i S (yr) I represents the set S (y)r) The potential of (c).
5b) Based on the MRF global energy segmentation model of the established local region model, introducing a consistent manifold constraint term of the local region of the image by utilizing a Lagrange multiplier method to obtain the MRF image segmentation model of the consistent manifold constraint of the local region as shown in the following formula:
Figure BDA0001467825490000085
Figure BDA0001467825490000086
as can be seen from the above equation, the local region manifold constraint MRF image segmentation model includes three terms: (1) in the Gaussian distribution likelihood model with local area weight, the weight wr(ys，yr) Takes into account spatial information between similar pixels; (2) the prior distribution of the local area effectively avoids the interference of noise or texture mutation, and keeps some obvious local structures of the natural image; (3) regularization term
Figure BDA0001467825490000087
More complex high-dimensional manifold structure information is introduced for spatial geometry structure prior of local region probability distribution, and over-smooth punishment of local region prior is avoided. λ is a regularization term parameter that controls the complexity of the implicit geometric function in the probability distribution. Therefore, the model fully utilizes the gray information and the complex spatial structure information of the image, has good robustness on the noise and the texture mutation of the image, and keeps the detail characteristics of the image.
Step 6: parameter estimation for proposed models
6a) Initializing and estimating GMM parameters by adopting K-means algorithm
Figure BDA0001467825490000088
6b) Iterative estimation of GMM parameters using EM algorithm
Figure BDA0001467825490000091
The estimation formula is as follows:
Figure BDA0001467825490000092
Figure BDA0001467825490000093
Figure BDA0001467825490000094
wherein, | δsAnd | is the number of neighborhood nodes of the central node s.
Step 7, optimizing the proposed model by adopting a Gibbs sampling algorithm
7a) Setting the maximum iteration number t of the Gibbs sampling algorithmmaxInitial temperature T04.0, annealing speed 0.95.
7b) Sampling a local region consistency manifold constraint MRF segmentation model by adopting a Gibbs sampling algorithm, and performing MAP criterion
Figure BDA0001467825490000095
For the estimated optimal label, the node y corresponding to the central pixelsAccept a new tag k according to the following probability:
Figure BDA0001467825490000096
in the formula, ELocal(k) Local region energy given a central pixel label of k;
7c) computing global energy of a segmentation model
Figure BDA0001467825490000097
If it is not
Figure BDA0001467825490000098
(ε is a small threshold, typically 10-6) Or a maximum number of iterations t is reachedmaxThen, then
Figure BDA0001467825490000099
And outputting a segmentation result. Otherwise, the temperature T is reduced to 0.95T(t)Returning to step 7b) and continuing the iteration.
The effect of the present invention will be further described with reference to fig. 2.
FIG. 2(a) shows a natural image to be segmented, wherein three images from left to right are respectively segmented into 4 classes, 4 classes and 6 classes; FIG. 2(b) is the result of the Pairwise MRF based segmentation model; FIG. 2(c) is a segmentation result based on a Local Spatial Adaptive MRF (LSAMLF) model; FIG. 2(d) shows the segmentation result of the present invention.
From the comparison result of the segmentation experiment, the segmentation result based on the Pairwise MRF segmentation model is the worst, because the point pair interaction structure of the Pairwise MRF model is too simple, the region and the global prior of a complex image are difficult to effectively express, and the image segmentation result is greatly interfered by factors such as noise or texture mutation of the image. As shown in the segmentation result of the "beach" image in fig. 2(b), the segmentation regions such as "coconut leaf" and "sea water" have strong abrupt texture changes, so that the segmentation effect of the "coconut leaf" and "sea water" regions is poor, and partial erroneous segmentation occurs. In the segmentation result of the "mountain" image in fig. 2(b), the "grassland" and "rock" regions have significant segmentation noise. In the segmentation result of the "windsurfing" image in fig. 2(b), the segmentation of the "sea water" region has more segmentation speckle noise, and particularly, the upper half part of the "sail" has obvious segmentation errors. The LSAMRF segmentation model has the advantages that the region characteristics of the image are introduced and more image region information is contained, so that the model has better robustness to sudden changes of noise or texture signals, and the better image segmentation result reflects the superiority of the model. The segmentation results are respectively shown in fig. 2(c), and it can be seen from the segmentation results that the "coconut leaf" and "sea water" of the "beach" image, "grassland" and "rock" region of the "mountain" image, "sea water" region of the "windsurfing" image, etc. have a smoother segmentation effect, and the upper half of the "sail" in the "windsurfing" image can be segmented more correctly, but because of the solution process of the region MRF model, the energy minimization of the local region easily causes the "sitting competition" phenomenon, which causes the phenomenon of "edge band" at the segmentation edge of some images, as shown in the "mountain" image segmentation result of fig. 2(c), an edge band appears between the "sky" and "mountain". The model provided by the invention firstly considers the spatial information among similar pixels by using the local spatial adaptive GMM, effectively avoids the interference of noise or texture mutation, and avoids the prior over-smooth punishment of a conventional local area; then, a local manifold constraint term of the image is established, complex space geometric structure prior of a local area is effectively described, and some obvious local structures of a natural image are kept. From the image segmentation result, the model provided by the invention effectively solves the edge banding phenomenon of the image segmentation result of "mountain" in fig. 2(c), and in the image segmentation result of "windsurfing" in fig. 2(a), the model not only has better robustness in the segmentation of the "ocean" region, but also keeps some detail features of the image, such as the "horizontal handle" in the "windsurfing" image, and is effectively extracted. Therefore, the model provided by the invention fully utilizes the gray information and the complex spatial structure information of the image, has good robustness on the noise and the texture mutation of the image, and keeps the detail characteristics of the image.

Claims (7)

1. The image segmentation method based on the local region consistency manifold constraint MRF model is characterized by comprising the following steps of:
step 1: inputting a natural image X to be segmented as X ═ X1,x2,…xN}；
Step 2: initializing parameters: number of segmentation class K, local area priorInitial temperature T of Potts model parameter beta, Lagrange multiplier lambda and Gibbs sampling algorithm0；
And step 3: constructing a nearest neighbor graph G which represents the local geometric structure of the image data manifold, wherein V is a vertex set, E is an edge set, and W is a weight matrix of the graph G;
and 4, step 4: searching low-dimensional representation of manifold through graph embedding, projecting sample data in high-dimensional space complex distribution to low-dimensional space, establishing a dimension reduction mapping relation in a local area by utilizing the homomorphism of the manifold in the local area of an image and a Euclidean space, establishing a geometric structure relation representing the manifold in the low-dimensional space, and establishing a manifold regular term under a probability frame;
and 5: based on a pairwise MRF model, modeling the dependency relationship of an image structure on an expansion neighborhood, expressing more complex image region characteristics, and establishing a region-based MRF energy segmentation model; introducing a consistent manifold constraint term of a local area of the image by utilizing a Lagrange multiplier method to obtain a consistent manifold constraint MRF image segmentation model of the local area;
step 6: method for estimating GMM parameter of local region consistency manifold constraint MRF image segmentation model provided by the invention by adopting expectation maximization algorithm
Figure FDA0002903294760000011
And 7, optimizing the consistent manifold constraint MRF segmentation model of the local area by adopting a Gibbs sampling algorithm, and outputting an image segmentation result.
2. The image segmentation method based on the local region consistency manifold constraint MRF model according to claim 1, wherein the step 2 specifically comprises:
2a) let Ω ═ {1,2, …, K } denote the pixel node label space, and determine the segmentation class number K;
2b) the prior Potts model parameter beta of the local region belongs to [0.1,5], and the Lagrangian multiplier lambda of the manifold consistency region constraint term of the local region belongs to [10,100 ];
2c) initial temperature of Gibbs sampling algorithmT0＝4.0。
3. The image segmentation method based on the local region consistency manifold constraint MRF model according to claim 2, wherein the step 3 specifically comprises:
giving a natural image X to be segmented as X1,x2,…xNConstructing a nearest neighbor graph G (V, E, W) representing a local geometric structure of an image data manifold in a natural image X to be segmented based on manifold learning theory, wherein V is a vertex set, E is a side set, and W is a weight matrix of the graph G;
Figure FDA0002903294760000021
in the formula, Nk(xs) Is a sample point xsK neighbor set of (1), if xs∈Nk(xr) Or xr∈Nk(xs) Then sample point xsAnd xrIs two adjacent sample points with weight wsrAccording to the thermal kernel function representation method weight wsrThe definition is as follows:
Figure FDA0002903294760000022
wherein t is 5, which is a thermonuclear parameter.
4. The image segmentation method based on the local region consistency manifold constraint MRF model according to claim 3, wherein the step 4 specifically comprises:
4a) under a probability framework, a natural image X to be segmented is made to be { X ═ X1,x2,…xNThe corresponding implicit variable set is Y ═ Y1,y2,…yNIn which y iss∈{1,2,…K}；
4b) Let the smooth insert fk(x) Is a conditional probability distribution p (y ═ k | x), i.e.：
Figure FDA0002903294760000023
4c) Based on a spectrogram theory, utilizing Laplacian feature mapping, establishing a nearest neighbor graph describing the local geometric structure of the image based on the step 3, and then searching for low-dimensional representation of the manifold through graph embedding; local information measure S of the established conditional probability distribution p (y ═ k | x)kThe definition is as follows:
Figure FDA0002903294760000031
in the formula:
Figure FDA0002903294760000032
D(p(k|xs),p(k|xr))2representing two adjacent nodes xs,xrConditional probability distribution p (y) ofs|xs) And p (y)r|xr) The distance of (c).
5. The image segmentation method based on the local region consistency manifold constraint MRF model according to claim 4, wherein the step 5 specifically comprises the following steps:
5a) based on a pairwise MRF model, more complex image region characteristics are expressed by utilizing the dependency relationship of an image structure on an expansion neighborhood, and the established region-based MRF energy segmentation model is shown as the following formula:
Figure FDA0002903294760000033
in the formula: eDataRepresenting the likelihood energy term of the MRF model in the local region, theta being a parameter of the conditional likelihood distribution, deltasA set of neighborhood nodes representing a node s; eSmoothIs the a priori smoothed energy term of the MRF model,beta is a prior parameter of MRF; w is ar(ys,yr) As a weight function of the center node s and the neighborhood nodes r, a standard normal distribution function is described as follows:
Figure FDA0002903294760000034
in the formula:
Figure FDA0002903294760000035
representing a local area deltasA set of labels of neighborhood nodes with equal label values of the central node s is neutralized; i S (y)r) I denotes the set S (y)r) A potential of (d);
5b) based on the MRF global energy segmentation model of the established local region model, introducing a consistent manifold constraint term of the local region of the image by utilizing a Lagrange multiplier method to obtain the MRF image segmentation model of the consistent manifold constraint of the local region as shown in the following formula:
Figure FDA0002903294760000041
6. the image segmentation method based on the local region consistency manifold constraint MRF model according to claim 5, wherein the step 6 specifically comprises:
6a) initializing and estimating GMM parameters by adopting K-means algorithm
Figure FDA0002903294760000042
6b) Iterative estimation of GMM parameters using EM algorithm
Figure FDA0002903294760000043
The estimation formula is as follows:
Figure FDA0002903294760000044
Figure FDA0002903294760000045
Figure FDA0002903294760000046
wherein, | δsAnd | is the number of neighborhood nodes of the central node s.
7. The image segmentation method based on the local region consistency manifold constraint MRF model according to claim 6, wherein the step 7 specifically comprises:
7a) setting the maximum iteration number t of the Gibbs sampling algorithmmaxInitial temperature T04.0, annealing speed 0.95;
7b) sampling a consistent manifold constraint MRF segmentation model of a local area by adopting a Gibbs sampling algorithm, wherein a node y corresponding to a central pixelsAccept a new tag k according to the following probability:
Figure FDA0002903294760000051
in the formula, ELocal(k) Local region energy given a central pixel label of k;
7c) computing global energy of a segmentation model
Figure FDA0002903294760000052
If it is not
Figure FDA0002903294760000053
Or a maximum number of iterations t is reachedmaxThen, then
Figure FDA0002903294760000054
Output ofDividing a result; otherwise, the temperature T is reduced to 0.95T(t)Returning to step 7b) and continuing the iteration.
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