CN101699513A - Level set polarization SAR image segmentation method based on polarization characteristic decomposition - Google Patents

Abstract

A level set polarization SAR image segmentation method based on polarization characteristic decomposition, belonging to the radar remote sensing technology or the image processing technology. In the invention, a polarization characteristic vector v which is composed of three polarization characteristics: H, alpha and A is obtained by the polarization characteristic decomposition of each pixel point of the original polarization SAR image; the polarization characteristic vectors v of all the pixel points are combined into a polarization characteristic matrix omega so as to convert the segmentation problem of the polarization SAR image from data space to polarization characteristic vector space; and the condition that the characteristic vector definition is suitable for energy functional of the polarization SAR image segmentation is utilized and a level set method is adopted to realize the numerical value solution of partial differential equation, thus realizing the polarization SAR image segmentation. The method provided by the invention takes full use of the polarization information of the polarization SAR image; therefore, the image edge obtained by segmentation is relatively complete so that the local characteristic is maintained better, the robustness for noise is stronger, the stability of the arithmetic is higher and the segmentation result is accurate; and the invention reduces the complexity of data and can effectively improve the image segmentation speed.

Description

A kind of level set polarization SAR image segmentation method that decomposes based on polarization characteristic

Technical field

The invention belongs to radar remote sensing or image processing techniques, promptly use image processing techniques Analysis of Radar observation information, be specifically related to the application of Level Set Method in polarimetric synthetic aperture radar (SAR) image segmentation.

Background technology

Polarization information is a kind of important information resource in the radar echo signal, and full spectrum of threats that faces and the acquisition of signal ability that improves radar have crucial meaning to solving current radar for it.Than traditional synthetic aperture radar (SAR), polarization SAR obtains a multiple scattering matrix by the combination of multiple polarization emission and polarization receiving antenna to each scattering unit, thereby has obtained the more target scattering information of horn of plenty.Along with the continuous development of complete polarization SAR theory, full polarimetric SAR is carried out decipher become in recent years research focus, and image segmentation (or classification) is a wherein very crucial step.Because the influence of serious coherent speckle noise, the polarization SAR image to cut apart (or classification) very difficult.Often need to determine empirical value when the polarization SAR image being cut apart (or classification) based on the edge detection method of local with based on the clusters of pixels method, very easily be subjected to the influence of coherent speckle noise, lack dirigibility and robustness, often can not form continuous border, also can't obtain effective area information, the object of same coordinate position often is divided into plurality of classes.Though can improve classification results by image pre-service (polarization filtering processing) and aftertreatment, can not fundamentally address the above problem.Though the methods such as zone merging based on area information can reduce The noise, segmentation result is subjected to the influence of initial over-segmentation, and segmentation result is independently single zone, can not really accomplish the atural object of same classification is divided into a class.

Level Set Method can overcome the number of drawbacks of traditional images dividing method, thereby is introduced in the cutting apart among the application of SAR image.Utilize Level Set Method research SAR image segmentation problem, can effectively utilize the probability model of coherent speckle noise, make full use of the image self-information, simultaneously because Level Set Method generally uses the symbolic distance function as the level set curved surface that develops, can express border and zone naturally, thereby the inherent structural information that has comprised image also can automatically be handled for the change in topology in zone, can obtain better segmentation effect.For general SAR image, the level set dividing method utilizes usually and mixes statistical model that Gamma distributes and construct the energy functional number that level set cuts apart and can obtain segmentation effect preferably.But for the polarization SAR image, because data mode is very complicated, and comprise important image feature information---polarization information, and therefore present existing Level Set Method can not directly apply to cutting apart of polarization SAR image all less than the utilization of considering polarization information.People such as I.B.Ayed have proposed a kind of Level Set Method that can be applicable to the polarization SAR image segmentation.This method is directly handled scattering matrix or coherence matrix, utilizes the target covariance matrix of polarization data and the multiple Wishart distribution of coherence matrix obedience to set up the energy function of image segmentation and utilized Level Set Method to find the solution.Because target covariance matrix and coherence matrix have comprised whole polarization informations, therefore this method is comparatively abundant to the utilization of polarization information, but its shortcoming also is very tangible, because target covariance matrix and coherence matrix all are one 3 * 3 complex matrix at each data point place, therefore its mathematical derivation and computing are very complicated, particularly along with the increase of data volume, it is more obvious that this shortcoming will become.People such as Cloude have proposed the another kind of characterizing method-H-α feature decomposition method of polarization characteristic, can obtain three important invariable rotary polarization characteristic parameters by decomposing: scattering entropy H, average scattering angle α and anti-entropy A, they have described the scattering properties of polarization SAR scene from different aspects.

Summary of the invention

The objective of the invention is in order to overcome the weak point of existing polarization SAR image segmentation method, to improve the accuracy of polarization SAR image segmentation, the spy provides a kind of level set polarization SAR image segmentation method that decomposes based on polarization characteristic.The basic ideas of this method are to utilize the relevant decomposition of polarization complex data to obtain polarization characteristic: scattering entropy H, average scattering angle α and anti-entropy A and with its composition characteristic vector, utilize the eigenvector definition to be applicable to the energy functional number of polarization SAR image segmentation, thereby the polarization SAR characteristics of image can be described accurately, adopt Level Set Method to realize the numerical solution of partial differential equation, thereby realize accurately cutting apart of polarization SAR image.

Detailed technology scheme of the present invention is as follows:

A kind of level set polarization SAR image segmentation method that decomposes based on polarization characteristic as shown in Figure 1, may further comprise the steps:

Step 1:, do following processing at each pixel in the original polarization SAR image:

Step 1-1:, calculate the polarization coherence matrix T of this pixel according to the polarization scattering matrix S of single pixel in the original polarization SAR image.

The data of each pixel are multiple scattering matrix, the generally form that can be expressed as of target in the full polarimetric SAR:

, wherein: s _HhBe Vertical Launch and the vertical polarization components that receives, s _HvBe the polarization components that Vertical Launch and level receive, s _VhBe level emission and the vertical polarization components that receives, s _VvIt is the polarization components that level emission and level receive.Using the Pauli base decomposes scattering matrix S and obtains the Polarization scattering vector and be

K can generate the polarization coherence matrix by the Polarization scattering vector:

$T=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{k}_i{k_i}^H=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{T}_i$

Wherein L is the number of looking of polarization SAR image, k _iIt is the Scattering of Vector that i looks.

Step 1-2: the polarization coherence matrix T that obtains among the step 1-1 is carried out characteristic value decomposition.

T carries out characteristic value decomposition to the resulting polarization coherence matrix of step 1-1:

$T=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{u}_i{u}_i^T$

Wherein

Be the unit character vector after the polarization coherence matrix T process Hermite orthogonalization, λ _iFor the eigenwert of polarization coherence matrix T and satisfy λ ₁〉=λ ₂〉=λ ₃, α _iThe scattering signatures of expression target, β _iBe target direction angle, φ _i, δ _iAnd γ _iPhasing degree for target.On the basis of feature decomposition, calculate polarization entropy H, average scattering angle α and anisotropy A:

$H=-\underset{i=0}{\overset{3}{\mathrm{\Σ}}}{p}_i{\log }_3{p}_i;$ $\mathrm{\α}=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{p}_i{\mathrm{\α}}_i;$ $A=\frac{{\mathrm{\λ}}_2-{\mathrm{\λ}}_3}{{\mathrm{\λ}}_2+{\mathrm{\λ}}_3};$

Wherein Polarization entropy H, average scattering angle α and anisotropy A that decomposition is obtained are combined into polarization characteristic vector v=[H α A] ^T

Step 2: the polarization characteristic vector v of each pixel of step 1 gained is combined by each pixel corresponding coordinate position in original polarization SAR image, obtain a polarization characteristic matrix Ω.

Step 1 is decomposed three polarization characteristic H, α obtaining and the atural object characteristic and the structure of A and observation scene is closely related, and the diverse location of polarization characteristic vector in feature space at different coordinates place characterized the atural object classification that this pixel belongs in the polarization SAR image.Polarization characteristic matrix Ω can be regarded as the vector image that a width of cloth has three passages (H, α and A), each pixel is the polarization characteristic vector v of a three-dimensional.By the relevant combination of decomposing with polarization characteristic that polarizes, thereby the polarization SAR image is transformed into feature space by data space, thereby the segmentation problem of polarization SAR image is converted into pattern classification problem at the polarization characteristic vector space.Utilized the polarization information of polarization SAR image so on the one hand preferably, avoided direct polarization scattering matrix S to handle on the other hand, can accelerate the speed of image segmentation for complexity.

Step 3: according to step 2 gained polarization characteristic matrix Ω, in conjunction with the energy functional E of C-V active contour parted pattern calculating about polarization characteristic matrix Ω.

For the dual area situation, have:

E＝μE _o+E _i；

And

$E_o=\∫{\∫}_{\mathrm{\Ω}}\mathrm{\δ}\left(\mathrm{\φ}(x,y)\right)|\▿\mathrm{\φ}(x,y)|\mathrm{dxdy};$

$E_i={\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v-v_1\left|\right|}^2\right)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+{\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v-v_2\left|\right|}^2\right)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy};$

Wherein || || be vector norm; μ is the weighting coefficient of border energy term, gets the number between [0.1,0.5] usually; φ () is a level set function, and curve is cut apart in the null set representative of level set function φ (); V is the polarization characteristic vector, v ₁, v ₂Be respectively the mean value vector of cutting apart the inside and outside polarization characteristic vector v of curve, and:

$v_1=\frac{{\∫}_{\mathrm{\Ω}}v(x,y)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}},$ $v_2=\frac{{\∫}_{\mathrm{\Ω}}v(x,y)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}};$

H () is the Heaviside function; δ () is the Dirac function; It is the image gradient operator; M is the dimension of polarization characteristic vector v, M=3 here.

For the multizone situation, have:

$E=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{E}_n=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}(\mathrm{\μ}{E}_o^n+E_i^n)$

And

$E_o^n={\∫\∫}_{\mathrm{\Ω}}\mathrm{\δ}\left({\mathrm{\φ}}_n\right)|\▿{\mathrm{\φ}}_n|\mathrm{dxdy};$

$E_i^n=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v-v_n\left|\right|}^2\right)H_n({\mathrm{\φ}}_1,{\mathrm{\φ}}_2,\·\·\·,{\mathrm{\φ}}_n)\mathrm{dxdy}+{\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v{-v}_{N+1}\left|\right|}^2\right)H_{N+1}({\mathrm{\φ}}_1,{\mathrm{\φ}}_2,...{\mathrm{\φ}}_N)\mathrm{dxdy}$

Wherein || || be vector norm; μ is the weighting coefficient of border energy term, gets the number between [0.1,0.5] usually; φ _n() is level set function, level set function φ _nOn behalf of the n bar, () null set cut apart curve; V is the polarization characteristic vector, v _nBe the mean value vector that the n bar is cut apart the polarization characteristic vector v of curve inside, and:

$v_n=\frac{{\∫}_{\mathrm{\Ω}}v(x,y)H\left({\mathrm{\φ}}_n(x,y)\right)\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}H\left({\mathrm{\φ}}_n(x,y)\right)\mathrm{dxdy}};$

H () is the Heaviside function; δ () is the Dirac function;

It is the image gradient operator; M is the dimension of polarization characteristic vector v, M=3 here; N is level set function φ _nThe quantity of ();

H _n(φ ₁，φ ₂，...φ _n)＝H(-φ ₁)H(-φ ₂)...H(-φ _n-1)H(φ _n)；

H′ _N(φ ₁，φ ₂，...φ _N)＝H(-φ ₁)H(-φ ₂)...H(-φ _N-1)H(-φ _N)；n＝1，2...N

Step 4: the employing variational method minimizes the energy functional E of step 3 gained, obtains the EVOLUTION EQUATION of level set function.

For the dual area situation, according to the energy functional E of step 3 gained, by variational principle Obtain the EVOLUTION EQUATION (being the active contour EVOLUTION EQUATION) of level set function by the minimization of energy functional:

Wherein,

Be the curvature of object boundary curve, t is a time variable.

For the multizone situation, according to the energy functional E of step 3 gained, by variational principle

Obtain the EVOLUTION EQUATION of level set function by the minimization of energy functional:

$\frac{{\∂\mathrm{\φ}}_n}{\∂t}=-\frac{\∂E}{\∂{\mathrm{\φ}}_n}=\mathrm{\δ}\left({\mathrm{\φ}}_n\right)[\mathrm{\μ}{K}_n+H(-{\mathrm{\φ}}_1)H(-{\mathrm{\φ}}_2)\·\·\·H(-{\mathrm{\φ}}_{n-1})(-{\mathrm{\ρ}}_n+{\mathrm{\ξ}}_n)],$

Wherein: t is a time variable; 1≤n≤N;

Be the curvature of object boundary curve;

ξ _n=H (φ _N+1) ρ _N+1+ H (φ _N+1) H (φ _N+2) ρ _N+2+ ...+H (φ _N+1) H (φ _N+2) ... H (φ _N-1) H (φ _N) ρ _N

Step 5: the level set function EVOLUTION EQUATION to step 4 gained is carried out numerical solution, obtains final image segmentation curve.

For the dual area situation, in solution procedure, the iterative process of level set function is: For the multizone situation, the iterative process of each level set function is:

N=1 wherein, 2..., N; Δ t is the time variable of discretize, gets the value between [1,5] usually.

When

(ε is that value is [0.001,0.01] between threshold value) or the iterations of level set function reaches setting value D, and (the common span of D is [50,200] in the time of), stop the iteration of level set function, this moment, the null set of level set function was final image segmentation curve.

Step 6: utilize the final image segmentation curve of step 5 gained that original polarization SAR image is cut apart, obtain final polarization SAR image segmentation result.

Core of the present invention is to combine polarization information to realize accurately cutting apart of polarization SAR image in level set image segmentation method.By being decomposed, the polarization characteristic of original each pixel of polarization SAR view data obtains the polarization characteristic vector v that constitutes by H, α and three polarization characteristics of A, polarization characteristic vector v with all pixels is combined into polarization characteristic matrix Ω then, thereby the segmentation problem of polarization SAR image is transformed into the polarization characteristic vector space by data space, reach the purpose of fully effectively utilizing polarization characteristic, can real polarization SAR image accurately cut apart.Meanwhile, when having kept polarization characteristic, reduce complexity of data, can effectively improve image segmentation speed.With compare based on the analytical approach of pixel cluster, the image border that utilizes the polarization SAR image segmentation method of level set to obtain is more complete, the characteristic of retaining zone has stronger robustness for noise better.And the employing of Level Set Method is converted into the process of non-plane motion with curvilinear motion, even object boundary division or merge in image segmentation, the topological structure of curved surface does not change, and algorithm stability is higher.Illustrate that thus advantage of the present invention is more outstanding, be applicable to the dividing processing of polarization SAR image.

Description of drawings

Fig. 1 is the process flow diagram of polarization SAR image segmentation method of the present invention.

Fig. 2 adopts this method and the operation time of the polarization SAR image segmentation method that distributes based on Wishart to compare.

Embodiment

The present invention is described further below in conjunction with accompanying drawing and embodiment.

Experimental data is area, San Francisco full polarimetric SAR that the airborne L-band STR_C/X of NASA-JPL system obtained in November, 1994, and this image is widely used among polarization SAR image classification/split-run test.This image mainly is made up of three major types atural object: ocean, city and vegetation region, wherein the city is divided into dense city and sparse city again, in addition, can also see the Gold Gate Bridge on the bay.This image is handled according to technical solution of the present invention step 1 and step 2, can obtain scattering entropy H, the average scattering angle α of this image and image and the polarization characteristic matrix Ω of anti-entropy A, wherein less entropy appears at the sea area, the entropy of urban area shows as the characteristics that height interweaves, and the vegetation area then shows bigger scattering entropy.Mainly by each regional scattering mechanism decision, tranquil ocean surface is mainly the Bragg diffraction model that is similar to in-plane scatter, the Polarization scattering randomness minimum of this model for this; Vegetation is that main zone mainly is the volume scattering model, the randomness maximum of its Polarization scattering; The situation of urban architecture object area is more complicated then, though the scattering of buildings mainly is the even scattering that is similar to dihedral angle, but owing to be located the varied of direction, and be studded with some plants in the city, so the Polarization scattering entropy of such kind of area can show various variation.The alpha parameter in area, ocean is comparatively even, and numerical value approaches zero; City and vegetation area have comprised higher alpha parameter value.Anti-entropy A has reflected the scattering unevenness of target, is an important supplement of H parameter, and special under the situation of higher scattering entropy, analysis has bigger help to target scattering characteristics for it.

Adopt method of the present invention, can obtain the segmentation result of this image.Therefore this image defines two level set functions because main atural object classification is three classes, can see that two evolution curves become three zones with image segmentation.Segmentation result and actual atural object are compared, and the present invention well has been partitioned into three kinds of different type of ground objects zones, and is consistent with actual conditions, and it is comparatively accurately complete to cut apart the edge that obtains.Wherein the Gold Gate Bridge is divided into and the same classification of urban district buildings, and two main street are also split preferably in the urban district.For cutting apart of city, because the city on the image left side is the building dense district, and the urban area on the right is sparse construction area, wherein comprised more vegetation, therefore the urban area on the left side has obtained dividing preferably, and the city on the right has also obtained in the zone of buildings comparatively dense dividing preferably.This has illustrated that this method has comparatively careful separating capacity.

Fig. 2 be this method with the computing velocity of the level set polarization SAR image segmentation method that distributes based on Wishart relatively, the advantage of this method on computing velocity as can be seen therefrom.Because the method that distributes based on Wishart is directly to handle the polarization SAR data in the energy functional of image segmentation, the data that is to say its processing are one 3 * 3 complex matrix at each pixel place, this not only causes it very complicated when the derivation of curve evolvement equation, also causes increase significantly its operation time simultaneously.Can see, increase along with picture size, its, curve had than the bigger slope of this method curve operation time operation time, and that is to say will increase operation time more fast, thus make the big shortcoming of its operand its get more obvious in image appearance of handling large-size.

Claims (4)

1. level set polarization SAR image segmentation method that decomposes based on polarization characteristic may further comprise the steps:

Step 1:, do following processing at each pixel in the original polarization SAR image:

Step 1-1:, calculate the polarization coherence matrix T of this pixel according to the polarization scattering matrix S of single pixel in the original polarization SAR image;

The data of each pixel are multiple scattering matrix, the generally form that can be expressed as of target in the full polarimetric SAR:

Wherein: s _HhBe Vertical Launch and the vertical polarization components that receives, s _HvBe the polarization components that Vertical Launch and level receive, s _VhBe level emission and the vertical polarization components that receives, s _VvIt is the polarization components that level emission and level receive; Using the Pauli base decomposes scattering matrix S and obtains the Polarization scattering vector and be

K can generate the polarization coherence matrix by the Polarization scattering vector:

$T=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{k}_i{k_i}^H=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{T}_i$

Wherein L is the number of looking of polarization SAR image, k _iIt is the Scattering of Vector that i looks;

Step 1-2: the polarization coherence matrix T that obtains among the step 1-1 is carried out characteristic value decomposition;

T carries out characteristic value decomposition to the resulting polarization coherence matrix of step 1-1:

$T=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{\mathrm{\λ}}_i{u}_i{u}_i^T$

Wherein

Be the unit character vector after the polarization coherence matrix T process Hermite orthogonalization, λ _iFor the eigenwert of polarization coherence matrix T and satisfy λ ₁〉=λ ₂〉=λ ₃, α _iThe scattering signatures of expression target, β _iBe target direction angle, φ _i, δ _iAnd γ _iPhasing degree for target; I=1,2,3; On the basis of feature decomposition, calculate polarization entropy H, average scattering angle α and anisotropy A:

$H=-\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{p}_i{\log }_3{p}_i;$ $\mathrm{\α}=\underset{i=1}{\overset{3}{\mathrm{\Σ}}}{p}_i{\mathrm{\α}}_i;$ $A=\frac{{\mathrm{\λ}}_2-{\mathrm{\λ}}_3}{{\mathrm{\λ}}_2+{\mathrm{\λ}}_3};$

Wherein Polarization entropy H, average scattering angle α and anisotropy A that decomposition is obtained are combined into polarization characteristic vector v=[H α A] ^T

Step 2: the polarization characteristic vector v of each pixel of step 1 gained is combined by each pixel corresponding coordinate position in original polarization SAR image, obtain a polarization characteristic matrix Ω;

Step 3: according to step 2 gained polarization characteristic matrix Ω, in conjunction with the energy functional E of C-V active contour parted pattern calculating about polarization characteristic matrix Ω;

For the dual area situation, have:

E＝μE _o+E _i；

And

$E_o={\∫\∫}_{\mathrm{\Ω}}\mathrm{\δ}\left(\mathrm{\φ}(x,y)\right)|\▿\mathrm{\φ}(x,y)|\mathrm{dxdy};$

$E_i={\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v-v_{\mathrm{out}}\left|\right|}^2\right)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}+{\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v-v_{\mathrm{in}}\left|\right|}^2\right)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy};$

Wherein || || be vector norm; μ is the weighting coefficient of border energy term; φ () is a level set function, and curve is cut apart in the null set representative of level set function φ (); V is the polarization characteristic vector, v ₁, v ₂Be respectively the mean value vector of cutting apart the inside and outside polarization characteristic vector v of curve, and:

$v_1=\frac{{\∫}_{\mathrm{\Ω}}v(x,y)H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}(x,y)\right)\mathrm{dxdy}},$ $v_2=\frac{{\∫}_{\mathrm{\Ω}}v(x,y)(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}(1-H\left(\mathrm{\φ}(x,y)\right))\mathrm{dxdy}};$

H () is the Heaviside function; δ () is the Dirac function; It is the image gradient operator; M is the dimension of polarization characteristic vector v, M=3 here;

For the multizone situation, have:

$E=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{E}_n=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}(\mathrm{\μ}{E}_o^n+E_i^n)$

And

$E_o^n={\∫\∫}_{\mathrm{\Ω}}\mathrm{\δ}\left({\mathrm{\φ}}_n\right)\left|{\▿\mathrm{\φ}}_n\right|\mathrm{dxdy};$

$E_i^n=\underset{n=1}{\overset{N}{\mathrm{\Σ}}}{\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v-v_n\left|\right|}^2\right)H_n({\mathrm{\φ}}_1,{\mathrm{\φ}}_2,...,{\mathrm{\φ}}_n)\mathrm{dxdy}+{\∫\∫}_{\mathrm{\Ω}}\left(\frac{1}{M}{\left|\right|v-v_{N+1}\left|\right|}^2\right)H_{N+1}({\mathrm{\φ}}_1,{\mathrm{\φ}}_2,...{\mathrm{\φ}}_N)\mathrm{dxdy}$

Wherein || || be vector norm; μ is the weighting coefficient of border energy term; φ _n() is level set function, level set function φ _nOn behalf of the n bar, () null set cut apart curve; V is the polarization characteristic vector, v _nBe the mean value vector that the n bar is cut apart the polarization characteristic vector v of curve inside, and:

$v_n=\frac{{\∫}_{\mathrm{\Ω}}v(x,y)H\left({\mathrm{\φ}}_n(x,y)\right)\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}H\left({\mathrm{\φ}}_n(x,y)\right)\mathrm{dxdy}};$

H () is the Heaviside function; δ () is the Dirac function; It is the image gradient operator; M is the dimension of polarization characteristic vector v, M=3 here; N is level set function φ _nThe quantity of ();

H _n(φ ₁，φ ₂，...φ _n)＝H(-φ ₁)H(-φ ₂)...H(-φ _n-1)H(φ _n)；

H′ _N(φ ₁，φ ₂，...φ _N)＝H(-φ ₁)H(-φ ₂)...H(-φ _N-1)H(-φ _N)；n＝1，2...N

Step 4: the employing variational method minimizes the energy functional E of step 3 gained, obtains the EVOLUTION EQUATION of level set function;

For the dual area situation, according to the energy functional E of step 3 gained, by variational principle

Obtain the EVOLUTION EQUATION of level set function by the minimization of energy functional:

Wherein,

Be the curvature of object boundary curve, t is a time variable;

For the multizone situation, according to the energy functional E of step 3 gained, by variational principle Obtain the EVOLUTION EQUATION of level set function by the minimization of energy functional:

$\frac{{\∂\mathrm{\φ}}_n}{\∂t}=-\frac{\∂E}{{\∂\mathrm{\φ}}_n}\mathrm{\δ}\left({\mathrm{\φ}}_n\right)[\mathrm{\μ}{K}_n+H(-{\mathrm{\φ}}_1)H(-{\mathrm{\φ}}_2)...H(-{\mathrm{\φ}}_{n-1})(-{\mathrm{\ρ}}_n+{\mathrm{\ξ}}_n)],$

Wherein: t is a time variable; 1≤n≤N;

Be the curvature of object boundary curve;

ξ _n＝H(φ _n+1)ρ _n+1+H(-φ _n+1)H(φ _n+2)ρ _n+2+…+H(-φ _n+1)H(-φ _n+2)…H(-φ _N-1)H(φ _N)ρ _N；

Step 5: the level set function EVOLUTION EQUATION to step 4 gained is carried out numerical solution, obtains final image segmentation curve;

For the dual area situation, in solution procedure, the iterative process of level set function is: For the multizone situation, the iterative process of each level set function is:

N=1 wherein, 2..., N; Δ t is the time variable of discretize;

As (φ _n ^T+1-φ ' _n) when reaching setting value D, stopping the iteration of level set function less than the iterations of threshold epsilon or level set function, this moment, the null set of level set function was final image segmentation curve;

Step 6: utilize the final image segmentation curve of step 5 gained that original polarization SAR image is cut apart, obtain final polarization SAR image segmentation result.

2. according to claim 1 based on the relevant level set polarization SAR image segmentation method that decomposes, it is characterized in that the span of the weighting coefficient μ of the energy term of border described in the step 3 is [0.1,0.5].

3. according to claim 1 based on the relevant level set polarization SAR image segmentation method that decomposes, it is characterized in that the time variable Δ t span of discretize described in the step 5 is [1,5].

4. according to claim 1 based on the relevant level set polarization SAR image segmentation method that decomposes, it is characterized in that the span of threshold epsilon described in the step 5 is [0.001,0.01]; The span of the setting value D of the iterations of described level set function is [50,200].

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