CN103745472B - SAR image segmentation method based on condition triple Markov field - Google Patents

SAR image segmentation method based on condition triple Markov field Download PDF

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CN103745472B
CN103745472B CN201410018003.8A CN201410018003A CN103745472B CN 103745472 B CN103745472 B CN 103745472B CN 201410018003 A CN201410018003 A CN 201410018003A CN 103745472 B CN103745472 B CN 103745472B
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吴艳
王凡
廉肖洁
李明
张强
吉新涛
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Xidian Univ
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Abstract

The invention discloses a kind of SAR image segmentation method based on condition triple Markov field, mainly solve the problem that in prior art, cut zone concordance is not enough.Implementation step is: 1. input SAR image, and initialization tag field and auxiliary field;2. extract the textural characteristics of SAR image, build the joint posterior distribution under Label Field and auxiliary field synergy;3. utilize Gibbs sampling that joint posterior distribution is sampled, obtain Label Field and several samples of auxiliary field;4. utilize maximum a posteriori marginal probability MPM criterion more new samples, obtain Label Field and the auxiliary field updated;5. Label Field and auxiliary field before utilizing sampling carry out parameter training, and judge whether the Label Field updated meets exit criteria, if meeting, exporting final segmentation result, otherwise returning the 3rd step and continuing iteration.The present invention improves concordance and the accuracy of location, edge of SAR image cut zone, can be used for SAR image object detection and recognition.

Description

SAR image segmentation method based on condition triple Markov field
Technical field
The invention belongs to technical field of image processing, further relate to SAR image segmentation method, can be used for target is examined Survey and target recognition.
Background technology
Along with synthetic aperture radar SAR is in the extensive application of every field, SAR image Interpretation Technology is increasingly subject to people's Pay attention to.SAR image segmentation is the basis and premise being interpreted SAR image, is a very important step.Pass through image Segmentation can provide image overall structure information and find target area interested, for classification and the identification in SAR image later stage Lay the foundation.Imaging characteristics yet with SAR makes SAR image comprise a large amount of coherent speckle noise, to image Segmentation Technology band Carry out the biggest difficulty.
At present, SAR image dividing processing technology has had more achievement in research, wherein Markov random field MRF mould Type has been obtained for being widely applied in SAR image is split, and it is to describe the pass that interdepends on image neighborhood pixels spatial domain System provides an effective modeling method.But this model does not accounts for the non-stationary of image, processing non-stationary SAR figure As time seem the simplest.For non-stationary image, triple Markov field TMF model is suggested.TMF model introduces the 3rd The non-stationary of image is modeled by individual random field, defines the different of image distribution by the several different values of auxiliary field Homogeneity.Therefore, TMF model has preferably processed non-stationary, and various statistical model can be used to carry out data Accurate Model, therefore achieves gratifying result when processing SAR image segmentation problem.
But, classical TMF model, when to image modeling, usually assumes that observation data are only about given label field condition Stand, do not take into full account the dependency between view data.At present, some extended models based on TMF model have also been emerged in large numbers And the model combined with other theories, such as layering TMF model, wavelet field TMF model, fuzzy TMF model etc..These are studied into Really utilize different methods to introduce the correlation information between the overall situation or yardstick or textural characteristics in TMF not have to solve classical TMF There is the deficiency utilizing observation data dependence, in the emulation to actual measurement SAR image, also obtained satisfied segmentation result, but The data dependence of they captures is limited in scope, and have impact on the concordance of cut zone.
Summary of the invention
Present invention aims to above-mentioned the deficiencies in the prior art, propose a kind of based on condition triple Markov field SAR image segmentation method, with ensure segmentation accuracy while, improve segmentation result region consistency.
The technical scheme realizing the object of the invention is: directly to the Label Field of non-stationary SAR image and combining of auxiliary field Posterior distrbutionp models;According to observing data dependence arbitrarily, introduce image texture characteristic, redefine auxiliary field in condition three Meaning in weight Markov Random Fields, builds Label Field and the unitary under auxiliary field synergy and binary potential function;According to maximum Posterior marginal probability criterion completes the segmentation to SAR image.Concrete steps include the following:
(1) input SAR image Y ', Y '={ yi| i ∈ S}, yiFor the gray value of pixel i, yi∈ [0,1 ..., 255], S For SAR image pixel point set;
(2) initialize: SAR image Y ' is carried out initial segmentation, it is thus achieved that dividing mark field X, X={xi| i ∈ S}, xiFor picture The segmentation label of vegetarian refreshments i, xi∈ [1,2 ..., K '], K ' is total classification number of segmentation label;Auxiliary field U is initialized, U={ui | i ∈ S}, uiFor the auxiliary field label of pixel i, ui∈[λ12,...,λM], λ12,…,λMRepresent the mark in auxiliary field U Number, M is the stationary state number comprised in SAR image;
(3) SAR image semivariance textural characteristics v at each pixel is extractedt(i);
3a) centered by pixel i, calculate its 5 × 5 sliding window Nei Dong-west, north-south, northeast-southwestern, western respectively The absolute value variogram value of north-southeast four direction:
γ E - W ( h ) = 1 2 N E - W ( h ) Σ i ′ = 1 N E - W ( h ) | Y ′ ( i ′ , j ′ ) - Y ′ ( i ′ + h , j ′ ) | ,
γ N - S ( h ) = 1 2 N N - S ( h ) Σ i ′ = 1 N N - S ( h ) | Y ′ ( i ′ , j ′ ) - Y ′ ( i ′ , j ′ + h ) | ,
γ NE - SW ( h ) = 1 2 N NE - SW ( h ) Σ i ′ = 1 N NE - SW ( h ) | Y ′ ( i ′ + h , j ′ ) - Y ′ ( i ′ , j ′ + h ) | ,
γ NE - SW ( h ) = 1 2 N NE - SW ( h ) Σ i ′ = 1 N NE - SW ( h ) | Y ′ ( i ′ , j ′ ) - Y ′ ( i ′ + H , j ′ + h ) | ,
Wherein, γE-W(h) represent east-west to absolute value variogram value, γN-SH () represents the exhausted of north-south direction To value variogram value, γNE-SWH () represents the absolute value variogram value of northeast-southwestward, γNW-SE(h) expression northwest- The absolute value variogram value of southeastern direction, h is the delay distance of any direction, h value 2, NE-W(h), NN-S(h), NNE-SW(h) And NNW-SEH () represents that the interior pixel at four direction h apart of sliding window is to number respectively;Y ' (i ', j ') represents that SAR image exists The gray value at coordinate (i ', the j ') place in sliding window, Y ' (i '+h, j ') represent SAR image sliding window internal coordinate (i '+ H, j ') gray value at place, Y ' (i ', j '+h) represents the SAR image gray value at two-dimensional coordinate (i ', j '+h) place, Y ' (i '+h, J '+h) represent the SAR image gray value at sliding window internal coordinate (i '+h, j '+h) place;
Absolute value variogram value 3b) utilizing four direction represents the semivariance textural characteristics at pixel i: vt(i) =[γE-W(h),γN-S(h),γNE-SW(h),γNW-SE(h)];
(4) Label Field X and unitary potential function f under auxiliary field U synergy are utilizedi(xi,ui| y) with binary potential function fij (xi,xj,ui,uj| y), build Label Field X with auxiliary field U joint posterior distribution function p (x, u | y):
p ( x , u | y ) = 1 Z exp { Σ i ∈ S f i ( x i , u i | y ) + α Σ i ∈ S Σ j ∈ N i f ij ( x i , x j , u i , u j | y ) } ,
Wherein, x is an example of Label Field X, and u is an example of auxiliary field U, and y is a reality of SAR image Y ' Example, S is the pixel point set in SAR image, NiRepresenting the neighborhood of pixel i, α is to regulate described unitary and the impact of binary potential function Coefficient, Z = Σ y exp { Σ i ∈ S f i ( x i , u i | y ) + α Σ i ∈ S Σ j ∈ N i f ij ( x i , x j , u i , u j | y ) } It it is the partition letter of condition triple Markov field Number, xjRepresent the segmentation label of pixel j, ujRepresent the auxiliary field label of pixel j;
(5) utilize the Gibbs method of sampling to joint posterior distribution function p (x, u | y) sample, obtain Label Field X with T the sample of auxiliary field U: [X1,…,XT] and [U1,…,UT];
(6) Bayesian MAP marginal probability criterion MPM T the sample to Label Field X with auxiliary field U is utilized [X1,…,XT] and [U1,…,UT] be updated, Label Field X ' and auxiliary field U ' after being updated;
(7) using the Label Field X before sampling and auxiliary field U as training data, to the parameter in unitary and binary potential function Carry out parameter training, prepare for next iteration;
(8) the pixel number that in the Label Field before and after statistical updating, classification changes, calculates change pixel number Pixel number purpose ratio total with SAR image, using this ratio as the testing conditions terminated, if this ratio is less than the threshold value set ε=10-6, the Label Field X ' after output renewal and auxiliary field U ', as final segmentation result;Otherwise, the Label Field X ' after updating Replace the Label Field X before updating and auxiliary field U with auxiliary field U ', return step (5) and continue iteration.
The present invention compared with prior art has the advantage that
First, the present invention is when splitting non-stationary SAR image, and the associating posteriority of direct construction Label Field and auxiliary field divides Cloth, it is to avoid traditional triple Markov field building process to likelihood function, thus it is independent to assume to observe data qualification, Can consider to observe arbitrary dependent feature between data so that the present invention improves accuracy and the region of segmentation result Concordance;
Second, the present invention has taken into full account the non-stationary of SAR image, has redefined the meaning of auxiliary field so that right In any SAR image, the most only consider two stationary states, and zone boundary is also labeled out, improves segmentation result The accuracy of boundary alignment;
3rd, the Label Field that the present invention builds has self adaptation with the unitary under auxiliary field synergy and binary potential function Property, the action intensity of unitary and binary potential function can be adaptively adjusted according to the similarity of neighborhood territory pixel, therefore, and the present invention The steric interaction relation of SAR image pixel can be described more accurately;
Simulation result shows, the present invention, compared with tradition triple Markov field dividing method, can suppress phase well Dry spot noise, improves the accuracy of location, edge, it is thus achieved that the most smooth cut zone, makes region consistency more preferable.
Accompanying drawing explanation
Fig. 1 is the flow chart of present invention SAR image based on condition triple Markov field segmentation;
Fig. 2 is the segmentation result figure to farmland actual measurement SAR image by the present invention and existing triple Markov field method;
Fig. 3 is the segmentation result to plains region actual measurement SAR image by the present invention and existing triple Markov field method Figure;
Fig. 4 is the segmentation result figure to grassland actual measurement SAR image by the present invention and existing triple Markov field method;
Fig. 5 is the segmentation result figure to highway actual measurement SAR image by the present invention and existing triple Markov field method.
Detailed description of the invention
Below in conjunction with the accompanying drawings the present invention is embodied as and effect is further described:
With reference to Fig. 1, the enforcement step of the present invention is as follows:
Step 1. inputs a width SAR image Y '.
The SAR image Y ' of input is 256 gray level images, the gray value y of each pixel iiThe most whole for taking from 0 to 255 All pixels in this SAR image are designated as gathering S by number, then this SAR image Y ' is expressed as Y '={ yi| i ∈ S}, yi∈[0, 1,...,255]。
Step 2. carries out initial segmentation to SAR image Y ', it is thus achieved that Label Field X, initializes auxiliary field U according to Label Field X.
2a) use histogram divion method that SAR image Y ' carries out initial segmentation, i.e. SAR image carried out the segmentation of K ' class, K ' is total classification number of segmentation label, and value is positive integer;
2b) determine the marginal value of each class according to the grey level histogram of SAR image, according to marginal value by SAR image pixel Point is divided into K ' class, obtains initial segmentation Label Field X, X={xi| i ∈ S}, xiFor the segmentation label of pixel i, xi∈[1, 2,...,K′];
2c) initialize auxiliary field U according to Label Field X, i.e. add up in 5 × 5 neighborhoods centered by pixel i and have not With the pixel of label to number, if pixel to number more than threshold tau=18 set, then it is assumed that this pixel i belongs to a kind of Stationary state is also labeled as 1, otherwise it is assumed that it belongs to another kind of stationary state and is labeled as 0, obtains two of any SAR image steadily State.
Step 3. extracts the SAR image semivariance textural characteristics v at each pixelt(i)。
In SAR image is split, outside ash disposal angle value, textural characteristics is also the Main Basis of segmentation, and application texture is permissible Describing the spatial information in SAR image more accurately, semivariance textural characteristics is a kind of textural characteristics being suitable for SAR image, Extracting method is as follows:
3a) centered by pixel i, calculate its 5 × 5 sliding window Nei Dong-west, north-south, northeast-southwestern, western respectively The absolute value variogram value of north-southeast four direction:
γ E - W ( h ) = 1 2 N E - W ( h ) Σ i ′ = 1 N E - W ( h ) | Y ′ ( i ′ , j ′ ) - Y ′ ( i ′ + h , j ′ ) | ,
γ N - S ( h ) = 1 2 N N - S ( h ) Σ i ′ = 1 N N - S ( h ) | Y ′ ( i ′ , j ′ ) - Y ′ ( i ′ , j ′ + h ) | ,
γ NE - SW ( h ) = 1 2 N NE - SW ( h ) Σ i ′ = 1 N NE - SW ( h ) | Y ′ ( i ′ + h , j ′ ) - Y ′ ( i ′ , j ′ + h ) | ,
γ NE - SW ( h ) = 1 2 N NE - SW ( h ) Σ i ′ = 1 N NE - SW ( h ) | Y ′ ( i ′ , j ′ ) - Y ′ ( i ′ + H , j ′ + h ) | ,
Wherein, γE-W(h) represent east-west to absolute value variogram value, γN-SH () represents the exhausted of north-south direction To value variogram value, γNE-SWH () represents the absolute value variogram value of northeast-southwestward, γNW-SE(h) expression northwest- The absolute value variogram value of southeastern direction, h is the delay distance of any direction, h value 2, NE-W(h), NN-S(h), NNE-SW(h) And NNW-SEH () represents that the interior pixel at four direction h apart of sliding window is to number respectively;Y ' (i ', j ') represents that SAR image exists The gray value at coordinate (i ', the j ') place in sliding window, Y ' (i '+h, j ') represent SAR image sliding window internal coordinate (i '+ H, j ') gray value at place, Y ' (i ', j '+h) represents the SAR image gray value at two-dimensional coordinate (i ', j '+h) place, Y ' (i '+h, J '+h) represent the SAR image gray value at sliding window internal coordinate (i '+h, j '+h) place;
Absolute value variogram value 3b) utilizing four direction represents the semivariance textural characteristics at pixel i: vt(i) =[γE-W(h),γN-S(h),γNE-SW(h),γNW-SE(h)]。
Step 4. utilizes Label Field X and unitary potential function f under auxiliary field U synergyi(xi,ui| y) with binary gesture letter Number fij(xi,xj,ui,uj| y), build Label Field X with auxiliary field U joint posterior distribution function p (x, u | y).
Minimum distance classifier 4a) is utilized to obtain unitary potential function:
f i ( x i , u i | y ) = log p ′ ( x i , u i | v t ( i ) , v g ( i ) ) = - log ( Σ k , l δ ( x i , k ) δ ( u i , l ) ( ( v g ( i ) - m ( k , l ) ) 2 σ g ( k , l ) + | | v t ( i ) - ω ( k , l ) | | 2 σ t ( k , l ) ) ) ,
Wherein, xiFor the segmentation label of pixel i, xi∈ [1,2 ..., K '], K ' is total classification number of segmentation label, ui For the auxiliary field label of pixel i, ui∈ [0,1], p ' (xi,ui|vt(i),vg(i)) represent local label distribution, vt(i) and vg I () is SAR image at the semivariance textural characteristics of i point and gray value respectively;K ∈ [1,2 ..., K '], l is integer, l ∈ [0, 1];δ () function equal to 1, is otherwise equal to 0 when two input parameters are equal; m → = { m ( 1 . 1 ) , · · · , m ( K ′ , M ) } With ω → = { ω ( 1 . 1 ) , · · · , ω ( K ′ , M ) } Presentation class center, M is the stationary state number in SAR image, M = 2 , σ → g = { σ g ( 1 . 1 ) , · · · , σ g ( K ′ , M ) } With σ → t = { σ t ( 1 . 1 ) , · · · , σ t ( K ′ , M ) } It is the variance of gray value and textural characteristics respectively;
4b) definition binary potential function is as follows:
fij(xi,xj,ui,uj| y)=W ' (xi,xj,ui,uj|θ′)gij(vg,vt),
Wherein, W ' (xi,xj,ui,uj| θ ') represent the interaction between label:
W ′ ( x i , x j , u i , u j | θ ′ ) = Σ k , l δ ( x i , k ) δ ( u i , l ) ( 2 δ ( x i , x j ) - 1 ) × ( β 1 δ * ( u i , u j , 0 ) + β 2 δ * ( u i , u j , 1 ) + β ( 1 - δ ( u i , u j ) ) ) ,
δ*() function equal to 1, is otherwise equal to 0 when three input parameters are equal;θ '=(β, β12), parameter beta, β1With β2Represent the pixel being positioned at region intersection, smooth region and the texture region degree of dependence to neighbor, g respectivelyij (vg,vt) represent the dependency between SAR image data:
g ij ( v g , v t ) = exp ( - d g ( i , j ) 2 σ g ( k , l ) - d t ( i , j ) 2 σ t ( k , l ) ) ,
Wherein, dg(i, j)=| | vg(i)-vg(j) | | represent two neighbor pixel i, the Euclidean distance of the gray scale of j;dt (i, j)=| | vt(i)-vt(j) | | represent two neighbor pixel i, the Euclidean distance of the textural characteristics of j;When two adjacent pictures When vegetarian refreshments i, j have similar textural characteristics and gray scale, function gij(vg,vt) there is bigger value, on the contrary less by having Value, is equivalent to be applied with an adaptive constraint in binary potential function, between the intensity of constraint is according to neighborhood territory pixel point Similarity is adaptively adjusted;
4c) according to unitary potential function fi(xi,ui| y) with binary potential function fij(xi,xj,ui,uj| y) obtain associating posteriority and divide Cloth function p (x, u | y) such as following formula:
p ( x , u | y ) = 1 Z exp { Σ i ∈ S f i ( x i , u i | y ) + α Σ i ∈ S Σ j ∈ N i f ij ( x i , x j , u i , u j | y ) } ,
Wherein, x is an example of dividing mark field X, and u is an example of auxiliary field U, and y is of SAR image Y ' Example, Z = Σ y exp { Σ i ∈ S f i ( x i , u i | y ) + α Σ i ∈ S Σ j ∈ N i f ij ( x i , x j , u i , u j | y ) } It is the partition function of condition triple Markov field, S For the pixel point set in SAR image, α is to regulate described unitary and the coefficient of binary potential function impact, NiRepresent the neighbour of pixel i Territory, xjRepresent the segmentation label of pixel j, ujRepresent the auxiliary field label of pixel j.
Step 5. utilize the Gibbs method of sampling to joint posterior distribution function p (x, u | y) sample, obtain Label Field X T the sample with auxiliary field U: [X1,…,XT] and [U1,…,UT]。
5a) calculate at each pixel joint posterior distribution p under different labels and different auxiliary fields label (x, u | y);
5b) in the joint posterior distribution under obtained different situations, search and make joint posterior distribution obtain maximum Label, as new label, obtain the Posterior distrbutionp p (x | y) of label, i.e. a sample of Label Field X;
5c) in the joint posterior distribution under obtained different situations, search and make joint posterior distribution obtain maximum Auxiliary field label, as new auxiliary field label, obtain assisting the Posterior distrbutionp p (u | y) of field label, i.e. auxiliary field U A sample;
5d) carry out T time to search, obtain Label Field X and assist T the sample of field U: [X1,…,XT] and [U1,…,UT]。
Step 6. utilizes Bayesian MAP marginal probability criterion MPM T the sample to Label Field X with auxiliary field U [X1,…,XT] and [U1,…,UT] be updated, Label Field X ' and auxiliary field U ' after being updated.
6a) utilize T the sample [X of Label Field X and auxiliary field U1,…,XT] and [U1,…,UT], create two discrete horses Markov's chain X (t)={ X1,X2,…,XTAnd U (t)={ U1,U2,…,UT, wherein, T is the sum of sample, t ∈ [1 ..., T];
6b) according to discrete joint network model X (t) and U (t), calculate the label x of pixel iiPosterior distrbutionp p (xi| y) and Auxiliary field label uiPosterior distrbutionp p (ui| y):
Order: μ k , i ( t ) = 1 , X t ( i ) = k 0 , X t ( i ) ≠ k , μ k , i ′ ( t ) = 1 , U t ( i ) = l 0 , U t ( i ) ≠ l ,
Wherein k ∈ [1,2 ..., K '], K ' be segmentation label total classification number, integer l ∈ [0,1], XtI () represents discrete The t sample in Markov chain X (t) is at the segmentation label of pixel i, UtI () represents in discrete joint network model U (t) The t sample at the auxiliary field label of pixel i;
Then: p ( x i | y ) ≈ 1 T Σ t μ k , i ( t ) , p ( u i | y ) ≈ 1 T Σ t μ l , i ′ ( t ) ,
Wherein, T is the sum of sample;
6c) by p (xi| y) with p (ui| y) obtain Label Field X ' and the approximation of auxiliary field U ' updated, it may be assumed that X '= (x′i)i∈S, x 'i=argmaxp (xi| y), U '=(u 'i)i∈S, u 'i=argmaxp (ui|y)。
Step 7. will sampling before Label Field X and auxiliary field U as training data, to the ginseng in unitary and binary potential function Number carries out parameter training, prepares for next iteration.
Stochastic gradient descent method SGD 7a) is utilized to estimate the parameter in unitary potential functionAnd α:
7a1) given average grayTextural characteristics meansigma methodsAdjustment factor α ∈ [1 ..., 5] and learning rate η ∈ (0,1), wherein, α be [1 ..., 5] in the arbitrary value that arranges, η be the arbitrary value of setting, iterations p=in (0,1) 1;
7a2) calculate average gray respectivelyTextural characteristics meansigma methodsGradient with adjustment factor αWith
s m p = &eta; &Sigma; i ( log p ( v g ( i ) | x i , u i m &RightArrow; p ) - < log p ( v g ( i ) | x i , u i , m &RightArrow; p ) > ) ,
s &omega; p = &eta; &Sigma; i ( log p ( v g ( i ) | x i , u i &omega; &RightArrow; p ) - < log p ( v g ( i ) | x i , u i , &omega; &RightArrow; p ) > ) ,
s &alpha; p = &eta; &Sigma; i &Sigma; j &Element; N i ( f ij ( x i , x j , u i , u j | y ) - < f ij ( x i , x j , u i , u j | y ) > ) ,
Wherein, p is iterations, and i, j represent pixel, vt(i) and vgI () is that SAR image is at the half of pixel i respectively Variance textural characteristics and gray value, xiRepresent pixel i label in Label Field X, uiRepresent that pixel i is in auxiliary field U Label, xjRepresent pixel j label in Label Field X, ujRepresent pixel j label in auxiliary field U,Represent pth The average gray of secondary iteration,Represent the textural characteristics meansigma methods of pth time iteration, NiRepresenting the neighborhood of pixel i, y represents One example of SAR image Y ', and<>expression Posterior distrbutionp p (x, u | expectation y); p ( v g ( i ) | x i , u i , m &RightArrow; p ) = ( v g ( i ) - m ( k , l ) ) 2 &sigma; g ( k , l ) , p ( v t ( i ) | x i , u i , &omega; &RightArrow; p ) = = | | v t ( i ) - &omega; ( k , l ) | | 2 &sigma; t ( k , l ) , Wherein, k ∈ [1,2 ..., K '], K ' is total classification number of segmentation label, integer l ∈ [0, 1], m &RightArrow; = { m ( 1 . 1 ) , &CenterDot; &CenterDot; &CenterDot; , m ( K &prime; , M ) } With &omega; &RightArrow; = { &omega; ( 1 . 1 ) , &CenterDot; &CenterDot; &CenterDot; , &omega; ( K &prime; , M ) } It it is classification center; &sigma; &RightArrow; g = { &sigma; g ( 1 . 1 ) , &CenterDot; &CenterDot; &CenterDot; , &sigma; g ( K &prime; , M ) } With &sigma; &RightArrow; t = { &sigma; t ( 1 . 1 ) , &CenterDot; &CenterDot; &CenterDot; , &sigma; t ( K &prime; , M ) } It is the variance of gray value and textural characteristics respectively;
7a3) set average grayGrads threshold d1=103, textural characteristics meansigma methodsGrads threshold d2=103With The Grads threshold d of adjustment factor α3=102If,GradientGradientAnd regulation system The gradient of number αThen learning rate η is reduced to original 90%;Otherwise update average grayTexture is special Levy meansigma methodsAnd adjustment factorI.e.
m &RightArrow; p + 1 = m &RightArrow; p - &eta; s m p ,
&omega; &RightArrow; p + 1 = &omega; &RightArrow; p - &eta; s &omega; p ,
&alpha; p + 1 = &alpha; p - &eta; s &alpha; p ,
And make p+1=p;
ICE method estimates the parameter θ ' in binary potential function=(β, β 7b) to utilize iterated conditional to estimate12):
7b1) given θ '=(β, β12) initial value, i.e. β, β1And β2Arbitrary value in [0,1], if iterations p=1, The then parameter θ ' of pth time iteration(p)=θ ';
7b2) update the parameter θ ' of+1 iteration of pth(p+1), i.e. calculate the θ ' expectation about SAR image Y 'Wherein, y is an example of SAR image Y ';If this be desirable to calculate, then obtain pth+ The parameter θ ' of 1 iteration(p+1), it is this desired value of calculation;Statistical method is otherwise utilized to calculate θ '(p+1)Approximation, i.e. For t given sample (x1,u1),…,(xt,ut), calculate θ '(p)Conditional expectation θ '(p+1)=[θ '(p)(x1,u1,y)+… +θ′(p)(xt,ut, y)] and/t, wherein, θ '(p)(x1,u1, y) represent the parameter in first sample, θ ' in pth time iteration(p)(xt, ut, y) represent the parameter in the t sample in pth time iteration;
If 7b3) | θ '(p+1)-θ′(p)| < 10-2, i.e. think that result of calculation is basicly stable, terminate above-mentioned steps 7b1)- 7b2);Otherwise make iterations p from increasing 1, return step 7b2) continue executing with.
The pixel number that in Label Field before and after step 8. statistical updating, classification changes, calculates change pixel number Mesh and SAR image total pixel number purpose ratio, using this ratio as the testing conditions terminated, if this ratio is less than the threshold set Value ε=10-6, the Label Field X ' after output renewal and auxiliary field U ', as final segmentation result;Otherwise, the labelling after updating Field X ' and auxiliary field U ' replaces the Label Field X before updating and auxiliary field U, returns step (5) and continues iteration.
Effect of the present invention can be further illustrated by following emulation:
1. simulated conditions
The emulation of the present invention is the hardware environment at dominant frequency 2.5GHz Intel (R) Pentium (R) Dual-Core CPU And carry out under the software environment of MATLAB R2009b, Window XP Professional.
2. emulation content and interpretation of result
Emulation 1, uses the inventive method and existing triple Markov field method to carry out the actual measurement SAR image in farmland point Cutting, segmentation result is as shown in Figure 2.Wherein Fig. 2 (a) is actual measurement SAR image in farmland to be split, and size is 256 × 256, Fig. 2 B (), for utilize the existing triple Markov field method segmentation result figure to Fig. 2 (a), Fig. 2 (c) is for utilizing the present invention to Fig. 2 The segmentation result figure of (a).
As it is clear from fig. 2 that the texture in Fig. 2 (a) is relatively simple, including substantial amounts of homogeneous region, the region of division is more, Boundary line between each region is the most obvious, in Fig. 2 (b), comprises more speckle noise in cut zone, by mistake segmentation picture Element is more, and region consistency is poor, and in Fig. 2 (c), it is consistent that each cut zone has more preferable region compared with Fig. 2 (b) Property, in region, speckle noise reduces, and the location, edge in region also more accurately and smooths than Fig. 2 (b).
Emulation 2, uses the inventive method and existing triple Markov field method to enter the actual measurement SAR image of plains region Row segmentation, segmentation result is as shown in Figure 3.Wherein Fig. 3 (a) is plains region to be split actual measurement SAR image, size is 256 × 256, Fig. 3 (b), for utilize the existing triple Markov field method segmentation result figure to Fig. 3 (a), Fig. 3 (c) is for utilizing the present invention The method segmentation result figure to Fig. 3 (a).
It can be seen from figure 3 that Fig. 3 (a) contains texture close quarters and simple textures region, in Fig. 3 (b), simply simultaneously The segmentation result of texture region still comprises a large amount of speckle noise, and region consistency is poor, in Fig. 3 (c), in simple textures region Speckle noise considerably reduce compared with Fig. 3 (b), region consistency is preferable, and texture close quarters is essentially identical with Fig. 3 (b), Maintain the detailed information of SAR image.
Emulation 3, uses the inventive method and existing triple Markov field method to carry out the actual measurement SAR image on grassland point Cutting, simulation result is as shown in Figure 4.Wherein Fig. 4 (a) is actual measurement SAR image in grassland to be split, and size is 256 × 256, Fig. 4 B (), for utilize the existing triple Markov field method segmentation result to Fig. 4 (a), Fig. 4 (c) is for utilizing the inventive method to Fig. 4 The segmentation result of (a).
As seen from Figure 4, the texture of Fig. 4 (a) is simple, but the edge in major part region is fuzzyyer, in Fig. 4 (b), point Cutting and comprise a large amount of speckle noise in region, the border in a part of region is fuzzyyer, in Fig. 4 (c), and the concordance of cut zone Significantly better than Fig. 4 (b), each cut zone edge is also the most clearly.
Emulation 4, uses the inventive method and existing triple Markov field method to carry out the actual measurement SAR image of highway point Cutting, simulation result is as shown in Figure 5.Wherein Fig. 5 (a) is highway actual measurement SAR image to be split, and size is 512 × 512, Fig. 5 B (), for utilize the existing triple Markov field method segmentation result to Fig. 5 (a), Fig. 5 (c) is for utilizing the inventive method to Fig. 5 The segmentation result of (a).
From figure 5 it can be seen that Fig. 5 (a) contains curved road, across grain region and simple textures region, in Fig. 5 (b), horizontal In texture region and simple textures region, speckle noise is more, and region consistency is poor, and in Fig. 5 (c), across grain region shows Relatively sharp, curve is the most smoother, and the speckle noise in simple textures region is considerably less than Fig. 5 (b), cut zone concordance More preferably.
Above four emulation show: the inventive method due to any dependency considering between SAR image data, from Two different stationary states of SAR image set out, and construct and have adaptivity under Label Field and auxiliary field synergy Unitary potential function and binary potential function, improve the concordance to SAR image cut zone, makes cut zone the most smooth, by mistake Segmentation reduces, and also improves the accuracy of edges of regions location simultaneously.

Claims (4)

1. a SAR image segmentation method based on condition triple Markov field, comprises the steps:
(1) input SAR image Y ', Y '={ yi| i ∈ S}, yiFor the gray value of pixel i, yi∈ [0,1 ..., 255], S is SAR image pixel point set;
(2) SAR image Y ' is carried out initial segmentation, it is thus achieved that Label Field X, initializes according to Label Field X and assist field U:
2a) using histogram divion method that SAR image Y ' carries out initial segmentation, SAR image i.e. carries out the segmentation of K ' class, K ' is Total classification number of segmentation label, value is positive integer;
2b) determine the marginal value of each class according to the grey level histogram of SAR image, according to marginal value by SAR image pixel dot-dash It is divided into K ' class, obtains initial segmentation Label Field X, X={xi| i ∈ S}, xiFor the segmentation label of pixel i, xi∈[1,2,..., K′];
2c) initializing auxiliary field U according to Label Field X, i.e. in 5 × 5 neighborhoods centered by pixel i, statistics has different mark Number pixel to number, if pixel to number more than threshold tau=18 set, then it is assumed that this pixel i belong to a kind of steadily State is also labeled as 1, otherwise it is assumed that it belongs to another kind of stationary state and is labeled as 0, obtains two stationary states of any SAR image;
U={ui| i ∈ S}, uiFor the auxiliary field label of pixel i, ui∈[λ12,...,λM], λ12,…,λMRepresent auxiliary Label in the U of field, M is the stationary state number comprised in SAR image;
(3) SAR image semivariance textural characteristics v at each pixel is extractedt(i);
3a) centered by pixel i, calculate its 5 × 5 sliding window Nei Dong-west, north-south, northeast-southwest, northwest-east respectively The absolute value variogram value of south four direction:
&gamma; E - W ( h ) = 1 2 N E - W ( h ) &Sigma; i &prime; = 1 N E - W ( h ) | Y &prime; ( i &prime; , j &prime; ) - Y &prime; ( i &prime; + h , j &prime; ) | ,
&gamma; N - S ( h ) = 1 2 N N - S ( h ) &Sigma; i &prime; = 1 N N - S ( h ) | Y &prime; ( i &prime; , j &prime; ) - Y &prime; ( i &prime; , j &prime; + h ) | ,
&gamma; N E - S W ( h ) = 1 2 N N E - S W ( h ) &Sigma; i &prime; = 1 N N E - S W ( h ) | Y &prime; ( i &prime; + h , j &prime; ) - Y &prime; ( i &prime; , j &prime; + h ) | ,
&gamma; N W - S E ( h ) = 1 2 N N W - S E ( h ) &Sigma; i &prime; = 1 N N W - S E ( h ) | Y &prime; ( i &prime; , j &prime; ) - Y &prime; ( i &prime; + h , j &prime; + h ) | ,
Wherein, γE-W(h) represent east-west to absolute value variogram value, γN-SH () represents the absolute value in north-south direction Variogram value, γNE-SWH () represents the absolute value variogram value of northeast-southwestward, γNW-SEH () represents northwest-southeast The absolute value variogram value in direction, h is the delay distance of any direction, h value 2, NE-W(h), NN-S(h), NNE-SW(h) and NNW-SEH () represents that the interior pixel at four direction h apart of sliding window is to number respectively;Y ' (i ', j ') represents that SAR image is being slided The gray value at coordinate (i ', the j ') place in dynamic window, Y ' (i '+h, j ') represent SAR image sliding window internal coordinate (i '+h, J ') gray value at place, Y ' (i ', j '+h) represents the SAR image gray value at two-dimensional coordinate (i ', j '+h) place, Y ' (i '+h, j '+ H) SAR image gray value at sliding window internal coordinate (i '+h, j '+h) place is represented;
Absolute value variogram value 3b) utilizing four direction represents the semivariance textural characteristics at pixel i: vt(i)= [γE-W(h),γN-S(h),γNE-SW(h),γNW-SE(h)];
(4) Label Field X and unitary potential function f under auxiliary field U synergy are utilizedi(xi,ui| y) with binary potential function fij(xi, xj,ui,uj| y), build Label Field X with auxiliary field U joint posterior distribution function p (x, u | y):
4a) obtain unitary potential function f with minimum distance classifieri(xi,ui| y):
f i ( x i , u i | y ) = log p &prime; ( x i , u i | v t ( i ) , v g ( i ) ) = - log ( &Sigma; k , l &delta; ( x i , k ) &delta; ( u i , l ) ( ( v g ( i ) - m ( k , l ) ) 2 &sigma; g ( k , l ) + | | v t ( i ) - &omega; ( k , l ) | | 2 &sigma; t ( k , l ) ) ) ,
Wherein, xiFor the segmentation label of pixel i, xi∈ [1,2 ..., K '], K ' is total classification number of segmentation label, uiFor pixel i Auxiliary field label, ui∈ [0,1], p ' (xi,ui|vt(i),vg(i)) represent local label distribution, vt(i) and vgI () is SAR figure respectively As at the semivariance textural characteristics of i point and gray value;K ∈ [1,2 ..., K '], l is integer, l ∈ [0,1];δ () function is at two Equal to 1 when input parameter is equal, otherwise equal to 0;With Presentation class center, M is the stationary state number in SAR image, M=2,WithIt is the variance of gray value and textural characteristics respectively;
4b) definition binary potential function is as follows:
fij(xi,xj,ui,uj| y)=W ' (xi,xj,ui,uj|θ′)gij(vg,vt),
Wherein, W ' (xi,xj,ui,uj| θ ') represent the interaction between label:
W &prime; ( x i , x j , u i , u j | &theta; &prime; ) = &Sigma; k , l &delta; ( x i , k ) &delta; ( u i , l ) ( 2 &delta; ( x i , x j ) - 1 ) &times; ( &beta; 1 &delta; * ( u i , u j , 0 ) + &beta; 2 &delta; * ( u i , u j , 1 ) + &beta; ( 1 - &delta; ( u i , u j ) ) ) ,
δ*() function equal to 1, is otherwise equal to 0 when three input parameters are equal;θ '=(β, β12), parameter beta, β1And β2Point Biao Shi not be positioned at the pixel degree of dependence to neighbor of region intersection, smooth region and texture region, gij(vg,vt) Dependency between expression SAR image data:
g i j ( v g , v t ) = exp ( - d g ( i , j ) 2 &sigma; g ( k , l ) - d t ( i , j ) 2 &sigma; t ( k , l ) ) ,
Wherein, dg(i, j)=| | vg(i)-vg(j) | | represent two neighbor pixel i, the Euclidean distance of the gray scale of j;dt(i,j) =| | vt(i)-vt(j) | | represent two neighbor pixel i, the Euclidean distance of the textural characteristics of j;
4c) according to unitary potential function fi(xi,ui| y) with binary potential function fij(xi,xj,ui,uj| y) obtain joint posterior distribution letter Number p (x, u | y) such as following formula:
p ( x , u | y ) = 1 Z exp { &Sigma; i &Element; S f i ( x i , u i | y ) + &alpha; &Sigma; i &Element; S &Sigma; j &Element; N i f i j ( x i , x j , u i , u j | y ) } ,
Wherein, x is an example of dividing mark field X, and u is an example of auxiliary field U, and y is a reality of SAR image Y ' Example,Being the partition function of condition triple Markov field, S is Pixel point set in SAR image, α is to regulate described unitary and the coefficient of binary potential function impact, NiRepresent the neighbour of pixel i Territory, xjRepresent the segmentation label of pixel j, ujRepresent the auxiliary field label of pixel j;
(5) utilize the Gibbs method of sampling to joint posterior distribution function p (x, u | y) sample, obtain Label Field X and auxiliary T the sample of field U: [X1,…,XT] and [U1,…,UT];
(6) Bayesian MAP marginal probability criterion MPM T the sample [X to Label Field X with auxiliary field U is utilized1,…,XT] [U1,…,UT] be updated, Label Field X ' and auxiliary field U ' after being updated;
(7) using the Label Field X before sampling and auxiliary field U as training data, the parameter in unitary and binary potential function is carried out Parameter training, prepares for next iteration;
(8) the pixel number that in the Label Field before and after statistical updating, classification changes, calculates change pixel number and SAR Image total pixel number purpose ratio, using this ratio as terminate testing conditions, if this ratio less than set threshold epsilon= 10-6, the Label Field X ' after output renewal and auxiliary field U ', as final segmentation result;Otherwise, will update after Label Field X ' and Auxiliary field U ' replaces the Label Field X before updating and auxiliary field U, returns step (5) and continues iteration.
SAR image segmentation method based on condition triple Markov field the most according to claim 1, it is characterised in that: Described in step (5) utilize the Gibbs method of sampling to joint posterior distribution function p (x, u | y) sample, enter as follows OK:
5a) calculate at each pixel joint posterior distribution p under different labels and different auxiliary fields label (x, u | y);
5b) in the joint posterior distribution under obtained different situations, search the mark making joint posterior distribution obtain maximum Number, as new label, obtain the Posterior distrbutionp p (x | y) of label, i.e. a sample of Label Field X;
5c) in the joint posterior distribution under obtained different situations, search and make joint posterior distribution obtain the auxiliary of maximum Help a label, as new auxiliary field label, obtain assisting the Posterior distrbutionp p (u | y) of field label, i.e. assist the one of field U Individual sample;
5d) carry out T time to search, obtain Label Field X and assist T the sample of field U: [X1,…,XT] and [U1,…,UT]。
SAR image segmentation method based on condition triple Markov field the most according to claim 1, it is characterised in that: Utilizing Bayesian MAP marginal probability criterion MPM update mark field X ' and assisting field U ' described in step (6), by following step Suddenly carry out:
6a) utilize T the sample [X of Label Field X and auxiliary field U1,…,XT] and [U1,…,UT], create two discrete Markov Chain X (t)={ X1,X2,…,XTAnd U (t)={ U1,U2,…,UT, wherein, T is the sum of sample, t ∈ [1,2 ..., T];
6b) according to discrete joint network model X (t) and U (t), calculate the label x of pixel iiPosterior distrbutionp p (xi| y) and auxiliary Field label uiPosterior distrbutionp p (ui| y):
Order:
Wherein k ∈ [1,2 ..., K '], K ' be segmentation label total classification number, l is integer, l ∈ [0,1], XtI () represents discrete horse The t sample in Markov's chain X (t) is at the segmentation label of pixel i, UtI () represents in discrete joint network model U (t) The t sample is at the auxiliary field label of pixel i;
Then:
Wherein, T is the sum of sample;
6c) by p (xi| y) with p (ui| y) obtain Label Field X ' and the approximation of auxiliary field U ' updated, it may be assumed that X '=(x 'i )i∈S, x 'i=arg maxp (xi| y), U '=(u 'i)i∈S, u 'i=arg maxp (ui|y)。
SAR image segmentation method based on condition triple Markov field the most according to claim 1, it is characterised in that: Described in step (7), the parameter in unitary and binary potential function is carried out parameter training, carries out as follows:
Stochastic gradient descent method SGD 7a) is utilized to estimate the parameter in unitary potential functionAnd α:
7a1) given average grayTextural characteristics meansigma methodsAdjustment factor α ∈ [1 ..., 5] and learning rate η ∈ (0, 1), wherein, α be [1 ..., 5] in the arbitrary value that arranges, η be the arbitrary value of setting, iterations p=1 in (0,1);
7a2) calculate average gray respectivelyTextural characteristics meansigma methodsGradient with adjustment factor αWith
s m p = &eta; &Sigma; i ( log p ( v g ( i ) | x i , u i , m &RightArrow; p ) - < log p ( v g ( i ) | x i , u i , m &RightArrow; p ) > ) ,
s &omega; p = &eta; &Sigma; i ( log p ( v t ( i ) | x i , u i , &omega; &RightArrow; p ) - < log p ( v t ( i ) | x i , u i , &omega; &RightArrow; p ) > ) ,
s &alpha; p = &eta; &Sigma; i &Sigma; j &Element; N i ( f i j ( x i , x j , u i , u j | y ) - < f i j ( x i , x j , u i , u j | y ) > ) ,
Wherein, p is iterations, and i, j represent pixel, vt(i) and vgI () is that SAR image is at the half of pixel i respectively Variance textural characteristics and gray value, xiRepresent pixel i label in Label Field X, uiRepresent that pixel i is in auxiliary Label in the U of field, xjRepresent pixel j label in Label Field X, ujRepresent pixel j mark in auxiliary field U Number,Represent the average gray of pth time iteration,Represent the textural characteristics meansigma methods of pth time iteration, NiRepresent pixel The neighborhood of some i, y represents an example of SAR image Y ',<>expression Posterior distrbutionp p (x, u | expectation y);Wherein, k ∈ [1, 2 ..., K '], K ' is total classification number of segmentation label, and l is integer, l ∈ [0,1],WithIt it is classification center;With It is the variance of gray value and textural characteristics respectively;
7a3) set average grayGrads threshold d1=103, textural characteristics meansigma methodsGrads threshold d2=103And tune The Grads threshold d of joint factor alpha3=102If,Gradient GradientAnd adjustment factor α GradientThen learning rate η is reduced to original 90%;Otherwise update average grayTextural characteristics is put down AverageWith adjustment factor αp+1, i.e.
m &RightArrow; p + 1 = m &RightArrow; p - &eta;s m p ,
&omega; &RightArrow; p + 1 = &omega; &RightArrow; p - &eta;s &omega; p ,
&alpha; p + 1 = &alpha; p - &eta;s &alpha; p ,
And make p+1=p;
ICE method estimates the parameter θ ' in binary potential function=(β, β 7b) to utilize iterated conditional to estimate12):
7b1) given θ '=(β, β12) initial value, i.e. β, β1And β2Arbitrary value in [0,1], if iterations p=1, then The parameter θ ' of p iteration(p)=θ ';
7b2) update the parameter θ ' of+1 iteration of pth(p+1), i.e. calculate the θ ' expectation θ ' about SAR image Y '(p+1)=Eθ′(p)(θ ′(p)| Y '=y), wherein, y is an example of SAR image Y ';If this is desirable to calculate, then obtain the ginseng of+1 iteration of pth Number θ '(p+1), it is this desired value of calculation;Statistical method is otherwise utilized to calculate θ '(p+1)Approximation, i.e. for given t Individual sample (x1,u1),…,(xt,ut), calculate θ '(p)Conditional expectation θ '(p+1)=[θ '(p)(x1,u1,y)+…+θ′(p)(xt,ut, Y)]/t, wherein, θ '(p)(x1,u1, y) represent the parameter in first sample, θ ' in pth time iteration(p)(xt,ut, y) represent pth Parameter in the t sample in secondary iteration;
If 7b3) | θ '(p+1)-θ′(p)| < 10-2, i.e. think that result of calculation is basicly stable, terminate above-mentioned steps 7b1) and-7b2);No Then make iterations p from increasing 1, return step 7b2) continue executing with.
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