CN103745472B  SAR image segmentation method based on condition triple Markov field  Google Patents
SAR image segmentation method based on condition triple Markov field Download PDFInfo
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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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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
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 nonstationary of image, processing nonstationary SAR figure
As time seem the simplest.For nonstationary image, triple Markov field TMF model is suggested.TMF model introduces the 3rd
The nonstationary 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 nonstationary, 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 abovementioned 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 nonstationary 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 '={ y_{i} i ∈ S}, y_{i}For the gray value of pixel i, y_{i}∈ [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={x_{i} i ∈ S}, x_{i}For picture
The segmentation label of vegetarian refreshments i, x_{i}∈ [1,2 ..., K '], K ' is total classification number of segmentation label；Auxiliary field U is initialized, U={u_{i}
 i ∈ S}, u_{i}For the auxiliary field label of pixel i, u_{i}∈[λ_{1},λ_{2},...,λ_{M}], λ_{1},λ_{2},…,λ_{M}Represent 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 extracted_{t}(i)；
3a) centered by pixel i, calculate its 5 × 5 sliding window Nei Dongwest, northsouth, northeastsouthwestern, western respectively
The absolute value variogram value of northsoutheast four direction:
Wherein, γ_{EW}(h) represent eastwest to absolute value variogram value, γ_{NS}H () represents the exhausted of northsouth direction
To value variogram value, γ_{NESW}H () represents the absolute value variogram value of northeastsouthwestward, γ_{NWSE}(h) expression northwest
The absolute value variogram value of southeastern direction, h is the delay distance of any direction, h value 2, N_{EW}(h), N_{NS}(h), N_{NESW}(h)
And N_{NWSE}H () 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 twodimensional 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: v_{t}(i)
=[γ_{EW}(h),γ_{NS}(h),γ_{NESW}(h),γ_{NWSE}(h)]；
(4) Label Field X and unitary potential function f under auxiliary field U synergy are utilized_{i}(x_{i},u_{i} y) with binary potential function f_{ij}
(x_{i},x_{j},u_{i},u_{j} y), build Label Field X with auxiliary field U joint posterior distribution function p (x, u  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, N_{i}Representing the neighborhood of pixel i, α is to regulate described unitary and the impact of binary potential function
Coefficient, $Z=\underset{y}{\mathrm{\Σ}}\mathrm{exp}\{\underset{i\∈S}{\mathrm{\Σ}}{f}_{i}({x}_{i},{u}_{i}y)+\mathrm{\α}\underset{i\∈S}{\mathrm{\Σ}}\underset{j\∈{N}_{i}}{\mathrm{\Σ}}{f}_{\mathrm{ij}}({x}_{i},{x}_{j},{u}_{i},{u}_{j}y)\}$ It it is the partition letter of condition triple Markov field
Number, x_{j}Represent the segmentation label of pixel j, u_{j}Represent 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: [X_{1},…,X_{T}] and [U_{1},…,U_{T}]；
(6) Bayesian MAP marginal probability criterion MPM T the sample to Label Field X with auxiliary field U is utilized
[X_{1},…,X_{T}] and [U_{1},…,U_{T}] 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 nonstationary 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 nonstationary 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 i_{i}The 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 '={ y_{i} i ∈ S}, y_{i}∈[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={x_{i} i ∈ S}, x_{i}For the segmentation label of pixel i, x_{i}∈[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 pixel_{t}(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 Dongwest, northsouth, northeastsouthwestern, western respectively
The absolute value variogram value of northsoutheast four direction:
Wherein, γ_{EW}(h) represent eastwest to absolute value variogram value, γ_{NS}H () represents the exhausted of northsouth direction
To value variogram value, γ_{NESW}H () represents the absolute value variogram value of northeastsouthwestward, γ_{NWSE}(h) expression northwest
The absolute value variogram value of southeastern direction, h is the delay distance of any direction, h value 2, N_{EW}(h), N_{NS}(h), N_{NESW}(h)
And N_{NWSE}H () 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 twodimensional 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: v_{t}(i)
=[γ_{EW}(h),γ_{NS}(h),γ_{NESW}(h),γ_{NWSE}(h)]。
Step 4. utilizes Label Field X and unitary potential function f under auxiliary field U synergy_{i}(x_{i},u_{i} y) with binary gesture letter
Number f_{ij}(x_{i},x_{j},u_{i},u_{j} 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:
Wherein, x_{i}For the segmentation label of pixel i, x_{i}∈ [1,2 ..., K '], K ' is total classification number of segmentation label, u_{i}
For the auxiliary field label of pixel i, u_{i}∈ [0,1], p ' (x_{i},u_{i}v_{t}(i),v_{g}(i)) represent local label distribution, v_{t}(i) and v_{g}
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； $\stackrel{\→}{m}=\{m(1.1),\·\·\·,m({K}^{\′},M)\}$ With $\stackrel{\→}{\mathrm{\ω}}=\{\mathrm{\ω}(1.1),\·\·\·,\mathrm{\ω}({K}^{\′},M)\}$ Presentation class center, M is the stationary state number in SAR image, $M=2,{\stackrel{\→}{\mathrm{\σ}}}_{g}=\{{\mathrm{\σ}}_{g}(1.1),\·\·\·,{\mathrm{\σ}}_{g}({K}^{\′},M)\}$
With ${\stackrel{\→}{\mathrm{\σ}}}_{t}=\{{\mathrm{\σ}}_{t}(1.1),\·\·\·,{\mathrm{\σ}}_{t}({K}^{\′},M)\}$ It is the variance of gray value and textural characteristics respectively；
4b) definition binary potential function is as follows:
f_{ij}(x_{i},x_{j},u_{i},u_{j} y)=W ' (x_{i},x_{j},u_{i},u_{j}θ′)g_{ij}(v_{g},v_{t}),
Wherein, W ' (x_{i},x_{j},u_{i},u_{j} θ ') represent the interaction between label:
δ^{*}() function equal to 1, is otherwise equal to 0 when three input parameters are equal；θ '=(β, β_{1},β_{2}), parameter beta, β_{1}With
β_{2}Represent the pixel being positioned at region intersection, smooth region and the texture region degree of dependence to neighbor, g respectively_{ij}
(v_{g},v_{t}) represent the dependency between SAR image data:
Wherein, d_{g}(i, j)=  v_{g}(i)v_{g}(j)   represent two neighbor pixel i, the Euclidean distance of the gray scale of j；d_{t}
(i, j)=  v_{t}(i)v_{t}(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 g_{ij}(v_{g},v_{t}) 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 f_{i}(x_{i},u_{i} y) with binary potential function f_{ij}(x_{i},x_{j},u_{i},u_{j} y) obtain associating posteriority and divide
Cloth function p (x, u  y) such as following formula:
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, $Z=\underset{y}{\mathrm{\Σ}}\mathrm{exp}\{\underset{i\∈S}{\mathrm{\Σ}}{f}_{i}({x}_{i},{u}_{i}y)+\mathrm{\α}\underset{i\∈S}{\mathrm{\Σ}}\underset{j\∈{N}_{i}}{\mathrm{\Σ}}{f}_{\mathrm{ij}}({x}_{i},{x}_{j},{u}_{i},{u}_{j}y)\}$ 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, N_{i}Represent the neighbour of pixel i
Territory, x_{j}Represent the segmentation label of pixel j, u_{j}Represent 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: [X_{1},…,X_{T}] and [U_{1},…,U_{T}]。
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: [X_{1},…,X_{T}] and [U_{1},…,U_{T}]。
Step 6. utilizes Bayesian MAP marginal probability criterion MPM T the sample to Label Field X with auxiliary field U
[X_{1},…,X_{T}] and [U_{1},…,U_{T}] 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 U_{1},…,X_{T}] and [U_{1},…,U_{T}], create two discrete horses
Markov's chain X (t)={ X_{1},X_{2},…,X_{T}And U (t)={ U_{1},U_{2},…,U_{T}, 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 i_{i}Posterior distrbutionp p (x_{i} y) and
Auxiliary field label u_{i}Posterior distrbutionp p (u_{i} y):
Order: ${\mathrm{\μ}}_{k,i}\left(t\right)=\left\{\begin{array}{c}1,{X}_{t}\left(i\right)=k\\ 0,{X}_{t}\left(i\right)\≠k\end{array}\right.,$ ${\mathrm{\μ}}_{k,i}^{\′}\left(t\right)=\left\{\begin{array}{c}1,{U}_{t}\left(i\right)=l\\ 0,{U}_{t}\left(i\right)\≠l\end{array}\right.,$
Wherein k ∈ [1,2 ..., K '], K ' be segmentation label total classification number, integer l ∈ [0,1], X_{t}I () represents discrete
The t sample in Markov chain X (t) is at the segmentation label of pixel i, U_{t}I () represents in discrete joint network model U (t)
The t sample at the auxiliary field label of pixel i；
Then: $p\left({x}_{i}\righty)\≈\frac{1}{T}\underset{t}{\mathrm{\Σ}}{\mathrm{\μ}}_{k,i}\left(t\right),$ $p\left({u}_{i}\righty)\≈\frac{1}{T}\underset{t}{\mathrm{\Σ}}{\mathrm{\μ}}_{l,i}^{\′}\left(t\right),$
Wherein, T is the sum of sample；
6c) by p (x_{i} y) with p (u_{i} 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 (x_{i} y), U '=(u '_{i})_{i∈S}, u '_{i}=argmaxp (u_{i}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
Wherein, p is iterations, and i, j represent pixel, v_{t}(i) and v_{g}I () is that SAR image is at the half of pixel i respectively
Variance textural characteristics and gray value, x_{i}Represent pixel i label in Label Field X, u_{i}Represent that pixel i is in auxiliary field U
Label, x_{j}Represent pixel j label in Label Field X, u_{j}Represent 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, N_{i}Representing the neighborhood of pixel i, y represents
One example of SAR image Y ', and<>expression Posterior distrbutionp p (x, u  expectation y)； $p\left({v}_{g}\left(i\right)\right{x}_{i},{u}_{i},{\stackrel{\→}{m}}^{p})=\frac{{({v}_{g}\left(i\right)m(k,l))}^{2}}{{\mathrm{\σ}}_{g}(k,l)},$ $p\left({v}_{t}\left(i\right)\right{x}_{i},{u}_{i},{\stackrel{\→}{\mathrm{\ω}}}^{p})=$ $=\frac{{\left\right{v}_{t}\left(i\right)\mathrm{\ω}(k,l)\left\right}^{2}}{{\mathrm{\σ}}_{t}(k,l)},$ Wherein, k ∈ [1,2 ..., K '], K ' is total classification number of segmentation label, integer l ∈ [0,
1], $\stackrel{\→}{m}=\{m(1.1),\·\·\·,m({K}^{\′},M)\}$ With $\stackrel{\→}{\mathrm{\ω}}=\{\mathrm{\ω}(1.1),\·\·\·,\mathrm{\ω}({K}^{\′},M)\}$ It it is classification center； ${\stackrel{\→}{\mathrm{\σ}}}_{g}=\{{\mathrm{\σ}}_{g}(1.1),\·\·\·,{\mathrm{\σ}}_{g}({K}^{\′},M)\}$
With ${\stackrel{\→}{\mathrm{\σ}}}_{t}=\{{\mathrm{\σ}}_{t}(1.1),\·\·\·,{\mathrm{\σ}}_{t}({K}^{\′},M)\}$ It is the variance of gray value and textural characteristics respectively；
7a3) set average grayGrads threshold d_{1}=10^{3}, textural characteristics meansigma methodsGrads threshold d_{2}=10^{3}With
The Grads threshold d of adjustment factor α_{3}=10^{2}If,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.
And make p+1=p；
ICE method estimates the parameter θ ' in binary potential function=(β, β 7b) to utilize iterated conditional to estimate_{1},β_{2}):
7b1) given θ '=(β, β_{1},β_{2}) initial value, i.e. β, β_{1}And β_{2}Arbitrary 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 (x^{1},u^{1}),…,(x^{t},u^{t}), calculate θ '^{(p)}Conditional expectation θ '^{(p+1})=[θ '^{(p)}(x^{1},u^{1},y)+…
+θ′^{(p)}(x^{t},u^{t}, y)] and/t, wherein, θ '^{(p)}(x^{1},u^{1}, y) represent the parameter in first sample, θ ' in pth time iteration^{(p)}(x^{t},
u^{t}, 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 abovementioned 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) DualCore 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 '={ y_{i} i ∈ S}, y_{i}For the gray value of pixel i, y_{i}∈ [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 dotdash
It is divided into K ' class, obtains initial segmentation Label Field X, X={x_{i} i ∈ S}, x_{i}For the segmentation label of pixel i, x_{i}∈[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={u_{i} i ∈ S}, u_{i}For the auxiliary field label of pixel i, u_{i}∈[λ_{1},λ_{2},...,λ_{M}], λ_{1},λ_{2},…,λ_{M}Represent 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 extracted_{t}(i)；
3a) centered by pixel i, calculate its 5 × 5 sliding window Nei Dongwest, northsouth, northeastsouthwest, northwesteast respectively
The absolute value variogram value of south four direction:
Wherein, γ_{EW}(h) represent eastwest to absolute value variogram value, γ_{NS}H () represents the absolute value in northsouth direction
Variogram value, γ_{NESW}H () represents the absolute value variogram value of northeastsouthwestward, γ_{NWSE}H () represents northwestsoutheast
The absolute value variogram value in direction, h is the delay distance of any direction, h value 2, N_{EW}(h), N_{NS}(h), N_{NESW}(h) and
N_{NWSE}H () 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 twodimensional 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: v_{t}(i)=
[γ_{EW}(h),γ_{NS}(h),γ_{NESW}(h),γ_{NWSE}(h)]；
(4) Label Field X and unitary potential function f under auxiliary field U synergy are utilized_{i}(x_{i},u_{i} y) with binary potential function f_{ij}(x_{i},
x_{j},u_{i},u_{j} 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 classifier_{i}(x_{i},u_{i} y):
Wherein, x_{i}For the segmentation label of pixel i, x_{i}∈ [1,2 ..., K '], K ' is total classification number of segmentation label, u_{i}For pixel i
Auxiliary field label, u_{i}∈ [0,1], p ' (x_{i},u_{i}v_{t}(i),v_{g}(i)) represent local label distribution, v_{t}(i) and v_{g}I () 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:
f_{ij}(x_{i},x_{j},u_{i},u_{j} y)=W ' (x_{i},x_{j},u_{i},u_{j}θ′)g_{ij}(v_{g},v_{t}),
Wherein, W ' (x_{i},x_{j},u_{i},u_{j} θ ') represent the interaction between label:
δ^{*}() function equal to 1, is otherwise equal to 0 when three input parameters are equal；θ '=(β, β_{1},β_{2}), parameter beta, β_{1}And β_{2}Point
Biao Shi not be positioned at the pixel degree of dependence to neighbor of region intersection, smooth region and texture region, g_{ij}(v_{g},v_{t})
Dependency between expression SAR image data:
Wherein, d_{g}(i, j)=  v_{g}(i)v_{g}(j)   represent two neighbor pixel i, the Euclidean distance of the gray scale of j；d_{t}(i,j)
=  v_{t}(i)v_{t}(j)   represent two neighbor pixel i, the Euclidean distance of the textural characteristics of j；
4c) according to unitary potential function f_{i}(x_{i},u_{i} y) with binary potential function f_{ij}(x_{i},x_{j},u_{i},u_{j} y) obtain joint posterior distribution letter
Number p (x, u  y) such as following formula:
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, N_{i}Represent the neighbour of pixel i
Territory, x_{j}Represent the segmentation label of pixel j, u_{j}Represent 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: [X_{1},…,X_{T}] and [U_{1},…,U_{T}]；
(6) Bayesian MAP marginal probability criterion MPM T the sample [X to Label Field X with auxiliary field U is utilized_{1},…,X_{T}]
[U_{1},…,U_{T}] 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: [X_{1},…,X_{T}] and [U_{1},…,U_{T}]。
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 U_{1},…,X_{T}] and [U_{1},…,U_{T}], create two discrete Markov
Chain X (t)={ X_{1},X_{2},…,X_{T}And U (t)={ U_{1},U_{2},…,U_{T}, 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 i_{i}Posterior distrbutionp p (x_{i} y) and auxiliary
Field label u_{i}Posterior distrbutionp p (u_{i} y):
Order:
Wherein k ∈ [1,2 ..., K '], K ' be segmentation label total classification number, l is integer, l ∈ [0,1], X_{t}I () represents discrete horse
The t sample in Markov's chain X (t) is at the segmentation label of pixel i, U_{t}I () 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 (x_{i} y) with p (u_{i} 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 (x_{i} y), U '=(u '_{i})_{i∈S}, u '_{i}=arg maxp (u_{i}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
Wherein, p is iterations, and i, j represent pixel, v_{t}(i) and v_{g}I () is that SAR image is at the half of pixel i respectively
Variance textural characteristics and gray value, x_{i}Represent pixel i label in Label Field X, u_{i}Represent that pixel i is in auxiliary
Label in the U of field, x_{j}Represent pixel j label in Label Field X, u_{j}Represent 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, N_{i}Represent 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 d_{1}=10^{3}, textural characteristics meansigma methodsGrads threshold d_{2}=10^{3}And tune
The Grads threshold d of joint factor alpha_{3}=10^{2}If,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 α^{p+1}, i.e.
And make p+1=p；
ICE method estimates the parameter θ ' in binary potential function=(β, β 7b) to utilize iterated conditional to estimate_{1},β_{2}):
7b1) given θ '=(β, β_{1},β_{2}) initial value, i.e. β, β_{1}And β_{2}Arbitrary 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)}=E_{θ′(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 (x^{1},u^{1}),…,(x^{t},u^{t}), calculate θ '^{(p)}Conditional expectation θ '^{(p+1)}=[θ '^{(p)}(x^{1},u^{1},y)+…+θ′^{(p)}(x^{t},u^{t},
Y)]/t, wherein, θ '^{(p)}(x^{1},u^{1}, y) represent the parameter in first sample, θ ' in pth time iteration^{(p)}(x^{t},u^{t}, 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 abovementioned steps 7b1) and7b2)；No
Then make iterations p from increasing 1, return step 7b2) continue executing with.
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