CN102426700B - Level set SAR image segmentation method based on local and global area information - Google Patents

Abstract

The invention discloses a level set SAR (Synthetic Aperture Radar) image segmentation method based on local and global area information, which mainly solves the problem that the existing level set method is influenced by speckle and cannot segment the SAR images with uneven gray. The method comprises the following implementation steps of: firstly, initializing a level set function phi, and segmenting the SAR image into an internal area omega 1 and an external area omega 2; secondly, convolving intensity information of the internal area and the external area of the image through a Gaussian Kernel Function, taking the convolved information as local area information, and forming an energy term based on the local area; then, solving intensity mean values c1 and c2 and probability densities p1and p2 of the internal area and the external area, and forming the energy term of the global area; and finally, adding a bound term L (phi) of level set length and a penalty P (phi) which avoids renewed initialization, forming a total energy function ESAR, solving a gradient sinking equation through a variation method, and updating the level set phi. The obtained new segmented area and the experimental result show that the segmentation method provided by the invention can get more ideal segmentation effects, and the method can be used for SAR image segmentation and target identification.

Description

Level set SAR image partition method based on local and global area information

Technical field

The invention belongs to technical field of image processing, relate to the application in SAR image segmentation field, a kind of level set SAR image partition method that combines based on local and global area information specifically can be used for the cutting apart of SAR image, rim detection and target and identifies.

Background technology

Synthetic-aperture radar SAR is the active radar of a kind of high resolving power, but has the advantages such as round-the-clock, round-the-clock, the high side-looking imaging of resolution, can be applicable to the numerous areas such as military affairs, agricultural, navigation, geographical supervision.The SAR image is widely used in object detection field, and the SAR image segmentation then is the important step of processing graphical analysis from image, is the basis of target classification and identification.Because SAR is a kind of coherence imaging system, the SAR image is to the Electromagnetic Scattering Characteristics of target and the reaction of architectural characteristic in itself, and its imaging effect depends on radar parameter and region electromagnetic parameter to a great extent.Because the singularity of SAR imaging system, make information representation mode and the optical imagery of SAR image that very big-difference be arranged, and can be subject to the impact of many geometric properties such as coherent speckle noise and shade, just because of these factors make the dividing method that is applicable to optical imagery no longer applicable to the SAR image.

On the whole conventional SAR image partition method similar or with traditional parted pattern to the SAR Image Segmentation Using, as some based on the cutting apart of threshold value, based on the edge cut apart and based on dividing method of region growing etc., but a lot of dividing methods wherein easily are subject to the impact of coherent speckle noise in the SAR image, so these class methods all need to suppress coherent speckle noise by pre-service first.These preprocess methods have lost a lot of edges and target information inevitably when suppressing coherent speckle noise, affected segmentation effect.

Level set image segmentation method is one of important image processing method.The advantage of Level Set Method is the variation that can adapt to topological structure, and algorithm stability is higher.Utilize Level Set Method research SAR image segmentation problem, by setting up suitable energy functional, can in the definition of energy functional, introduce image area information, do not needing to obtain more accurately segmentation result for the SAR image that affected by coherent speckle noise in the pretreated situation of coherent spot.

Can be divided into based on regional area with based on the method for global area based on the Level Set Method in zone.Utilize the half-tone information structure energy function of the regional area of image based on the method for regional area, obtained preferably segmentation result at medical image and natural image, the CV model that Chan and Vese propose is a kind of level set dividing method based on the zone, as a kind of zone level collection parted pattern of energy Effective Raise curve evolvement topology adaptation ability, it has utilized the global area information of image.But it is the Shortcomings part equally also, the internal energy term of this model just guarantees zero level collection line smoothing, and do not consider the inwardness that level set function itself is intrinsic, also need in some applications level set function is reinitialized, so that it is near the symbolic distance function, guarantee the stability of numerical solution.

Although the level set dividing method has obtained huge success in optics and medical image segmentation, but in SAR image segmentation field, that studies is also fewer, the scholar who studies in the world at present based on the Level Set Method of area information has the people such as Chunming Li and Ayed, Chunming Li lays particular stress on the local two-value match LBF method of research in the application of medical image segmentation, because the SAR picture noise is multiplicative noise, be different from the additive noise in medical image and the natural image, the regional area method is vulnerable to the impact of the property taken advantage of coherent speckle noise, so the LBF method is not suitable for the SAR image.The Level Set Method of the people such as Ayed research easily produces more complicated SAR image Lou cuts apart phenomenon, is not very desirable to the segmentation result of complex region SAR image.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, a kind of level set SAR image partition method that combines based on local and global area information is provided, with accurately cutting apart of the fuzzy SAR image-region of realization edge, improve the positioning performance at edge, thereby improve the quality of SAR image segmentation.

Realize that the object of the invention technical thought is: according to the half-tone information of SAR image, use a local window function gaussian kernel function strength information of exterior domain in the image is carried out convolution, as local region information, again according to the statistical property of SAR image, the estimated value of the probability density in two zones that obtain is divided in calculating by level set, with the logarithm of each estimated value as global area information, last bound term and the penalty term of avoiding reinitializing in conjunction with level set length, this four partial information combined carry out the modeling of energy function, thereby reach desirable segmentation result.Its concrete implementation procedure comprises as follows:

(1) level set function φ is initialized to the symbolic distance functional form, positive and negative according to the level set function value is divided into interior zone Ω with the whole image-region Ω of SAR image I to be split ₁With perimeter Ω ₂

(2) according to described two regional Ω ₁With _Ω2, the energy of local area function E that structure is corresponding _L:

$E_L={\mathrm{\λ}}_1{\∫\∫}_{{\mathrm{\Ω}}_1}K\left(\mathrm{\φ}\right)*{|I-f_1\left(\mathrm{\φ}\right)|}^{2}H\left(\mathrm{\φ}\right)+{\mathrm{\λ}}_2{\∫\∫}_{{\mathrm{\Ω}}_2}K\left(\mathrm{\φ}\right)*{|I-f_2\left(\mathrm{\φ}\right)|}^2(1-H\left(\mathrm{\φ}\right)),$

Wherein, λ ₁And λ ₂Be the weights of local energy item, φ is level set function, and K (φ) is gaussian kernel function, and I is image to be split, f ₁(φ) be regional Ω ₁The local gray level average, f ₂(φ) be regional Ω ₂The local gray level average, H (φ) is the Heaviside function;

(3) according to described two regional Ω ₁And Ω ₂, the global area energy function E that structure is corresponding _G:

$E_G=-{\mathrm{\λ}}_1{\∫\∫}_{{\mathrm{\Ω}}_1}\log \left(p_1\left(I\right)\right)-{\mathrm{\λ}}_2{\∫\∫}_{{\mathrm{\Ω}}_2}\log \left(p_2\left(I\right)\right),$

Wherein, λ ₁And λ ₂The weights of global energy item, p ₁(I) be regional Ω ₁Estimated probability density, p ₂(I) be regional Ω ₂Estimated probability density;

(4) the energy of local area function E of integrating step two structures _LGlobal area energy function E with the step 3 structure _G, the structure total energy function:

4a) according to the formula of asking level set length L (φ) in the local two-value match LBF method, calculated level collection length item L (φ):

$L\left(\mathrm{\φ}\right)={\∫\∫}_{\mathrm{\Ω}}|\▿H\left(\mathrm{\φ}\right)|,$

Wherein

Be gradient operator, H (φ) is the Heaviside function;

4b) according to asking the formula of avoiding the penalty term P (φ) that reinitializes in the local two-value match LBF method, calculate penalty term P (φ):

$P\left(\mathrm{\φ}\right)={\∫\∫}_{\mathrm{\Ω}}\frac{1}{2}{\left(\right|\▿\mathrm{\φ}|-1)}^2,$

Wherein

That level set function φ is asked gradient;

4c) the energy of local area function E that tries to achieve of integrating step two _L, the global area energy function E that step 3 is tried to achieve _G, step 4a) and the bound term L (φ) and the step 4b that try to achieve) the penalty term P (φ) that tries to achieve, construct complete total energy function E _SAR:

E _SAR＝αE _L+(1-α)E _G++μL(φ)+νP(φ)，

Wherein α is used for regulating the ratio of local and global energy item, and μ is the weights of bound term, is used for regulating the value of length constraint item, and ν is the weights of penalty term, is used for regulating the value of penalty term, and the value of μ and ν obtains by experiment.

(5) the total energy function E that constructs according to step (4) _SARThe SAR image I is cut apart:

5a) to total energy function E _SARUtilize the variational method, obtain the Gradient Descent flow equation

$\frac{\∂\mathrm{\φ}}{\∂t}=\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_1\log \left(P_1\left(I\right)\right)-{\mathrm{\λ}}_2\log \left(P_2\left(I\right)\right))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)),$

Wherein: δ (φ) is the Dirac function, e ₁And e ₂Be intermediate variable, its expression formula is respectively:

e ₁＝∫∫ _ΩK(φ)*|I-f ₁(φ)| ²，e ₂＝∫∫ _ΩK(φ)*|I-f ₂(φ)| ²，

5b) to the Gradient Descent flow equation

Discretize obtains following expression:

$\frac{{\mathrm{\φ}}^{n+1}-{\mathrm{\φ}}^n}{\mathrm{\Δt}}=\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_1\log \left(P_1\left(I\right)\right)-{\mathrm{\λ}}_2\log \left(P_2\left(I\right)\right))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)),$

Wherein: φ ^N+1Represent the level set function after the iteration the n+1 time, φ ⁿRepresent the level set function after the iteration the n time, Δ t is iteration step length;

5c) according to step 5b) discretization equation that obtains Try to achieve φ ^N+1Expression formula be:

${\mathrm{\φ}}^{n+1}={\mathrm{\φ}}^n+\mathrm{\Δt}\·(\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_1\log \left(P_1\left(I\right)\right)-{\mathrm{\λ}}_2\log \left(P_2\left(I\right)\right))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right))),$

5d) according to step 5c) try to achieve new level set function φ ^N+1, by φ ^N+1Positive negative value namely obtain new cut zone

With

5e) whether the determined level set function is restrained and is reached maximum iterations 100 times, does not then forward step (2) to if do not satisfy, and uses

With

Substitute Ω ₁And Ω ₂Continue iteration, otherwise stop iteration, obtain

With

It namely is final segmentation result.

The present invention has the following advantages compared with prior art:

1, the gaussian kernel function K (φ) of utilization of the present invention with fine local effect makes convolution to field strength information inside and outside the SAR image, as local region information, can guarantee to obtain enough segmenting edge.

2, the present invention combines the Gamma statistical probability density information of SAR image coherent speckle noise, directly constructed the global area energy function of level set function, parted pattern is carried out in the pretreated situation coherent speckle noise not needing, can obtain relatively accurate segmentation result to the SAR image that the property taken advantage of coherent speckle noise affects.

3, the present invention had both used local region information, used again global area information, made the region energy item structure of total energy function model more reasonable.The present invention takes full advantage of the area information of image, not only the image border is had and well cut apart the localization effect, improve again the accuracy to object edge location, also improved simultaneously segmentation effect and the robustness of fuzzy and the SAR image that gray scale is inhomogeneous of edge.

Through with the simulation comparison of existing level set dividing method, verified that the present invention can obtain better segmentation effect to the SAR image segmentation.

Description of drawings

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the first width of cloth test pattern;

Fig. 3 is with the present invention and the existing method segmentation effect comparison diagram to Fig. 2;

Fig. 4 is the second width of cloth test pattern;

Fig. 5 is with the present invention and the existing method segmentation effect comparison diagram to Fig. 4;

Embodiment

With reference to Fig. 1, specific implementation step of the present invention is as follows:

Step 1 is initialized to the symbolic distance functional form with level set function φ, and positive and negative according to the level set function value is divided into two regional Ω with the whole image-region Ω of SAR image I to be split ₁And Ω ₂

The detailed process that realizes this step is expressed as follows: do a rectangle with PC Tools in image I to be split, this rectangle equation is as initialization level set function φ, when φ＞0, and expression rectangle perimeter Ω ₁, when φ＜0, expression rectangle interior zone Ω ₂, therefore, positive and negative according to the level set function value is divided into two regional Ω with the SAR image ₁And Ω ₂

Step 2 is according to described two regional Ω ₁And Ω ₂, the energy of local area function E that structure is corresponding _L:

2a) choose the karyomerite function:

Suppose that K () is a kernel function, have local characteristics, this kernel function need meet the following conditions:

K(-x)＝K(x)

K(x)≤K(y)，if|x|＞|y|，

K(x)＝0，if|x|→∞

Wherein x and y are two independents variable, and y is the point of the regional area centered by x;

Analyzing above character draws: if decentering point x is far away, its kernel function value is less as can be known by the character of karyomerite function, if instead decentering point x is nearer, its kernel function value is larger.Usually the kernel function that satisfies this character is gaussian kernel function, so the present invention chooses gaussian kernel function commonly used as the karyomerite function, and its expression formula is as follows:

$K\left(\mathrm{\φ}\right)=\frac{1}{{\left(2\mathrm{\π}\right)}^{n/2}{\mathrm{\σ}}^n}\exp (-\frac{{\left|\mathrm{\φ}\right|}^2}{2{\mathrm{\σ}}^2}),$

Wherein φ is level set function, and n is positive integer, and σ is the standard variance of gaussian kernel function;

2b) according to karyomerite function K (φ), zoning Ω ₁And Ω ₂Local strength's average:

$f_1\left(\mathrm{\φ}\right)=\frac{K\left(\mathrm{\φ}\right)*\left[H\left(\mathrm{\φ}\right)I\right]}{K\left(\mathrm{\φ}\right)*H\left(\mathrm{\φ}\right)}$

$f_2\left(\mathrm{\φ}\right)=\frac{K\left(\mathrm{\φ}\right)*\left[\left(1-H\left(\mathrm{\φ}\right)\right)I\right]}{K\left(\mathrm{\φ}\right)*[1-H\left(\mathrm{\φ}\right)]},$

Wherein H (φ) is the Heaviside function, and I is SAR image to be split, and * is convolution algorithm;

2c) integrating step 2b) the local strength's average that obtains obtains the energy of local area function as follows:

$E_L={\mathrm{\λ}}_1{\∫\∫}_{{\mathrm{\Ω}}_1}K\left(\mathrm{\φ}\right)*{|I-f_1\left(\mathrm{\φ}\right)|}^{2}H\left(\mathrm{\φ}\right)+{\mathrm{\λ}}_2{\∫\∫}_{{\mathrm{\Ω}}_2}K\left(\mathrm{\φ}\right)*{|I-f_2\left(\mathrm{\φ}\right)|}^2(1-H\left(\mathrm{\φ}\right)),$

λ wherein ₁And λ ₂The weights of local energy item.

Step 3 is according to described two regional Ω ₁And Ω ₂, the global area energy function E that structure is corresponding _G:

3a) according to the formula that calculates SAR image intensity average in the statistical method, zoning Ω ₁Strength mean value c ₁With regional Ω ₂Strength mean value c ₂:

$\left\{\begin{array}{c}{c}_1=\frac{{\∫\∫}_{{\mathrm{\Ω}}_1}I(x,y)\mathrm{dxdy}}{{\∫\∫}_{{\mathrm{\Ω}}_1}\mathrm{dxdy}}\\ c_2=\frac{{\∫\∫}_{{\mathrm{\Ω}}_2}I(x,y)\mathrm{dxdy}}{{\∫\∫}_{{\mathrm{\Ω}}_2}\mathrm{dxdy}}\end{array}\right.,$

Wherein (x, y) is the coordinate of SAR image I to be split;

3b) according to step 3a) the strength mean value c that tries to achieve ₁, c ₂With the formula that calculates SAR image probability density function in the statistical method, zoning Ω ₁And Ω ₂Estimated probability density p ₁(I) and p ₂(I):

$\left\{\begin{array}{c}{p}_1\left(I\right)=\frac{L^L}{c_1\mathrm{\Γ}\left(L\right)}{\left(\frac{I}{c_1}\right)}^{L-1}{e}^{-\mathrm{LI}/c_1}\\ p_2\left(I\right)=\frac{L^L}{c_2\mathrm{\Γ}\left(L\right)}{\left(\frac{I}{c_2}\right)}^{L-1}{e}^{-\mathrm{LI}/c_2}\end{array}\right.,$

Wherein L is the number of looking of SAR image, and Γ () is the Gamma function;

3c) integrating step 3a)-3b), construct energy function model E based on the global area _G:

$E_G=-{\mathrm{\λ}}_1{\∫\∫}_{{\mathrm{\Ω}}_1}\log \left(p_1\left(I\right)\right)-{\mathrm{\λ}}_2{\∫\∫}_{{\mathrm{\Ω}}_2}\log \left(p_2\left(I\right)\right),$

λ wherein ₁And λ ₂The weights of global energy item, p ₁(I) be regional Ω ₁Estimated probability density, p ₂(I) be regional Ω ₂Estimated probability density.

Step 4, the energy of local area function E of integrating step two structures _LGlobal area energy function E with the step 3 structure _G, the structure total energy function:

4a) according to the formula of asking level set length L (φ) in the local two-value match LBF method, calculated level collection length item L (φ):

$L\left(\mathrm{\φ}\right)={\∫\∫}_{\mathrm{\Ω}}|\▿H\left(\mathrm{\φ}\right)|,$

Wherein

Be gradient operator, H (φ) is the Heaviside function;

4b) according to asking the formula of avoiding the penalty term P (φ) that reinitializes in the local two-value match LBF method, calculate penalty term P (φ):

$P\left(\mathrm{\φ}\right)={\∫\∫}_{\mathrm{\Ω}}\frac{1}{2}{\left(\right|\▿\mathrm{\φ}|-1)}^2,$

Wherein

That level set function φ is asked gradient;

4c) the energy of local area function E that tries to achieve of integrating step two _L, the global area energy function E that step 3 is tried to achieve _G, step 4a) and the bound term L (φ) and the step 4b that try to achieve) the penalty term P (φ) that tries to achieve, construct complete total energy function E _SAR:

E _SAR＝αE _L+(1-α)E _G++μL(φ)+νP(φ)，

Wherein α is used for regulating the ratio of local and global energy item, and μ is the weights of bound term, is used for regulating the value of length constraint item, and ν is the weights of penalty term, is used for regulating the value of penalty term, and the value of μ and ν obtains by experiment.

Step 5 is according to the total energy function E of step 4 structure _SARThe SAR image I is cut apart:

5a) to total energy function E _SARUtilize the variational method, try to achieve the Gradient Descent flow equation and be:

$\frac{\∂\mathrm{\φ}}{\∂t}=\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_1\log \left(P_1\left(I\right)\right)-{\mathrm{\λ}}_2\log \left(P_2\left(I\right)\right))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)),$

Wherein: δ (φ) is the Dirac function, e ₁And e ₂Be intermediate variable, its expression formula is respectively:

e ₁＝∫∫ _ΩK(φ)*|I-f ₁(φ)| ²，e ₂＝∫∫ _ΩK(φ)*|I-f ₂(φ)| ²，

5b) to the Gradient Descent flow equation

Discretize obtains following expression:

$\frac{{\mathrm{\φ}}^{n+1}-{\mathrm{\φ}}^n}{\mathrm{\Δt}}=\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_1\log \left(P_1\left(I\right)\right)-{\mathrm{\λ}}_2\log \left(P_2\left(I\right)\right))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)),$

φ wherein ^N+1Represent the level set function after the iteration the n+1 time, φ ⁿRepresent the level set function after the iteration the n time, Δ t is iteration step length;

5c) according to step 5b) discretization equation that obtains

Try to achieve φ ^N+1Expression formula be:

${\mathrm{\φ}}^{n+1}={\mathrm{\φ}}^n+\mathrm{\Δt}\·(\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_1\log \left(P_1\left(I\right)\right)-{\mathrm{\λ}}_2\log \left(P_2\left(I\right)\right))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right))),$

5d) according to step 5c) try to achieve new level set function φ ^N+1, by φ ^N+1Positive and negative value obtain new cut zone

With Be φ ^N+1＞0, obtain cut zone

φ ^N+1＜0 obtains cut zone

Step 6 judges whether convergence.

The fundamental purpose of this step is the iteration situation according to level set, and whether the determined level set function is restrained and reached maximum iterations, if the Gradient Descent flow equation does not reach steady state (SS) and do not reach maximum iterations, then forwards step 2 to, uses

With Substitute Ω ₁And Ω ₂Continue iteration, otherwise stop iteration, obtain final zone With

It namely is final segmentation result.

Effect of the present invention can further specify by following emulation:

1, simulated conditions

Hardware platform is: Intel Core2 Duo CPU E65502.33GHZ, 2GB RAM.

Software platform is: MATLAB 7.9.

2, emulation content and interpretation of result

Emulation one: use the present invention and existing local two-value match LBF method and existing statistical method and respectively the test pattern of Fig. 2 is carried out split-run test, its segmentation result as shown in Figure 3, wherein: Fig. 3 (a) is that local two-value match LBF method is to the segmentation result of Fig. 2; Fig. 3 (b) is that existing statistical method is to the segmentation result of Fig. 2; Fig. 3 (c) is that the inventive method is to the segmentation result of Fig. 2.

Can be found out by Fig. 3 (a), existing local two-value match LBF method is very sensitive to SAR image coherent speckle noise, has detected many false edges.Can be found out by Fig. 3 (b), existing Statistical Techniques can only detect partial contour to the zone than more rich SAR image, and can not obtain complete segmentation result.Comparison diagram 3 (a) and Fig. 3 (c), because the present invention combines the global area information that suppresses the SAR picture noise, inhibited to noise, so the present invention too much false edge can not occur, comparison diagram 3 (b) and Fig. 3 (c), because the present invention combines local region information, can guarantee to obtain enough edges, thereby obtain relatively accurate segmentation result.

Emulation two: use the present invention and existing local two-value match LBF method and existing statistical method and respectively the test pattern of Fig. 4 is carried out split-run test, its segmentation result as shown in Figure 5, wherein: Fig. 5 (a) is that local two-value match LBF method is to the segmentation result of Fig. 4; Fig. 5 (b) is that existing statistical method is to the segmentation result of Fig. 4; Fig. 5 (c) is that the inventive method is to the segmentation result of Fig. 4.

Can be found out by Fig. 5 (a), existing local two-value match LBF method is very sensitive to SAR image coherent speckle noise, so detected many false edges.Can be found out by Fig. 5 (b), existing Statistical Techniques can only detect partial contour to the SAR image, and can not obtain complete segmentation result.Can be found out by Fig. 5 (c), inhibited and can obtain enough edges to noise because the present invention combines local and global area information, the positioning performance at enhancing edge, thus obtain relatively accurate segmentation result.

Claims (3)

1. level set SAR image partition method that combines based on local and global area information may further comprise the steps:

(1) level set function φ is initialized to the symbolic distance functional form, positive and negative according to the level set function value is divided into interior zone Ω with the whole image-region Ω of SAR image I to be split ₁With perimeter Ω ₂

(2) according to described two regional Ω ₁And Ω ₂, the energy of local area function E that structure is corresponding _L:

$E_L={\mathrm{\λ}}_1{\∫\∫}_{{\mathrm{\Ω}}_1}K\left(\mathrm{\φ}\right)*{|I-f_1\left(\mathrm{\φ}\right)|}^{2}H\left(\mathrm{\φ}\right)+{\mathrm{\λ}}_2{\∫\∫}_{{\mathrm{\Ω}}_2}K\left(\mathrm{\φ}\right)*{|I-f_2\left(\mathrm{\φ}\right)|}^2(1-H\left(\mathrm{\φ}\right)),$

Wherein, λ ₁And λ ₂Be the weights of local energy item, φ is level set function, and K (φ) is gaussian kernel function, and I is image to be split, f ₁(φ) be regional Ω ₁The local gray level average, f ₂(φ) be regional Ω ₂The local gray level average, H (φ) is the Heaviside function;

(3) according to described two regional Ω ₁And Ω ₂, the global area energy function E that structure is corresponding _G:

$E_G=-{\mathrm{\λ}}_3{\∫\∫}_{{\mathrm{\Ω}}_1}\log \left(p_1\left(I\right)\right)-{\mathrm{\λ}}_4{\∫\∫}_{{\mathrm{\Ω}}_2}\log \left(p_2\left(I\right)\right),$

Wherein, λ ₃And λ ₄The weights of global energy item, p ₁(I) be regional Ω ₁Estimated probability density, p ₂(I) be regional Ω ₂Estimated probability density;

(4) the energy of local area function E of integrating step (2) structure _LAnd the global area energy function E of step (3) structure _G, the structure total energy function:

4a) according to the formula of asking level set length L (φ) in the local two-value match LBF method, calculated level collection length item L (φ):

$L\left(\mathrm{\φ}\right)={\∫\∫}_{\mathrm{\Ω}}|\▿H\left(\mathrm{\φ}\right)|,$

Wherein

Be gradient operator, H (φ) is the Heaviside function;

4b) according to asking the formula of avoiding the penalty term P (φ) that reinitializes in the local two-value match LBF method, calculate penalty term P (φ):

$P\left(\mathrm{\φ}\right)={\∫\∫}_{\mathrm{\Ω}}\frac{1}{2}{\left(\right|\▿\mathrm{\φ}|-1)}^2,$

Wherein

That level set function φ is asked gradient;

4c) the energy of local area function E that tries to achieve of integrating step (2) _L, the global area energy function E that step (3) is tried to achieve _G, step 4a) and the bound term L (φ) and the step 4b that try to achieve) the penalty term P (φ) that tries to achieve, construct complete total energy function E _SAR:

E _SAR＝αE _L+（1-α）E _G++μL(φ)+νP(φ)，

Wherein α is used for regulating the ratio of local and global energy item, and μ is the weights of bound term, is used for regulating the value of length constraint item, and ν is the weights of penalty term, is used for regulating the value of penalty term, and the value of μ and ν obtains by experiment;

(5) the total energy function E that constructs according to step (4) _SARThe SAR image I is cut apart:

5a) to total energy function E _SARUtilize the variational method, obtain the Gradient Descent flow equation

$\frac{\∂\mathrm{\φ}}{\∂t}=\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_3\log \left(p_1\left(I\right)\right)-{\mathrm{\λ}}_4\log \left(p_2\left(I\right)\right)))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)),$

Wherein: δ (φ) is the Dirac function, λ ₁And λ ₂Be the weights of local energy item, λ ₃And λ ₄Be the weights of global energy item, e ₁And e ₂Be intermediate variable, its expression formula is respectively:

$e_1={\∫\∫}_{{\mathrm{\Ω}}_1}K\left(\mathrm{\φ}\right)*|I-f_1{\left(\mathrm{\φ}\right)|}^2,e_2={\∫\∫}_{{\mathrm{\Ω}}_2}K\left(\mathrm{\φ}\right)*{|I-f_2\left(\mathrm{\φ}\right)|}^2;$

5b) to the Gradient Descent flow equation Discretize obtains following expression:

$\frac{{\mathrm{\φ}}^{n+1}-{\mathrm{\φ}}^n}{\mathrm{\Δt}}=\mathrm{\δ}\left(\mathrm{\φ}\right)(\mathrm{\α}(-({\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2))+(1-\mathrm{\α})({\mathrm{\λ}}_3\log \left(p_1\left(I\right)\right)-{\mathrm{\λ}}_4\log \left(p_2\left(I\right)\right)))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)),$

Wherein: φ ^N+1Represent the level set function after the iteration the n+1 time, φ ⁿRepresent the level set function after the iteration the n time, λ ₁And λ ₂Be the weights of local energy item, λ ₃And λ ₄Be the weights of global energy item, Δ t is iteration step length;

5c) according to step 5b) discretization equation that obtains

Try to achieve φ ^N+1Expression formula be:

${\mathrm{\φ}}^{n+1}={\mathrm{\φ}}^n+\mathrm{\Δt}\·\left(\mathrm{\δ}\left(\mathrm{\φ}\right)\right)\left(\mathrm{\α}(-{\mathrm{\λ}}_1{e}_1-{\mathrm{\λ}}_2{e}_2)\right)+(1-\mathrm{\α})({\mathrm{\λ}}_3\log \left(p_1\left(I\right)\right)-{\mathrm{\λ}}_4\log \left(p_2\left(I\right)\right))$

$+\mathrm{\μ\δ}\left(\mathrm{\φ}\right)\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right)+v({\▿}^2\mathrm{\φ}-\mathrm{div}\left(\frac{\▿\mathrm{\φ}}{|\▿\mathrm{\φ}|}\right));$

5d) according to step 5c) try to achieve new level set function φ ^N+1, by φ ^N+1Positive negative value namely obtain new cut zone

With

5e) whether the determined level set function is restrained and is reached maximum iterations 100 times, does not then forward step (2) to if do not satisfy, and uses

With

Substitute Ω ₁And Ω ₂Continue iteration, otherwise stop iteration, obtain

With

It namely is final segmentation result.

2. level set SAR image partition method according to claim 1, energy of local area function corresponding to the described structure of step (2) wherein, carry out as follows:

2a) choose gaussian kernel function commonly used as the karyomerite function, its expression formula is as follows:

$K\left(\mathrm{\φ}\right)=\frac{1}{{\left(2\mathrm{\π}\right)}^{n/2}{\mathrm{\σ}}^n}\exp (-\frac{{\left|\mathrm{\φ}\right|}^2}{{2\mathrm{\σ}}^2}),$

Wherein φ is level set function, and n is positive integer, and σ is the standard variance of gaussian kernel function;

2b) according to the karyomerite function, zoning Ω ₁And Ω ₂Local strength's average:

$f_1\left(\mathrm{\φ}\right)=\frac{K\left(\mathrm{\φ}\right)*\left[H\left(\mathrm{\φ}\right)I\right]}{K\left(\mathrm{\φ}\right)*H\left(\mathrm{\φ}\right)}$

$f_2\left(\mathrm{\φ}\right)=\frac{K\left(\mathrm{\φ}\right)*\left[(1-H\left(\mathrm{\φ}\right))I\right]}{K\left(\mathrm{\φ}\right)*[1-H\left(\mathrm{\φ}\right)]},$

Wherein H (φ) is the Heaviside function, and I is SAR image to be split, and * is convolution algorithm;

2c) integrating step 2b) the local strength's average that obtains obtains the energy of local area function as follows:

$E_L={\mathrm{\λ}}_1{\∫\∫}_{{\mathrm{\Ω}}_1}K\left(\mathrm{\φ}\right)*{|I-f_1\left(\mathrm{\φ}\right)|}^{2}H\left(\mathrm{\φ}\right)+{\mathrm{\λ}}_2{\∫\∫}_{{\mathrm{\Ω}}_2}K\left(\mathrm{\φ}\right)*{|I-f_2\left(\mathrm{\φ}\right)|}^2(1-H\left(\mathrm{\φ}\right)),$

λ wherein ₁And λ ₂The weights of local energy item.

3. level set SAR image partition method according to claim 1, global area energy function corresponding to the described structure of step (3) wherein, carry out as follows:

3a) zoning Ω ₁And Ω ₂Strength mean value:

$c_i=\frac{{\∫\∫}_{{\mathrm{\Ω}}_i}I(x,y)\mathrm{dxdy}}{{\∫\∫}_{{\mathrm{\Ω}}_i}\mathrm{dxdy}},$

I=1 wherein, 2, (x, y) is the coordinate of SAR image I to be split;

3b) according to strength mean value c _i, zoning Ω ₁And Ω ₂Estimated probability density p ₁(I) and p ₂(I):

$p_i\left(I(x,y)\right)=\frac{L^L}{c_i\mathrm{\Γ}\left(L\right)}{\left(\frac{I(x,y)}{c_i}\right)}^{L-1}{e}^{-\mathrm{LI}(x,y)/c_i},i=\mathrm{1,2},$

Wherein L is the number of looking of SAR image, and I (x, y) is the pixel value that coordinate is located pixel in the image for (x, y), and Γ () is the Gamma function;

3c) integrating step 3a)-3b) construct the energy function model E based on the global area _G:

$E_G=-{\mathrm{\λ}}_1{\∫\∫}_{{\mathrm{\Ω}}_1}\log \left(p_1\left(I\right)\right)-{\mathrm{\λ}}_2{\∫\∫}_{{\mathrm{\Ω}}_2}\log \left(p_2\left(I\right)\right),$

λ wherein ₁And λ ₂The weights of global energy item, p ₁(I) be regional Ω ₁Estimated probability density, p ₂(I) be regional Ω ₂Estimated probability density.

Images