CN110136146B - SAR image water area segmentation method based on sinusoidal SPF distribution and level set model - Google Patents

SAR image water area segmentation method based on sinusoidal SPF distribution and level set model Download PDF

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CN110136146B
CN110136146B CN201910414750.6A CN201910414750A CN110136146B CN 110136146 B CN110136146 B CN 110136146B CN 201910414750 A CN201910414750 A CN 201910414750A CN 110136146 B CN110136146 B CN 110136146B
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吕文涛
任佳伟
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Hangzhou Huicui Intelligent Technology Co ltd
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Zhejiang University of Technology ZJUT
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Abstract

The invention discloses a sinusoidal SPF distribution and level setA method for segmenting a model SAR image water area. Establishing a global steady state minimum segmentation model based on sine SPF distribution and a level set model, wherein the model is fused with G0Weighted sum of both the area energy term and the regularization term of the probability density distribution and the sinusoidal SPF distribution: and (4) minimizing the energy functional to obtain a level set evolution equation, and solving by an iterative method to obtain an accurate target region and a background region of the SAR image. The method overcomes the inherent characteristics of inherent multiplicative speckle noise, target intensity heterogeneity change and the like of the SAR image and the defects that a traditional level set model based on statistical information is easy to fall into a local minimum value and the curve evolution speed is slow, and can improve the accuracy of SAR image segmentation.

Description

SAR image water area segmentation method based on sinusoidal SPF distribution and level set model
Technical Field
The invention relates to the field of image processing, in particular to a Synthetic Aperture Radar (SAR) image water area segmentation method based on sinusoidal Symbolic Pressure Function (SPF) distribution and a level set model.
Background
Image segmentation is the basis of the image research field, and effective segmentation results can provide key and effective information for processes such as image analysis and recognition. Image segmentation is an image processing technique for decomposing an image into several mutually disjoint regions to extract a target required by a user.
SAR image segmentation is important content of SAR image research and plays a vital role in subsequent SAR image analysis, identification and other processes. In recent years, research on SAR image segmentation at home and abroad has achieved abundant research results. The study found G0The probability density distribution can better fit the intensity statistical characteristics of the SAR image, and therefore is based on G0The distributed level set model is widely applied to segmentation of SAR images. Conventional G-based0The distributed level set model can better segment the SAR image target area, but for different SAR images, the model still faces various challenges, for example, the curve evolution of the model is easy to fall into a local minimum value, and the global steady-state segmentation result is difficult to obtain; for SAR images with rough background areas, strong speckle noise and fuzzy target boundaries, accurate segmentation can not be obtained by applying the model; in addition, the model is time consuming to process SAR images. Therefore, an efficient level set model needs to be built to adapt to the complexity of the SAR image.
Disclosure of Invention
In order to solve the problems in the background art, the invention provides an SAR image water area segmentation method based on sine SPF distribution and a level set model, which effectively realizes global minimum segmentation of a complex SAR image and simultaneously improves the evolution speed of a boundary curve in the image.
As shown in fig. 1, the present invention is realized by the following technical scheme, which comprises the following specific steps:
step 1, establishing a global steady state minimum segmentation model based on sine SPF distribution and a level set model, wherein the model is fused with G0Weighted sum of both the area energy term and the regularization term of the probability density distribution and the sinusoidal SPF distribution:
E＝Eregion(φ)+Ereg(φ)
where φ is a level set function, Eregion(phi) represents the regional energy term, Ereg(φ) represents the regularization term, E represents the total energy of the model;
1, A, the regional energy term Eregion(phi) the SAR image with complex background texture, strong speckle noise and fuzzy target contour can be segmented effectively and rapidly, and the segmentation is represented as follows:
Figure GDA0002783115660000021
wherein, x represents a pixel point in the image, and I (x) is the gray value of the pixel point x in the image; omega is an SAR image area and represents a target area/background area; a and b are first and second weight coefficients, beta is a regularization parameter and is taken as any smaller positive number, omega and lambda are weight coefficients of a sinusoidal SPF distribution term in a target area and a background area of the image respectively, and a, b, beta, omega and lambda can be adjusted according to different SAR images;
Figure GDA0002783115660000022
is G of the target area0The function of the probability density distribution is,
Figure GDA0002783115660000023
g as background region0A probability density distribution function, R (x) representing a sinusoidal SPF distribution term;
two G0The probability density distribution functions are respectively expressed as:
Figure GDA0002783115660000024
Figure GDA0002783115660000025
wherein the content of the first and second substances,
Figure GDA0002783115660000026
g for representing x gray value of pixel point in target area0The distribution of the probability density is such that,
Figure GDA0002783115660000027
g for representing x gray value of pixel point in background area0Probability density distribution, n is equivalent view, alpha1Is a shape parameter of the target region, gamma1Is a scale parameter of the target region, alpha2As a shape parameter of the background region, gamma2As scale parameters of the background area, gamma (·) is a gamma function;
the sinusoidal SPF distribution term R (x) is a novel sinusoidal SPF distribution, R (x) ranges from [ -1,1], as follows:
Figure GDA0002783115660000028
wherein, c1And c2Mean gray values respectively representing a target region and a background region in the SAR image are represented as:
Figure GDA0002783115660000029
wherein H (phi) represents a Heaviside function, and the value of epsilon in the invention is 1, and the Heaviside function is represented as:
Figure GDA00027831156600000210
wherein e represents epsilon parameter, epsilon is selected as a smaller positive number during numerical calculation;
1, B, said regularization term Ereg(φ) is used to smooth the level set function, expressed as:
Figure GDA0002783115660000031
wherein the content of the first and second substances,
Figure GDA0002783115660000032
is a gradient operator, v is a weight coefficient of a regular term, | calculation of the luminance2Represents the square of the gradient mode of phi;
and fusing the two energy terms, and comprehensively expressing the global steady-state minimization segmentation model as follows:
Figure GDA0002783115660000033
Figure GDA0002783115660000034
Figure GDA0002783115660000035
Figure GDA0002783115660000036
Figure GDA0002783115660000037
Figure GDA0002783115660000038
and 2, minimizing the energy functional obtained in the step 1 to obtain a level set evolution equation, and solving by an iterative method to obtain an accurate target region and a background region of the SAR image.
The step 2 specifically comprises the following steps:
step 2-1, randomly generating an initial level set contour in the SAR image, namely:
Figure GDA0002783115660000039
wherein phi is0Represents the initial level set profile, Ω1Is a target region in the SAR image, C is a boundary between the target region and a background region in the SAR image, omega2As background regions in the SAR image, c0Constant values representing the interior of the initial level set profile, -c0A constant value representing an outside of the initial level set profile;
step 2-2, setting parameters a, b, beta, omega and lambda according to the SAR image; a. b, beta, omega and lambda can all be adjusted according to different SAR images.
Step 2-3 according to formula
Figure GDA0002783115660000041
Calculating the equivalent vision n of the SAR image, wherein mu is the mean value of the SAR image, sigma2Is the variance of the SAR image;
step 2-4, G of target area is estimated by using moment0The distribution parameters are estimated according to the equivalent vision n and the formula
Figure GDA0002783115660000042
And gamma1＝-(α1+1)E(x1) Calculating to obtain the shape parameter alpha of the target area1And a scale parameter gamma1，E(x1) First moment, E (x), representing target region of SAR image1 2) Representing a second moment of a target area of the SAR image;
step 2-5, G of background area is estimated by using moment0The distribution parameters are estimated according to the equivalent vision n and the formula
Figure GDA0002783115660000043
And gamma2＝-(α2+1)E(x2) Calculating to obtain the shape parameter alpha of the background area2And a scale parameter gamma2，E(x2) First moment, E (x), representing background area of SAR image2 2) Representing a second moment of a background area of the SAR image;
step 2-6, using the estimated G of the target area0Distribution parameter calculation target region G0Probability density distribution, i.e. according to formula
Figure GDA0002783115660000044
-α1,γ1,n,I(x)>0, calculating probability density distribution of the target area;
step 2-7, using the estimated G of the background area0Distributed parameter calculation of G of background region0Probability density distribution, i.e. according to formula
Figure GDA0002783115660000045
-α2,γ2,n,I(x)>0, calculating the probability density distribution of the background area;
step 2-8 according to formula
Figure GDA0002783115660000046
And
Figure GDA0002783115660000047
respectively calculating the mean value of the gray values of a target area and a background area in the image;
step 2-9 according to formula
Figure GDA0002783115660000051
Calculating a sinusoidal SPF distribution term;
step 2-10, minimizing an energy functional by utilizing an Euler-Lagrange method, and obtaining the following level set evolution equation according to a gradient descent flow equation:
Figure GDA0002783115660000052
wherein t represents time and div (·) represents divergence;
taking the divergence of the gradient of the level set function phi as the Laplace operation of phi
Figure GDA0002783115660000053
The terms are removed so that the level set evolution equation becomes:
Figure GDA0002783115660000054
and finally, carrying out level set evolution iterative processing according to the level set evolution equation to obtain an optimal target region omega in the SAR image1And background region omega2And a boundary C between the target region and the background region.
In the iterative processing process, the method is according to the formula
Figure GDA0002783115660000055
Calculating an energy difference Δ φ to obtain a level set function φ, wherein τ represents the number of iterations currently performed, φτRepresents the level set function phi, phi in the τ th iterationτ+1Represents the level set function phi in the tau +1 th iteration calculation;
then judging whether to terminate iteration according to the energy difference delta phi of the level set function phi:
if the condition satisfies that delta phi is more than or equal to e0，e0If the energy difference threshold value is represented, returning to the step 2-4;
if not, delta phi is more than or equal to e0And outputting the segmentation result of the target area and the background area.
The level set function phi is smoothed with a gaussian convolution kernel, expressed as:
φ＝φ*Gσ
wherein G isσIs a gaussian kernel function, and sigma is a width parameter of the gaussian kernel function and is used for adjusting the smoothness degree.
The SAR image is a water area SAR image collected by aiming at rivers, lakes, canals, channels, reservoirs, ponds and the like.
The main idea of the invention is to utilize G0The intensity statistical characteristics of the foreground area and the background area of the image are fitted in a distribution mode to establish an energy functional, then a level set function phi is introduced, and the newly constructed sinusoidal SPF distribution is blended into G0And constructing a global steady state minimization model to obtain a new energy functional, then minimizing the energy functional by adopting an Euler-Lagrange variational method to obtain a level set evolution equation, and finally continuously carrying out iterative solution on the level set evolution equation until an iteration termination condition is met.
The innovation points of the invention mainly comprise the following three aspects: first, adopt G0Modeling the water area and the non-water area in the SAR image by distribution, which is a novel modeling mode in the field of water area segmentation; secondly, introducing a novel sinusoidal SPF distribution to enhance the acquisition of the target profile and accelerate the evolution speed of the curve; and thirdly, realizing global steady state minimum segmentation by designing a convex optimization energy model.
The invention has the beneficial effects that:
the method overcomes the inherent characteristics of inherent multiplicative speckle noise, target intensity heterogeneity change and the like of the SAR image and the defects that a traditional level set model based on statistical information is easy to fall into a local minimum value and the curve evolution speed is slow, so as to improve the accuracy of SAR image segmentation.
Drawings
FIG. 1 is a flow chart of an implementation of the present invention.
FIG. 2 is an original image according to an embodiment of the present invention.
FIG. 3 is an initial level set profile of an embodiment of the present invention.
Fig. 4 is a diagram of the final level set evolution result of the embodiment of the present invention.
Fig. 5 is a water area segmentation result diagram of the final SAR image according to the embodiment of the present invention.
Detailed Description
The following describes embodiments of the present invention in detail with reference to the accompanying drawings.
As shown in fig. 1, the embodiment of the present invention and its implementation are as follows: in the embodiment, the SAR image of the coastal scene is processed, and the SAR image is acquired by a sentinel No. 1 satellite SAR system.
The embodiment comprises the following steps:
step 1, establishing a global steady state minimum segmentation model based on sine SPF distribution and a level set model, wherein the model is fused with G0Weighted sum of both the area energy term and the regularization term of the probability density distribution and the sinusoidal SPF distribution:
E＝Eregion(φ)+Ereg(φ)
1, A, the regional energy term Eregion(φ) is expressed as:
Figure GDA0002783115660000061
in this embodiment, a has a value range of [0,0.1], b has a value range of [0,0.1], β has a value range of [1,3], ω has a value range of [0,100], and λ has a value range of [0,55 ].
1, B, regularization term Ereg(φ) is expressed as:
Figure GDA0002783115660000071
and 2, minimizing the energy functional obtained in the step 1 to obtain a level set evolution equation, and solving by an iterative method to obtain an accurate target region and a background region of the SAR image.
Step 2-1, randomly generating an initial level set contour in the SAR image, namely:
Figure GDA0002783115660000072
wherein phi is0Represents the initial level set profile, Ω1Is a target region in the SAR image, C is a boundary between the target region and a background region in the SAR image, omega2As background regions in the SAR image, c0Constant values representing the interior of the initial level set profile, -c0A constant value representing an outside of the initial level set profile;
in this example c0The value is 1.
Step 2-2, setting parameters a, b, beta, omega and lambda according to the SAR image; in this embodiment, a is 0.1, b is 0.05, β is 1, ω is 25, and λ is 5.
Step 2-3 according to formula
Figure GDA0002783115660000073
Calculating the equivalent vision n of the SAR image, wherein mu is the mean value of the SAR image, sigma2Is the variance of the SAR image;
step 2-4, G of target area is estimated by using moment0The distribution parameters are estimated according to the equivalent vision n and the formula
Figure GDA0002783115660000074
And gamma1＝-(α1+1)E(x1) Calculating to obtain the shape parameter alpha of the target area1And a scale parameter gamma1，E(x1) First moment, E (x), representing target region of SAR image1 2) Representing a second moment of a target area of the SAR image;
step 2-5, G of background area is estimated by using moment0The distribution parameters are estimated according to the equivalent vision n and the formula
Figure GDA0002783115660000075
And gamma2＝-(α2+1)E(x2) Calculating to obtain the shape parameter alpha of the background area2And a scale parameter gamma2，E(x2) First moment, E (x), representing background area of SAR image2 2) Representing a second moment of a background area of the SAR image;
step 2-6, using the estimationTo the target area G0Distribution parameter calculation target region G0Probability density distribution, i.e. according to formula
Figure GDA0002783115660000081
-α1,γ1,n,I(x)>0, calculating probability density distribution of the target area;
step 2-7, using the estimated G of the background area0Distributed parameter calculation of G of background region0Probability density distribution, i.e. according to formula
Figure GDA0002783115660000082
-α2,γ2,n,I(x)>0, calculating the probability density distribution of the background area;
step 2-8 according to formula
Figure GDA0002783115660000083
And
Figure GDA0002783115660000084
respectively calculating the mean value of the gray values of a target area and a background area in the image;
step 2-9 according to formula
Figure GDA0002783115660000085
Calculating a sinusoidal SPF distribution term;
step 2-10, minimizing an energy functional by utilizing an Euler-Lagrange method, and obtaining the following level set evolution equation according to a gradient descent flow equation:
Figure GDA0002783115660000086
the divergence of the gradient of the level set function phi is equivalent to the Laplace operation of phi, and will
Figure GDA0002783115660000087
The terms are removed so that the level set evolution equation becomes:
Figure GDA0002783115660000088
the level set function φ is smoothed with a Gaussian convolution kernel, expressed as:
φ＝φ*Gσ
wherein G isσThe value is a Gaussian kernel function, sigma is a width parameter of the Gaussian kernel function, and in the specific implementation, sigma is 1.
And finally, carrying out level set evolution iterative processing according to the level set evolution equation to obtain an optimal target region omega in the SAR image1And background region omega2And a boundary C between the target region and the background region.
During the iterative processing according to formula
Figure GDA0002783115660000091
Calculating an energy difference Δ φ to obtain a level set function φ, wherein τ represents the number of iterations currently performed, φτRepresents the level set function phi, phi in the τ th iterationτ+1Represents the level set function phi at the time of the τ +1 th iteration calculation.
In the iteration processing process, whether the iteration is terminated is judged according to the energy difference delta phi of the level set function phi:
if the condition satisfies that delta phi is more than or equal to e0，e0If the energy difference threshold value is represented, returning to the step 2-4;
if not, delta phi is more than or equal to e0And outputting the segmentation result of the target area and the background area.
Example e0Value of 10-3。
Fig. 2 shows a raw SAR image as an embodiment of the invention. The original SAR image size is 1522 × 1522, and the black area in the image is the water area, i.e. the target area.
Fig. 3 shows an initial level set profile as an embodiment of the invention.
Fig. 4 shows a diagram of the evolution result of the final level set as an embodiment of the invention.
FIG. 5 is a water area segmentation result diagram of the final SAR image according to the embodiment of the present invention. Where the black part represents the target area and the white part represents the background area.
As can be seen from fig. 4 and 5, the present invention can completely divide the water area. Aiming at the defects of the existing SAR image level set segmentation model in a complex scene, the accuracy of SAR image segmentation is improved. The method is not influenced by the initial contour, has stable parameter value and good robustness.

Claims (5)

1.A SAR image water area segmentation method based on sine SPF distribution and a level set model is characterized in that:
step 1, establishing a global steady state minimum segmentation model based on sine SPF distribution and a level set model, wherein the model is fused with G0Weighted sum of both the area energy term and the regularization term of the probability density distribution and the sinusoidal SPF distribution:
E＝Eregion(φ)+Ereg(φ)
where φ is a level set function, Eregion(phi) represents the regional energy term, Ereg(φ) represents the regularization term, E represents the total energy of the model;
1, A, the regional energy term Eregion(φ) is expressed as:
Figure FDA0002783115650000011
wherein, x represents a pixel point in the image, and I (x) is the gray value of the pixel point x in the image; omega is an SAR image area and represents a target area/background area; a and b are first and second weight coefficients, beta is a regularization parameter, and omega and lambda are the weight coefficients of the sinusoidal SPF distribution term in the target region and the background region of the image respectively;
Figure FDA0002783115650000012
is G of the target area0The function of the probability density distribution is,
Figure FDA0002783115650000013
g as background region0A probability density distribution function, R (x) representing a sinusoidal SPF distribution term;
two G0The probability density distribution functions are respectively expressed as:
Figure FDA0002783115650000014
Figure FDA0002783115650000015
wherein the content of the first and second substances,
Figure FDA0002783115650000016
g for representing x gray value of pixel point in target area0The distribution of the probability density is such that,
Figure FDA0002783115650000017
g for representing x gray value of pixel point in background area0Probability density distribution, n is equivalent view, alpha1Is a shape parameter of the target region, gamma1Is a scale parameter of the target region, alpha2As a shape parameter of the background region, gamma2As scale parameters of the background area, gamma (·) is a gamma function;
the sinusoidal SPF distribution term r (x) is expressed as follows:
Figure FDA0002783115650000018
wherein, c1And c2Mean gray values respectively representing a target region and a background region in the SAR image are represented as:
Figure FDA0002783115650000021
wherein H (φ) represents the Heaviside function, which is expressed as:
Figure FDA0002783115650000022
wherein ε represents an epsilon parameter;
1, B, said regularization term Ereg(φ) is expressed as:
Figure FDA0002783115650000023
wherein the content of the first and second substances,
Figure FDA0002783115650000024
is a gradient operator, v is a weight coefficient of a regular term, | calculation of the luminance2Represents the square of the gradient mode of phi;
and 2, minimizing the energy functional obtained in the step 1 to obtain a level set evolution equation, and solving by an iterative method to obtain an accurate target region and a background region of the SAR image.
2. The SAR image water area segmentation method based on the sinusoidal SPF distribution and the level set model according to claim 1, characterized in that: the step 2 specifically comprises the following steps:
step 2-1, randomly generating an initial level set contour in the SAR image, namely:
Figure FDA0002783115650000025
wherein phi is0Represents the initial level set profile, Ω1Is a target region in the SAR image, C is a boundary between the target region and a background region in the SAR image, omega2As background regions in the SAR image, c0Constant values representing the interior of the initial level set profile, -c0A constant value representing an outside of the initial level set profile;
step 2-2, setting parameters a, b, beta, omega and lambda according to the SAR image;
step 2-3 according to formula
Figure FDA0002783115650000026
Calculating the equivalent vision n of the SAR image, wherein mu is the mean value of the SAR image, sigma2Is the variance of the SAR image;
step 2-4, G of target area is estimated by using moment0The distribution parameters are estimated according to the equivalent vision n and the formula
Figure FDA0002783115650000027
And gamma1＝-(α1+1)E(x1) Calculating to obtain the shape parameter alpha of the target area1And a scale parameter gamma1，E(x1) First moment, E (x), representing target region of SAR image1 2) Representing a second moment of a target area of the SAR image;
step 2-5, G of background area is estimated by using moment0The distribution parameters are estimated according to the equivalent vision n and the formula
Figure FDA0002783115650000031
And gamma2＝-(α2+1)E(x2) Calculating to obtain the shape parameter alpha of the background area2And a scale parameter gamma2，E(x2) First moment, E (x), representing background area of SAR image2 2) Representing a second moment of a background area of the SAR image;
step 2-6, using the estimated G of the target area0Distribution parameter calculation target region G0Probability density distribution, i.e. according to formula
Figure FDA0002783115650000032
Calculating probability density distribution of the target area;
step 2-7, using the estimated G of the background area0Distributed parameter calculation of G of background region0Probability density distribution, i.e.According to the formula
Figure FDA0002783115650000033
Calculating the probability density distribution of the background area;
step 2-8 according to formula
Figure FDA0002783115650000034
And
Figure FDA0002783115650000035
respectively calculating the mean value of the gray values of a target area and a background area in the image;
step 2-9 according to formula
Figure FDA0002783115650000036
Calculating a sinusoidal SPF distribution term;
step 2-10, minimizing an energy functional by utilizing an Euler-Lagrange method to obtain the following level set evolution equation:
Figure FDA0002783115650000037
wherein t represents time and div (·) represents divergence;
taking the divergence of the gradient of the level set function phi as the Laplace operation of phi
Figure FDA0002783115650000041
The terms are removed so that the level set evolution equation becomes:
Figure FDA0002783115650000042
and finally, carrying out level set evolution iterative processing according to the above steps to obtain an optimal target region omega in the SAR image1And background region omega2And a boundary C between the target region and the background region.
3. The SAR image water area segmentation method based on the sinusoidal SPF distribution and the level set model according to claim 1, characterized in that:
in the iterative processing process, the method is according to the formula
Figure FDA0002783115650000043
Calculating an energy difference Δ φ to obtain a level set function φ, wherein τ represents the number of iterations currently performed, φτRepresents the level set function phi, phi in the τ th iterationτ+1Represents the level set function phi in the tau +1 th iteration calculation;
then judging whether to terminate iteration according to the energy difference delta phi of the level set function phi:
if the condition satisfies that delta phi is more than or equal to e0，e0If the energy difference threshold value is represented, returning to the step 2-4;
if not, delta phi is more than or equal to e0And outputting the segmentation result of the target area and the background area.
4. The SAR image water area segmentation method based on the sinusoidal SPF distribution and the level set model according to claim 1, characterized in that: the level set function phi is smoothed with a gaussian convolution kernel, expressed as:
φ＝φ*Gσ
wherein G isσIs a gaussian kernel function, and σ is a width parameter of the gaussian kernel function.
5. The SAR image water area segmentation method based on the sinusoidal SPF distribution and the level set model according to claim 1, characterized in that: the SAR image is a water area SAR image collected by aiming at rivers, lakes, canals, channels, reservoirs, ponds and the like.
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