Poisson reconstruction based fusion method for polarimetric SAR images. 2.1 The definition of local .... data processing
Target Enhancement Oriented Fusion Method using Polarimetric SAR Data Yilun Chen, Jian Yang Department of Electronic Engineering, Tsinghua University Beijing, 100084, P.R.China
[email protected]
Abstract—Polarimetric Synthetic Aperture Radar (SAR) can provide multi-dimensional radar images with different transmitting and receiving polarization states of antennas. For the application of target detection, an essential problem is to combine multi-dimensional images into a single one to enhance the contrast between the target and the clutters. In this paper, a novel fusion method is proposed for the enhancement of local contrast. The optimal local contrast of each pixel is first defined based on the ratio between neighboring pixels. Then the problem is formulated in a least square minimization framework. It is proved that the solution can be obtained by solving a discrete Poisson equation via the Fast Fourier Transform (FFT) implementation. With polarimetric synthetic aperture radar data, we demonstrate the effectiveness of our method for target enhancement, where road detection is used as an example.
1. Introduction Synthetic Aperture Radar (SAR) has attracted more and more attention in recent years for its all-day and all-weather capability of earth observation. Polarimetric synthetic aperture radar can provide multi-dimensional data by transmitting and receiving electromagnetic waves with different polarizations, which can be especially helpful in the application of target detection. An important problem for target detection using polarimetric SAR data is how to fuse information from different channels to make the target more salient from the background, i.e., to enhance the target/clutter contrast by combining data from different channels in a proper way. For years researchers have devised several methods to utilize the polarimetric information for target enhancement. Optimal polarimetric contrast enhancement (OPCE) is to choose optimal polarization states for enhancing a desired target versus an undesired target/clutter [1]- [5]. By incorporating more parameters, Yang et al. extends the OPCE into a more general form with more encouraging results [6]. However, traditional methods tend to enhance the contrast between single target and single clutter and require the statistics of these targets first, which limits their use. Because in practice the statistical characteristics of different targets may vary significantly, and so do the clutters. For the problem of multi-targets/multi-clutters enhancement, traditional methods might not work well. In this paper, a new fusion method is proposed to solve this problem. The optimal local contrast for polarimetric SAR data is first defined. A fused image is then reconstructed from the obtained optimal local contrast. The problem is formulated in a least square minimization framework. The fused image can be obtained by solving a discrete Poisson equation with the Fast Fourier Transform (FFT) implementation. We use polarimetric SAR data from the NASA/JPL L-band AirSAR to demonstrate the effectiveness of the proposed method.
2. Poisson reconstruction based fusion method for polarimetric SAR images 2.1 The definition of local contrast The local contrast is defined to measure the difference of neighboring pixels. For a SAR image with intensity value I, the horizontal contrast and the vertical contrast of the pixel(i, j) are defined as x ri,j =
Ii,j Ii,j , ry = , Ii−1,j i,j Ii,j−1
respectively. The ratio form in eq.(1) is adopted due to the multiplicative speckle noise of SAR images. For polarimetric SAR data, a Sinclair scattering matrix [S] can be obtained from each pixel:
(1)
· [S] =
sHH sV H
sHV sV V
¸ .
(2)
In a reciprocal isotropic medium for the monostatic case, the reciprocity theorem holds and thus the Sinclair scattering matrix is symmetric, i.e., sHV = sV H . Therefore, we have three images from independent channel denoted as HH, HV and V V , respectively. With these images from three different channels, the optimal horizontal local contrast Rx is defined as ½ x x Mi,j if Mi,j > 1/mxi,j x , (3) Ri,j = mxi,j else where
and
¯ ¯ ¯ ¯ ¯¾ ½¯ ¯ HHi,j ¯ ¯ HVi,j ¯ ¯ V Vi,j ¯ x ¯,¯ ¯,¯ ¯ Mi,j = max ¯¯ HHi−1,j ¯ ¯ HVi−1,j ¯ ¯ V Vi−1,j ¯
(4)
¯ ¯ ¯ ¯ ¯¾ ½¯ ¯ HHi,j ¯ ¯ HVi,j ¯ ¯ V Vi,j ¯ ¯,¯ ¯,¯ ¯ . mxi,j = min ¯¯ HHi−1,j ¯ ¯ HVi−1,j ¯ ¯ V Vi−1,j ¯
(5)
Similarly, the optimal horizontal local contrast Ry is defined as ½ y y Mi,j if Mi,j > 1/myi,j y Ri,j = , y mi,j else where
(6)
y Mi,j
¯ ¯ ¯ ¯ ¯¾ ½¯ ¯ HHi,j ¯ ¯ HVi,j ¯ ¯ V Vi,j ¯ ¯ ¯ ¯ ¯ ¯ ¯ = max ¯ , , HHi,j−1 ¯ ¯ HVi,j−1 ¯ ¯ V Vi,j−1 ¯
(7)
myi,j
¯ ¯ ¯ ¯ ¯¾ ½¯ ¯ HHi,j ¯ ¯ HVi,j ¯ ¯ V Vi,j ¯ ¯ ¯ ¯ ¯ ¯ ¯ . , , = min ¯ HHi,j−1 ¯ ¯ HVi,j−1 ¯ ¯ V Vi,j−1 ¯
(8)
and
2.2 The reconstruction framework Based on the optimal local contrast Rx and Ry defined in the above subsection, the fusion problem is to reconstruct the fused image P from Rx and Ry , i.e., to find an image P with its local contrast (defined in eq.(1)) closest to Rx and Ry : Pi,j Pi,j y x → Ri,j , → Ri,j . Pi−1,j Pi,j−1
(9)
Let f = ln P , g x = ln Rx and g y = ln Ry , we use the following form to approximate eq.(9) for the convenience of calculation, y x . fi,j − fi−1,j → gi,j , fi,j − fi,j−1 → gi,j
The approximation is implemented by minimizing the following energy function ´ X ³¡ ¢ ¡ y ¢2 x 2 . min E = fi,j − fi−1,j − gi,j + fi,j − fi,j−1 − gi,j
(10)
(11)
i,j ∂E = 0, it can be proved that the optimization of eq.(11) is equivalent to the solution of the following Let ∂f i,j linear equations y y x x , 4fi,j − fi−1,j − fi,j−1 − fi+1,j − fi,j+1 = gi+1,j − gi,j − gi,j + gi,j+1
(12)
which turns to be the discrete form of Poisson equation [7]. The log image f can be solved by Poisson reconstruction using the Fast Fourier Transform (FFT). Define a set of image operators as follows
−1 h = −1 4 −1 , hx = 0 −1 1 , hy = −1
0 −1 1
.
(13)
Expressing eq.(12) in the convolution form h ∗ f = hx ∗ g x + hy ∗ g y ,
(14)
and applying the Fourier Transform on both sides, there is H · F = H x · Gx + H y · Gy ,
(15)
where H, H x , H y , Gx and Gy are the Fourier Transformation of h, hx , hy , g x and g y , respectively. f is then reconstructed by ¡ ¢ f = if f t H −1 (H x · Gx + H y · Gy ) ,
(16)
and the fused image P can thus be obtained: P = exp (f ) .
(17)
3. Experimental results A National Aeronautics and Space Administration SIR-C/X-SAR L-band image of a forest area is used for validating the effectiveness of the proposed method. In this area, several roads pass through the forest area. Fig.1(a) - Fig.1(d) show HH image, HV image, VV image and the span image of this area, respectively. The fusion result obtained from the proposed method is shown in Fig.1(f). From this image, one can easily find the roads in the forest area which are more clear than those in Fig.1(a) to Fig.1(d). For comparison, we also use the OPCE to enhance the contrast between forest area and non-forest area, and the result is shown in Fig.1(e). We can see that difference of the OPCE and the proposed method: only a limited number of roads are enhanced from the background in OPCE results. That is because the statistics of targets vary from region to region, OPCE tries to enhance the contrast of only two types of targets which fails in the multiple targets/multiple clutters enhancement scenarios, as the experiment shows. To see the results more clearly, we zoom a selected sub-region, as shown in Fig.2. Two roads are marked with arrows. The first road is clear to see in the HH image but blurred in the HV image, while the second road is easy to be found in the HV image but is not distinct in the HH image. For the scattering characteristics of the two roads are different with each other, OPCE could enhance only one of them from the background (see Fig.2(c)). By taking advantage of local contrast from all the polarizations, the proposed method achieves the best contrast-preserving fusion result, where all the roads are easy to be found in Fig.2(d).
4. Conclusion In this paper, we have presented a new fusion method for target enhancement in polarimetric SAR images. The basic idea is to fuse the local contrast of image from each channel to obtain an optimal contrast image. A fused image is then reconstructed from the optimal contrast image, by solving a discrete Poisson equation. The proposed method focuses its attention on enhancing local contrast between the target and its neighboring pixels and does not require prior statistical knowledge of the targets to be enhanced. The effectiveness of the proposed method is demonstrated by experimental results using polarimetric SAR data. The algorithm is applied to polarimetric SAR images in this paper, however, it can be naturally extended to general multi-channel SAR data processing, such as multi-frequency and etc.
Acknowledgment This work was supported by the National Important Fundamental Research Plan of China (2001CB309401) and by the Fundamental Research Foundation of Tsinghua University.
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(f)
Figure 1: Experimental results.(a) The HH image.(b)The HV image.(c) The VV image. (d) The span image. (e) Result obtained by OPCE. (f) Result from the proposed method.
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(d)
Figure 2: Results from a selected region of the area. (a) The HH image .(b)The HV image. (c) Result by OPCE. (d) Result by the proposed method. REFERENCES
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