# A Novel Mosaic Method for Spaceborne ScanSAR Images Based on Homography Matrix Compensation
## 3 Traditional Feature-Based Mosaic Process for SAR Images
### Image Preprocessing Based on an Improved Wallis Filter  
The wide swath of ScanSAR was composed of multiple subswaths. However, the radiation intensities of the different subswath images were still inconsistent even though the intrinsic periodic scalloping in the azimuth and the effect of the roll angle error on the range were corrected. This phenomenon is caused by many factors, such as the slant range from the satellite to the target, the radar looking angle, different antenna gain patterns and inconsistent processor parameterizations. Therefore, the radiation intensity of adjacent images should be balanced during preprocessing to avoid inconsistency after mosaicking.  
The Wallis filter, which can equalize the intensity and contrast of images, is a pixel-value processing algorithm based on the reference image [39]. We used \(I_{\alpha}\) and \(I_{\beta}\) to represent the reference image and the image to be stitched, respectively; then, the classic Wallis filter can be shown as:  
\[I^{\prime}_{\beta}(i,j)=\left(I_{\beta}(i,j)-m_{\beta}\right)\frac{s_{\alpha}} {s_{\beta}}+m_{\alpha} \tag{4}\]  
where \(I^{\prime}_{\beta}\) is the filtered image, \(m_{\alpha}\) and \(m_{\beta}\) represent the mean of the pixel values in \(I_{\alpha}\) and \(I_{\beta}\), and \(s_{\alpha}\) and \(s_{\beta}\) are the standard deviations of the pixel values.  
As shown in Figure 3a, the classic Wallis filter worked well when two images with similar intensity trends along the stitching seam were processed. However, when the seam was too long and the intensity trends were opposites, there would still be obvious intensity inconsistencies even when the means and standard deviations of the two images were adjusted to the same, as shown in Figure 3b.  
It can be analyzed from Equation (4), when \(m_{\alpha}=m_{\beta}\) and \(s_{\alpha}=s_{\beta}\), \(I^{\prime}_{\beta}(i,j)=I_{\beta}(i,j)\), which means that the classic Wallis filter will be invalid if the means and standard deviations of \(I_{\alpha}\) and \(I_{\beta}\) are equal. This could happen in the situation of opposite intensity trends. Thus, these two parameters were not enough to accurately describe the differences between images.  
In this paper, a ratio of the mean was multiplied by the classic Wallis filter to implement the description of intensity trends along the stitching seam:  
\[I^{\prime\prime}_{\beta}(i,j)=I^{\prime}_{\beta}(i,j)\frac{M_{\alpha}}{M_{ \beta}} \tag{5}\]  
where \(I^{\prime\prime}_{\beta}\) is the result of the improved Wallis filter, \(I^{\prime}_{\beta}\) is the result of the classic Wallis filter, and \(M_{\alpha}\) and \(M_{\beta}\) are the mean pixel values of \(I_{\alpha}\) and \(I^{\prime}_{\beta}\) perpendicular to the stitching seam (if the stitching seam is along the column, \(M_{\alpha}\) and \(M_{\beta}\) are the mean pixel values of every row). The improved Wallis filter performed well regardless of whether the intensity trends were similar or opposite, so that the inconsistency in the intensity could be successfully eliminated and the effect of the mosaic result would be improved.