# Multi-Source Image Fusion Based on BEMD and Region Sharpness Guidance Region Overlapping Algorithm
## 4 Multi-Source Image Fusion Algorithm  
### Selection Strategy by Sharpness Comparison  
In order to reduce the noise and suppress the halo artifacts in the interpolation process, the salient map is calculated by Gaussian filter. GBIMF is obtained to facilitate subsequent clarity contrast and fusion. The Gaussian filter [9] model is as follows:  
\[G(x,y)=\frac{1}{2\pi\sigma^{2}}e^{-\frac{x^{2}+y^{2}}{2\sigma^{2}}} \tag{7}\]  
where \(\sigma\) represents the standard deviation of a bidimensional image matrix and is set to 1. Gaussian filtering is convolved with the image by A \(\times\) A gaussian kernel. The sum of all elements of the kernel is 1, and the kernel window size is set to 5 \(\times\) 5. The filtered BIMFs and residual are denoted as GBIMFs and GRes, respectively, and can be collectively referred to as G-layers. Precisely speaking, each image layer includes a pair of image layers from source image A or B. Each G-layer is segmented into multiple small regions. And the sharpness value of image layer pairs, namely the corresponding regions of the same G-layer from image A or B, are calculated by an improved Sobel operator of the Tenengrad function. The regions with higher sharpness are selected. The whole procedure is shown in Figure 3.  
Sharpness value calculation is usually based on the gray gradient, and the values of feature edge pixels are usually higher than that of non-edge pixels. Existing evalua  
Figure 3: Multi-source image fusion based on BEMD and region sharpness guidance region overlapping algorithm. tion functions are vulnerable to noise and, generally, the gray gradient is evaluated for the whole image, resulting in large evaluation errors. As for small image regions, the traditional Tenengrad gradient function selects the region with a larger gradient value rather than the region with higher sharpness. Misjudgment occurs and results in unsmooth or blur in the border region for the fused image, especially in the adjacent area of the foreground and background. Therefore, it is necessary to improve the sharpness evaluation function to improve its applicability to ensure that the regions with higher sharpness can be correctly selected. The Tenengard function extracts the gradient values of pixels in each direction by convolution of the Sobel operator [10], which can reduce the influence of noise interference. The Tenengard function can be expressed as:  
\[\mathrm{F}=\sum_{\mathrm{x}}\sum_{\mathrm{y}}\mathrm{G}_{\mathrm{x}}^{2}( \mathrm{x},\mathrm{y})+\mathrm{G}_{\mathrm{y}}^{2}(\mathrm{x},\mathrm{y}) \tag{8}\]  
where \(\mathrm{Gx}(\mathrm{x},\mathrm{y})\) and \(\mathrm{Gy}\) (\(\mathrm{x},\mathrm{y}\)) are the gradient values at pixel (x,y) in the horizontal and vertical direction. \(\mathrm{Gx}(\mathrm{x},\mathrm{y})\) and \(\mathrm{Gy}(\mathrm{x},\mathrm{y})\) are formulated as:  
\[\mathrm{G}_{\mathrm{x}}(\mathrm{x},\mathrm{y})=\mathrm{f}(\mathrm{x},\mathrm{ y})\otimes\mathrm{g}_{\mathrm{x}} \tag{9}\]  
\[\mathrm{G}_{\mathrm{y}}(\mathrm{x},\mathrm{y})=\mathrm{f}(\mathrm{x},\mathrm{ y})\otimes\mathrm{g}_{\mathrm{y}} \tag{10}\]  
where \(\mathrm{f}\) (\(\mathrm{x},\mathrm{y}\)) is the image pixel; \(\otimes\) is the convolution symbol; \(\mathrm{gx}\) and \(\mathrm{gy}\) are the horizontal and vertical templates of Sobel operators and are defined as:  
\[\mathrm{g}_{\mathrm{x}}= \begin{pmatrix}-1&-2&-1\\ 0&0&0\\ 1&2&1\end{pmatrix}  \tag{11}\]  
\[\mathrm{g}_{\mathrm{y}}= \begin{pmatrix}1&0&-1\\ 2&0&-2\\ 1&0&-1\end{pmatrix}  \tag{12}\]  
Due to the limitation of the traditional Sobel operator, the gradient changes in each direction of the image tend to appear poorly non-uniform. In the process of image sharpness calculation, the gradient calculation of each direction of the image cannot achieve a more accurate sharpness value, which leads to mistakes in the selection of the segmented image.