# Multi-Source Image Fusion Based on BEMD and Region Sharpness Guidance Region Overlapping Algorithm
## 4 Multi-Source Image Fusion Algorithm
### Improved Sobel Weighting Operator  
BEMD decomposes the input images into multiple BIMFs and a residual component from a high-frequency layer to a low-frequency layer. And the high-frequency layers contain contour information and rich energy information. Thus, the fusion of high-frequency layer decides whether the feature information and the background information of the image can be retained. The Tenengard function is selected to distinguish contour sharpness. When performing image fusion, the image is segmented into small regions, and the salient parts of the image are extracted for image fusion to minimize the influence of background information. However, many regions with low gradient information need to be saved. For instance, the hat body regions in image A and image B both show low gradient information. The difference of the gradient information of the hat body in image A or B may be very small. But the hat body of image A needs to be saved and that of image B needs to be removed. It is easy to make mistakes in judging the regions to be preserved and produce noise in the final image. To address this issue, an improved Sobel operator of the Tenengrad function is designed. As depicted in Figure 4, the operator template is different from that of  
Figure 4: Improved Sobel operator of Tenengrad function. There are 8 operator templates in 8 directions. Figure 5: (**a**) DFT operator, (**b**) Laplacian operator, and (**c**) improved Sobel operator. Equations (9) and (10). There are eight operator templates in eight directions. To obtain the gradient values G(x,y) according to the operator templates shown in Figure 4 by  
\[\text{G}_{\text{i}}(\text{x},\text{y})=\text{f}(\text{x},\text{y})\otimes\text{ g}_{\text{i}},\text{i}=1,\cdots,8. \tag{14}\]  
it is found that the operators take into account the gray change trend in eight directions and are used to convolve with the G-layers, respectively. Then, the pixel gradient value Gi(x,y) is obtained. The eight operators act on the same regions and we can obtain eight pixel gradient values Gi(x,y). It is necessary to integrate them together to obtain the only one. To obtain appropriate normalized gradient weighting coefficient, the maximum absolute value scheme is generally used. This strategy is sensitive to noise and some feature information may also be lost. To obtain the neighborhood average value, the correlation analysis between pixel points and its neighborhood is carried out. Based on this idea, an algorithm named optimal mean of neighborhood grayscale is proposed. By calculating the correlation between the optimal mean grayscale values of the pixel and its neighborhood, the gradient weighting coefficient Q is obtained, as follows:  
\[\text{Q}=1-\frac{2\times\text{f}(\text{x},\text{y})\times\text{f}_{\text{ avg}}}{\text{f}^{2}(\text{x},\text{y})+\text{f}^{2}_{\text{avg}}} \tag{15}\]  
By this method, it can effectively enhance the sensitivity and noise resistance of the gradient weighting algorithm. To obtain the optimal mean value \(\text{f}_{\text{avg}}\), the pixel values in the neighborhood are filtered to ensure the reliability of the neighborhood grayscale mean, as shown in Equation (16). \[\text{f}_{\text{avg}}=\frac{1}{8}\sum_{(\text{i},\text{j})\in\text{S}}\text{ f}(\text{x}+\text{i},\text{y}+\text{j})\times\text{\psi}_{\text{i},\text{j}} \tag{16}\]  
where f(x,y) is the gray value of the pixel, S is the set of eight neighborhoods of the pixel, and i and j are the horizontal and vertical coordinates of the neighborhood of the pixel, respectively. The maximum gray value \(\text{f}_{\text{max}}\) and the minimum gray value \(\text{f}_{\text{min}}\) are found by traversing the gray value of the eight neighborhoods, and using them as the standard to judge the effective grayscale values of the neighborhood, finally to eliminate the interference of noise points, and enhance the quality of image fusion. This process can be expressed as:  
\[\text{\psi}_{\text{i},\text{j}}=