# Multi-Source Image Fusion Based on BEMD and Region Sharpness Guidance Region Overlapping Algorithm
## 4 Multi-Source Image Fusion Algorithm
### The Maximum Sharpness Value Guidance of the Region Overlapping Fusion Algorithm  
To merge two original images \(\rm I_{A}\) and \(\rm I_{B}\) into one image \(\rm I=(I_{A},I_{B})\), based on the above sharpness value maximum layer, the formula can be expressed as:  
\[\rm I_{f}=\sum_{i=1}^{K}H_{i}+H_{R} \tag{20}\]  
When implementing sharpness comparison selection, the region method can finely capture prominent features in the corresponding regions of the same layer in two input images. Namely, the regions with rich and sharp information should be taken as the fused image. The region fusion method may lead to gray and feature discontinuity at the junction of different regions, resulting in an uneven transition of the concatenated boundaries. For example, the region in row 1 and column 1 are all taken from image \(\rm I_{1}\), including the IMF layer 1 to K and residual layer. The regions in row 1 and column 2 are all taken from image \(\rm I_{2}\), including the IMF layer 1 to K and residual layer. The fused image is prone to forming obvious splicing marks at the boundaries between the first column and second column of the first row. To solve the problem that the boundary transition of different regions is not smooth, the region overlapping method [12] can be used. Slide over the layer \(\rm H_{i}\) to \(\rm H_{R}\) obtained by the sharpness value selection strategy using the M \(\times\) M size window. In the traversal of the two-dimensional layer matrix, if the step size of each step is S, which is less than M, then the overlapping area is formed between adjacent regions and the number of overlapping rows or columns N is M-S. The choice of overlapping value N may directly affect the degree of the splicing mark; therefore, appropriate value is crucial. The region overlapping method is illustrated in Figure 6. If window size is 6 \(\times\) 6 and sliding step size is 2, when the window slides on the image, it can ensure that there are overlapping areas between adjacent regions, and there is even region stacking. The overlapping number of different regions in the image is shown in Table 1. The gray value of each region divided by its overlapping number is the final gray value of corresponding region. The region overlapping fusion can reduce the splicing marks compared with the method without overlapping. The comparison of pixel-based fusion strategy, region energy comparison strategy, and region sharpness comparison strategy are given in Figure 7. Pixel  
Figure 6: Region overlapping for 7 \(\times\) 12 image with window size of 6 \(\times\) 6 and sliding step size of 2.  
based fusion strategy is based on the selection strategy of maximum pixel values. Therefore, for the image in the first row of Figure 7, when the gray value of the clock digit in image A is smaller than that in image B, the fusion method selects the clock digit with a blurred appearance of image B, resulting in blurred numbers in the fused image. The extracted numbers are unclear and the fused image is not so satisfactory. The fusion performance of the region energy comparison method is superior to the above method. However, in terms of sharpness and smoothness, it is still inferior to the region sharpness comparison method.