## 2 Proposed Method
### Review of the Fusion Method
#### 2.1.3 Selector  
To choose the best-fit intensity image, a selector is designed to measure the information loss of the pre-fused images to select the best-fit intensity image as the final output of the fused image. Because AFAM fusion aims is to combine the information of the cell, the regions of the cells should be extracted, and the fusion problem could be simplified to the fusion problem in the regions of cells. To acquire the position and shape of the cell, a cell extraction algorithm based on [PERSON]'s approach [14] was developed. Erosion and dilation steps are used to reduce the influence of the noise and smoothen the boundary of the cell region. Our cell extraction method is a triple-step process. The first step is detection. [PERSON]'s threshold is used to segment the morphology image into \(CEL_{0}\) and \(BKG\) at gray level \(t\), which is defined as follows:  
\[BKG=\left\{0,1,2,\ldots,t\right\}\, \tag{3}\]  
\[CEL_{0}=\left\{t+1,t+2,\ldots,L-1\right\}\, \tag{4}\]  
where \(t\) is the threshold of classifying background and the cell. To clarifiy, [PERSON]'s threshold is not an accurate segmentation method because it does not perform well in segmenting smooth boundary. Our method is not sensible to the segmentation accuracy. However, the small object, which is not the region of interest in the view of content but has the same gray level section, does harm to the fusion performance. To clear them, we apply the erosion step. We assume that the main part of the morphology image is the cell, and noise occupies small and separated regions. To clear these areas, the erosion step is defined as follows:  
\[CEL_{1}=I_{m}\oplus\left(BKG\oplus A\right)\, \tag{5}\]  
\[L_{A}=round\left(\sqrt{\sum(CEL_{0})\times\left(\sqrt{p_{1}}-1\right)}\right)\, \tag{6}\]  
where \(A\) is a disk-shaped structuring element, \(L_{A}\) is the size of \(A\), and \(p_{1}=1.2\) is the multiple coefficient that determines the narrowing of the original segmentation of the cell. The function of \(A\) is to clear the noise regions which have a similar intensity feature of the cells, and the proper value of \(p_{1}\) is to clear all the noise regions but still preserve the region of the cells. According to our hypothesis, the noise regions are removed during the erosion process but the cell region is narrowed either. Therefore, the dilation step, which is the third step, is used to recover the cell region. It is defined as follows:  
\[CEL=CEL_{1}\oplus B\, \tag{7}\]  
\[L_{B}=round\left(\sqrt{\sum(CEL_{1})\times\left(1-\sqrt{p_{2}}\right)}\right)\, \tag{8}\]  
where \(B\) is a disk-shaped structuring element, \(L_{B}\) is the size of \(B\), and \(p_{2}\) is a multiple coefficient that determines the extension of \(CEL_{1}\). The function of \(B\) is to recover the region of cells and make the boundary of the cells smooth. The value of \(p_{2}\) is determined by \(p_{1}\), and it is defined as follows:  
\[p_{2}=\frac{1}{p_{1}}. \tag{9}\]  
At last, we obtain \(CEL\), which represents the region of cell, and \(BKG\), representing the background. The relationship of morphology image, \(BKG\) and \(CEL\) is defined as follows:  
\[I_{m}=\left\{CEL,BKG\right\}. \tag{10}\]  
Next, to set the standard of the best-fit intensity image among the pre-fused images, we define a multi-regional information loss (MRIL) to measure the information loss. It is a double-stage algorithm, which would calculate the total information loss of the inner and outer cells. To define the set of thecriterion of the pre-fused images, characteristic of inverted morphology and acoustic image should be taken into consideration. As it is shown in Figure 2, inverted morphology and acoustic images show different information in different regions. In the cell region, because of grayscale inversion, the intensities of inverted morphology are weaker than those in the background and provide little information about the inner structures. By contrast, the acoustic image provides much richer details in the region of the cell.