# Classification of Mineral Foam Flotation Conditions Based on Multi-Modality Image Fusion
## 3 Results
### Experimental Data
#### 3.2.1 Image Fusion  
The parameters of the image fusion algorithm are set. Two main parameters are set: (1) the number of NSST decomposition sub-band levels, and (2) the number of iterations of PAPCNN. (1) The level K of NSST decomposition sub-band levels is from 1 to 4 respectively, and the direction number of each decomposition level is determined. The direction number generally decreases from fine scale to coarse scale. In this paper, the number of directions is set to 16, 16, 8, and 8 from fine to coarse. The number of directions of each level corresponding to different decomposition sub-band stages is shown in Table 1.  
In this experiment, the fusion image is evaluated based on Peak Signal to Noise Ratio (PSNR), Mutual Information (MI), Average Gradient (AG), Mean Square Error (MSE), Standard Deviation (SD), and Visual Quality Fidelity (VIF) [7]. PSNR is the ratio of peak \begin{table}
\begin{tabular}{c c} \hline \hline
**Number of Decomposition Sub-Bands** & **The Direction Number of Each Level** \\ \hline
1 & 16 \\
2 & 16, 16 \\
3 & 16, 16, 8 \\
4 & 16, 16, 8, 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The number of NSST decomposition sub-band levels and the direction number of each level. Figure 8: Schematic of the foam image fusion and classification. power to noise power in the fused image, which reflects the distortion in the fusion process. The larger the value is, the closer the fused image is to the source image, and the less distortion is produced by the fusion method. MI is a quality index that measures the amount of information transferred from the source image to the fused image. A larger value indicates that more information is transferred from the source image to the fused image, indicating a good fusion performance. AG quantifies the gradient information of the fused image to represent its details and textures. The larger the value, the more gradient information the fused image contains and the better the performance of the fusion algorithm. MSE indicates the error between the fused image and the source images. The smaller the value, the better the fusion performance, which means that the fused image is closer to the source image and the error in the fusion process is smaller. SD is based on the statistical concept that reflects the distribution and contrast of the fused image. The higher the contrast of the fused image, the higher the SD value, which means that the fused image achieves good visuals. VIF measures the information fidelity of the fused image, which is consistent with the human visual system. By measuring the fidelity of visual information between the fused image and each source image, the higher the value, the better the performance. Figure 9 shows the effect of parameter \(K\) on the fused image indices, and the number of iterations \(N\) of PAPCNN is fixed at 110. In the case of \(N=4\), most of the indices of the sample data are the best except for the MI index which gradually decreases. From the above information, it can be seen that when \(K=4\), most of the indices of image fusion are better and the effect of image fusion is better. (2) Number of PAPCNN iterations, is set to 70, 90, 110, 130, and 150. The results are shown in Figure 10, where fixed \(K=4\). As shown in Figure 10, the sample foam images have the best performance, where data 1 has the best performance except MI at \(N=110\), data 2 has the best performance except PSNR at \(N=110\), and data 3 has the best performance at \(N=110\) except MI. Therefore, combining Figures 9 and 10, we can get the best effect of image fusion when \(K=4\) and \(N=110\). Figure 9: The influence of parameters \(K\) on the performance of fused image. The image fusion method in this paper is compared with the method of [18], the method of [36], and the maximum fusion method. The fused image indexes are shown in Figure 11. For the PSNR, the fusion method in this paper is the best. For most of the samples, the MI index is the best.