# Structural Information Reconstruction of Distorted Underwater Images Using Image Registration
## 4 Discussion
### Number of Iterations and Running Time  
For the purpose of raising efficiency, the \(\updownarrow\), which presents the difference between the frames and the mean of the current sequence \(V\), is applied to determine the end of the registration process. The value can be obtained from Equation (14). The threshold is set to 0.025, the same as Oreifej [20]. As long as the \(\updownarrow\) is less than the threshold, it means that the registration tends to be stable, then the post-processing is carried out. The comparison of convergence results is listed in Table 3.  
\[\updownarrow(V)=\frac{\sum_{k}\sum_{x\in\Omega}\abs{I_{k}(x)-M(x)}}{h\times w \times n} \tag{13}\]  
From Table 3, we can see that the iteration numbers of the proposed method are obviously less than other methods, and neither of the data sets has more iterations than the preset maximum iteration times.  
We think the reason that, in the Oreifej method, the numbers of iterations keep a high level is because frame blurring is used. In our previous study, using the higher quality reference frame could speed up the registration. However, due to the continuous improvement of the overall definition of the reference frame, the nature of registration being guided to the sharper region is weakened, resulting in a decrease of later iteration velocity. However, a processed reference frame, which has preserved edges and smoothed non-edges simultaneously, is employed to the registration of our proposed method. The edges of reference are always sharper than other parts as the iterations go on,  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Data sets** & **Methods** & **GMSD (L)** & **FSIM (H)** & **UISM (H)** & **UIConM (H)** & **UIGQM (H)** \\ \hline \multirow{3}{*}{Middle fonts} & Oreifej [20] & 0.1530 & 0.8239 & 6.7602 & 0.6896 & 4.4619 \\  & Our previous & 0.2100 & 0.7291 & 6.6876 & 0.6774 & 4.3968 \\  & Proposed method & 0.1938 & 0.7613 & 6.8826 & 0.7002 & 4.5358 \\ \hline \multirow{3}{*}{Small fonts} & Oreifej [20] & 0.1349 & 0.8068 & 6.6793 & 0.8195 & 4.9022 \\  & Our previous & 0.2033 & 0.7073 & 6.5596 & 0.7959 & 4.7825 \\  & Proposed method & 0.1850 & 0.7389 & 6.7231 & 0.8225 & 4.9259 \\ \hline \multirow{3}{*}{Tiny fonts} & Oreifej [20] & 0.1524 & 0.7537 & 6.8084 & 0.5654 & 4.0321 \\  & Our previous & 0.1798 & 0.7168 & 6.7185 & 0.5508 & 3.9533 \\  & method [21] & 0.1679 & 0.7439 & 7.1807 & 0.6256 & 4.3571 \\ \hline \multirow{3}{*}{Large fonts} & Oreifej [20] & X & X & 6.4618 & 0.4136 & 3.3870 \\  & Our previous & X & X & 6.6355 & 0.4003 & 3.3906 \\  & Proposed method & X & X & 6.9208 & 0.4395 & 3.6151 \\ \hline \multirow{3}{*}{checkboard} & Oreifej [20] & X & X & 6.8788 & 0.6291 & 4.2804 \\  & Our previous & 0.70863 & 0.6161 & 4.2953 \\ \cline{1-1}  & Proposed method & X & X & 7.0246 & 0.6308 & 4.3295 \\ \hline \hline \end{tabular}  
* Because the true image of “Large fonts” is unavailable, the PSNR, GMSD, FSIM are presented with “X”. The “L” means that the low value is good, whereas the “H” means that the high value is good.  
\end{table}
Table 2: Comparison of image quality metrics among the Oreifej method [20], the proposed method, and the previous method [21] 1.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Checkboard** & **Large Fonts** & **Middle Fonts** & **Small Fonts** & **Tiny Fonts** \\ \hline Oreifej method [20] & 2 & \(>\)5 & \(>\)5 & 2 & 4 \\ Our previous & 4 & 5 & 5 & 2 & 3 \\ method [21] & 2 & 4 & 4 & 2 & 2 \\ Proposed method & 2 & 4 & 4 & 2 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The number of iterations when termination conditions are met.  
thus further shortening the registration time. It is also shown by the decreasing trend of iteration time, as shown in Figure 3.  
Therefore, the proposed method has better performance on computing speed and greater development potential when the numbers of iterations are the same or unknown.