# Structural Information Reconstruction of Distorted Underwater Images Using Image Registration
## 4 Discussion
### Analysis of Restoration Results  
The results shown in Figure 2 suggest that the proposed method performed better than our previous study and the Oreifej method in the adjacent letter reconstruction. The mean frame of frame sequence was selected as the reference frame of the Oreifej method, and the originally sharp letter boundaries in the image sequence were destroyed by bringing blur to the frames. It is difficult in the registration process to act precisely on the edge of text, even causing some mismatches. The fuzzy and double image caused by mismatches gets worse as the iteration step goes on. Our previous study adds a deblur step to the reference image before registration, which makes the registration pay too much attention to the nonboundary part and neglects the restoration of the border. In other words, Oreifej adds blurring to the original sequence and registers the blurred image sequence against the mean frame of the original sequence. Our previous method registers the original sequence against the reconstructed image using lucky patches fusion and blind deconvolution. However, Figure 2 shows that the above methods fail to deal with the fuzzy of structural information, especially the outline of adjacent letters. We think the reason is that the regions registered preferentially, which are relatively sharper, are random and irregular because of the uncertainty of sharper region generation and lack of explicit information priority. Therefore, considering the integrity of structural edge information is useful to improve the visual effect, we decided to intentionally raise the status of edge registration and guarantee the priority of boundary reconstruction to recover the edge information to a greater extent. We spliced the patches with less distortion into an image. Then the guided filter was used to keep the boundary information with great gradient change and ensure the edges of the character were clearer than non-edges. The registration process of edges took precedence over other positions, and with increasing iterations, the reference quality was constantly improved. Nevertheless, because the nonuniform geometric degradation in the first iteration was unable to be completely compensated by lucky patches fusion, and guided filter directed the registration to focus on the structural details instead of regional distortion, some of the migrated boundaries were mistaken for correct ones and partial distortion was retained, leading to some letters suffering from deformations shown in the result of the \"Large fonts\". Although there are still some local distortions in the results, slight distortions are more conducive to be observed than blurring. To quantify the results of all methods, gradient magnitude similarity deviation (GMSD) [31], and feature similarity (FSIM) [32], were chosen as relevant quality metrics. Above metrics belong to full-reference, which reflect the difference between the evaluated image and the ideal image, were defined as follows:  
Figure 4: Reference selected by different methods. GMSD is a metric that estimates image quality score by gradient magnitude, which presents structural information. The formal can be shown as:  
\[\text{GMS}(i)=\frac{2m_{r}(i)m_{d}(i)+c}{m_{r}{}^{2}(i)+m_{d}{}^{2}(i)+c} \tag{9}\]  
\[\text{GMSD}=\sqrt{\frac{1}{N}{\sum}_{i=1}^{N}{(\text{GSM}(i)-\text{GMSM})}^{2}} \tag{10}\]  
where \(m_{r}\) and \(m_{d}\) denote gradient magnitude of the reference image and the distorted image, respectively, \(c\) represents constant, and GMSM denotes the mean of gradient magnitude similarity. FSIM is an expression for emphasizing the structural features of visual interest, to estimate the frame quality. It can be expressed as:  
\[PC_{m}=\max(PC_{1}(x),PC_{2}(x)) \tag{11}\]  
\[\text{FSIM}=\frac{\sum_{x\in\Omega}S_{L}(x)\cdot PC_{m}(x)}{\sum_{x\in\Omega} PC_{m}(x)} \tag{12}\]  
where \(PC\) represents phase congruency, \(\Omega\) denotes the entire image, and \(S_{L}\) denotes similarity that is determined by phase congruency similarity and GMS.