# Blind Image Deblurring Based on Local Edges Selection
## 3 Results and Discussion
### Image Deblurring Results  
In all the tests, the size of the image patch N(w) equals \(5\times 5\). The parameters in Formula (11) are set to be the same in all the experiments: \(\alpha=0.008\), \(\beta=0.7\). The parameters of the comparison methods in this section are selected according to the references. The first test is based on the dataset of [PERSON] [5] which is shown in Figure 6--the blurred images are obtained by using eight blurring kernels and four ground truth gray value images. In the deblurring of gray value images, the dark channel and bright channel are obtained by Equations (9) and (10). The comparison algorithms include the methods in [7; 9; 19; 20; 22; 27; 31; 33; 36]. Figure 7 shows the visual results of one motion blurred image in [PERSON]'s dataset. From the estimated clear images, the proposed method outperforms others. The clarity of the estimated clear images by some methods are relatively poor, such as [7; 19]. The clear images obtained by the methods in [22; 31] are too smooth, which may lead to the loss of some details. The brightness of the image has changed a lot in the image obtained by [36]. The blurring kernels estimated by the proposed method are also closer to the real kernels and have fewer noise points. Table 1 shows quantitative comparison results of the clear image and blurring kernel in Figure 7, the metrics include structure similarity (SSIM) [37], Peak Signal to Noise Ratio (PSNR) [38] and kernel similarity (KS). It can be seen from the results that the proposed method outperforms competing methods. Then, tests are carried out based on all the 32 synthetic blurred images in [PERSON]'s dataset. In addition to SSIM, PSNR, and KS, success rates are obtained based on the dataset. The success rate is measured by error ratio [5], which is defined in Equation (18), \(x_{p}^{e}\), \(x_{p}^{t}\) are the clear images obtained by the estimated blurring kernel and the ground truth blurring kernel, respectively, for each pixel \(p\). \(x_{p}^{g}\) is the ground truth clear image for each pixel \(p\). Empirically, when the error ratio is lower than 3, the algorithm is considered to be successful. Figure 8 shows the average SSIM, PSNR, KS, and success rate. From the comparison results, the proposed method can deblur the gray value images well, and all the  
Figure 5: The convergence of the proposed method: (**a**) the convergence of image, and (**b**) the convergence of blurring kernel. indices are dominant among the methods. In the proposed method, when the error ratio equals to 2.5, the success rate reaches 100%, and the proposed method outperforms others consistently. \[r=\frac{\sum\limits_{p}\left\|x_{p}^{e}-x_{p}^{g}\right\|_{2}^{2}}{\sum\limits_{ p}\left\|x_{p}^{t}-x_{p}^{g}\right\|_{2}^{2}} \tag{18}\]  
Figure 6: [PERSON]’s dataset. Figure 7: _Cont._ \begin{table}
\begin{tabular}{c c c c} \hline  & **SSIM** & **PSNR** & **KS** \\ \hline [PERSON] et al. & 0.485 & 28.57 & 0.556 \\ [PERSON] and [PERSON] & 0.789 & 26.53 & 0.623 \\ [PERSON] et al. & 0.654 & 31.69 & 0.583 \\ [PERSON] et al. & 0.697 & 30.77 & 0.633 \\ [PERSON] et al. & 0.800 & 31.72 & 0.699 \\ [PERSON] et al. & 0.732 & 26.86 & 0.691 \\ [PERSON] et al. & 0.588 & 26.33 & 0.621 \\ [PERSON] et al. & 0.624 & 30.10 & 0.612 \\ [PERSON] et al. & 0.769 & 30.53 & 0.705 \\ [PERSON] & 0.823 & 31.82 & 0.713 \\ \hline \end{tabular}
\end{table} 
Table 1: Quantitative comparison of the deblurring results in Figure 7.  
Figure 7: The deblurring results of [PERSON]’s dataset. Figure 8: _Cont._  
Then, experiments are carried out based on the 48 color images in the dataset of [PERSON] et al. [39], which includes four ground truth color images and 12 blurring kernels. The 48 synthetic images in [PERSON]'s dataset are deblurred by the proposed method and other methods in [1; 7; 9; 19; 20; 22; 31; 40; 41; 42]. Figure 9 shows the visualization results of one blurred image in the dataset. The results show that the proposed method can effectively restore detailed information of images.