## 8 Discussion and Conclusions  
The use of image databases for different applications in industrial, educational, and medical problems is more relevant than ever due to the ease of image capturing and storage. Enormous numbers of degraded images are captured unintentionally or by mistake and in the long run, there is a need to clean a large quantity of data from unwanted images. In this paper, we studied the unintentional defocus or out-of-focus blur problem. The cause of blurring effects was expressed as a hypothesis based on geometrical optics. We showed that the unintentional blur caused a shifting and scaling of the DOF, which in turn resulted in a motion and defocused blur on the captured images. We proved the validity of the hypothesis by an independent method used to compare the sharp and blurred images. In Appendix A, Figure A4 shows the result of the independent method and Figures A2 and A3 show the hypothesis principles. In the independent method, we calculated the depth from a single image. We showed that an optimal range for a virtual DOF can be estimated by several virtually recaptures of the image. The recapturing of the image was achieved by using a Gaussian model for the lens. We argued that such recapturing process had strong effect on the amplitude of edges. Therefore, the ratio of the amplitude of edges for two virtual recaptured images, in the range of the virtual DOF, was argued to be a significant parameter in the estimation of the relative depth on the edges. We showed how a network of such edges could be propagated to the whole image to generate a depth image. The histogram of depth values in the depth image was used as a feature parameter for blur classification. A database of historical documentation was used for the verification of the hypothesis and blur classification. The use of documentation images was shown to be very useful in the simplification of a scene with its two major planes, the document and its background. The orientation of the two planes in the sharp and blurred images was easy to detect and compare, see Figure 10. In the classification of blur effects of the database, we faced a common problem in big data: the imbalance of classes. The numbers of blurred images as mixed blur, motion blur, and defocused blur were 47, 22, and 15 whereas the number of sharp images was 827 images. We used a probabilistic RUSBoost classification approach to solve the classification problem. The result of the blur classification was presented in Table 1. It should be noted that in the classification between sharp and mixed blur images, 44 of 47 of possible blurred images, between sharp and \begin{table}
\begin{tabular}{l l l l l} \hline \hline \multirow{2}{*}{**Classification between**} & \multicolumn{4}{c}{**Classifications Results**} \\ \cline{2-5}  & **TP\({}_{\text{rate}}\)** & **TN\({}_{\text{rate}}\)** & **FP\({}_{\text{rate}}\)** & **FN\({}_{\text{rate}}\)** \\ \hline Sharp and mixed blur & 44/47 = 0.9362 & 798/827 = 0.9649 & 29/827 = 0.0351 & 3/47 = 0.0638 \\ Sharp and motion blur & 20/22 = 0.9091 & 839/852 = 0.9836 & 13/852 = 0.0153 & 2/22 = 0.0909 \\ Sharp and defocused blur & 14/15 = 0.9333 & 854/859 = 0.9942 & 5/859 = 0.0058 & 1/15 = 0.0667 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classification results between sharp and mixed blur, motion blur, and defocused blur images. motion blur, 20 of 22 possible images, and between sharp and defocused, 14 of 15 possible images were classified. However, this indicates that the statistical results are sensitive to the number of blurred images, and there is a need to examine the methodology on more extensive databases which include a larger number of blurred images. Conceptualization, S.K. ; Methodology, S.K. and W.W.; Software, W.W.; Validation, W.W.; Formal analysis, S.K. and S.M.E. ; Investigation, S.K. and S.M.E. ; Resources, S.K. ; Writing--original draft, S.K. ; Writing--review & editing, W.W. and S.M.E. ; Supervision, S.K. ; Project administration, S.K. ; Funding acquisition, S.K.