## 4 Discussion  
The sizes of the dual-window are two important parameters of CRD, which depend on the size of the anomaly in the image of each dataset and determine the anomaly detection availability of CRD. It is necessary to discuss the effect of dual-window sizes on the anomaly detection performance. Tables 1-3 display the AUC values of CRD, CRBORAD, and SSCRD, respectively, with varying window sizes on the three images. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Win\_Size**} & \multicolumn{2}{c}{**CRD**} & \multicolumn{2}{c}{**CRBORAD**} & \multicolumn{2}{c}{**SSCRD**} \\ \hline \(\mathbf{W_{out}}\) & \(\mathbf{W_{in}}\) & **AUC** & **Time** & **AUC** & **Time** & **AUC** & **Time** \\ \hline \multirow{3}{*}{15} & 13 & 96.90 & 12.58 & **98.38** & 15.50 & 98.19 & 29.15 \\  & 11 & 91.38 & 26.71 & **95.94** & 25.85 & 95.73 & 42.80 \\  & 11 & 94.10 & 9.61 & **97.49** & 11.01 & 97.41 & 25.96 \\  & 9 & 84.07 & 20.36 & 93.26 & 20.77 & **94.88** & 36.88 \\  & 9 & 88.51 & 7.60 & 94.99 & 8.96 & **97.12** & 23.58 \\  & 7 & 71.81 & 14.88 & 85.48 & 16.74 & **94.77** & 33.61 \\  & 7 & 80.90 & 4.97 & 89.03 & 7.32 & **96.73** & 23.65 \\  & 5 & 64.35 & 10.31 & 71.46 & 12.55 & **96.47** & 29.05 \\  & 5 & 78.76 & 4.05 & 80.12 & 5.56 & **98.59** & 21.07 \\  & 3 & 62.42 & 6.81 & 64.22 & 8.56 & **99.13** & 22.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: AUC values (in %) and computing times (in seconds) for San Diego-I image. Figure 7: ROC curves for ABU Airport image dataset with dual-window sizes (11,15) for CRD, CRBORAD, and SSCRD. For the San Diego-I image, the AUC values (in percent) of CRD range from 62.42 to 96.90, and the AUC values (in percent) of CRBORAD range from 64.22 to 98.38 when the size of the dual-window varies. Moreover, the AUC values (in percent) of the proposed SSCRD range from 94.88 to 99.13 as the size of the dual-window changes. When the size of the dual-window is set to (15,13), (15,11), or (13,11), the AUC values of the three algorithms are not significantly different, and all are at a high level. This is because the inner window with a relatively large size covers those nearby anomaly pixels when the pixel to be measured is abnormal, so there are almost no abnormal pixels in the local background framed by the dual-window. In this case, purification processing of the local background is superfluous. However, improper selection of the dual-window sizes results in a lower AUC value, meaning the deterioration of detection performance of CRD and CRBORAD. As the size of the dual-window decreases, the AUC values of CRD and CRBORAD both decrease. For example, the AUC values (in percent) of CRD and CRBORAD are 64.35 and 71.46 when the size of the dual-window is (5,9). The AUC value of CRBORAD deteriorates slightly less than that of CRD. The small size of the inner window could not frame the nearby abnormal pixels when the size of the anomaly to be detected is relatively large, resulting in some abnormal pixels within the outer window and the impurity of the local background. Due to the selective search process, the AUC of SSCRD has a stable high-level value, meaning that the dependence of the CRD anomaly detection performance on the size of the dual window is greatly reduced. When the size of the dual-window is (5,9), the AUC value (in percent) of SSCRD is 96.47, which is more than 25% higher than that of CRD and CROBORAD. In addition, different sizes of dual-window correspond to different local background dictionaries and slightly different detection performances of SSCRD. From Table 1, we calculate the average improvement effect of SSCRD on CRD to be 21.8% under