## 3 Results
### Detection Performance  
The segmentation parameters \(K\) for three images are all set as 2 since the sizes of them are the same. The regularization parameter \(\lambda\) for CRD, CRBORAD, and SSCRD are all set as \(10^{-6}\) according to the original literature [23]. All of the settings for parameter \(T\) correspond to the optimal label map \(P\) for each image, which are obtained by traversal of the range of parameter values. In addition, pixels with a higher background probability are representedby black, and pixels with a higher abnormal probability are represented by white to more prominently display the label map \(P\). The colour detection graphs for the San Diego-I image, the corresponding false color image, the ground-truth map, the result of graph-based over-segmentation, and the corresponding label map \(P\) obtained from the selective search are shown in Figure 2. The threshold \(T\) in the region fusion is set at 1.15 for the San Diego-I image because of the optimal regional fusion effect. The color detection graphs of CRD-based methods are shown in Figure 2, and are obtained when the sizes of the dual-window are (7,11), which is a typical sample of unbeffiting dual-window sizes for CRD in the San Diego-I image. Since the proposed SSCRD aims to make up for the defect that the local background in CRD is abnormally polluted, and then to improve the anomaly detection accuracy of CRD, the sizes of the dual-window for the representation of detection results are set to present the intuitive and effective improvement of SSCRD compared with CRD. Compared with the ground-truth map, the anomaly detection performance of CRD is unsatisfactory because of the blurred aircraft shapes and the difficulty in distinguishing the aircraft from pixels misjudged as anomalies. As shown in Figure 2, the detection graph of CRBORAD is slightly improved compared with that of CRD, and more pixels of three aircraft are identified. However, the shapes of the aircraft remain unidentifiable, and some background pixels are misjudged as abnormal, which seriously affects the correct judgment of the anomaly. By contrast, SSCRD successfully detects more abnormal pixels compared with CRD and CRBORAD, making the shape of the aircraft more complete and clearer. Furthermore, the detection performance of LRSRD is passable because of the recognizable locations and shapes of the three aircraft. However, some background pixels on the bottom left edge of the image have extremely high scores to be misjudged as anomalies. This could be attributed to an inaccurate and incomplete background dictionary. The ROC curves of the anomaly detectors for the San Diego-I image are shown in Figure 3 for the quantitative comparison of detection performance under the situation that the sizes of the dual-window are (7,11) as well. As shown in Figure 3, the probability of detection for CRD is less than 0.3 when the false alarm rate is 0.1, while the probability of detection for CRD is 0.78 when the false alarm rate rises to 0.5. In general, the ROC curve of the detection results of the CRD on the San Diego-I image shows a large gap from the upper left corner of the coordinate axis, meaning that the CRD fails to accurately detect the anomalies. The corresponding AUC value (in percent) of the CRD is 71.81. Compared with the ROC curve of CRD, the ROC curve of CRBORAD is closer to the top left corner, indicating a slight improvement in anomaly detection performance. Concretely, the probability of detection reaches 0.55 when the false alarm rate is 0.1, while the probability of detection is 0.8 when the false alarm rate is 0.25. The AUC value (in percent) of CRBORAD is 85.48. Based on the ROC curve of SSCRD, the detection effect is significantly improved by the selective search compared with CRD and CRBORAD. When the false alarm rate is 0.1, the probability of detection reaches 0.87, and the curve is closest to the upper left corner of the coordinate axis.