*3.4. Experimental Results*

The brighter pixels in the detection maps of Figures 14 and 15 represent the higher probability of NGL and highlight the pixels of targets hit in red points, the pixels of a false alarm in blue points, the pixels of targets missing in yellow points in Regions 1. By visually inspecting the Figures, the Subset CEM and SW CEM detectors seemed to perform slightly better than traditional CEM in terms of NGL pixel detection. Figures 16 and 17 represent the higher probability of NGL and highlight the pixels of targets in Region 2. Obviously, the results of ASW CEM in Figures 15d and 17d reduce plenty of false alarm pixels.

**Figure 14.** Detection maps of 4 algorithms in Region 1. (**a**) CEM (**b**) Subset CEM (**c**) Sliding Window-based CEM (SW CEM) (**d**) Adaptive Window-based CEM (ASW CEM).

**Figure 15.** Detection results highlighted with different colors of 4 algorithms in Region 1. (**a**) CEM (**b**) Subset CEM (**c**) Sliding Window-based CEM (SW CEM) (**d**) Adaptive Window-based CEM (ASW CEM).

**Figure 16.** Detection maps of 4 algorithms in Region 2. (**a**) CEM (**b**) Subset CEM (**c**) Sliding Window-based CEM (SW CEM) (**d**) Adaptive Window-based CEM (ASW CEM).

**Figure 17.** Detection results highlighted with different colors of 4 algorithms in Region 2. (**a**) CEM (**b**) Subset CEM (**c**) Sliding Window-based CEM (SW CEM) (**d**) Adaptive Window-based CEM (ASW CEM).

Figures 18 and 19 show the ROC curves of traditional CEM and our proposed three window based CEMs. Tables 4 and 5 show the AUC calculated, according to the ROC Curve in the experimental images of different regions and the evaluation of PD, PF, overall accuracy (ACC), and kappa under the optimum threshold.

**Figure 18.** ROC curves of local and global CEMs on Region 1.

**Figure 19.** ROC curves of local and global CEMs on Region 2.

**Table 4.** Detection results of traditional CEM and our proposed CEMs in the image of Region 1.


**Table 5.** Detection results of traditional CEM and our proposed CEMs in the image of Region 2.


The performance of each detection method can be judged according to its ROC curve. Different target detection algorithms have different AUCs (Area under the Curve of ROC). Generally speaking, the value of AUC is 0~1, and the performance of a detection method can be judged according to the AUC value. If AUC = 1, then the detector is almost perfect. When this detector is used, there are at least two thresholds, so the result appears to be ideal. If AUC is 0.5~1, then this detector is better than a random guess. If AUC is just equal to 0.5—as shown in Figure 13, when the detection power (PD) is equal to the false alarm probability (PF), meaning that the result is the same as a random guess, like flipping a coin—then the probability of front and back is 1/2. If AUC < 0.5, then the result is worse than a random guess, and the resulting target and the background may be inverted. Put briefly, the larger the AUC value is, the more correct is the detection method. According to Figures 16 and 17, the three proposed CEMs have higher AUC than the traditional CEM.

Finally, according to the data of ROC, kappa, and the error matrix in Tables 4 and 5, in the three images of different resolutions of the two regions, respectively, ASW performs better than the other algorithms. The performance of TPR is slightly different from that of the other algorithms. However, in terms of the false alarm, ASW CEM can effectively reduce the detection of non NGL pixels, which thus can increase overall accuracy and the Kappa value of image detection. This result means that ASW CEM has a better detection result than the other algorithms. Figures 20 and 21 illustrate the comparison of traditional CEM and our proposed three window based CEMs in the results of AUC and Kappa.

**Figure 20.** Area under curve (AUC) detection results of Region 1 and Region 2.

**Figure 21.** Kappa detection results of Region 1 and Region 2.

Figures 22 and 23 highlight parts of two regions where a false alarm is likely to occur. In those regions where the false alarm is likely to occur in the two images, it is observed that the CEM algorithm is likely to misrecognize similar RGB values as NGL. Our proposed algorithms using local autocorrelation matrix **S** in Equation (10), such as Subset CEM, SW CEM, and ASW CEM, are likely to suppress the background of the region, so as to reduce the false alarm rate. Based on the experimental results, ASW CEM performs the best effect.

**Figure 22.** Resulting images of the region where a false alarm is likely to occur in Region 1: (**a**) Traditional CEM; (**b**) Subset CEM; (**c**) SW CEM; (**d**) ASW CEM.

*Remote Sens.* **2018**, *10*, 96

**Figure 23.** Resulting images of the region where a false alarm is likely to occur in Region 2: (**a**) Traditional CEM; (**b**) Subset CEM; (**c**) SW CEM; and, (**d**) ASW CEM.

In order to the validate the influence of the window size for Subset CEM and SW CEM, Tables 6 and 7 tabulate the detection results of various window sizes in Region 1. As seen, various window sizes of Subset CEM and SW CEM produce very similar results. On the other hand, the window size of Subset CEM and SW CEM are not sensitive to the final performance; thus, it is not the critical parameter for the detectors.

**Table 6.** Detection results of Subset CEM with various window sizes.



**Table 7.** Detection results of SW CEM with various window sizes.
