## 3 Results
### Shadow Detection Combining Topography and Spectra  
The proposed CTS method has two inputs: the image and the DEM corresponding to the image's geographic location. We used six \(512\times 512\) size mountainous images to conduct the experiments. The six images contain two types of features that easily cause shadow \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Image** & **Method** & \(P_{s}\)**(\%)** & \(P_{n}\)**(\%)** & \(U_{s}\)**(\%)** & \(U_{n}\)**(\%)** & \(E_{c}\)**(\%)** & \(E_{o}\)**(\%)** & \(\tau\)**(\%)** & \(kappa\) \\ \hline \multirow{4}{*}{3} & [PERSON] & 81.83 & 91.06 & 94.43 & 73.02 & 8.94 & 18.17 & 85.06 & 0.69 \\  & [PERSON] & 94.78 & 83.93 & 91.61 & 89.68 & 16.07 & 5.22 & 90.98 & 0.80 \\  & [PERSON] & 93.25 & 92.31 & 95.74 & 88.07 & 7.69 & 6.75 & 92.92 & 0.85 \\  & [PERSON] & 79.87 & 93.68 & 95.90 & 71.54 & 6.32 & 20.13 & 84.71 & 0.69 \\  & ECA & 75.78 & 98.09 & 98.66 & 68.63 & 1.91 & 24.22 & 83.61 & 0.67 \\  & [PERSON] (MC3) & **95.06** & 89.15 & 94.19 & **90.69** & 10.85 & **4.94** & **92.98** & **0.85** \\ \hline \multirow{4}{*}{4} & [PERSON] & 99.08 & 56.18 & 28.91 & 99.71 & 43.82 & 0.92 & 62.72 & 0.28 \\  & [PERSON] & 94.50 & 73.63 & 39.19 & 98.67 & 26.37 & 5.50 & 76.81 & 0.43 \\  & [PERSON] & 89.84 & 81.82 & 47.06 & 97.82 & 18.18 & 10.16 & 83.04 & 0.52 \\  & [PERSON] & 44.66 & 98.73 & 86.32 & 90.84 & 1.27 & 55.34 & 90.48 & 0.54 \\  & ECA & 40.14 & 99.39 & 92.23 & 90.23 & 0.61 & 59.86 & 90.36 & 0.51 \\  & Ours (MC3) & 91.48 & 89.10 & 60.15 & 98.31 & 10.90 & 8.52 & 89.46 & **0.66** \\ \hline \multirow{4}{*}{5} & [PERSON] & 67.70 & 66.47 & 64.48 & 69.60 & 33.53 & 32.30 & 67.05 & 0.34 \\  & [PERSON] & 70.05 & 98.47 & 97.63 & 78.53 & 1.53 & 29.95 & 85.01 & 0.70 \\  & [PERSON] & 96.60 & 91.64 & 91.21 & 96.78 & 8.36 & 3.40 & 93.99 & 0.88 \\  & [PERSON] & 95.32 & 95.07 & 94.56 & 95.77 & 4.93 & 4.68 & 95.19 & 0.90 \\  & ECA & 91.41 & 97.15 & 96.64 & 92.64 & 2.85 & 8.59 & 94.43 & 0.89 \\  & [PERSON] (MC3) & 95.36 & 96.65 & 96.23 & 95.86 & 3.36 & 4.64 & **96.04** & **0.92** \\ \hline \multirow{4}{*}{6} & [PERSON] & 91.68 & 71.00 & 34.87 & 98.06 & 28.99 & 8.32 & 74 & 0.37 \\  & [PERSON] & 83.90 & 98.32 & 89.45 & 97.30 & 1.68 & 16.10 & 96.24 & 0.84 \\ \cline{1-1}  & [PERSON] & 96.98 & 97.03 & 84.69 & 99.48 & 2.97 & 3.02 & 97.02 & 0.89 \\ \cline{1-1}  & [PERSON] & 91.16 & 96.34 & 80.83 & 98.47 & 3.66 & 8.84 & 95.59 & 0.83 \\ \cline{1-1}  & ECA & 87.76 & 98.31 & 89.78 & 97.94 & 1.69 & 12.24 & 96.78 & 0.87 \\ \cline{1-1}  & [PERSON] (MC3) & 92.90 & **98.44** & **90.98** & 98.79 & **1.56** & 7.10 & **97.64** & **0.91** \\ \hline \end{tabular} Note: The values in **bold** indicate the best performance.  
\end{table} 
Table 2: Quantitative evaluation results of shadow detection. Figure 11: Shadow detection results for four images. confusion, which are vegetation and water body. Table 3 presents the center longitude and latitude of the images and the province where they are located. Figure 12a illustrates these six images. Image 7 has two triangular shapes of shadows in the center and left. The middle portion of Image 8 is actually a vegetation area surrounded by shadows, and the lower part of the dark area in Image 9 is also vegetation rather than shadows. In Image 10, the right side of the river is a large hillside shadow. Image 11 has long shadows on both sides of the river. Image 12 contains small shadows cast by urban buildings in addition to the hillside shadows. The corresponding ground truth images are shown in Figure 12b. The detection results of Silva, Wang, Zhou, Guan, ECA, MC3, and CTS are shown in Figure 12c-i, respectively. Figure 13 illustrates the process diagrams of CTS  
Figure 13: Process diagrams of CTS.