## 5 Conclusions  
In this paper, we propose a DEM-based shadow coarse detection method, an MC3-based shadow fine detection method, and a shadow detection method combining topography and spectra (CTS) for remote sensing images in mountainous environments. The DEM-based shadow coarse detection method obtains a rough shadow mask corresponding to the image by utilizing DEM data and the Sun's position at the moment of image acquisition. The MC3-based shadow fine detection method includes image enhancement with linear and logarithmic stretching, multi-scale superpixel segmentation (FNEA based on SLIC), and MC3 index calculation. The CTS method takes the superpixel as a bridge connecting the DEM rough shadow mask and the MC3 index map, and the fusion map can reflect the probability of superpixels belonging to shadow both topographically and spectrally. After the experiments of three shadow detection methods on several images, the following three conclusions can be drawn:  
1. The DEM-based shadow coarse detection method can locate the main shadow region in images. Compared with the 12.5 m and 30 m DEM, the shadow extracted by 5 m DEM is more refined and has a better fit with the original image. The shadow \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Detection Time (s)** \\ \hline [PERSON] et al. [20] & 0.20 \\ \hline [PERSON] et al. [22] & 6.89 \\ \hline [PERSON] et al. [18] & 1.98 \\ \hline [PERSON] et al. [34] & 3.46 \\ \hline [PERSON] et al. [35] (ECA) & 1.57 \\ \hline Ours(MC3) & 0.84 \\ \hline \multirow{2}{*}{Ours (CTS)} & 0.97 (DEM rough shadow mask) \\ \cline{2-3}  & 0.91 (shadow detection perform) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The average detection time of five methods. extracted by the 30 m DEM is slightly coarser than 12.5 m, but it does not affect the effectiveness of the DEM method in locating the main shadow regions. 2. The MC3-based shadow fine detection method extracts shadows in the image meticulously and completely. It can avoid the problem of dark objects being mistakenly detected as shadows to some extent. Compared to the methods proposed by [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] (ECA), the MC3-based approach demonstrates superior performance across most evaluation metrics, with a significant reduction in omitted errors. The overall accuracy and kappa coefficient have reached the best among the six methods. 3. The CTS method can accurately recognize shadows and avoid the misdetection of dark objects, such as vegetation and water body. The method obtains a Joint Shadow probability Map (JSM) by combining the Shadow pixel Proportion Map (SPM) and the MC3 mean map, and it utilizes both topographic and spectral factors to make the distinction between shadows and dark objects more obvious. The experiments confirm that the detection performance of CTS is further improved on the basis of the MC3-based method. In the future research work, we will conduct more experiments on the other sources of DEM data (e.g., Lidar) or time-sensitive data to assess the robustness and applicability of our methods. We have compared CTS with CNN-based deep learning methods, and in the future, we can compare it with GAN-based deep models to observe its accuracy and robustness. In addition, CTS is also fully applicable to urban areas if high-resolution DEMs of urbanized areas are obtained, which has the immediate effect of separating the shadows of buildings from the urban greenery and artificial lakes. Conceptualization, H.X., F.W., H.Y. and W.W.; methodology, H.X. ; software, H.X. and J.Z. ; validation, H.X. ; formal analysis, H.X. ; investigation, H.X. ; resources, H.X. and J.Z. ; data curation, H.X. ; writing--original draft preparation, H.X. ; writing--review and editing, H.X., F.W., H.Y. and W.W.; visualization, H.X. ; supervision, H.X. ; project administration, F.W., H.Y. and W.W.; funding acquisition, F.W., H.Y. and W.W. All authors have read and agreed to the published version of the manuscript.