## 4 Discussion
### Experimental Results Analysis
Its higher \(P_{s}\) and \(U_{n}\) and lower \(E_{o}\) demonstrate its ability to effectively recognize shadows. In the shadow detection results of Images 7-12, both [PERSON] and [PERSON]'s methods recognize vegetation and water bodies as shadows. Compared to those, [PERSON]'s method effectively mitigates vegetation misdetection by virtue of the large difference in brightness between vegetation and shadows in the NIR band, but it still cannot avoid the misdetection of water bodies as shadows. [PERSON]'s method does not show any case of vegetation and water bodies being misdetected as shadows in the other five images except for Image 7 because it recommends error-prone dark regions through the Dark-Region Recommendation (DRR) module. However, at the same time, it also excludes brighter shadow regions, such as the hillside shadow on the left side of the river in Image 11 and the thin shadow cast by the bridge across the river in Image 12. The ECA method does not have too many shadow misdetections in any of the six images, but there are more shadow omissions, such as the hillside shadow on the right side of Image 12. The MC3 method, like [PERSON], [PERSON], and [PERSON], has many shadow misdetections due to the presence of dark vegetation and water bodies. This exemplifies the drawbacks of only using spectral features to detect shadows, where large dark objects in the image can make shadow recognition more difficult. Our CTS is able to exclude dark vegetation and water bodies from interfering with shadow recognition. In addition to correctly detecting hillside shadows, CTS also ensures that the small and non-terrain-induced shadows can be detected, such as the small patch of shadows above Image 10 and the shadows of the bridge in Image 12. Thus, the shadows detected by CTS are both real and complete and are generally consistent with the results of visual interpretation. The quantitative evaluation results provided by Table 4 also show that CTS performs best among the seven methods. The average overall accuracy is 95.81%, which is 21.65%, 23.18%, 18.19%, and 13.65% higher than the [PERSON], [PERSON], Zhou, and MC3 methods, respectively. The kappa coefficients of all six images remain above 0.8. Compared with other traditional methods, the committed error of CTS is significantly lower, basically staying around 2%, whereas the others are 20% or more. On the six images, CTS achieves a mean overall accuracy of 95.81% compared with 90.14% for [PERSON]'s method and 94.04% for ECA. CTS maintains a high overall accuracy over multiple images compared to [PERSON]'s model and ECA, which shows that CTS is also the most robust. The MC3 method behaves better on Images 3-6 (the average overall accuracy is 94.03%) but worse on Images 7-12 (the average overall accuracy is 82.16%). This may be due to the fact that there are fewer dark features affecting shadow extraction in Images 3-6, whereas the opposite is true in Images 7-12. Large areas of dark vegetation and water bodies make it more difficult to accurately extract shadows. Generally, the shadows in urban area images are mainly building shadows, and the areas of vegetation and water bodies are smaller compared to mountainous images. So it is perfectly fine for MC3 to be applied to urban area images. The CTS method needs to be used in conjunction with DEM corresponding to the images, and its advantages become apparent when there are large areas of dark objects that hinder the extraction of true shadows. In our CTS experiment, we used the DEM with a resolution of 12.5 m, which is open-source and relatively easy to obtain. In the DEM-based shadow coarse detection experiment, the detection performance between the 30 m DEM and the 12.5 m DEM showed little difference, and the gap became even smaller after generating the SPM. Therefore, the impact of the resolution of the DEM on CTS detection performance can be considered negligible. If high-resolution urban DEMs are available, CTS can also be used in urban areas.