## 4 Discussion
### Sensitivity Analysis of the Morphological Operation  
The shadow detection results are usually subsequently processed with a certain denoising algorithm, such as the morphological operation [29] and the box filtering process [22]. In our study, the final shadow detection results are achieved through optimizing shadow candidates with a certain morphological operation. However, the structuring element is a significant influential factor for the effective utilization of the morphological operation. Therefore, both the morphological structuring element type and the morphological structuring element scale \(\alpha\) should be taken into consideration. In this part, we deliver the sensitivity analysis about the impact of the morphological structuring element on the \(LSI\) shadow detection algorithm through carrying out additional experiments in several invariant color spaces (i.e., HIS, HSV, CIELCh, YCbCr and YIQ) with various structuring element types (i.e., cube, diamond, disk, sphere and square types) and different structuring element scales \(\alpha\) set from 1 to 20 with an interval of 1 for test images Tripoli-1 and Tripoli-2. Figure 10 presents the sensitivity of the \(LSI\) algorithm to the morphological structuring element for test images Tripoli-1 and Tripoli-2, respectively.  
Figure 10: _Cont._  
Figure 9: The sensitivity of the \(LSI\) algorithm to the neighborhood parameter \(m\) for test images. (a) Tripoli-1. (b) Tripoli-2.  
Figure 10: The sensitivity of the \(LSI\) algorithm to the morphological structuring element in variant color space for test images. (**a**) Tripoli-1 in HIS. (**b**) Tripoli-2 in HIS. (**c**) Tripoli-1 in HSV. (**d**) Tripoli-1 in HSV. (**e**) Tripoli-1 in CIELCh. (**f**) Tripoli-2 in CIELCh. (**g**) Tripoli-1 in YCbCr. (**h**) Tripoli-2 in YCbCr. (**i**) Tripoli-1 in YIQ. (**j**) Tripoli-2 in YIQ.  
As depicted in Figure 10a,c,e,g,i for Tripoli-1, the higher overall accuracies of shadow detection results by the morphological operation with the structuring element type of both cube and square state the better performance of the _LSI_ algorithm optimized with the morphological operation of the structuring element types of cube and square, and the decreasing trend of the overall accuracy along with the increase of the structuring element scale \(\alpha\) reveals that more effective information is processed as noise with a bigger structuring element scale. Additionally, the similarity of the overall accuracy in Figure 10a,c,e,g,i for Tripoli-1 proves the excellent performance and good stability of the _LSI_ algorithm for Tripoli-1 in these invariant color spaces. Similarly, the same phenomenon appears for Tripoli-2, as presented in Figure 10b,d,f,h,j. In accordance with the decreasing trend of the overall accuracy along with the increase of the structuring element scale for various structuring element types in these invariant color spaces for test images presented in Figure 10a-j, we optimize the binary shadow detection results by applying the morphological operation with a structuring element type of cube and a structuring element scale \(\alpha=1\), which results in the final shadow detection image.