## 3 Experiments and Performance Assessment
### Quantitative Evaluation
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Method** & **Color Space** & \(\rho_{\mathbf{s}}\)**(\%) & \(\rho_{\mathbf{n}}\)**(\%) & \(\mu_{\mathbf{s}}\)**(\%) & \(\mu_{\mathbf{n}}\)**(\%) & \(\tau\) & \(e_{\mathbf{c}}\)**(\%) & \(e_{\mathbf{o}}\)**(\%) \\ \hline  & HIS & 83.94 & 95.53 & 87.21 & 94.24 & 92.44 & 4.47 & 16.06 \\  & HSV & 83.67 & 95.75 & 87.73 & 94.17 & 92.53 & 4.25 & 16.33 \\ _LSI_ & CIELCh & 84.24 & 95.61 & 87.45 & 94.35 & 92.58 & 4.39 & 15.76 \\  & YCbCr & 80.98 & 96 & 88.03 & 93.29 & 92 & 4 & 19.02 \\  & YIQ & 83.66 & 95.65 & 87.48 & 94.16 & 92.46 & 4.35 & 16.34 \\ \hline MC3 [18] & C1C2C3 & 85.52 & 87.47 & 71.26 & 94.33 & 86.96 & 12.53 & 14.48 \\ NSVDI [25] & HSV & 96.41 & 63.67 & 49.08 & 97.99 & 72.39 & 36.33 & 3.59 \\ LSRI [24] & CIELCh & 63.69 & 97.65 & 90.77 & 88.1 & 88.6 & 2.35 & 36.31 \\ SDI [26] & _NIR_-RGB & 99.2 & 33.73 & 35.22 & 99.14 & 51.17 & 66.27 & 0.8 \\ SRI [20] & HIS & 87.91 & 65.15 & 47.82 & 93.69 & 71.22 & 34.85 & 12.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Shadow detection accuracy measurements of various shadow detection algorithms for the test image Tripoli-1. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Method** & **Color Space** & \(\rho_{\mathbf{s}}\)**(\%) & \(\rho_{\mathbf{n}}\)**(\%) & \(\mu_{\mathbf{s}}\)**(\%) & \(\mu_{\mathbf{n}}\)**(\%) & \(\tau\) & \(e_{\mathbf{c}}\)**(\%) & \(e_{\mathbf{o}}\)**(\%) \\ \hline  & HIS & 73.39 & 98.21 & 94.53 & 89.75 & 90.85 & 1.79 & 26.61 \\  & HSV & 73.48 & 98.23 & 94.58 & 89.78 & 90.89 & 1.77 & 26.52 \\ _LSI_ & CIELCh & 72.89 & 98.43 & 95.15 & 89.6 & 90.86 & 1.57 & 27.11 \\  & YCbCr & 72.54 & 97.97 & 93.78 & 89.43 & 90.43 & 2.03 & 27.46 \\  & YIQ & 72.64 & 98.32 & 94.8 & 89.5 & 90.71 & 1.68 & 27.36 \\ \hline MC3 & C1C2C3 & 94.19 & 20.96 & 33.44 & 89.53 & 42.68 & 79.04 & 5.81 \\ NSVDI & HSV & 92.04 & 65.49 & 52.92 & 95.12 & 73.36 & 34.51 & 7.96 \\ LSRI & CIELCh & 75.06 & 94.84 & 85.99 & 90.02 & 88.98 & 5.16 & 24.94 \\ SDI & _NIR_-RGB & 97.61 & 40.35 & 40.82 & 97.56 & 57.33 & 59.65 & 2.39 \\ SRI & HIS & 79.61 & 65.14 & 49.05 & 88.34 & 69.43 & 34.86 & 20.39 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Shadow detection accuracy measurements of various shadow detection algorithms for the test image Tripoli-2. terms of the nonshadow producer's accuracy (about 95%), the nonshadow user's accuracy (about 94%) and the overall accuracy (over 92%). Additionally, relatively high and stable values are also obtained in terms of the shadow producer's accuracy and the shadow user's accuracy, and relatively low values are also acquired in terms of the committed error and the omitted error. Generally speaking, ideal shadow detection accuracy measurements are achieved for shadow detection results by the _LSI_ algorithm in these invariant color spaces (i.e., HIS, HSV, CIELCh, YCbCr and YIQ) for the test image Tripoli-1, which not only reveals the good capability of these invariant color spaces in decoupling chromaticity and luminance, but also states the excellent performance and robustness of the _LSI_ algorithm. Similarly, as presented in Table 2, relatively high and consistent accuracy measurements are also acquired for the test image Tripoli-2 for shadow detection results by the proposed _LSI_ algorithm in these invariant color spaces (i.e., HIS, HSV, CIELCh, YCbCr and YIQ). In particular, not only very high values are obtained in terms of the nonshadow producer's accuracy (about 98%), the shadow user's accuracy (about 94%) and the overall accuracy (approximately 91%), but also relatively low values (less than 2%) is acquired for the committed error measurement. In general, the proposed _LSI_ approach acquires relatively ideal and stable shadow detection accuracy measurements for the test image Tripoli-2 in these invariant color spaces (i.e., HIS, HSV, CIELCh, YCbCr and YIQ).