## 5 Discussions
### The Positive Impact of \(\alpha\) and \(\beta\) on the Proposed Model  
Taking \(I\) as an example, the compensation experiment continued on the shadow image TIGS in Figure 2a and TICS in Figure 2c to verify the influence of \(\alpha\)and \(\beta\). A comparison of the compensation results by assigning different values to \(\alpha\) and \(\beta\) was implemented, as visually shown in Tables 3 and 4. The figures in the table show how the brightness and contrast changes with the change of the parameter. When fixing \(\beta\)and changing \(\alpha\)in compensation model of Equation (5), \(B\) and \(T\) are both improved with the increase of \(\alpha\); when fixing \(\alpha\)and changing \(\beta\), \(T\)decreases, and \(B\) remains unchanged with the rise of \(\beta\). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Image Name** & \begin{tabular}{c} **Shadow Rate** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Length \(\times\) Width** \\ **(pixel)** \\ \end{tabular} & \begin{tabular}{c} **OWC** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **GMC** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **HMT** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **LCC** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **CRM** \\ **(s)** \\ \end{tabular} & \
\begin{tabular}{c} **OOPR** \\ **(s)** \\ \end{tabular} &
\begin{tabular}{c} **Ours** \\ **(s)** \\ \end{tabular} \\ \hline
1 & 50.563 & 823\(\times\)576 & 0.075 & **0.033** & 0.034 & 0.179 & 4.627 & 1.102 & 0.893 \\
2 & 38.979 & 686\(\times\)601 & 0.076 & 0.038 & **0.033** & 0.082 & 1.650 & 0.889 & 0.677 \\
3 & 45.893 & 894\(\times\)634 & 0.143 & 0.065 & **0.064** & 0.159 & 2.336 & 1.604 & 1.338 \\
4 & 26.783 & 1437\(\times\)937 & 0.297 & **0.172** & 0.186 & 0.375 & 33.469 & 5.034 & 4.688 \\
5 & 22.352 & 937\(\times\)1437 & 0.186 & **0.105** & 0.108 & 0.234 & 20.276 & 1.903 & 1.641 \\
6 & 27.077 & 1004\(\times\)1188 & 0.263 & **0.129** & 0.129 & 0.269 & 32.886 & 1.525 & 1.264 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Shadow compensation time comparison of different images in Figures 4–10. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Image Name** & \begin{tabular}{c} **Shadow Rate** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Length \(\times\) Width** \\ **(pixel)** \\ \end{tabular} & \begin{tabular}{c} **OWC** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **GMC** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **HMT** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **LCC** \\ **(s)** \\ \end{tabular} & \begin{tabular}{c} **CRM** \\ **(s)** \\ \end{tabular} & \
\begin{tabular}{c} **OOPR** \\ **(s)** \\ \end{tabular} &
\begin{tabular}{c} **Ours** \\ **(s)** \\ \end{tabular} \\ \hline
1 & 50.563 & 823\(\times\)576 & 0.075 & **0.033** & 0.034 & 0.179 & 4.627 & 1.102 & 0.893 \\
2 & 38.979 & 686\(\times\)601 & 0.076 & 0.038 & **0.033** & 0.082 & 1.650 & 0.889 & 0.677 \\
3 & 45.893 & 894\(\times\)634 & 0.143 & 0.065 & **0.064** & 0.159 & 2.336 & 1.604 & 1.338 \\
4 & 26.783 & 1437\(\times\)937 & 0.297 & **0.172** & 0.186 & 0.375 & 33.469 & 5.034 & 4.688 \\
5 & 22.352 & 937\(\times\)1437 & 0.186 & **0.105** & 0.108 & 0.234 & 20.276 & 1.903 & 1.641 \\
6 & 27.077 & 1004\(\times\)1188 & 0.263 & **0.129** & 0.129 & 0.269 & 32.886 & 1.525 & 1.264 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Shadow compensation time comparison of different images in Figures 4–10. Figure 12 describes the influence of \(\alpha\) and \(\beta\) on the compensation results. Figure 12a,b show that \(\alpha\) affects both \(B\) and \(T\) linearly and positively. However, for the values for \(\alpha\) that were too high, the brightness and contrast compensation was excessive, while the values that were too low for \(\alpha\) made the brightness and contrast compensation insufficient. As shown Figure 12c, with the increasing value of \(\alpha\), \((\Delta B)^{2}\) and \((\Delta T)^{2}\) decreased until they reached the lowest points; and the increasing \(\alpha\) led to an increase in \((\Delta B)^{2}\) and \((\Delta T)^{2}\).