## 3 Results
### Effects of the Background on LAI Estimation  
#### 3.2.1 The Impact of Background on CIs  
To investigate the impact of background on CIs, we employed image segmentation techniques to separate the Retinex-corrected images into rice plants and backgrounds. By analyzing the changes in CIs before and after segmentation, we could assess the influence of background on the CIs of the rice fields. Figure 5 presents a boxplot of the CIs of rice and background. There were significant differences between the CIs of rice and background. This indicated that segmenting images into rice and background reduces the range of CI variation compared to non-segmented images. We further analyzed the difference in CI between rice and background using a \(t\)-test, and the results are presented in Table 4. Significant differences were observed between rice and background in most CIs. At the tilleering stage, the pixel values of rice plants and background pixels showed no significant differences except for C6, C18, and C20. At the booting, heading, and filling stages, significant differences were observed in C7, C12, C14, and C22.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**CIs** & **Tillering** & **Elongation** & **Booting** & **Heading** & **Grouting** \\ \hline C1 & \(-8.098\)** & \(-9.641\)** & \(-6.951\)** & \(-6.716\)** & \(-9.719\)** \\ C2 & \(6.007\)** & \(7.835\)** & \(6.148\)** & \(5.495\)** & \(5.118\)** \\ C3 & \(8.574\)** & \(9.865\)** & \(6.839\)** & \(6.859\)** & \(8.886\)** \\ C4 & \(8.509\)** & \(9.723\)** & \({}^{**}\) & \(6.708\)** & \(6.848\)** & \(9.78\)** \\ C5 & \(4.415\)** & \(6.435\)** & \(3.805\)** & \(3.956\)** & \(2.036\)** \\ C6 & \(1.146\) & \(2.145\)** & \(3.434\)** & \(4.195\)** & \(5.179\)** \\ C7 & \(4.550\)** & \(3.508\)** & \(1.506\) & \(0.467\) & \(1.531\) \\ C8 & \(6.083\)** & \(8.847\)** & \(7.583\)** & \(5.725\)** & \(3.827\)** \\ C9 & \(3.470\)** & \(6.568\)** & \(6.847\)** & \(7.080\)** & \(11.185\)** \\ C10 & \(4.101\)** & \(7.181\)** & \(6.842\)** & \(7.081\)** & \(11.044\)** \\ C11 & \(8.716\)** & \(10.317\)** & \(8.399\)** & \(7.581\)** & \(11.303\)** \\ C12 & \(3.265\)** & \(3.46\)** & \(1.1\) & \(0.372\) & \(0.159\) \\ C13 & \(2.473\)* & \(1.221\) & \(1.396\) & \(1.406\)** & \(1.885\)** \\ C14 & \(3.051\)** & \(2.369\)* & \(0.776\) & \(-0.168\) & \(-0.142\) \\ C15 & \(4.823\)* & \(6.638\)** & \(6.464\)** & \(6.176\)** & \(11.352\)** \\ C16 & \(2.866\)** & \(2.526\)* & \(-1.233\) & \(-0.464\) & \(-2.390\)* \\ C17 & \(3.266\)** & \(6.471\)** & \(1.894\) & \(2.143\)* & \(2.793\)** \\ C18 & \(0.738\) & \(2.615\)* & \(1.868\) & \(2.163\)* & \(2.042\)* \\ C19 & \(3.106\)** & \(3.173\)** & \(-3.21\)** & \(-0.691\) & \(-3.752\)** \\ C20 & \(-1.984\) & \(0.038\) & \(-7.274\)** & \(-3.552\)** & \(-5.415\)** \\ C21 & \(4.224\)** & \(7.565\)** & \(7.312\)** & \(7.655\)** & \(11.146\)** \\ C22 & \(2.900\)** & \(1.106\) & \(0.622\) & \(0.062\) & \(-0.044\) \\ C23 & \(1.620\)** & \(0.146\) & \(-2.257\)** & \(-1.955\) & \(-3.755\)** \\ C24 & \(-7.669\)** & \(-9.385\)** & \(-8.219\)** & \(-6.752\)** & \(-9.043\)** \\ C25 & \(7.467\)** & \(8.009\)* & \(8.170\)** & \(3.564\)** & \(4.443\)** \\ \hline \hline \end{tabular}  
* behind a number indicates that the correlation was significant at \(p<0.01\);
* indicates significant at \(p<0.05\).  
\end{table}
Table 3: Coefficient of determination (R\({}^{2}\)) of the multiple linear regression model between the different CIs and LAI.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stage** & **Original CIs** & **Retinex-Corrected CIs** & **Segmented CIs** \\ \hline Tillering & \(0.47\) & \(0.57\) & \(0.64\) \\ Elongation & \(0.31\) & \(0.50\) & \(0.58\) \\ Booting & \(0.38\) & \(0.52\) & \(0.63\) \\ Heading & \(0.33\) & \(0.51\) & \(0.60\) \\ Grouting & \(0.46\) & \(0.55\) & \(0.61\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Coefficient of determination (R\({}^{2}\)) of the multiple linear regression model between the different CIs and LAI.