## 2 Materials and Methods
The name of each digital image index and the formula used to calculate it are shown in Table 2 below:  
The study examined plant parameters, including leaf area (PLA), leaf area index (LAI), chlorophyll SPAD, dry matter accumulation (DMA), fluorescence parameters (F\({}_{\rm v}\)/F\({}_{\rm m}\)), intercellular CO\({}_{2}\), concentration (C\({}_{\rm i}\)), stomatal conductance (Gs), net photosynthetic rate (NPR), transpiration rate (T\({}_{\rm r}\)/E), water use efficiency (WUE), spike number (PN), grain number (GN), thousand grain weight (TKW), yield (Y), and plant nitrogen content (NC). The study also measured the stem and leaf nitrogen content (SLNC), stem and leaf phosphorus content (SLPC), stem and leaf potassium content (SLKC), seed nitrogen content (KNC), seed phosphorus content (KPC), kernel potassium content (KKC), plume nitrogen content (GNC), phosphorus content of plumes (GPC), potassium content of plumes (GKC), number of spikes (PN), number of grains in spikes (GN), thousand kernel weight (TKW), and yield (Y), with corresponding vegetation indices. The study utilized the correlation coefficient (r) to measure the degree of correlation between wheat digital image indices and physiological growth characterization parameters. The coefficient was calculated using the following formula:  
\[\rm r=\frac{\sum{(x-\overline{x})(y-\overline{y})}}{\sqrt{\sum{(x-\overline{x} )^{2}\cdot\sum{(y-\overline{y})^{2}}}}} \tag{1}\]  
The correlation coefficient (r) indicates the degree of linear relationship between two variables. A correlation between two variables can be positive, negative, or non-existent, indicated by \(\rm 1\geq r>0\), \(\rm-1\leq r<0\), and \(\rm r=0\), respectively. The absolute value of r indicates the strength of the correlation. To determine the significance of the correlation coefficient, refer to the critical value table for correlation coefficients. Significance levels are denoted by * and ** at the 0.05 and 0.01 levels, respectively. As indicated in Table 3, the analysis of variance (ANOVA) demonstrated significant differential effects of fertilization treatments on the digital image indices G, B, and INT. No significant effects were observed on the remaining indices. \begin{table}
\begin{tabular}{c c c c} \hline
**Digital Image Index** & **Description** & **Calculating Formula** & **Source Literature Reference** \\ \hline R & Red & R & - \\ G & Green & G & - \\ B & Blue & B & - \\ r & Normalized Red Index & R/(R + G + B) & [15] \\ g & Normalized Green Index & G/(R + G + B) & [15] \\ b & Normalized Blue Index & B/(R + G + B) & [15] \\ ExG & Excess Green & \(\rm 2\times G\) - R - B & [8] \\ GRRI & Green-Red Ratio Index & G/R & [8] \\ GRRI & Green-Blue Ratio Index & G/B & [8] \\ RBRI & Red-Blue Ratio Index & R/B & [8] \\ GRVI & Green–Red Vegetation Index & (G - R)/(G + R) & [8] \\ INT & Intensity & (R + G + B)/(3) & [15] \\ IKAW & Normalized Red–Blue Index & (R - B)/(R + B) & [8] \\ MGRVI & Modified Green–Red Vegetation Index & (G - R)/(G + R) & [8] \\ RGRVI & Red–Green-Blue Vegetation Index & (G\({}^{2}-\rm B\times R\))/(G + R + B) & [8] \\ GLA & Green Leaf Area & (\(\rm 2\times G\) – R – B)/(\(\rm 2\times G\) + R + B) & [8] \\ CIVE & Color Index of Vegetation Extraction & 0.441R – 0.881G + 0.385B + 18.7875 & [8] \\ \hline \end{tabular}
\end{table} 
Table 2: Calculation of digital image indices and cited literature sources. R, G, B, and near infrared (NIR) indicate the measured reflectance (digital numbers) in red, green, blue, and near-infrared wavelength ranges, respectively.