# Rapid Detection of Key Phenotypic Parameters in Wheat Grains Using Linear Array Camera
## 3 Results
Through the traversal calculation of the major semi-axis value, \(r_{1}\), determined by the fitted ellipse and distance, d, from the center point to the marked germination point, we found that setting k to 0.72 provides an optimal fit for the wheat germination point locations, as illustrated in Figure 16. To further validate the accuracy of coefficient k, images of germinated grains were matched with their corresponding ungerminated seeds. The actual germination point positions were manually marked in Halcon, and deviations between these points and the predicted germination points after applying the correction coefficient were calculated. Specifically, both angular and distance differences were computed by connecting the annotated and predicted germination points to the center point of each wheat grain. The entire experimental processing workflow is detailed in Figure 14. The resulting deviations were compiled and analyzed in Excel, where average angular and distance differences for each category were calculated. These summarized results are presented in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Category**} & **Mean Grain** & **Average Error of** & **Mean Particle** & **Average Error of** & **Mean Grain** & **Average Error of** \\  & **Length Error (mm)** & **Grain Length (\%)** & **Width Error (mm)** & **Grain Width (\%)** & **Weight Error (mg)** & **Grain Weight (\%)** \\ \hline hm20 & 0.063 & 0.796\% & 0.039 & 0.796\% & 2.42 & 0.796\% \\ hm44 & 0.065 & 0.988\% & 0.050 & 0.988\% & 2.24 & 0.988\% \\ nhm237 & 0.051 & 0.675\% & 0.036 & 0.675\% & 3.24 & 0.675\% \\ nhm432 & 0.058 & 0.808\% & 0.043 & 0.808\% & 2.08 & 0.808\% \\ xm35 & 0.091 & 1.392\% & 0.045 & 1.392\% & 1.67 & 1.392\% \\ all & 0.066 & 0.932\% & 0.043 & 0.932\% & 3.15 & 0.932\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Error analysis of wheat grain shape parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{3}{c}{**Number of Grains (pcs)**} & **Number of Correctly Identified Units (pcs)** & **Accuracy (\%)** \\ \hline hm20 & 40 & 38 & 95\% \\ hm44 & 40 & 38 & 95\% \\ nhm237 & 40 & 40 & 100\% \\ nhm432 & 40 & 40 & 100\% \\ xm35 & 40 & 39 & 97.5\% \\ all & 200 & 195 & 97.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Wheat bud-point direction determination test. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{3}{c}{**Number of Grains (pcs)**} & **Number of Correctly Identified Units (pcs)** & **Accuracy (\%)** \\ \hline hm20 & 40 & 38 & 95\% \\ hm44 & 40 & 38 & 95\% \\ nhm237 & 40 & 40 & 100\% \\ nhm432 & 40 & 40 & 100\% \\ xm35 & 40 & 39 & 97.5\% \\ all & 200 & 195 & 97.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Wheat bud point validation test. During image processing, the irregular shape of certain wheat grains can cause slight deviations in the calculated bud-point position within localized areas. While the bud point determined through ellipse fitting may exhibit minor positional errors, these deviations minimally impact the accuracy of bud-point angle calculations. As shown in Table 3, using the bud-point direction determination method proposed in Section 2.3.2, only two misjudments occurred out of 120 grains, corresponding to an accuracy rate of 98.33%. The coefficient k was initially established during the research and validated through traversal analysis using Halcon. The data indicate that with k at 0.72, the mean positional error between the predicted and actual bud points across the five wheat varieties remains within 0.10 mm. Additionally, the mean angular error between the predicted and actual bud-point directions is confined within \(\pm 3^{\circ}\). Altogether, the experimental results confirm that this method reliably and accurately localizes wheat grain bud points. The high accuracy and low error margins indicate their suitability for precise phenotypic analysis and related applications in wheat breeding and quality assessment.