Research on stem/tiller number measurement technology of cereal crops based on capacitance principle

Stem/tiller number is a critical component of cereal crop yield, and high-throughput monitoring of crop density is essential for variety selection and cultivation management. However, traditional manual counting methods are inefficient, while existing automated measurement methods suffer from bottlenecks such as insufficient accuracy in high-density scenarios, high equipment costs, and limited field dynamic monitoring capabilities. Therefore, there is an urgent need to develop efficient and low-cost stem/tiller number measurement technologies. This study proposes a novel stem/tiller number measurement technology based on the capacitance principle, systematically validated using wheat and oats as objects through theoretical modeling, indoor stem simulation, pot density experiments, field variety-density combined trials, and stem/tiller number estimation model construction. Theoretical model construction reveals that the linear relationship between stem/tiller number and capacitance value originates from differences in dielectric constants and electric field modulation effects. Both Maxwell-Garnett theory and circuit models indicate a linear positive correlation between stem/tiller number and capacitance variation. Analysis of measurement results under different experimental conditions (electrode configurations, measurement setups, etc.) shows that the best linear relationship between capacitance and stem/tiller number (R²≥0.92, RMSE≤29 stem∙m⁻², P<0.01) was achieved using 6 mm diameter, 3 cm spacing, 30 cm length electrode rods with random contact measurement. Field experiments demonstrated that the measurement setup combining a digital bridge with a four-terminal bridge method, parallel electrodes, and a grounding electrode rod yielded the highest linear correlation between stem/tiller number and capacitance (R²=0.69, P<0.01, RMSE=79 stem∙m⁻²). Additionally, measurements across different growth stages showed linear correlations between stem/tiller number and capacitance for both crops, particularly during vigorous tillering stages, where capacitance responses to stem/tiller number were statistically significant (wheat tillering stage: R²=0.46, RMSE=103 stem∙m⁻², MAE=80 stem∙m⁻², P<0.01; oat tillering stage: R²≥0.55, RMSE≤149 stem∙m⁻², MAE≤117 stem∙m⁻², P<0.01). When establishing field stem/tiller number estimation models, the random forest regression model accurately measured stem/tiller number for wheat and oats (wheat: R²=0.76, RMSE=160 stem∙m⁻², MAE=123 stem∙m⁻², P<0.05, n=102; oats: R²=0.74, RMSE=110 stem∙m⁻², MAE=89 stem∙m⁻², P<0.05, n=143). The results of this study fully demonstrate that the capacitance principle can effectively measure stem/tiller number of field cereal crops. The stable linear relationship between stem/tiller number and capacitance provides new insights for developing low-cost and efficient stem/tiller number measurement technologies.