# Winter Wheat Take-All Disease Index Estimation Model Based on Hyperspectral Data
## 3 Results
### Validation of Inversion Model of Winter Wheat Take-All Disease Index  
Fit test was performed on the 15 sample data in the validation group using the six models selected above and the coefficient of determination, root mean square error and mean absolute error between the estimated value and the measured value of the disease indices were obtained. The optimal disease index estimation model was obtained by comparing the verification accuracy and the three groups with the highest accuracy were selected for summary (Table 5).  
The three models with high determination coefficients all contain the green-red composite spectral index NDSI(R\({}_{534}\),R\({}_{742}\)), which has a great influence on the disease index inversion.  
Compared with the binary parameter model, the near infrared NDSI(R\({}_{810}\),R\({}_{834}\)) and green NDSI(R\({}_{590}\),R\({}_{598}\)) were combined with NDSI(R\({}_{534}\),R\({}_{742}\)) and it was found that the near infrared was better. Comparing binary variables with ternary variables, adding near infrared NDSI(R\({}_{810}\),R\({}_{834}\)) variable can effectively improve the accuracy of the model, increase \(R^{2}\) and decrease RMSEP of the model. The best estimate model was \(Y=134.577-70.301\) NDSI(R\({}_{590}\),R\({}_{598}\)) - 533 NDSI(R\({}_{534}\),R\({}_{742}\)) + 51.584 NDSI(R\({}_{810}\),R\({}_{834}\)) (\(R^{2}=0.743\), RMSEP = 0.094). It was the optimal disease index prediction model and Figure 5 showed the linear fitting results of this model. The following estimate models were \(Y=133.059+32.751\) NDSI(R\({}_{810}\),R\({}_{834}\)) \(-219.736\) NDSI(R\({}_{834}\),R\({}_{742}\)) (\(R^{2}=0.728\), RMSEP = 0.106) and \(Y=137.507-65.786\) NDSI(R\({}_{590}\),R\({}_{598}\)) \(-228.808\) NDSI(R\({}_{534}\),R\({}_{742}\)) (\(R^{2}=0.726\), RMSEP = 0.108).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Band Combination** & **Fitting Formula** & \(R^{2}\) \\ \hline G-BR & \(Y=137.507-65.786\) NDSI(R\({}_{890}\),R\({}_{598}\)) \(-228.808\) NDSI(R\({}_{834}\),R\({}_{742}\)) & 0.759 \\ N-BR & \(Y=133.059+32.751\) NDSI(R\({}_{810}\),R\({}_{834}\)) \(-219.736\) NDSI(R\({}_{834}\),R\({}_{742}\)) & 0.755 \\ B-GR & \(Y=113.968+35.529\) NDSI(R\({}_{590}\),R\({}_{598}\)) \(-211.716\) NDSI(R\({}_{854}\),R\({}_{742}\)) & 0.758 \\ N-GR & \(Y=111.824+11.54\) NDSI(R\({}_{810}\),R\({}_{834}\)) \(-193.693\) NDSI(R\({}_{854}\),R\({}_{742}\)) & 0.750 \\ G-BR-N & \(Y=134.577-70.301\) NDSI(R\({}_{890}\),R\({}_{598}\)) \(-223.533\) NDSI(R\({}_{834}\),R\({}_{742}\)) & 0.760 \\  & \(+51.584\) NDSI(R\({}_{810}\),R\({}_{834}\)) & 0.760 \\ B-GR-N & \(Y=107.966+53.344\) NDSI(R\({}_{890}\),R\({}_{898}\)) \(-206.922\) NDSI(R\({}_{534}\),R\({}_{742}\)) & 0.762 \\  & \(+51.584\) NDSI(R\({}_{810}\),R\({}_{834}\)) & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Optimal band combinations and fitting formulas.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Band Combination** & **Spectral Index** & \(R^{2}\) & **RMSEP** \\ \hline G-BR &
\begin{tabular}{c} NDSI(R\({}_{890}\),R\({}_{988}\)), \\ NDSI(R\({}_{534}\),R\({}_{742}\)) \\ NDSI(R\({}_{810}\),R\({}_{834}\)), \\ NDSI(R\({}_{534}\),R\({}_{742}\)) \\ NDSI(R\({}_{590}\),R\({}_{598}\)), \\ NDSI(R\({}_{534}\),R\({}_{742}\)) \\ NDSI(R\({}_{810}\),R\({}_{834}\)) \\ \hline \hline \end{tabular}
\end{table}
Table 5: Band combinations with the highest validation accuracy.