## 4 Results and Discussion  
### Comparison of Identification Results of Nine Classifiers  
Figure 7 shows the relative errors of identified maize and sunflower planting areas from 2009 to 2015 using the above nine classifiers. For the training years, the mean relative errors of classifiers normalized with mean values of farmland, grassland and forest are 6.18%, 6.70%, and 4.62% for maize, and 5.32%, 3.35%, and 5.25% for sunflower, respectively. For the testing years, the corresponding mean relative errors are 14.55%, 14.08% and 13.79% for maize, and 9.19%, 8.72% and 8.87% for sunflower, respectively. Compared with the results of [PERSON] et al. [11] with the mean relative error for maize of 15.91%, our identification results of maize are significantly better. Moreover, we also obtained better identification results of sunflower than maize. Consequently, our classifiers of maize and sunflower are superior to [PERSON] et al. [11]. One possible reason for more precise identification results may be the higher spatial resolution data of 30 m that can reduce the impact of mixed pixels and enhance the capability in identifying small areas of maize and sunflower.  
Considering the overall identification performance of maize and sunflower, the mean relative errors of the above three normalization approaches are 5.75%, 4.85%, and 4.94% for the training years, and 11.87%, 11.40%, and 11.33% for the testing years. Therefore, the relative errors of the second and third normalization approaches were quite close, which are both smaller than the first one. This is because the growth of farmland is not only affected by climatic factors, but also affected by plant structure, irrigation conditions, and other factors, resulting in instability of its normalized results. While the growth of grassland and forest are mainly affected by climatic factors, using grassland and forest indexes can eliminate the influence of different meteorological conditions after normalization. In addition, the forest area is relative small, while the area of grassland is the second largest and only smaller than the farmland in the study area (Figure 2). Therefore, the mean values of grassland indexes are more representative than forest, which was chosen for normalization.  
For three classifiers normalized with grassland indexes, the mean relative errors during the training and testing years using the classifiers of NDVI_max-FGP, NDVI_inf-FGP and ANDVI-FGP are 11.46%, 10.82% and 10.48% for maize, and 4.37%, 4.38% and 10.50% for sunflower, respectively. The mean relative errors of maize and sunflower in the above three methods are 7.92%, 7.60% and 10.49%, respectively. The relative error from the \(\Delta\)NDVI-FGP classifier are higher than the  
Figure 7: Performance of different classifiers for maize (**a**) and sunflower (**b**).  
NDVI_max\(\sim\)FGP and NDVI_inf-FGP classifiers, and the NDVI_inf-FGP classifier has slightly better performance than the NDVI_max\(\sim\)FGP classifier. Consequently, the NDVI_inf-FGP classifier (b2) based on the normalization of grassland indexes was selected as the optimal classifier, and the corresponding ellipse equations of maize and sunflower are  
\[895x^{2}+673y^{2}+484 xy-2821x-1832y+2608=0 \tag{15}\]  
\[940x^{2}+426y^{2}-292 xy-1939x-1000y+1298=0 \tag{16}\]