*3.2. Plant Density, Canopy Cover, and Yield*

Figure 4 shows the correlation coefficient at 47 and 79 days after sowing between the canopy cover, plant density, and yield; it also shows the correlation coefficient between the applied nitrogen dose and grain yield per plant. The canopy cover calculated through the TGI index is closely related to the density and grain yield of corn; the higher the density, the higher the cover and yield for 47 and 79 DAS. Therefore, corn yield has a direct response to canopy cover and planting density. For the period from 47 to 79 DAS, the canopy cover increased by an average of 15% with a standard deviation of 5%. The correlation coefficient for canopy cover was similar for both flight dates, around 0.76. Plant density, according to Figure 4c, showed a high correlation with a coefficient of 0.94; thus, at a higher density, an increase in grain yield is expected. This means that plant density explained 94% of the yield. Positive yield responses have been reported with an increase in planting density, a significant increase of 4.5–6, moderate of 6–7.5, and low of 7.5 to 9 plants per square meter [14]. The different nitrogen treatments applied to the experiment influenced grain yield per plant; as the nitrogen dose increases, there is a positive gain in grain yield per plant, as observed in Figure 4d, with mean grain weight yield per plant of 109.3, 134.0, 135.6, 137.1, and 138.3 g per plant for 140, 200, 260, 320, and 380 kg ha−<sup>1</sup> , for the conditions of the experimental site and the variety used.

## *3.3. Vegetation Indices and Yield*

For flights at 47 DAS and 79 DAS, six vegetation indices (NDVI, NDRE, WDRVI, EXG, TGI, VARI) were generated; three multispectral indices and three indices in the visible spectrum (RGB). Figure 5 shows the correlation coefficient between the vegetation indices corresponding to the corn class and the observed grain yield at 47 DAS. During the 47 DAS, the WDRVI index presented values ranging from −0.45 to −0.63 with a correlation coefficient of 0.54, thus presenting the highest correlation at this crop stage. Meanwhile, the NDRE index showed a low correlation of 0.23 with values ranging from 0.15 to 0.24. The NDVI ranged from 0.36 to 0.55. In the study carried out by Maresma et al. [72], they found that the WDRVI better explained the corn grain yield with different nitrogen treatments; on the other hand, the index is reported to be sensitive to the leaf area index (LAI) and the canopy cover [53].

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**Figure 4.** (**a**) Correlation between the canopy cover at 47 days after sowing (DAS) and yield; (**b**) correlation between the canopy cover at 79 DAS and yield; (**c**) correlation between plant density and yield; (**d**) correlation between the applied nitrogen dose and grain weight per plant. **Figure 4.** (**a**) Correlation between the canopy cover at 47 days after sowing (DAS) and yield; (**b**) correlation between the canopy cover at 79 DAS and yield; (**c**) correlation between plant density and yield; (**d**) correlation between the applied nitrogen dose and grain weight per plant.

*3.3. Vegetation Indices and Yield*  For flights at 47 DAS and 79 DAS, six vegetation indices (NDVI, NDRE, WDRVI, EXG, TGI, VARI) were generated; three multispectral indices and three indices in the visible spectrum (RGB). Figure 5 shows the correlation coefficient between the vegetation indices corresponding to the corn class and the observed grain yield at 47 DAS. During the 47 DAS, the WDRVI index presented values ranging from −0.45 to −0.63 with a correlation coefficient of 0.54, thus presenting the highest correlation at this crop stage. Meanwhile, the NDRE index showed a low correlation of 0.23 with values ranging from 0.15 to 0.24. The NDVI ranged from 0.36 to 0.55. In the study carried out by Maresma et al. [72], they found that the WDRVI better explained the corn grain yield with different nitrogen treatments; on the other hand, the index is reported to be sensitive to the leaf area index (LAI) and the canopy cover [53]. At 72 DAS, the correlation coefficient of the vegetation indices with respect to the observed corn grain yield increases slightly for all the indices, which is related to the increase in canopy cover and the presence of more pixels in the corn class and fewer pixels in the soil category. In Figure 6, the NDVI, NDRE, and WDRVI showed correlation coefficients of 0.68, 0.31, and 0.65, respectively, and the indices values resulted in ranges of 0.86–0.92, 0.21–0.31, and −0.241 to 0.003, respectively. These increases in the vegetation indices are related to the increase in biomass, leaf area index (LAI), leaf chlorophyll content (LCC), canopy cover (CC), and yield [23,50,72–74]. The NDVI can explain 0.68 of the corn grain yield. Figure 6 shows a proportional relation between an increase in grain yield and an increase in the NDVI index; the same is true for the NDRE and WDRVI. Regarding the normalized EXG, TGI, and VARI indices computed in the visible spectrum (RGB) for 47 DAS, Figure 5d,e show that EXG and TGI presented low correlation coefficients, 0.22 and 0.23, respectively. The VARI in Figure 5f showed a better fit regarding to these indices, with a correlation coefficient of 0.52. In Figure 6, the values of the indices were found between 0.338–0.503, 0.335–0.501, and 0.02–0.19 for EXG, TGI, and VARI, respectively, according to the sampled polygons. In Figure 6 at 79 DAS, 0.71 of the yield can be explained by the EXG index, while VARI showed a value of 0.67. TGI showed a low correlation coefficient. The values of the indices ranged as follows: 0.47–0.60, 0.51–0.55, and 0.10–0.18 for EXG, TGI, and VARI, respectively. Some research works indicate that the VARI has a high correlation with grain yield, chlorophyll content, and the fraction of photosynthetically active radiation intercepted [75,76].

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**Figure 5.** Correlation of vegetation indices and yield at 47 DAS. (A) Normalized difference red edge index (NDRE); (**b**) normalized difference vegetation index (NDVI); (**c**) wide dynamic range vegetation index (WDRVI); (**d**) excess green (ExG); (**e**) triangular greenness index (TGI); (**f**) visible atmospherically resistant index (VARI). **Figure 5.** Correlation of vegetation indices and yield at 47 DAS. (**a**) Normalized difference red edge index (NDRE); (**b**) normalized difference vegetation index (NDVI); (**c**) wide dynamic range vegetation index (WDRVI); (**d**) excess green (ExG); (**e**) triangular greenness index (TGI); (**f**) visible atmospherically resistant index (VARI).

At 72 DAS, the correlation coefficient of the vegetation indices with respect to the observed corn grain yield increases slightly for all the indices, which is related to the increase in canopy cover and the presence of more pixels in the corn class and fewer pixels in the soil category. In Figure 6, the NDVI, NDRE, and WDRVI showed correlation coefficients of 0.68, 0.31, and 0.65, respectively, and the indices values resulted in ranges of 0.86–0.92, 0.21–0.31, and −0.241 to 0.003, respectively. These increases in the vegetation indices are related to the increase in biomass, leaf area index (LAI), leaf chlorophyll content (LCC), canopy cover (CC), and yield [23,50,72–74]. The NDVI can explain 0.68 of the corn grain yield. Figure 6 shows a proportional relation between an increase in grain yield and an increase in the NDVI index; the same is true for the NDRE and WDRVI. Regarding the normalized EXG, TGI, and VARI indices computed in the visible spectrum (RGB) for 47 DAS, Figure 5d,e show that EXG and TGI presented low correlation coefficients, 0.22 and 0.23, respectively. The VARI in REVIEW

[75,76].

Figure 5f showed a better fit regarding to these indices, with a correlation coefficient of 0.52. In Figure 6, the values of the indices were found between 0.338–0.503, 0.335–0.501, and 0.02–0.19 for EXG, TGI, and VARI, respectively, according to the sampled polygons. In Figure 6 at 79 DAS, 0.71 of the yield can be explained by the EXG index, while VARI showed a value of 0.67. TGI showed a low correlation coefficient. The values of the indices ranged as follows: 0.47–0.60, 0.51-0.55, and 0.10–0.18 for EXG, TGI, and VARI, respectively. Some research works indicate that the VARI has a high correlation with

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**Figure 6.** Correlation of vegetation indices and yield for 79 DAS for corn crops. (**a**) Normalized difference red edge index (NDRE); (**b**) normalized difference vegetation index (NDVI); (**c**) wide dynamic range vegetation index (WDRVI); (**d**) excess green (ExG); (e) triangular greenness index (TGI); (**f**) visible atmospherically resistant index (VARI). **Figure 6.** Correlation of vegetation indices and yield for 79 DAS for corn crops. (**a**) Normalized difference red edge index (NDRE); (**b**) normalized difference vegetation index (NDVI); (**c**) wide dynamic range vegetation index (WDRVI); (**d**) excess green (ExG); (**e**) triangular greenness index (TGI); (**f**) visible atmospherically resistant index (VARI).

### *3.4. Training, Validation, and Testing of the Artificial Neural Network for Estimating Yield 3.4. Training, Validation, and Testing of the Artificial Neural Network for Estimating Yield*

A feed-forward neural network was created with 2 layers and 40 neurons, where a combination of the normalized vegetation indices, plant density, and canopy cover, according to Table 4 for 47 DAS, was entered as input parameters. Another neural network for 79 DAS was created to estimate A feed-forward neural network was created with 2 layers and 40 neurons, where a combination of the normalized vegetation indices, plant density, and canopy cover, according to Table 4 for 47 DAS, was entered as input parameters. Another neural network for 79 DAS was created to estimate the corn grain yield of 76 sampled polygons obtained from all of the experimental treatments. The results are shown in Table 4; in column one, we have the combination of input parameters: NDVI, NDRE, WDRVI, EXG, TGI, VARI, canopy cover (C), and plant density (D). The correlation coefficient for training, validation, testing, and total entered data is also presented, as well as the mean absolute error (MAE) and the root mean square error (RMSE).


**Table 4.** Training, validation, and testing of the artificial neural network with different input variables from vegetation indices, plant density, and canopy cover for

greenness index; VARI, visible atmospherically resistant index; C, canopy cover; D, plant density (plants \* m−2 ); MAE, mean absolute error; RMSE, root mean square error.

### *Agriculture* **2020**, *10*, 277

For 47 DAS, which is shown in Table 4 and Figure 7, the input parameters WDRVI, plant density, and canopy cover showed the highest correlation coefficient and the smallest errors for the corn grain yield estimation (R = 0.99, MAE = 0.028 t ha−<sup>1</sup> , RMSE = 0.125 t ha−<sup>1</sup> ) when the total data were used. Using the same parameters above, except plant density as input parameter in the neural network, the correlation coefficient decreased, and the errors increased (R = 0.87, MAE = 0.584 t ha−<sup>1</sup> , RMSE = 0.784 t ha−<sup>1</sup> ), which indicates that plant density is an important parameter in estimating yield for this flight date. A combination of six vegetation indices (NDVI, NDRE, WDRVI, EXG, TGI, VARI), plant density, and canopy cover generates a model with high correlation in yield estimation (R = 0.97), with a mean absolute error of 307 kg per hectare and a root mean square error of 400 kg per hectare. Doing the same analysis, but without plant density, a lower correlation was obtained with the total data (R = 0.92, MAE = 0.512 t ha−<sup>1</sup> y RMSE = 0.643 t ha−<sup>1</sup> ), having greater precision than the combination of WDRVI and canopy cover. On the other hand, a combination of only six vegetation indices as input parameters resulted in a correlation of 0.86 and an MAE of 0.622 t ha−<sup>1</sup> , with an RMSE of 0.809 t ha−<sup>1</sup> when using the total data in yield estimation. This is good if we consider that there is a decrease in computational cost in obtaining plant density and canopy cover. The EXG index, canopy cover, and plant density showed a correlation coefficient of 0.98. In general, combinations that include canopy cover presented high correlation coefficients (R ≥ 0.80), and incorporating plant density as an input parameter increased the value of the correlation coefficient (R ≥ 0.95). The multispectral indices without canopy cover and plant density as input parameters showed a good correlation (R = 0.73, MAE = 0.811 t ha−<sup>1</sup> , RMSE = 1.093 t ha−<sup>1</sup> ) in yield estimation. The RGB indices without canopy cover and plant density showed a lower correlation than the multispectral indices, explaining 0.67 of the corn grain yield. Plant density and canopy cover showed a high correlation (R = 0.96, MAE = 0.298 t ha−<sup>1</sup> , RMSE = 0.441 t ha−<sup>1</sup> ).

For 79 DAS, which is shown in Figure 8 and Table 4, the six vegetation indices, canopy cover, and plant density presented the highest correlation coefficient and the smallest errors (R = 0.97, MAE = 0.249 t ha−<sup>1</sup> , RMSE = 0.425 t ha−<sup>1</sup> ) when the total data were used. The EXG index, canopy cover, and plant density also showed a good correlation coefficient and small errors (R = 0.97, MAE = 0.280 t ha−<sup>1</sup> , RMSE = 0.431 t ha−<sup>1</sup> ) in yield estimation. Vegetation indices and canopy cover increased the correlation coefficient with respect to 47 DAS, while the indices without canopy cover and plant density maintained a similar correlation coefficient for all the data. The TGI index and canopy cover showed the lowest correlation and biggest errors (R = 0.54, MAE = 1.017 t ha−<sup>1</sup> , RMSE = 1.380 t ha−<sup>1</sup> ) in the yield estimate. The multispectral vegetation indices and the visible vegetation indices presented a high correlation in the estimation of corn grain yield at 47 and 79 DAS for the different nitrogen doses tested, presenting slightly higher correlations at 47 DAS.

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**Figure 7.** Yields estimated by the neural network during 47 DAS for all observed yield data. (**a**) Yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices, as well as planting density (D) and canopy cover (C); (**b**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, VARI vegetation indices, as well as C; (**c**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices; (**d**) yield estimated with the NDVI, NDRE, and WDRVI vegetation indices; (**e**) yield estimated with EXG, TGI, and VARI vegetation indices; (**f**) yield estimated with the WDRVI vegetation index, as well as D and C. **Figure 7.** Yields estimated by the neural network during 47 DAS for all observed yield data. (**a**) Yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices, as well as planting density (D) and canopy cover (C); (**b**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, VARI vegetation indices, as well as C; (**c**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices; (**d**) yield estimated with the NDVI, NDRE, and WDRVI vegetation indices; (**e**) yield estimated with EXG, TGI, and VARI vegetation indices; (**f**) yield estimated with the WDRVI vegetation index, as well as D and C.

REVIEW

For 79 DAS, which is shown in Figure 8 and Table 4, the six vegetation indices, canopy cover, and plant density presented the highest correlation coefficient and the smallest errors (R = 0.97, MAE = 0.249 t ha−1, RMSE = 0.425 t ha−1) when the total data were used. The EXG index, canopy cover, and plant density also showed a good correlation coefficient and small errors (R = 0.97, MAE = 0.280 t ha−1, RMSE = 0.431 t ha−1) in yield estimation. Vegetation indices and canopy cover increased the correlation coefficient with respect to 47 DAS, while the indices without canopy cover and plant density maintained a similar correlation coefficient for all the data. The TGI index and canopy cover showed the lowest correlation and biggest errors (R = 0.54, MAE = 1,017 t ha−1, RMSE = 1,380 t ha−1) in the yield estimate. The multispectral vegetation indices and the visible vegetation indices presented a high correlation in the estimation of corn grain yield at 47 and 79 DAS for the different

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**Figure 8.** Yields estimated by the neural network during 79 DAS for all observed yield data. (**a**) Yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices, as well as plant density (D) and canopy cover (C); (**b**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices, as well as C; (**c**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices; (**d**) yield estimated with the NDVI, NDRE, and WDRVI vegetation indices; (**e**) yield estimated with EXG, TGI, and VARI vegetation indices; (f) yield estimated with the WDRVI vegetation index, as well as D and C. **Figure 8.** Yields estimated by the neural network during 79 DAS for all observed yield data. (**a**) Yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices, as well as plant density (D) and canopy cover (C); (**b**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices, as well as C; (**c**) yield estimated with the NDVI, NDRE, WDRVI, EXG, TGI, and VARI vegetation indices; (**d**) yield estimated with the NDVI, NDRE, and WDRVI vegetation indices; (**e**) yield estimated with EXG, TGI, and VARI vegetation indices; (**f**) yield estimated with the WDRVI vegetation index, as well as D and C.

with 0.058 and 0.031 relative importance, respectively.

The importance of the predictor variables (NDVI, NDRE, WDRVI, EXG, TGI, VARI, density, and canopy cover) with respect to the predicted variable (yield) is shown in Figure 9; this was calculated using Garson's algorithm. The results show that the density is the most important predictor for the 47 and 79 DAS with a relative importance of 0.269 and 0.295, respectively; the WDRVI index (0.175) was the second best predictor in importance for the 47 DAS; while the NDVI index (0.184) for the 79 DAS. The VARI index was the least important predictor in the yield estimation for the 47 and 79 DAS

**4. Conclusions** 
