## 3 Results and Discussion
### Field and Crop Statistics  
One important use of the image workflow is the extraction of spectral and textural statistics for the characterization of crops and fields. This operation requires satellite images that are radiometrically and atmospherically corrected and that are highly aligned over time and over the fields. Otherwise, the extracted statistics from such small fields will be incoherent. For spectral statistics, we use multispectral images, and, for textural statistics, we use panchromatic images. To obtain pure results per field, a (negative) buffer of 2 m is applied to disregard potentially fuzzy pixels at the field boundary; this eliminates vegetation along the edges of the field to a large extent. Cloud and tree masks are applied at this stage. The first four statistical moments (i.e., pixel count, mean, variance, and skewness) of the surface reflectance contained within the field polygon are extracted, as well as the correlation and covariance matrices between the multispectral bands. Table 4 lists the spectral attributes extracted per field and per satellite image, and their values are delivered as a single.csv file for each image. Concurrently, the mean values and standard deviations of nine popular spectral vegetation indices are computed (NDVI, green NDVI, EVI, TCARI, NIR red, SARVI, MSAVI, WV2) (Table 5). Textural attributes are derived from the panchromatic images using the Gray-Level Co-Occurrence Matrix (GLCM) [60], which is a statistical approach to texture characterization suitable for regions with irregular shapes [61]. This applies well to smallholder fields. GLCM was calculated for four \begin{table}
\begin{tabular}{c c} \hline \hline
**Statistical Moment** & **Explanation** \\ \hline
0 & Number of pixels within the polygon \\
0 & Number of pixels contributing to the statistics \\  & (masked pixels excluded) \\
1 & Mean \\
2 & Variance \\
3 & Skewness \\ mixed & Band-to-band correlation (i,j) \\ mixed & Band-to-band covariance (i,j) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Spectral statistical moments extracted from the images. \begin{table}
\begin{tabular}{c c} \hline \hline
**Index** & **Reference** & **Formula** \\ \hline NDVI (Normalized Difference & \(\frac{R_{NII}-R_{R}}{R_{NII}+R_{R}}\) \\ Vegetation Index) & [52] & \(\frac{R_{NII}-R_{R}}{R_{NII}+R_{R}}\) \\ \hline Green NDVI (Green Normalized & \multirow{2}{*}{[53]} & \(\frac{R_{NII}-R_{R}}{R_{NII}+R_{R}}\) \\ Difference Vegetation Green & & \\ Index) & [53] & \(\frac{2.5*R_{NII}-R_{R}}{R_{NII}+6*R_{R}-7.5*R_{R}+1}\) \\ \hline EVI (Enhanced Vegetation Index) & [54] & \(3\Big{[}(R_{REDGE}-R_{R})-0.2(R_{REDGE}-R_{G})\Big{(}\frac{R_{REDGE}}{R_{R}} \Big{)}\Big{]}\) \\ \hline TCARI (Transformed Chlorophyll & \multirow{2}{*}{[55]} & \(3\Big{[}(R_{REDGE}-R_{R})-0.2(R_{REDGE}-R_{G})\Big{(}\frac{R_{REDGE}}{R_{R}} \Big{)}\Big{]}\) \\ Absorption Ratio Index) & \\ \hline Simple ratio (NIR/RED) & [56] & \(\frac{R_{NII}}{R_{R}}\) \\ \hline SARVI (Soil and Atmospherically & \multirow{2}{*}{[57]} & \(\frac{(1+1)(R_{NII}-R_{R})}{(R_{NII}+R_{R}+1)}\) \\ Resistant Vegetation Index) & & where \(R_{R}=R_{R}-gamma(R_{R}-R_{R})\) \\ \hline SAVI (Soil Adjusted Vegetation & \multirow{2}{*}{[58]} & \(\frac{(1+1)(R_{NII}-R_{R})}{(R_{NII}+R_{R}+1)}\) \\ Index) & & \\ \hline MSAVI2 (Improved Soil Adjusted & \multirow{2}{*}{[59]} & \(\frac{2R_{NII}+1-\sqrt{(2R_{NII}+1)^{2}-8(R_{NII}-R_{R})}}{2}\) \\ Vegetation Index) & & \\ \hline NDVI (Normalized Difference & \multirow{2}{*}{[52]} & \(\frac{R_{NII}-R_{R}}{R_{NII}+R_{R}}\) \\ Vegetation Index) based on NIR2 & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Empirical indices proposed frequently in remote sensing of agriculture. angles to cater for different directions along and perpendicular to the sowing rows.