# Fusion of Different Image Sources for Improved Monitoring of Agricultural Plots
## 2 Materials and Methods
### Description of the Fusion Process  
Once the above hypotheses have been accepted, both the histograms of the original image of May (orthophoto) and of the original image of September (drone) are adjusted  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Orthophoto** & **Drone Images** & **Sentinel 2 Images** \\ \hline \multirow{4}{*}{Camera} & UltraCamEagle, UCC-E-1- & \multirow{4}{*}{Parrot Sequoia} & MultiSpectral \\  & 50016095-f80. Quoptic & & multispectral & Instrument (MSI) \\  & & Digaton sensor & & \\ \cline{1-1} \cline{3-4}  & Near Infrared, Red & \multirow{2}{*}{Near Infrared, Red} & \multirow{2}{*}{88 (Near Infrared), \(\mathrm{B}\) (Red), B3 (Green)} \\ \cline{1-1} \cline{3-4}  & Green, Blue & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4} Original Nom. & \multirow{2}{*}{0.25 m} & \multirow{2}{*}{0.062 m} & \multirow{2}{*}{10 m} \\ Resolution employed & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4} Acquisition dates & \multirow{2}{*}{14 August 2019} & \multirow{2}{*}{31 October 2019} \\ \cline{1-1} \cline{3-4}  & & & (‘August’, validation) & (29 images, separated \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \cline{1-1} \cline{3-4}  & & & & \\ \hline \hline \end{tabular} \({}^{*}\)Available bands. Only underlined bands are used in this work.  
\end{table}
Table 2: Summary of main technical specifications of images and bands used in this work.  
using the histogram matching technique, with respect to the reference image ('original image of July', obtained from drone). From them, the so-called homogenized image of May and homogenized image of September are obtained (the image of July is not transformed since it is the reference).  
Subsequently, the fusion process starts. From hypothesis e) we have that in each of the bands we want Equation (1) to be fulfilled:  
\[\sum pf_{i}/numpy=S2_{j} \tag{1}\]  
\(pf_{i}\) being the value to be assigned to the pixel of coordinates \(i\) in that band, \(numpy\) the number of pixels of the image of higher resolution that is below the pixel \(S2_{j}\), of coordinates \(j\), in the corresponding band of Sentinel 2.  
Hypothesis (f) is formulated as follows, for each band:  
\[pf_{i}=po_{i}\times K_{j} \tag{2}\]  
being \(po_{i}\) the value of the pixel of coordinates \(i\) in a band of the high-resolution image and \(K_{j}\) the correction factor that must be applied to the high-resolution pixels of that band located under the \(S2_{j}\) pixel.  
Combining Equations (1) and (2) yields how to convert the grey level values of each band of the homogenized images into values consistent with the hypothesis (d):  
\[K_{j}=S2_{j}\times numpy\text{x}/\sum po_{i} \tag{3}\]  
\[pf_{i}=po_{i}\times S2_{j}\times numpy\text{x}/\sum po_{i}=po_{i}\times S2_{j} /avg_{i} \tag{4}\]  
being \(avg_{i}\) the average of the values of the pixels of the homogenized high-resolution band under the pixel \(S2_{j}\).  
The sentinel2 series of images are then merged with the high resolution homogenized images as follows:  
1. Sentinel 2 images from the period 1 May 2019-30 June 2019 (11 images) merge with the homogenized image of May, from the orthophoto.
2. Sentinel 2 images from the period 1 July 2019-31 August 2019 (12 images) merge with the original Image from July
3. Sentinel 2 images from the period 1 September 2019-31 October 2019 (6 images) merge with the homogenized image from September.  
Later the spectral indices known as NDVI, GNDVI and GCI are calculated on the synthetic images. Figure 1 shows the overall scheme of the procedure.  
Parallelly, for validation purposes, Sentinel 2 images from the period 1 August 2019-30 September 2019 (eight images) were merged with the homogenized image of August and the same indexes were calculated. This image series has a time overlap with series c in the period 1 September 2019-30 September 2019 (3 images). Hereinafter, this period is referred as the 'overlapping period'.