## 3 Results and Discussion
### The Validation of Results  
Table 3 shows the overall percentage of pixels for both the HRC and HRC_e raster that were correctly classified when compared to the validation polygons. On average, an improvement of 10% was achieved in the images, with an increase of up to 25% in one case. After editing, a mean value of 74% of correctly classified pixels with a standard deviation of 10% was accomplished in our study areas, although the lowest classification rate was about 58%. That value was observed in the oldest images of each study site. This suggests that image quality plays an important role, since newer images present better sharpness. The best classification result (85.2% accuracy) was achieved for the 'Urban' area in 2018. Contrary to our expectations, two images corresponding to the 'Sub-Urban' area show an improvement lower than 2% in the HRC_e. The last could not only be related to the image quality but also to the main characteristic of the study area. As can be seen in Figure 4, the 'Sub-Urban' area is mainly covered by high and low vegetation, followed by areas in process of erosion. The presences of streets, waterbodies, and buildings are scarce. This subject is related to the number of pixels defined as ROIs in both the training input and the validation polygons for the accuracy assessment. Due to the similarity of green color tones, the overall percentage of green areas, and the capacity of the algorithm to discern between vegetation classes, the results tended to misinterpret between 'HighVeg' and 'LowVeg.' In other words, the overall percentage of accuracy in this area was highly influenced by a misclassification of these two classes. In consequence, it is necessary to interpret not only the general accuracy of the results in comparison with manual randomly verification polygons but also to verify which LULC classes are mixed with each other. By doing so, it is possible to make clear if an inaccurate classification is distributed on other classes or tends to be misinterpreted with only one specific class. The point charts in Figure 5 display how a specific LULC class was categorized into any of the nine classes previously defined. Each point is associated with an image (corresponding to one of the three study areas and one year). The y-axis represents the matching ratio of a land cover class in regard to the validation polygons. For a specific chart, the numerator in the ratio indicates the number of pixels of an image within the boundaries of the validation polygons, which were classified as the land cover classes represented in the chart. The denominator is the total number of pixels of the validation polygons defined as one of the classes on the X-axis for each image. Two columns are shown in each category of this axis to designate the coefficients obtained for the HRC (left) and HRC_e (right) raster. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Study Area** & **Year** & **HRC (\%)** & **HRC\_e (\%)** \\ \hline \multirow{3}{*}{Urban} & 2009 & 44.2 & 69.9 \\  & 2015 & 71.7 & 81.7 \\  & 2018 & 72.2 & 85.2 \\ \hline \multirow{3}{*}{Transitional} & 2009 & 54.6 & 60.1 \\  & 2015 & 56.5 & 77.1 \\  & 2018 & 72.0 & 78.4 \\ \hline \multirow{3}{*}{Sub-Urban} & 2009 & 56.1 & 57.7 \\  & 2015 & 80.6 & 82.6 \\ \cline{1-1}  & 2018 & 68.3 & 76.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: General matching percentage obtained between polygons of validation and both HRC andFigure 4: Graphical results for the study area, ‘Sub-Urban,’ in 2015. (Left) *: Regions of interest (ROIs) in the training input of the HRC. (Middle) *: Randomly generated validation polygons. (Right): HRC_e raster. * Transparency of the images in the figure was increased by 10% for better visualization. Figure 5: Accuracy assessment of the LULC classification for each of the study areas and land cover classes. Each class on the x-axis is composed of two columns related to the HRC raster (left) and HRC_e raster (right).