## 3 Results and Discussion
### The Validation of Results
For example, a point located in the chart 'Building,' column HRC of the 'Paved' class has a coefficient equal to 0.48 (green triangle symbol in the left column). The point indicates that, from all the pixels in the validation polygons of HRC corresponding to 'Transitional' area in 2015 classified as buildings, 48% were classified as paved streets. Thus, the tendency of a specific land cover class to be classed as another one can be inferred. Some points were not displayed in Figure 5, since they were considered irrelevant and could lead to false conclusions due to the nature of the diagram. A value was discarded if the ratio between the correspondent percentage of the land class and the percentage of the maximum land class of its image was lower than a threshold. This threshold was assumed as 0.05 which represents a relative percentage in reference to the largest land cover class of an image. A specific point representing only a small portion of the validation pixels in comparison with other categories was rejected if that ratio was lower than the minimum threshold. The formula employed to define this ratio can be observed in Equation (1), where the subscripts \(i\) and \(j\) represent each \(m\) land classes and \(n\) HRC_e rasters, respectively. Nevertheless, this boundary was employed only for illustration purposes of depicting Figure 5 without any change on the HRC or HRC_e results. \[ratio_{(i,j)}=\left.\frac{\%LandClass_{HRC\_e(i,j)}}{Max\left(\%landClass_{ HRC\_e(j)}\right)}\right|_{i=1}^{m}\left|\right._{j=1}^{n}\geq Threshold \tag{1}\]  
The charts presented in Figure 5 illustrate how the results improved after post-processing. Clouds and shadows were reduced to zero as a result of replacing them by other LULC classes. For 'Water,' no variation is indicated because the random validation polygons did not lay in any of these areas, so no comparison was possible for this layer. The most relevant variation which tended to be erroneously classified in the HRC was found between buildings and paved streets. In the case of buildings, this land cover class was mostly classified as 'Buildings' and 'Paved' in the ranges of 20-80% and 0-45%, respectively. Those results improved after editing, achieving accuracy values higher than 60% for the first case and reducing the error to values lower than 20% in comparison with other classes (See Figure 5, 'Building' chart). Similar results can be observed for the validation areas corresponding to paved streets. In this case, the percentage of accuracy rose above 80% for 'Streets' while misclassified buildings in those areas were reduced to less than 5%, most likely due to the overlapping process. However, in the same layer, 'Bare land' showed an error on the accuracy of up to 16% in one case, which suggests that the misclassification between these two classes is higher in paved zones. This result was expected, since some sites, such as sidewalks, are still irregular unsealed areas among paved streets, which leads to an erroneous classification if the superimposing method is applied. The chart corresponding to 'Bare land' shows how it tends to be the least accurately classified. These areas are subject to misclassification with any of the other classes, except shadows, clouds, or waterbodies. Even after editing, these values did not decrease but actually rose for the classes 'HighVeg' and 'LowVeg.' The latter could be due to the random generation of areas which considered two land classes in the same polygon and were classified as just one class. Another factor for this increase could be related to the ambiguity of visually defining zones with soil degradation. Thus, if an area is considered as 'LowVeg' or 'Bare land' depends highly on the manual definition of ROIs driven by the user. There is no significant variation after editing in the areas classified as 'HighVeg' and 'LowVeg.' The charts associated with those two classes show that the ranges of accuracy improved only in certain cases.