## 2 Materials and Methods
### Method  
The main steps followed in the proposed methodology are presented in this section. The approach consists mainly in an algorithm that includes three major steps; (A) pre-processing of the remote sensing data, (B) land cover types generation based on relevant spectral indices, and (C) removal of all land use classes that are not urban related and extraction of built-up area. After the image datasets pre-processing and calibration, the next step of the algorithm is represented by extracting the urban associated land use and removal of any other type (Figure 2). For that purpose, we chose to start the analysis from a vegetation index and not from an urban related index, due to the fact that vegetation indices are most widely used and return the most accurate results if we refer to satellite remote sensing if there is an infra-red band (NIR) available. In the preliminary analysis, both urban and vegetation indexes were compared and for this study area, normalized difference vegetation index (NDVI) returned the best results as primary dataset. \[\text{NDVI}=(\text{NIR}-\text{RED})/(\text{NIR}+\text{RED}) \tag{1}\]  
There are many researchers who have used this type of approach; for example, using NDVI, SAVI (Soil Adjusted Vegetation Index) and VI (Vegetation Index) to determine manmade impervious surfaces in urban areas and achieved very good results [60; 61; 62; 63]. The analysis proceeds from the premise according to which, after calculating the NDVI, the next step is to remove all the areas where a considerable degree of vegetation is present. For that purpose, a single threshold is required that can be adjusted depending on the degree of vegetation coverage of the analyzed area and the data acquisition season. It is very well known that NDVI returns a raster dataset with values from \(-1\) to \(+1\) and in general low NDVI values, below 0-0.2 means no vegetation (built-up area, roads, water, bare land, arable land, etc. ), an approximate value between 0.2 to 0.5 means sparse vegetation and everything above 0.6-0.7 correspond to dense vegetation [64]. Given that the studied area does not correspond to areas with very high vegetation, in this analysis a threshold of 0.35 was chosen for the vegetation and no-vegetation areas delimitation. Of course, as we said above, in this category besides the built-up areas we will also have other types of land cover without vegetation (water bodies, bare land, arable land, etc.). The next step of the analysis will focus on eliminating those non-urban areas using specific indexes, such as the Modified Normalized Difference Water Index (MNDWI) for water bodies and the Bare Soil Index (BI) [65; 66] for bare land and arable land. The indices used for highlighting water bodies (MNDWI), respectively; bare lands (BI) were chosen and used due to the fact that they returned the best results within the analyzed area and compared to other indices from the same category. Therefore,  
Figure 2: Workflow of the semi-automatic model proposed for built-up area mapping. MNDWI best managed to highlight water bodies with variable dimensions both in area and depth and BI was best able to highlight bare and uncultivated agricultural land, in a relatively fragmented area in terms of land cover, characterized by medium density built-up areas that are often mixed with agricultural land, both cultivated and uncultivated. \[\text{MNDWI}=\left(\text{GREEN}-\text{NIR}\right)/\left(\text{GREEN}+\text{NIR}\right) \tag{2}\]  
\[\text{BI}=\left[\left(\text{SWIR}+\text{R}\right)-\left(\text{NIR}+\text{B} \right)\right]/\left[\left(\text{SWIR}+\text{R}\right)+\left(\text{NIR}+\text{ B}\right)\right] \tag{3}\]  
In the case of these indices, for both MNDWI and BI, the normalized values obtained will also be between \(-1\) and \(1\) and the analysis proceeds from the assumption that every value above \(0\) means the presence of the observed features and everything below that value means the lack of it.