# 4D Building Reconstruction with Machine Learning and Historical Maps
## 3 Data and Case Studies  
### Trento (Italy) Historic City Centre  
As a part of the TOTEM project, maps from four different years (1851, 1887, 1908, and 1936--Figure 1) were employed for this study. Throughout these years, the more significant changes in the city's structure have been related to (i) the alteration of the river's course, which conditioned the urban sprawl of the city and (ii) the progressive demolition of most of the defensive medieval walls. These changes in the urban pattern and the expansion of man-made structures are visible throughout the maps, whereas building functions or planned urban interventions are differently coded.  
While in the oldest map (the year 1851), the buildings' aggregation in blocks and their relation with the cultivated areas are quite detailed, the 1887 map features a more draft representation of the urban landscape (Figure 1), with buildings aggregated in large footprints. In this case, only a few significant civil and religious buildings are sufficiently mapped, while other structures can be identified only by comparing historical data. The informative level of the last two maps (years 1908 and 1936) is instead suitable enough for highlighting the main features and transformation of the built urban environment (Table 1).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Dataset** & **Total n. of Polygons** & **Average Polygons Area (m\({}^{2}\))** \\ \hline
1851 & 1274 & 197.18 \\
1887 & 632 & 499.97 \\
1908 & 1685 & 238.24 \\
1936 & 3112 & 236.62 \\ Actual & 4537 & 149.87 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The number of polygons and their average area in the four digitised historical maps and in the actual topographic data (2016).  
After the manual digitisation of building footprints and each historical map's georeferencing, several attributes (predictors--Section 4.2) were computed. For training the predictive models, footprints and their respective height values derived from the actual topographic data (2016) were employed (Table 2). From this data set (Figure 2), some temporally inconsistent constructions, as recent and industrial structures, were removed to avoid erroneous predictions.  
As reported in Section 5.1, two buildings' classes proved to be an under-represented category in the training data, namely religious structures and civil towers. A data augmentation approach was therefore applied to reach a more balanced class representation and more accurate reconstructions of these few but relevant buildings, describing the city-skyline and aspect.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Total n. of Polygons** & **Average Polygons Area (m2)** & **Average Height (m)** & **Median Height (m)** & **St. Deviation (m)** \\ \hline Actual & 4537 & 149.87 & 12.26 & 12.41 & 5.36 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The actual (2016) topographic data of man-made structures available for Trento.  
Figure 1: The four digitised historical maps of Trento (1851, 1887, 1908, and 1936). Please note the different levels of detail of building footprints, e.g., between 1851 and 1887: in the latter case, footprints are bigger and include multiple buildings with regard to the other maps.