# 4D Building Reconstruction with Machine Learning and Historical Maps
## 2 Related Works  
3D city models are simplified digital replicas of the urban environments, mainly defined by the building blocks' geometry, mutual relations, and the interaction with natural elements. 3D city modelling is a vast research area, centred on developing solutions to create models with several techniques, source data, and automation levels [7; 8; 9]. The application fields have extraordinarily increased in the last decades, bringing significant advantages in many domains (e.g., urban planning, crises and risks management, simulation studies) [10; 11; 12]. 3D city models are generally obtained from 3D surveyed reality-based data [13; 14], employing SAR (Synthetic-Aperture Radar) techniques [15], extruding 2D building footprints [16], through procedural modelling [17], or volunteered geoinformation [18]. Elevation data are mostly derived from LiDAR airborne scanning or image-based procedures and are differently used for modelling purposes. Based on the available source data, employed approach, and the field of application, buildings can be represented with five levels of detail (LoD) [19] and stored with well-defined standards, such as CityGML [20; 21] or CityISON [22]. For visualisation and simple data analyses, the LoD1 (i.e., prismatic block with flat roofs) is sufficient and preferred. According to the available elevation data, the simplest and most common approach for generating LoD1 modelsis the extrusion of building footprints, generally considering the median or maximum height value [23; 24]. When elevation data are missing, a rough building height estimation can be performed with other methods, e.g., counting the number of storeys, considering local regulations and related construction restrictions, or measuring the shadows' length in imagery data [25; 26; 27; 28]. The derived height values' quality is rarely verified and out of scope in many applications with these approaches.  
AI-based procedures were recently used to infer buildings' features and characteristics. Machine and deep learning methods were increasingly employed for predicting 3D urban geometries and semantics [29; 30; 31; 32], for energy performances [33; 34; 35], for models generalisation [36], or to infer some missing information, such as buildings' age [37; 38; 39; 40] and height [28; 41; 42; 43; 44]. Prediction algorithms are generally trained using satellite or aerial images [43; 44], LiDAR data [37; 42], or 2D data (such as photographs, maps, footprints, and attributes) available from historical archives, cadastre datasets, or volunteered geographic information databases [28; 38; 39; 45].  
For the 3D reconstruction of historical urban scenarios, buildings' footprints and some neighbours or categorical features are the only information usable for the prediction. In [28] and [46], buildings' heights are inferred exploiting some machine learning techniques, relying on cadastral and statistical data, as well as some geometrical information extracted from the footprints. We hereafter present a similar approach, based only on geometric, neighbour, and categorical features computable from the digitised historical buildings. With respect to other methods, the proposed approach does not include the number of storeys [28] (not always available and which could significantly vary in each regional contexts), and it only relies only on a set of features (\"predictors\"--Section 4.2) derived from the available building footprints, combined with data augmentation methods to derive accurate results over multiple years and locations.