# 4D Building Reconstruction with Machine Learning and Historical Maps
## 7 Conclusions  
Multi-temporal (4D) versions of the same urban area are of beneficial interest for landscape and urban analyses. This work presented a methodology for the digital reconstruction of buildings in 4D with machine learning algorithms and historical data.  
From digitised historical maps and information of the actual city situations, different regression algorithms were compared and employed for inferring missing building heights, using this information for the multi-temporal 3D reconstruction of two urban city centres.  
The reliability of the proposed approach was verified, testing the method on different datasets and epochs. Multiple quality evaluation methods were also proposed to tackle the issue of missing ground-truth data. The achieved results proved to be consistent with our accuracy targets and the complexity of such historical urban contexts. The implemented method is flexible and extendable, relying mainly on geometric and neighbour characteristics derivable from the datasets and adaptable categorical data.  
In future investigations, the method will be extended to tackle the several issues presented in the previous section, exploring:  
Figure 19: 3D view of the inferred building heights (pink) in Trento with respect to the ground truth data (white), using the actual Bologna dataset as training. Data augmentation was removed from the training set.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline
**Dataset** & **Dataset** & **RMSE TEST** & **MAE TEST (m)** & \(R^{2}\) TEST & **Median (m)** & **St. Dev. (m)** \\
**Prediction** & **Training** & **(m)** & & & & & \\ \hline Trento & Bologna & 3.90 & 2.98 & 0.47 & \(-\)0.03 & 2.49 \\ Bologna & Trento & 4.75 & 3.70 & 0.47 & \(-\)0.09 & 2.99 \\ \hline \end{tabular}
\end{table}
Table 19: Accuracy evaluation with the Random Forest regressor and inverted training data. In this case, augmented data were removed from the training.  
* automatic methods and deep learning techniques for replacing the time-consuming digitisation procedure of historical maps;
* the use of specific training data (e.g., prepared at a building-block level rather than using detailed cadastral maps) for historical datasets suffering from a low informative level;
* the prediction response assigning a lower weight to positional attributes, for avoiding possible mismatches related to different-scale maps and georeferencing issues; and
* the possible generalisation of the method, expanding the training set with data representative of different regional contexts, and applying the trained model in actual scenarios where no elevation data are available (e.g., remote areas).  
The article presents a research contribution that involved authors in equal measure. [PERSON] supervised the overall work and reviewed the entire paper, writing the introduction, aim, and conclusions of the paper; [PERSON] dealt with the state of the art, methodology, data processing, and results. [PERSON] was mainly involved in the development of the regressor analysis, methodology development, and paper revision. All authors have read and agreed to the published version of the manuscript.  
The presented work belongs to the TOTEM project activities which are financially supported by Fondazione CARITRO ([[https://www.fondazionecaritro.it/](https://www.fondazionecaritro.it/)]([https://www.fondazionecaritro.it/](https://www.fondazionecaritro.it/))).  
Not applicable.  
Authors are thankful to the Cadastral office and Superintendence for Cultural Heritage of the Autonomous Province of Trento, Fondazione Museo Storico del Trentino, Archivio Fotografico Storico, and Municipality of Trento.  
The authors declare no conflict of interest.