# 4D Building Reconstruction with Machine Learning and Historical Maps
## 6 Discussion  
The quality performance of several regressors for predicting height values from historical data was presented. Several evaluation approaches were proposed for tackling the issue of a lack of ground-truth information with historical data. The evaluation metrics proved that the Random Forest regressor inferred better building heights with regard to other algorithms. Comparing the prediction results with the Random Forest algorithm in the historical datasets (Tables 11 and 14), a general worsening of the metrics can be noticed when the polygon's area is much different from the training data (Tables 1 and 3). Therefore, the prediction quality is conditioned by the informative level of the historical maps and size of digitised polygons. The inferring methodology relies on some twenty predictors (Section 4.2). As typical in a machine learning application, a recursive feature elimination (RFE) approach can be employed to select and reduce the predictors. This technique helps remove irrelevant predictors, selecting only the most relevant ones and speeds up the overall prediction procedure. Figure 16 reports the predictors' importance for the Trento dataset. Some categorical features are more significant than other attributes. Therefore, an RFE approach was applied to optimise the algorithm's performance and reduce the number of predictors (Figure 17). Results and comparisons for both datasets are presented in Tables 16 and 17. Aside from no significant changes in the evaluation metrics, a general worsening in the predicted building heights' quality was verified by visually checking the results obtained after an RFE approach. Therefore, for the considered datasets, the RFE approach proved to be ineffective, and the different contributions of all predictors (Section 4.2) were shown to be relevant. Figure 15: Multi-temporal 3D reconstruction of Bologna with building heights inferred using machine learning and historical maps (1884 and 1945). Figure 16: Predictors importance of the Random Forest method in the Trento dataset. The most relevant are function (e.g., civil or religious), class (e.g., churches, palaces, castle), and distance (from a polygon’s centroid from the nearest centroid). On the y-axis, the features importance score is given, i.e., the normalised average scores indicating the weighted variance decrease in a decision tree. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Regressor** & **N. of Features** & **RMSE TEST (m)** & **MAE TEST (m)** & \(\mathbf{R^{2}}\)**TEST** & **St. Dev. (m)** \\ \hline Random Forest—without RFE & 20 & 3.59 & 2.83 & 0.57 & 2.07 \\ Random Forest—with RFE & 10 & 3.83 & 2.99 & 0.51 & 2.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 17: Evaluation metrics for the Bologna dataset with and without an RFE approach. Figure 17: Feature importance of the Random Forest method and RFE in the Trento dataset. The implemented method, although reliable and feasible, still presents some issues to be tackled:  
1. data preparation (i.e., the digitisation of historical maps) is demanding and time-consuming;
2. differences in the input data (i.e., different informative levels among the training data and the historical datasets) can affect the quality of the prediction;
3. the results can be influenced by the accuracy of the georeferenced maps, considering that positional attributes are included among the predictors; and
4. the method was tested on similar urban scenarios and using respective actual data as training. The applicability in different regional contexts and the prediction's quality employing other cities' training data need further investigations. About the latter issue, some preliminary tests were conducted to verify if, in similar built environments, the procedure can return satisfactory results using different cities' training data. The Random Forest performances' evaluation are presented in Table 18 where a training using Trento's data is used to predict heights of Bologna footprints, and vice-versa (removing the positional attributes).