## 3 Materials and Methods
### Dataset Design  
The acquisition of \"real-world\" AH period data poses significant logistical and technical challenges. When trying to gather LiDAR data, some parts are usually occluded from view. In addition, density in its point cloud output format is often impractical for virtual reconstruction tasks, with its point count usually in the billions. This, in turn, produces a significant amount of \"outlier\" points (or, in the ML language, noise), and processing these in an automated manner is a significant hurdle. A similar type of problem arises when performing photogrammetry to obtain AH building data; occluded points are a common and difficult hindrance due to camera positions and their respective ranges. We also note that both methods, by far the most popular, present similar equipment expertise-related issues, often being extremely expensive and complicated to operate, requiring specialized personnel to manipulate them. Hence, we opted to produce our synthetic dataset to simulate a video capture from a drone or smartphone and simplify the data capture method. The justification for using a synthetic dataset for training, instead of a photographic image set, is thoroughly addressed in our other publications [17]. Finally, our non-invasive strategy of developing synthetic training datasets provides, as a byproduct, the advantage of intervening even less directly in the studied building, overcoming a significant problem in AH processes. Concerning Romanesque-Mudejar churches, they were chosen as subjects because numerous churches remain in usable states, and there is significant historical documentation available showing them in their original state. We took advantage of this, as it was easier to collect data from the existing or documented buildings and to 3D model them for AI training.  
For these reasons, we built a synthetic dataset that comprises 60 Romanesque-Mudejar style medieval churches, which were 3D-modeled using photographs, surveyed \"as-built\" plans, sketches, and written descriptions as bases for the modeling of each church. These 3D models were then used to produce rendered images, displaying the building's materials, light, and shadows against a standard background environment. In turn, these were used to train the GS-SuGaR models, build 3D RFRs, and thereafter extract their respective meshes. To build a systematic dataset, we rendered each church, defining three building states (cf. \"snapshots\" of the building's decay process at specific points in time for each church, shown in Figure 2) as follows: building state 0 (complete building); building state 1 (missing roof and comice); building state 2 (mid-height walls); and counting 180 rendered images for each church. At 32,400 images in total, this dataset is relatively small, but this order of magnitude can be useful if its data framing and processing are adequately implemented, as [17; 43] noted. The criterion for selecting the number of images follows the same approach used by [23] in GS, as well as by [38] in Mip-NeRF360, taking every 8 th photo for testing, to ensure consistent and meaningful comparisons for the generation of error metrics.