## 2 3D Reference Model-TLS Survey  
In order to provide a 3D reference dataset for the assessment of the other two systems considered in this work, the interior of the Impossible bastion was fully surveyed with a Leica ScanStation C10  
Figure 2: **(a)** A section of the tunnel of the Impossible bastion. **(b)** Setup of the Leica ScanStation C10 over a traverse mark and target pole over the back target. TLS. Based on time-of-flight (TOF) measuring principle, this scanning system combines all-in-one portability with the ability of performing surveys similar to a total station (traverse and resection). The laser features a full 360\({}^{\circ}\)\(\times\) 270\({}^{\circ}\) field-of-view thanks to the adoption of the Smart X-Mirror design, low beam divergence (\(<\)6 mm @ 50 m), high accuracy (6 mm @ 50 m), long range (300 m @ 90% reflectivity), dual-axis compensator and high scan speed (50k pts/s). In addition, the total station-like interface and on-board graphic color touch screen display allow users on-site data viewing. Moreover, this scanner also has internal memory storage of 80 gigabytes, which is ideal for surveying large areas. The laser survey of the fortification was carried out by using the traversing method. This surveying procedure allows the user to take advantage of the Leica C10 built-in dual-axis compensator to use conventional surveying techniques to perform a traverse and establishing relationships between successive scanner positions within a known or assumed coordinate system. Because the dual-axis compensator automatically corrects scan data for the vertical displacements, the traverse procedure does not require as many targets as regular target-based registration. In this case study, an open traverse consisting of nine laser stations was set up to completely cover the study area. On each station, the laser scanner was set on a tripod and then carefully leveled and plumbed directly over the top of the traverse mark on the ground. Leveling of the instrument is required in order to enable automatic registration of acquired scans and to minimize measurement errors. After setting out the TLS, the bearing and coordinates of the back station were set in order to define the fore station. The positions of back and fore stations were measured by the laser scanner using proper Leica target poles (Figure 2b), whose sizes are automatically stored in the laser firmware. In order to meet the requirement of a clear line of sight between each target station (back and fore) and the laser station, scanner positions were carefully designed by taking into account the inner geometry of the fortification. From each laser station, a set of scans was acquired with an average spatial resolution of about 1 cm at a distance of 10 m. Following a few initial tests, this value was deemed the most suited to generate a 3D model with a good level of detail for subsequent analyses. Furthermore, in order to georeference the TLS-based 3D model, the traverse was properly connected to four control points (CPs) located outside of the bastion. Due to the morphological characteristics of the ancient structure and of the surrounding environment, three points were set at the tunnel entry, while the fourth one was placed in front of the left wing, being visible from the interior of the bastion through a small aperture. These CPs were measured both with a double frequency GNSS receiver (Topcon HiPer V) and with the Leica C10. In the latter case, specific Leica retroreflective 6\" circular targets were employed. At the four CPs, GNSS observations were collected in network real-time kinematic (NRTK) mode, i.e., receiving real-time corrections from a nation-wide network of permanent GNSS stations (Topcon NetGEO network [37]). The raw data collected with the ScanSation C10 were then imported in Leica Cyclone software for processing. First, the scan station sequence was assembled in the Cyclone Traverse Editor in order to build the traverse. To this aim, instrument and target heights measured in the field were set for each scanner position.