## 1 Introduction  
Digital-based architectural heritage (AH) restoration methods [1], specifically in what is called virtual reconstruction, have gained prominence in the past two decades [2]. This has been mainly due to novel data collection, computer graphics, and computer-aided design (CAD) technologies, and their wide adoption. The last of these is artificial intelligence (AI), which \"suggests a turning point that may change in the coming years the way we approach, from a scientific point of view, the question of virtual reconstruction\" [3]. In turn, the current AH practice is traversing a paradigm shift from \"by hand,\" craft-based methods, through 3D modeling and rendering, towards AI-based ones. Central to AH practice, virtual reconstruction is defined as a means of inferring or guessing, based on available information, a building's possible original state. The latter entails representing a prediction of its original appearance, or its intermediate states, from observation of its existing remains. Here, and this is the main point, \"virtual\" means that the building is not physically intervened, but it is immaterially invoked via drawing plans, perspectives, isometric views, paintings, or scale model representations [3]. Examples of the aforementioned advancements [4; 5; 6; 7] comprise mainly light detection and ranging (LiDAR) surveying and data capture [8], photogrammetry, videogrammetry [9], virtual reality [10], fractal mesh representation [11], and parametric modeling. These have significantly reduced the difficulty of studying decayed and even disappeared buildings such as Renaissance-era palaces [12], museums [6], and residential buildings [13], including the development of detailed finite element models aimed at the structural assessment of historical constructions at risk of disappearance [14; 15]. However, AH's most recent digital advancement came in the form of building information modeling (BIM), and the later advent of heritage BIM (HBIM), a heritage-specific BIM class system [16]; this means that within the BIM environment, specific classes--or families--are identified that go beyond traditional BIM elements. These recent methods have superseded \"traditional\" ones due to their further reduced invasiveness in comparison with earlier methods. Roughly speaking, the AH workflow usually works this way: LiDAR technicians, surveyors, art historians, and archaeologists capture data, mainly in the form of point clouds. Then, they submit these data to 3D artists and technicians who reconstruct a detailed digital representation of 3D models. Finally, AH professionals use these as a foundation and support material for their decision-making processes [4]. Benefits aside, non-automated CAD work is still the norm within these practices [10], and significant technical setbacks stem from this kind of 3D acquisition and modeling work. In addition, these conventional methods are usually labor-intensive, time-consuming, and often supported by few and thinly automated processes [2; 4; 6; 13]. Moreover, there have been documented difficulties in establishing precise geometry during mesh reconstruction, often taking significant amounts of time to complete [6]. Furthermore, scan cleaning-related noise problems (i.e., reducing excess points from the usual LiDAR-generated point cloud) and incomplete documentation [7] are commonplace. Last, but more importantly, is their non-reusability, meaning that each building has to be reconstructed from scratch every time a new project begins [17]. In this context, Scan to BIM has emerged in the last decade as a solution \"program\" to address these issues and automate the whole process. Scan-to-BIM is a process that converts digital point-cloud models obtained through laser scanning into BIM platforms, which analyze the data and incorporate them into a 3D model of the site or building to support development, design, and construction teams [18].