Digital 3D reconstruction as a research environment in art and architecture history: uncertainty classification and visualisation

The dissertation addresses the still not solved challenges concerned with the source-based digital 3D reconstruction, visualisation and documentation in the domain of archaeology, art and architecture history. The emerging BIM methodology and the exchange data format IFC are changing the way of collaboration, visualisation and documentation in the planning, construction and facility management process. The introduction and development of the Semantic Web (Web 3.0), spreading the idea of structured, formalised and linked data, offers semantically enriched human- and machine-readable data. In contrast to civil engineering and cultural heritage, academic object-oriented disciplines, like archaeology, art and architecture history, are acting as outside spectators. Since the 1990s, it has been argued that a 3D model is not likely to be considered a scientific reconstruction unless it is grounded on accurate documentation and visualisation. However, these standards are still missing and the validation of the outcomes is not fulfilled. Meanwhile, the digital research data remain ephemeral and continue to fill the growing digital cemeteries. This study focuses, therefore, on the evaluation of the source-based digital 3D reconstructions and, especially, on uncertainty assessment in the case of hypothetical reconstructions of destroyed or never built artefacts according to scientific principles, making the models shareable and reusable by a potentially wide audience. The work initially focuses on terminology and on the definition of a workflow especially related to the classification and visualisation of uncertainty. The workflow is then applied to specific cases of 3D models uploaded to the DFG repository of the AI Mainz. In this way, the available methods of documenting, visualising and communicating uncertainty are analysed. In the end, this process will lead to a validation or a correction of the workflow and the initial assumptions, but also (dealing with different hypotheses) to a better definition of the levels of uncertainty.

Implementazione del Sistema Informativo 3D: sviluppo di un lessico codificato per una funzionale e produttiva comparazione dei dati

Il progetto del dottorato di ricerca ha permesso di estendere il lavoro svolto sul Sistema Informativo 3D del Cantiere della Fontana del Nettuno al fine di definire la struttura concettuale e i relativi contenuti tematici di una piattaforma open source in grado di sviluppare la documentazione di restauro, sia per opere complesse caratterizzate dalla presenza di molti materiali costitutivi, sia per interventi più semplici nel quale preservare memoria e fornire libero accesso ai dati. Il confronto tra il SI del Cantiere della Fontana del Nettuno con le attuali metodologie utilizzate in campo nazionale ed internazionale ha permesso di ampliare i lessici necessari per la documentazione grafica e testuale da effettuare su diverse classi di materiali, creando delle cartelle integrate da combinare in base ai materiali costitutivi delle opere da restaurare. Il lavoro ha permesso la redazione di un lessico specifico per i diversi materiali costitutivi fornendo una banca dati informatizzata di facile consultazione.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.