MATH4CHARMA mathematical approach to inverse problems arising in cultural heritage preservation and dissemination

Piano Nazionale di Ripresa e Resilienza (PNRR) – Missione 4 “Istruzione e Ricerca” – Componente 2 “Dalla Ricerca all’Impresa” Investimento 1.1 “Fondo per il Programma Nazionale di Ricerca e Progetti di Rilevante Interesse Nazionale (PRIN)”.

Cultural heritage preservation and dissemination are becoming fundamental aspects of the human experience. Our purpose is to provide new scientific solutions for this effort. Our contribution will be twofold. Firstly, we will provide new and improved methods for identifying archaeological sites. These methods will require mostly inexpensive tools and will be non-invasive. Secondly, we will produce automatic software for analyzing sites’ artifacts and determining their nature and properties. The first point will allow for more extensive and profitable investigations by reducing their costs. Researchers who could not afford site-wide searches will have new tools to efficiently gather valuable archaeological information and enrich their contribution to the scientific community. The new methods will use the geophysical properties of the ground, i.e., its electrical conductivity and magnetic permeability. As new technological tools are developed for geophysical perspections, we need the mathematical models underlying the analysis methods and the algorithmic techniques for the reconstruction of the properties of the ground to be updated and improved. Our purpose is to provide new models and methods for analyzing geophysical data that will improve the accuracy of the reconstruction and reduce the computational effort. This will be achieved by employing new regularization methods and model reduction tools that were previously considered only for linear problems. The second point will provide new automatic tools for archaeologists to analyze findings. In particular, we are interested in constructing three-dimensional models of the findings obtained by photographs of the object taken under different light conditions and points of view, namely, photometric stereo and stereo-vision. Once these models are constructed, we will provide tools for the extraction and analysis of incisions and glyphs present on them. This extraction is now performed manually and can be long and tedious. We will develop and distribute software for the scientific community to extract glyphs and incisions from previously obtained three-dimensional models. These will be used in two ways. Firstly they can be used to determine the nature of the incisions themselves, e.g., the instruments or the techniques used to make them. Secondly, they can be printed in three-dimension to either accompany the real counterparts in museums and other educational facilities or be shared with other researchers easily. In summary, our main purpose is to furnish archaeologists with mathematically sound software and tools to discover new sites easily, analyze their findings automatically, and share their results with the public and other researchers efficiently.