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Dettaglio Insegnamento Context Academic Year 2021/2022 Name Dott. - MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering Programme Year 1 Course Details ID Code 053494 Course Title DISCRETE AND GEOMETRIC TOMOGRAPHY Course Type MONODISCIPLINARE Credits (CFU / ECTS) 5.0 Course Description Computerized Tomography and discretization The Radon transform and its inversion for X-ray image reconstruction. Applications and related problems. Discretization of the reconstruction process. The Matlab "radon" and "iradon" functions. Examples and applications. Reconstruction from a limited number of projections The problem of ghosts. Models for discrete tomography. The reconstruction problem in the grid model as a linear system of equations. Investigation of the space of ghosts. Algebraic approach in a finite lattice grid and polynomial characterization of switching components. Discrete tomography Uniqueness models. Uniqueness and additivity. A few notion of projective geometry. Cross-ratio and its invariance under projections and sections. The results of Gardner and Gritzmann in the integer lattice. A few remarks on polyominoes. Binary Tomography Bad configurations, weakly bad configurations, switching components, ghosts. Ryser algorithm and a few extensions. Examples of binary reconstruction and characterization of the set of solutions. A uniqueness theorem for binary tomography. Examples of reconstructions of differently shaped discrete binary objects in a finite grid, by exploiting suitable sets of four directions. Geometric Tomography Hammer's problem and related uniqueness problems. Mid-point construction. U-polygons and their properties. The theorem of Gardner-McMullen in the Euclidean plane. Projections of convex bodies with point X-rays. The theorem of Volcic in the Euclidean plane. P-polygons. Some results and examples Scientific-Disciplinary Sector (SSD) SSD Code SSD Description CFU MAT/03 GEOMETRY 5.0 Details Alphabetical group Professor Course details From (included) To (excluded) A ZZZZ Dulio Paolo

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Area Servizi ICT

23/05/2022