
Dettaglio Insegnamento
Academic Year 
2021/2022 
Name 
Dott.  MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering 
Programme Year 
1 
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 Xray 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. Crossratio 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. Midpoint construction. Upolygons and their properties. The theorem of GardnerMcMullen in the Euclidean plane. Projections of convex bodies with point Xrays. The theorem of Volcic in the Euclidean plane. Ppolygons. Some results and examples 
ScientificDisciplinary Sector (SSD)

SSD Code

SSD Description

CFU

MAT/03

GEOMETRY

5.0


Alphabetical group

Professor

Course details

From (included)

To (excluded)

A

ZZZZ

Dulio Paolo


