
Dettaglio Insegnamento
Anno Accademico 
2021/2022 
Corso di Studi 
Dott.  MI (1385) Modelli e Metodi Matematici per l'Ingegneria / Mathematical Models and Methods in Engineering 
Anno di Corso 
1 
Codice Identificativo 
053494 
Denominazione Insegnamento 
DISCRETE AND GEOMETRIC TOMOGRAPHY 
Tipo Insegnamento 
MONODISCIPLINARE 
Crediti Formativi Universitari (CFU) 
5.0 
Programma sintetico 
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 
Settori Scientifico Disciplinari (SSD) 
Codice SSD

Descrizione SSD

CFU

MAT/03

GEOMETRIA

5.0


Scaglione

Docente

Programma dettagliato

Da (compreso)

A (escluso)

A

ZZZZ

Dulio Paolo


