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CodiceQDD 108
TitoloINTERSECTING POLYTOPES AND TOMOGRAPHIC RECONSTRUCTIONS
Data2011-10-05
Autore/iDulio, P.; Peri, C.
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AbstractIn this paper we deal with the reconstruction problem in Tomography, focusing on some new classes of subsets of the n-dimensional real space. Such classes are formed by clusters of polytopes mutually intersecting according to a twisting notion. The importance for tomography comes from their additivity property, which implies uniqueness of reconstruction. In the case n=2 we give a detailed description of their geometric structure, with some insight in the lattice frame. In particular, for a finite set D of directions in two-dimensional lattice, we introduce the class of D-inscribable lattice sets, showing that such sets can be considered as the natural discrete counterpart of the same notion known in the continuous case. Due to their nice tomographic properties, clusters of twisted polytopes might represent good candidates for approximating real shapes, as well as for investigating stability problems.

Dipartimento di Matematica