Regions of Uniqueness Quickly Reconstructed by Three Directions in Discrete Tomography

• Autorzy: Dulio P. , Pagani S. M. C. , Frosini A.

Identyfikatory

DOI

10.3233/FI-2017-1592

• Języki publikacji: EN

Abstrakty

EN

In discrete tomographic image reconstruction, projections are taken along a finite set S of valid directions for a working grid A. In general, uniqueness cannot be achieved in the whole grid A. Usually, some information on the object to be reconstructed is introduced, that, sometimes, allows possible ambiguities to be removed. From a different perspective, one aims in finding subregions of A where uniqueness can be guaranteed, and obtained in linear time, only from the knowledge of S. When S consists of two lattice directions, the shape of any such region of uniqueness, say ROU, have been completely characterized in previous works by means of a double Euclidean division algorithm called DEDA. Results have been later extended to special triples of directions, under a suitable assumption on their entries. In this paper we remove the previous assumption, so providing a complete characterization of the shape of the ROU for such kind of triples. We also show that the employed strategy can be even applied to more general sets of three directions, where the corresponding ROU can be characterized as well. Independently of the combinatorial interest of the problem, the result can be exploited to define in advance, namely before using any kind of radiation, suitable sets of directions that allow regions of interest to be included in the corresponding ROU. Results have been proved in all details, and several experiments are considered, in order to support the theoretical steps and to clarify possible applications.

Słowa kluczowe

EN

discrete tomography; lattice grid; projection; uniqueness region

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2017
• Tom: Vol. 155, nr 4
• Strony: 407--423
• Opis fizyczny: Bibliogr. 12 poz., rys., tab.

Twórcy

autor

Dulio P.

• Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

autor

Pagani S. M. C.

• Dipartimento di Matematica “F. Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133 Milano, Italy

autor

Frosini A.

• Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, viale Morgagni 65, 50134 Firenze, Italy

Bibliografia

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• [2] Dulio P, Frosini A, Pagani SMC. Uniqueness regions under sets of generic projections in discrete tomography. In: Discrete geometry for computer imagery, volume 8668 of Lecture Notes in Comput. Sci., pp. 285–296. Springer, 2014. doi:10.1007/978-3-319-09955-2_24. URL http://dx.doi.org/10.1007/978-3-319-09955-224.
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• [10] Brunetti S, Dulio P, Peri C. Discrete tomography determination of bounded lattice sets from four X-rays. Discrete Appl. Math., 2013;161(15):2281–2292. doi:10.1016/j.dam.2012.09.010. URL http://dx.doi.org/10.1016/j.dam.2012.09.010.
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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).