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001-es BibID:BIBFORM067005
Első szerző:Brunetti, Sara
Cím:Ghosts in Discrete Tomography / Sara Brunetti, Paolo Dulio, Lajos Hajdu, Carla Peri
Dátum:2015
ISSN:0924-9907
Megjegyzések:Switching components, also named as bad configurations, interchanges, and ghosts (according to different scenarios), play a key role in the study of ambiguous configurations, which often appear in Discrete Tomography and in several other areas of research. In this paper we give an upper bound for the minimal size bad configurations associated to a given set SS of lattice directions. In the special but interesting case of four directions, we show that the general argument can be considerably improved, and we present an algebraic method which provides such an improvement. Moreover, it turns out that finding bad configurations is in fact equivalent to finding multiples of a suitable polynomial in two variables, having only coefficients from the set {1,0,1}{1,0,1} . The general problem of describing all polynomials having such multiples seems to be very hard (Borwein and Erdélyi, in Ill J Math 41(4):667?675, 1997). However, in our particular case, it is hopeful to give some kind of solution. In the context of Digital Image Analysis, it represents an explicit method for the construction of ghosts, and consequently might be of interest in image processing, also in view of efficient algorithms to encode data.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
Bad configuration
Discrete Tomography
Generating function
Ghost
X-ray
Megjelenés:Journal of Mathematical Imaging and Vision 53 : 2 (2015), p. 210-224. -
További szerzők:Dulio, Paolo Hajdu Lajos (1968-) (matematikus) Peri, Carla
Pályázati támogatás:OTKA-100339
OTKA
OTKA-NK101680
OTKA
TÁMOP-4.2.2.C-11/1/KONV-2012-0001
TÁMOP
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DOI
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2.

001-es BibID:BIBFORM106862
035-os BibID:(Scopus)85097749814
Első szerző:Pongrácz András (matematikus)
Cím:On the Reconstruction of the Center of a Projection by Distances and Incidence Relations / András Pongrácz, Csaba Vincze
Dátum:2021
ISSN:0924-9907
Megjegyzések:Up to an orientation-preserving symmetry, photographic images are produced by a central projection of a restricted area in the space into the image plane. To obtain reliable information about physical objects and the environment through the process of recording is the basic problem of photogrammetry. We present a reconstruction process based on distances from the center of projection and incidence relations among the points to be projected. For any triplet of collinear points in the space, we construct a surface of revolution containing the center of the projection. It is a generalized conic that can be represented as an algebraic surface. The rotational symmetry allows us to restrict the investigations to the defining polynomial of the profile curve in the image plane. An equivalent condition for the boundedness is given in terms of the input parameters, and it is shown that the defining polynomial of the profile curve is irreducible.
Tárgyszavak:Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
folyóiratcikk
Megjelenés:Journal Of Mathematical Imaging And Vision. - 63 : 4 (2021), p. 443-456. -
További szerzők:Vincze Csaba (1971-) (matematikus)
Pályázati támogatás:EFOP-3.6.2-16-2017-00015
EFOP
124814
OTKA
125160
OTKA
ÚNKP-19-4
Egyéb
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DOI
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