Discrete tomography: Determination of finite sets by X-rays
نویسندگان
چکیده
منابع مشابه
Discrete Tomography: Determination of Finite Sets by X-Rays
We study the determination of finite subsets of the integer lattice Zn, n ≥ 2, by X-rays. In this context, an X-ray of a set in a direction u gives the number of points in the set on each line parallel to u. For practical reasons, only X-rays in lattice directions, that is, directions parallel to a nonzero vector in the lattice, are permitted. By combining methods from algebraic number theory a...
متن کاملDetermination of Q-convex sets by X-rays
In this paper, the problem of the determination of lattice sets from X-rays is studied. We define the class of Q-convex sets along a set D of directions which generalizes classical lattice convexity and we prove that for any D, the X-rays along D determine all the convex sets if and only if it determines all the Q-convex sets along D. As a consequence, any algorithm which reconstructs Q-convex ...
متن کاملSuccessive Determination and Verification of Polytopes by their X-Rays
It is shown that each convex polytope P in E can be verified by ([d/(d— k)]+ 1) /odimensional X-rays. This means that P is uniquely determined by these X-rays and the choice of the direction of each X-ray depends only on P. Examples are constructed to show that in general this number cannot be reduced. Further, it is shown that each convex polytope P in E can be successively determined by only ...
متن کاملDetermination of Q-convex bodies by X-rays
The class of Q-convex bodies is defined, and the uniqueness result proved by Gardner and McMullen in 1980 for planar convex bodies is extended to this new class.
متن کاملDiscrete tomography of icosahedral model sets.
The discrete tomography of mathematical quasicrystals with icosahedral symmetry is investigated, placing emphasis on reconstruction and uniqueness problems. The work is motivated by the requirement in materials science for the unique reconstruction of the structures of icosahedral quasicrystals from a small number of images produced by quantitative high-resolution transmission electron microscopy.
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1997
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-97-01741-8