Download e-book for iPad: Advances in discrete tomography and its applications by Gabor T. Herman

By Gabor T. Herman

ISBN-10: 0817636145

ISBN-13: 9780817636142

Advances in Discrete Tomography and Its purposes is a unified presentation of recent tools, algorithms, and choose purposes which are the rules of multidimensional snapshot reconstruction by way of discrete tomographic equipment. The self-contained chapters, written by way of best mathematicians, engineers, and desktop scientists, current state of the art study and leads to the field.Three major components are coated: foundations, algorithms, and useful purposes. Following an advent that studies the new literature of the sector, the ebook explores a variety of mathematical and computational difficulties of discrete tomography together with new applications.Topics and Features:* advent to discrete aspect X-rays* area of expertise and additivity in discrete tomography* community stream algorithms for discrete tomography* convex programming and variational tools* functions to electron microscopy, fabrics technological know-how, nondestructive trying out, and diagnostic medicineProfessionals, researchers, practitioners, and scholars in arithmetic, desktop imaging, biomedical imaging, computing device technological know-how, and photograph processing will locate the e-book to be an invaluable advisor and connection with cutting-edge study, tools, and functions.

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5 is the same as the one published in [6] except for the last step (reduction to 2-SAT), which is faster and simpler in this chapter. 2 Definitions and Preliminaries We first give some notations and classical definitions we use in the chapter, and then we recall some known results that are relevant for our discussion. 1 Definitions A lattice direction is represented by a vector p = (a, b) = (0, 0) with a, b coprime integers. Any straight line parallel to p has equation bx − ay = k where k is a constant.

For example, there are sets P with as many as six noncollinear points in Z2 such that the corresponding discrete point X-rays do not determine convex lattice sets. 5 follows the extended abstract [6] of the full article [7] in which the authors introduce point Xrays. 6, containing brief remarks about instability results due to Katja Lord (to whom we are grateful for permission to include this summary), the possibility of measuring discrete point X-rays in practice, and our ideas for future work.

2 for the formal definition. When a lattice U -polygon exists, it is easy to construct two different convex lattice sets with equal discrete parallel X-rays in the directions in U . In [9] it was proved that in fact the nonexistence of a lattice U -polygon is necessary and sufficient for the discrete parallel X-rays in the directions in U to determine convex lattice sets (provided U has at least two nonparallel directions). It is easy to see that when |U | = 3, lattice U -polygons always exist. With tools from p-adic number theory, it was shown in [9] that they do not exist for certain sets of four lattice directions and any set of at least seven lattice directions, but can exist for certain sets of six lattice directions.

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Advances in discrete tomography and its applications by Gabor T. Herman

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