By Gabor T. Herman
Advances in Discrete Tomography and Its purposes is a unified presentation of latest equipment, algorithms, and choose functions which are the rules of multidimensional photograph reconstruction by means of discrete tomographic tools. The self-contained chapters, written via top mathematicians, engineers, and laptop scientists, current state of the art study and ends up in the field.Three major parts are lined: foundations, algorithms, and functional functions. Following an advent that experiences the hot literature of the sphere, the booklet explores numerous mathematical and computational difficulties of discrete tomography together with new applications.Topics and Features:* creation to discrete element X-rays* area of expertise and additivity in discrete tomography* community stream algorithms for discrete tomography* convex programming and variational equipment* purposes to electron microscopy, fabrics technology, nondestructive checking out, and diagnostic medicineProfessionals, researchers, practitioners, and scholars in arithmetic, computing device imaging, biomedical imaging, machine technological know-how, and picture processing will locate the ebook to be an invaluable consultant and connection with cutting-edge learn, tools, and purposes.
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Additional resources for Advances in discrete tomography and its applications
Trans. Amer. Math. , 349, 2271–2295 (1997). 10. : Uniqueness and complexity in discrete tomography. , Kuba, A. ), Discrete Tomography: Foundations, Algorithms, and Applications. Birkh¨ auser, Boston, MA, pp. 85–113 (1999). 11. , Kuba, A. ): Discrete Tomography: Foundations, Algorithms, and Applications. Birkh¨ auser, Boston, MA (1999). 12. : A three-point solution to Hammer’s X-ray problem. J. London Math. Soc. (2), 34, 349–359 (1986). 3 Reconstruction of Q-Convex Lattice Sets S. Brunetti and A.
Corollary 2. Let P be a set of points in Z2 in a line L. Then convex lattice sets in Z2 not meeting L are determined by discrete point X-rays at the points in P if either (a) |P | ≥ 7, or (b) |P | = 4 and there is no ordering of points in P such that their cross ratio is 2, 3, or 4. On the other hand, it is possible that |P | = 6 and there exist diﬀerent convex lattice sets with convex hulls disjoint from L and equal discrete point X-rays at points in P . Proof. Suppose that P is a set of points in Z2 in a line L, such that convex lattice sets in Z2 not meeting L are not determined by discrete point X-rays at the points in P .
Their absorbed projections. , Discrete Geometry for Computer Imagery, Springer, Berlin, Germany, pp. 79– 91 (2005). 135. : A new approach to SPECT attenuation correction without transmission measurements. In: Proc. IEEE Nuclear Sci. Symp. , pp. 62 (2000). 136. : Reconstruction of Label Images Using Gibbs Priors. D. Thesis, City University of New York, New York, USA (2005). 137. : Automated estimation of the parameters of Gibbs priors to be used in binary tomography. Electr. Notes Theor. Comput.