Preface Contributors Part I. Foundations Discrete Tomography: A Historical Overview Attila Kuba, Gabor T. Herman Sets of Uniqueness and Additivity in Integer Lattices Peter C. Fishburn, Lawrence A. Shepp Tomopgraphic Equivalence and Switching Operations T. Yung Kong, Gabor T. Herman Uniqueness and Complexity in Discrete Tomography Richard J. Gardner, Peter Gritzmann Reconstruction of Plane Figures from Two Projections Akira Kaneko, Lei Huang Reconstruction of Two-Valued Functions and Matrices Attila Kuba Reconstruction of Connected Sets from Two Projections Alberto Del Lungo, Maurice Nivat Part II. Algorithms Binary Tomography Using Gibbs Priors Samuel Matej, Avi Vardi, Gabor T. Herman, Eilat Vardi Probabilistic Modeling of Discrete Images Michael T. Chan, Gabor T. Herman, Emanuel Levitan Multiscale Bayesian Methods for Discrete Tomography Thomas Frese, Charles A. Bouman, Ken Sauer An Algebraic Solution for Discrete Tomography Andrew E. Yagle Binary Steering of Nonbinary Iterative Algorithms Yair Censor, Samuel Matej Reconstruction of Binary Images via the EM Algorithm Yehuda Vardi, Cun-Hui Zhang Part III. Applications CT-Assisted Engineering and Manufacturing Jolyon A. Browne, Mathew Koshy 3D Reconstruction from Sparse Radiographic Data James Sachs, Jr., Ken Sauer Heart Chamber Reconstruction from Biplane Angiography Dietrich G.W. Onnasch, Guido P.M. Prause Discrete Tomography in Electron Microscopy J.M. Carazo, C.O. Sorzano, E. Rietzel, R. Schröder, R. Marabini Tomopgraphy on the 3D-Torus and Crystals Pablo M. Salzberg, Raul Figueroa A Recursive Algorithm for Diffuse Planar Tomography Sarah K. Patch From Orthogonal Projections to Symbolic Projections Shi-KuoChang Index
Goals of the Book Overthelast thirty yearsthere has been arevolutionindiagnostic radiology as a result oftheemergenceofcomputerized tomography (CT), which is the process of obtaining the density distribution within the human body from multiple x-ray projections. Since an enormous variety of possible density values may occur in the body, a large number of projections are necessary to ensure the accurate reconstruction oftheir distribution. There are other situations in which we desire to reconstruct an object from its projections, but in which we know that the object to be recon structed has only a small number of possible values. For example, a large fraction of objects scanned in industrial CT (for the purpose of nonde structive testing or reverse engineering) are made of a single material and so the ideal reconstruction should contain only two values: zero for air and the value associated with the material composing the object. Similar as sumptions may even be made for some specific medical applications; for example, in angiography ofthe heart chambers the value is either zero (in dicating the absence of dye) or the value associated with the dye in the chamber. Another example arises in the electron microscopy of biological macromolecules, where we may assume that the object to be reconstructed is composed of ice, protein, and RNA. One can also apply electron mi croscopy to determine the presenceor absence ofatoms in crystallinestruc tures, which is again a two-valued situation.
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