Advances in Discrete Tomography and Its Applications

ISBN-13: 9780817636142 / Angielski / Twarda / 2007 / 392 str.

Gabor T. Herman; Attila Kuba

Opis

The book provides a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image construction and reconstruction. The self-contained survey chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field. Three main areas are covered: theoretical results, algorithms, and practical applications. Following an historical and introductory overview of the field, the book explores the various mathematical and computational problems of discrete tomography with an emphasis on new applications.

Recenzje

"This book is strongly recommended for all those who want to work [in] tomography and get solutions of problems in discrete situations."   -International Journal of Tomography & Statistics

"...The selected contributions are clear and complete. The editors wisely break the text into three sections, all covered with equal depth and breadth-foundational material, reconstruction algorithms, and applications. The text's exercises, exhaustive solutions, and expert remarks also make it a suitable reference for a special topics class. Guided by well-crafted chapter summaries, motivated students and professionals will find the text a welcome handbook and resource. ...Bringing together an enormous amount of theoretical and practical knowledge from DT applications, Advances in Discrete Tomography and Its Applications fulfills its commitment to report on the field's growth. Surely, students, programmers, scientists, and engineers from medicine, industry, and research will find something valuable in this total tomography handbook."  -Computing in Science & Engineering

Spis treści

ANHA Series Preface Preface List of Contributors Introduction / A. Kuba and G.T. Herman Part I. Foundations of Discrete Tomography An Introduction to Discrete Point X-Rays / P. Dulio, R.J. Gardner, and C. Peri Reconstruction of Q-Convex Lattice Sets / S. Brunetti and A. Daurat Algebraic Discrete Tomography / L. Hajdu and R. Tijdeman Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals / E. Vallejo Constructing (0, 1)-Matrices with Given Line Sums and Certain Fixed Zeros / R.A. Brualdi and G. Dahl Reconstruction of Binary Matrices under Adjacency Constraints / S. Brunetti, M.C. Costa, A. Frosini, F. Jarray, and C. Picouleau Part II. Discrete Tomography Reconstruction Algorithms Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components / P. Balázs Network Flow Algorithms for Discrete Tomography / K.J. Batenburg A Convex Programming Algorithm for Noisy Discrete Tomography / T.D. Capricelli and P.L. Combettes Variational Reconstruction with DC-Programming / C. Schnörr, T. Schüle, and S. Weber Part III. Applications of Discrete Tomography Direct Image Reconstruction-Segmentation, as Motivated by Electron Microscopy / Hstau Y. Liao and Gabor T. Herman Discrete Tomography for Generating Grain Maps of Polycrystals / A. Alpers, L. Rodek, H.F. Poulsen, E. Knudsen, G.T. Herman Discrete Tomography Methods for Nondestructive Testing / J. Baumann, Z. Kiss, S. Krimmel, A. Kuba, A. Nagy, L. Rodek, B. Schillinger, and J. Stephan Emission Discrete Tomography / E. Barcucci, A. Frosini, A. Kuba, A. Nagy, S. Rinaldi, M. Samal, and S. Zopf Application of a Discrete Tomography Approach to Computerized Tomography / Y. Gerard and F. Feschet Index

Blurb

Advances in Discrete Tomography and Its Applications is a unified presentation of new methods, algorithms, and select applications that are the foundations of multidimensional image reconstruction by discrete tomographic methods. The self-contained chapters, written by leading mathematicians, engineers, and computer scientists, present cutting-edge research and results in the field.

Three main areas are covered: foundations, algorithms, and practical applications. Following an introduction that reports the recent literature of the field, the book explores various mathematical and computational problems of discrete tomography including new applications.

Topics and Features:

* introduction to discrete point X-rays

* uniqueness and additivity in discrete tomography

* network flow algorithms for discrete tomography

* convex programming and variational methods

* applications to electron microscopy, materials science, nondestructive testing, and diagnostic medicine

Professionals, researchers, practitioners, and students in mathematics, computer imaging, biomedical imaging, computer science, and image processing will find the book to be a useful guide and reference to state-of-the-art research, methods, and applications.