Advances in Discrete Tomography and Its Applications / Edition 1

by Gabor T. Herman, Attila Kuba

Overview

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 include introduction to discrete point X-rays, uniqueness and additivity in discrete tomography, network flow algorithms for discrete tomography, convex programming and variational methods, and 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.

Product Details

ISBN-13:	9780817636142
Publisher:	Birkhäuser Boston
Publication date:	04/04/2007
Series:	Applied and Numerical Harmonic Analysis
Edition description:	2007
Pages:	392
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Foundations of Discrete Tomography.- An Introduction to Discrete Point X-Rays.- Reconstruction of Q-Convex Lattice Sets.- Algebraic Discrete Tomography.- Uniqueness and Additivity for n-Dimensional Binary Matrices with Respect to Their 1-Marginals.- Constructing (0,1)-Matrices with Given Line Sums and Certain Fixed Zeros.- Reconstruction of Binary Matrices under Adjacency Constraints.- Discrete Tomography Reconstruction Algorithms.- Decomposition Algorithms for Reconstructing Discrete Sets with Disjoint Components.- Network Flow Algorithms for Discrete Tomography.- A Convex Programming Algorithm for Noisy Discrete Tomography.- Variational Reconstruction with DC-Programming.- Applications of Discrete Tomography.- Direct Image Reconstruction-Segmentation, as Motivated by Electron Microscopy.- Discrete Tomography for Generating Grain Maps of Polycrystals.- Discrete Tomography Methods for Nondestructive Testing.- Emission Discrete Tomography.- Application of a Discrete Tomography Approach to Computerized Tomography.

Editorial Reviews

"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

From the Publisher