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Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics: a general presentation and introduction (Moscoso), X-ray tomography (Natterer), Electromagnetic imaging (Dorn, Bertete-Aguirre, Papanicolaou), coherent imaging in telecommunications in a multiple input-multiple output setup (Dorn), polarization based optical imaging (Moscoso), topological derivatives used in shape reconstruction related to inverse scattering problems (Carpio, Rapún), Point interactions (Dell’Antonio, Figari, Teta).

Tomography --- Geometric tomography --- Inverse problems (Differential equations) --- Tomography (Mathematics) --- Tomography, Geometric --- Convex geometry --- Integral transforms --- Mathematics. --- Mathematics, general. --- Math --- Science

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Geometric tomography. --- Inverse problems (Differential equations). --- Inverse problems (Differential equations) --- Tomography (Mathematics) --- Tomography, Geometric --- Differential equations --- Convex geometry --- Integral transforms --- Tomography

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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. .

Geometric tomography. --- Convex geometry. --- Geometry --- Tomography (Mathematics) --- Tomography, Geometric --- Convex geometry --- Integral transforms --- Tomography --- Computer vision. --- Engineering mathematics. --- Visualization. --- Fourier analysis. --- Signal, Image and Speech Processing. --- Image Processing and Computer Vision. --- Mathematical and Computational Engineering. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Visualisation --- Imagination --- Visual perception --- Imagery (Psychology) --- Engineering --- Engineering analysis --- Machine vision --- Vision, Computer --- Artificial intelligence --- Image processing --- Pattern recognition systems --- Mathematics --- Signal processing. --- Image processing. --- Speech processing systems. --- Optical data processing. --- Applied mathematics. --- Mathematics. --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Math --- Science --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical equipment

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Computer graphics --- Discrete geometry --- Infographie --- Géométrie discrète --- Congresses. --- Data processing --- Congrès --- Informatique --- Geometric tomography --- Applied Physics --- Technology - General --- Engineering & Applied Sciences --- Tomography (Mathematics) --- Tomography, Geometric --- Computer science. --- Algorithms. --- Computer science --- Computer simulation. --- Computer graphics. --- Image processing. --- Application software. --- Computer Science. --- Computer Applications. --- Image Processing and Computer Vision. --- Computer Graphics. --- Discrete Mathematics in Computer Science. --- Simulation and Modeling. --- Algorithm Analysis and Problem Complexity. --- Mathematics. --- Application computer programs --- Application computer software --- Applications software --- Apps (Computer software) --- Computer software --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Electromechanical analogies --- Mathematical models --- Simulation methods --- Model-integrated computing --- Computer mathematics --- Discrete mathematics --- Algorism --- Algebra --- Arithmetic --- Informatics --- Science --- Digital techniques --- Mathematics --- Foundations --- Convex geometry --- Integral transforms --- Tomography --- Geometry --- Combinatorial geometry --- Computer vision. --- Computational complexity. --- Computer software. --- Software, Computer --- Computer systems --- Complexity, Computational --- Machine theory --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Optical data processing. --- Computer science—Mathematics. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment

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This book constitutes the refereed proceedings of the 15th IAPR International Conference on Discrete Geometry for Computer Imagery, DGCI 2009, held in Montréal, Canada, in September/October 2009. The 42 revised full papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on discrete shape, representation, recognition and analysis; discrete and combinatorial tools for image segmentation and analysis; discrete and combinatorial Topology; models for discrete geometry; geometric transforms; and discrete tomography.

Computer graphics --- Discrete geometry --- Geometric tomography --- Technology - General --- Engineering & Applied Sciences --- Data processing --- Tomography (Mathematics) --- Tomography, Geometric --- Computer science. --- Algorithms. --- Computer science --- Computer graphics. --- Image processing. --- Pattern recognition. --- Computer Science. --- Computer Graphics. --- Pattern Recognition. --- Image Processing and Computer Vision. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Discrete Mathematics in Computer Science. --- Algorithm Analysis and Problem Complexity. --- Mathematics. --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Electronic data processing --- Engineering graphics --- Image processing --- Computer mathematics --- Discrete mathematics --- Algorism --- Algebra --- Arithmetic --- Informatics --- Science --- Digital techniques --- Mathematics --- Foundations --- Convex geometry --- Integral transforms --- Tomography --- Geometry --- Combinatorial geometry --- Optical pattern recognition. --- Computer vision. --- Computational complexity. --- Computer software. --- Software, Computer --- Computer systems --- Complexity, Computational --- Machine theory --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Pattern perception --- Perceptrons --- Visual discrimination --- Optical data processing. --- Computer science—Mathematics. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment