Handbook of Mathematical Methods in Imaging

Engineers and computer scientists working in imaging will also find this handbook useful. The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science.

Author: Otmar Scherzer

Publisher: Springer Science & Business Media

ISBN: 9780387929194

Category: Mathematics

Page: 1512

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The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

Mathematical Methods in Image Reconstruction

M. Abramowitz and I.A. Stegun (1970), Handbook of Mathematical Functions. Dover, New York. R.A. Adams (1975), Sobolev Spaces. Academic Press, New York. V. Aguilar and P. Kuchment (1995), Range conditions for the multidimensional ...

Author: Frank Natterer

Publisher: SIAM

ISBN: 9780898716221

Category: Computers

Page: 184

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This book provides readers with a superior understanding of the mathematical principles behind imaging.

Partial Differential Equation Methods for Image Inpainting

In O. Scherzer, ed., Handbook of Mathematical Methods in Imaging, 2nd ed., Chap. 22. SpringerVerlag, New York, 2015. Stanley Osher and James A Sethian. Fronts propagating with curvaturedependent speed: Algorithms based on HamiltonJacobi ...

Author: Carola-Bibiane Schönlieb

Publisher: Cambridge University Press

ISBN: 9781316404584

Category: Mathematics

Page:

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This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.

A Handbook of Mathematical Methods and Problem Solving Tools for Introductory Physics

How we know which one is the correct solution is that we already know that we placed the object to the left and it formed an image to the right. The lens that does this is a converging lens, so it has to be a positive focal length and ...

Author: Joshua F Whitney

Publisher: Morgan & Claypool Publishers

ISBN: 9781681742816

Category: Science

Page: 70

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This is a companion textbook for an introductory course in physics. It aims to link the theories and models that students learn in class with practical problem-solving techniques. In other words, it should address the common complaint that 'I understand the concepts but I can't do the homework or tests'. The fundamentals of introductory physics courses are addressed in simple and concise terms, with emphasis on how the fundamental concepts and equations should be used to solve physics problems.

Multi wave Medical Imaging Mathematical Modelling And Imaging Reconstruction

P. Kuchment and L. Kunyansky, Mathematics of photoacoustics and thermoacoustic tomography, in Handbook of Mathematical Methods in Imaging (Ed.) O. Scherzer, Springer, New York, 2011. P. Kunchment and L. Kunyansky, Mathematics of ...

Author: Nguyen Loc Hoang

Publisher: World Scientific

ISBN: 9781786342263

Category: Medical

Page: 688

View: 324

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Super-Resolution imaging refers to modern techniques of achieving resolution below conventional limits. This book gives a comprehensive overview of mathematical and computational techniques used to achieve this, providing a solid foundation on which to develop the knowledge and skills needed for practical application of techniques. Split into five parts, the first looks at the mathematical and probabilistic tools needed, before moving on to description of different types of imaging; single-wave, anomaly, multi-wave and spectroscopic and nanoparticle. As an important contribution to the understanding of super-resolution techniques in biomedical imaging, this book is a useful resource for scientists and engineers in the fields of biomedical imaging and super-resolution, and is self-contained reference for any newcomers to these fields.

The Radon Transform and Medical Imaging

O. Scherzer, M. Grasmair, H. Grossauer, M. Haltmeier, F. Lenzen, Variational Methods in Imaging, Appl. Math. Sci. ... O. Scherzer (Editor), Handbook of Mathematical Methods in Imaging, Springer-Verlag, Berlin, 2010.

Author: Peter Kuchment

Publisher: SIAM

ISBN: 9781611973280

Category: Computers

Page: 240

View: 285

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This book surveys the main mathematical ideas and techniques behind some well-established imaging modalities such as X-ray CT and emission tomography, as well as a variety of newly developing coupled-physics or hybrid techniques, including thermoacoustic tomography. The Radon Transform and Medical Imaging emphasizes mathematical techniques and ideas arising across the spectrum of medical imaging modalities and explains important concepts concerning inversion, stability, incomplete data effects, the role of interior information, and other issues critical to all medical imaging methods. For nonexperts, the author provides appendices that cover background information on notation, Fourier analysis, geometric rays, and linear operators. The vast bibliography, with over 825 entries, directs readers to a wide array of additional information sources on medical imaging for further study.

Mathematical Modeling in Biomedical Imaging II

34, 108–124 (2011) P. Kuchment, L. Kunyansky, in Mathematics of Photoacoustics and Thermoa- coustic Tomography, ed. by O. Scherzer. Handbook of Mathematical Methods in Imaging (Springer, New York, 2011) P. Kunchment, L. Kunyansky, ...

Author: Habib Ammari

Publisher: Springer Science & Business Media

ISBN: 9783642229893

Category: Mathematics

Page: 160

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This volume reports on recent mathematical and computational advances in optical, ultrasound, and opto-acoustic tomographies. It outlines the state-of-the-art and future directions in these fields and provides readers with the most recently developed mathematical and computational tools. It is particularly suitable for researchers and graduate students in applied mathematics and biomedical engineering.

Energy Minimization Methods in Computer Vision and Pattern Recognition

Firsov, D., Lui, S. H.: Domain Decomposition Methods in Image Denoising Using Gaussian Curvature. J. Comput. Appl. Math., 193 ... Physica D, 60, 259-268(1992) Scherzer, O.(editor): Handbook of Mathematical Methods in Imaging.

Author: Xue-Cheng Tai

Publisher: Springer

ISBN: 9783319146126

Category: Computers

Page: 506

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This volume constitutes the refereed proceedings of the 10th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition, EMMCVPR 2015, held in Hong Kong, China, in January 2015. The 36 revised full papers were carefully reviewed and selected from 45 submissions. The papers are organized in topical sections on discrete and continuous optimization; image restoration and inpainting; segmentation; PDE and variational methods; motion, tracking and multiview reconstruction; statistical methods and learning; and medical image analysis.

Scale Space and Variational Methods in Computer Vision

In: Handbook of Mathematical Methods in Imaging, pp. 1016–1057. Springer, New York (2011) 3. Chambolle, A., Caselles, V., Cremers, D., Novaga, M., Pock, T.: An introduction to total variation for image analysis.

Author: Jean-François Aujol

Publisher: Springer

ISBN: 9783319184616

Category: Computers

Page: 716

View: 206

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This book constitutes the refereed proceedings of the 5th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2015, held in Lège-Cap Ferret, France, in May 2015. The 56 revised full papers presented were carefully reviewed and selected from 83 submissions. The papers are organized in the following topical sections: scale space and partial differential equation methods; denoising, restoration and reconstruction, segmentation and partitioning; flow, motion and registration; photography, texture and color processing; shape, surface and 3D problems; and optimization theory and methods in imaging.