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Título : Mathematical Models for Registration and Applications to Medical Imaging Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Scherzer, Otmar Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Mathematics in Industry, ISSN 1612-3956 num. 10 Número de páginas: X, 191 p. 54 illus., 12 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-540-34767-5 Idioma : Inglés (eng) Palabras clave: Mathematics Radiology Computer graphics Mathematical models Modeling and Industrial Imaging, Vision, Pattern Recognition Graphics Imaging / Clasificación: 51 Matemáticas Resumen: Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets. This fuzzy de?nition of registration requires a mathematical modeling and in particular a mathematical speci?cation of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity p measures ranges from a simpleL distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine relevant and emerging image registration applications and to show new emerging mathematical technologies in these areas. Currently, many registration application are solved based on variational prin- ple requiring sophisticated analysis, such as calculus of variations and the theory of partial differential equations, to name but a few. Due to the numerical compl- ity of registration problems ef?cient numerical realization are required. Concepts like multi-level solver for partial differential equations, non-convex optimization, and so on play an important role. Mathematical and numerical issues in the area of registration are discussed by some of the experts in this volume. Moreover, the importance of registration for industry and medical imaging is discussed from a medical doctor and from a manufacturer point of view Nota de contenido: Numerical Methods -- A Generalized Image Registration Framework using Incomplete Image Information – with Applications to Lesion Mapping -- Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity -- Registration of Histological Serial Sectionings -- Computational Methods for Nonlinear Image Registration -- A Survey on Variational Optic Flow Methods for Small Displacements -- Applications -- Fast Image Matching for Generation of Panorama Ultrasound -- Inpainting of Movies Using Optical Flow -- Medical Applications -- Multimodality Registration in Daily Clinical Practice -- Colour Images En línea: http://dx.doi.org/10.1007/978-3-540-34767-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34984 Mathematical Models for Registration and Applications to Medical Imaging [documento electrónico] / SpringerLink (Online service) ; Scherzer, Otmar . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - X, 191 p. 54 illus., 12 illus. in color : online resource. - (Mathematics in Industry, ISSN 1612-3956; 10) .
ISBN : 978-3-540-34767-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Radiology Computer graphics Mathematical models Modeling and Industrial Imaging, Vision, Pattern Recognition Graphics Imaging / Clasificación: 51 Matemáticas Resumen: Image registration is an emerging topic in image processing with many applications in medical imaging, picture and movie processing. The classical problem of image registration is concerned with ?nding an appropriate transformation between two data sets. This fuzzy de?nition of registration requires a mathematical modeling and in particular a mathematical speci?cation of the terms appropriate transformations and correlation between data sets. Depending on the type of application, typically Euler, rigid, plastic, elastic deformations are considered. The variety of similarity p measures ranges from a simpleL distance between the pixel values of the data to mutual information or entropy distances. This goal of this book is to highlight by some experts in industry and medicine relevant and emerging image registration applications and to show new emerging mathematical technologies in these areas. Currently, many registration application are solved based on variational prin- ple requiring sophisticated analysis, such as calculus of variations and the theory of partial differential equations, to name but a few. Due to the numerical compl- ity of registration problems ef?cient numerical realization are required. Concepts like multi-level solver for partial differential equations, non-convex optimization, and so on play an important role. Mathematical and numerical issues in the area of registration are discussed by some of the experts in this volume. Moreover, the importance of registration for industry and medical imaging is discussed from a medical doctor and from a manufacturer point of view Nota de contenido: Numerical Methods -- A Generalized Image Registration Framework using Incomplete Image Information – with Applications to Lesion Mapping -- Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity -- Registration of Histological Serial Sectionings -- Computational Methods for Nonlinear Image Registration -- A Survey on Variational Optic Flow Methods for Small Displacements -- Applications -- Fast Image Matching for Generation of Panorama Ultrasound -- Inpainting of Movies Using Optical Flow -- Medical Applications -- Multimodality Registration in Daily Clinical Practice -- Colour Images En línea: http://dx.doi.org/10.1007/978-3-540-34767-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34984 Ejemplares
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Título : The Mathematics of Medical Imaging : A Beginner’s Guide Tipo de documento: documento electrónico Autores: Timothy G. Feeman ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2010 Colección: Springer Undergraduate Texts in Mathematics and Technology, ISSN 1867-5506 Número de páginas: XII, 141 p Il.: online resource ISBN/ISSN/DL: 978-0-387-92712-1 Idioma : Inglés (eng) Palabras clave: Mathematics Radiology Computer science graphics Functional analysis Integral transforms Operational calculus Biomedical engineering Analysis Imaging / Transforms, Calculus Math Applications in Science Imaging, Vision, Pattern Recognition and Graphics Engineering Clasificación: 51 Matemáticas Resumen: A Beginner's Guide to the Mathematics of Medical Imaging presents the basic mathematics of computerized tomography – the CT scan – for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. The text is self-contained with a range of practical exercises, topics for further study, and an ample bibliography, making it ideal for use in an undergraduate course in applied or engineering mathematics, or by practitioners in radiology who want to know more about the mathematical foundations of their field Nota de contenido: X-rays -- The Radon Transform -- Back Projection -- Complex Numbers -- The Fourier Transform -- Two Big Theorems -- Filters and Convolution -- Discrete Image Reconstruction -- Algebraic Reconstruction Techniques -- MRI#x2014;An Overview En línea: http://dx.doi.org/10.1007/978-0-387-92712-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33526 The Mathematics of Medical Imaging : A Beginner’s Guide [documento electrónico] / Timothy G. Feeman ; SpringerLink (Online service) . - New York, NY : Springer New York, 2010 . - XII, 141 p : online resource. - (Springer Undergraduate Texts in Mathematics and Technology, ISSN 1867-5506) .
ISBN : 978-0-387-92712-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Radiology Computer science graphics Functional analysis Integral transforms Operational calculus Biomedical engineering Analysis Imaging / Transforms, Calculus Math Applications in Science Imaging, Vision, Pattern Recognition and Graphics Engineering Clasificación: 51 Matemáticas Resumen: A Beginner's Guide to the Mathematics of Medical Imaging presents the basic mathematics of computerized tomography – the CT scan – for an audience of undergraduates in mathematics and engineering. Assuming no prior background in advanced mathematical analysis, topics such as the Fourier transform, sampling, and discrete approximation algorithms are introduced from scratch and are developed within the context of medical imaging. A chapter on magnetic resonance imaging focuses on manipulation of the Bloch equation, the system of differential equations that is the foundation of this important technology. The text is self-contained with a range of practical exercises, topics for further study, and an ample bibliography, making it ideal for use in an undergraduate course in applied or engineering mathematics, or by practitioners in radiology who want to know more about the mathematical foundations of their field Nota de contenido: X-rays -- The Radon Transform -- Back Projection -- Complex Numbers -- The Fourier Transform -- Two Big Theorems -- Filters and Convolution -- Discrete Image Reconstruction -- Algebraic Reconstruction Techniques -- MRI#x2014;An Overview En línea: http://dx.doi.org/10.1007/978-0-387-92712-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33526 Ejemplares
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Título : Visualization and Processing of Tensor Fields Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Joachim Weickert ; Hans Hagen Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2006 Colección: Mathematics and Visualization, ISSN 1612-3786 Número de páginas: XV, 481 p Il.: online resource ISBN/ISSN/DL: 978-3-540-31272-7 Idioma : Inglés (eng) Palabras clave: Mathematics Radiology Computer graphics Image processing Mathematical analysis Analysis (Mathematics) Visualization Differential geometry Imaging / Imaging, Vision, Pattern Recognition and Graphics Processing Vision Geometry Clasificación: 51 Matemáticas Resumen: Matrix-valued data sets - so-called second order tensor fields - have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state-of-the-art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students Nota de contenido: An Introduction to Tensors -- Feature Detection with Tensors -- Adaptive Structure Tensors and their Applications -- On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor -- Low-level Feature Detection Using the Boundary Tensor -- Diffusion Tensor Imaging -- An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond -- Random Noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections -- An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications -- Anatomy-Based Visualizations of Diffusion Tensor Images of Brain White Matter -- Variational Regularization of Multiple Diffusion Tensor Fields -- Higher Rank Tensors in Diffusion MRI -- Visualization of Tensor Fields -- Strategies for Direct Visualization of Second-Rank Tensor Fields -- Tensor Invariants and their Gradients -- Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields -- Degenerate 3D Tensors -- Locating Closed Hyperstreamlines in Second Order Tensor Fields -- Tensor Field Visualization Using a Metric Interpretation -- Tensor Field Transformations -- Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization -- Continuous Tensor Field Approximation of Diffusion Tensor MRI data -- Tensor Field Interpolation with PDEs -- Diffusion-Tensor Image Registration -- Image Processing Methods for Tensor Fields -- Tensor Median Filtering and M-Smoothing -- Mathematical Morphology on Tensor Data Using the Loewner Ordering -- A Local Structure Measure for Anisotropic Regularization of Tensor Fields -- Tensor Field Regularization using Normalized Convolution and Markov Random Fields in a Bayesian Framework -- PDEs for Tensor Image Processing En línea: http://dx.doi.org/10.1007/3-540-31272-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34936 Visualization and Processing of Tensor Fields [documento electrónico] / SpringerLink (Online service) ; Joachim Weickert ; Hans Hagen . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2006 . - XV, 481 p : online resource. - (Mathematics and Visualization, ISSN 1612-3786) .
ISBN : 978-3-540-31272-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Radiology Computer graphics Image processing Mathematical analysis Analysis (Mathematics) Visualization Differential geometry Imaging / Imaging, Vision, Pattern Recognition and Graphics Processing Vision Geometry Clasificación: 51 Matemáticas Resumen: Matrix-valued data sets - so-called second order tensor fields - have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state-of-the-art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students Nota de contenido: An Introduction to Tensors -- Feature Detection with Tensors -- Adaptive Structure Tensors and their Applications -- On the Concept of a Local Greyvalue Distribution and the Adaptive Estimation of a Structure Tensor -- Low-level Feature Detection Using the Boundary Tensor -- Diffusion Tensor Imaging -- An Introduction to Computational Diffusion MRI: the Diffusion Tensor and Beyond -- Random Noise in Diffusion Tensor Imaging, its Destructive Impact and Some Corrections -- An Introduction to Visualization of Diffusion Tensor Imaging and Its Applications -- Anatomy-Based Visualizations of Diffusion Tensor Images of Brain White Matter -- Variational Regularization of Multiple Diffusion Tensor Fields -- Higher Rank Tensors in Diffusion MRI -- Visualization of Tensor Fields -- Strategies for Direct Visualization of Second-Rank Tensor Fields -- Tensor Invariants and their Gradients -- Visualizing the Topology of Symmetric, Second-Order, Time-Varying Two-Dimensional Tensor Fields -- Degenerate 3D Tensors -- Locating Closed Hyperstreamlines in Second Order Tensor Fields -- Tensor Field Visualization Using a Metric Interpretation -- Tensor Field Transformations -- Symmetric Positive-Definite Matrices: From Geometry to Applications and Visualization -- Continuous Tensor Field Approximation of Diffusion Tensor MRI data -- Tensor Field Interpolation with PDEs -- Diffusion-Tensor Image Registration -- Image Processing Methods for Tensor Fields -- Tensor Median Filtering and M-Smoothing -- Mathematical Morphology on Tensor Data Using the Loewner Ordering -- A Local Structure Measure for Anisotropic Regularization of Tensor Fields -- Tensor Field Regularization using Normalized Convolution and Markov Random Fields in a Bayesian Framework -- PDEs for Tensor Image Processing En línea: http://dx.doi.org/10.1007/3-540-31272-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34936 Ejemplares
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Título : Handbook of Mathematical Methods in Imaging Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Scherzer, Otmar Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Número de páginas: eReference Il.: online resource ISBN/ISSN/DL: 978-0-387-92920-0 Idioma : Inglés (eng) Palabras clave: Mathematics Radiology Image processing Applied mathematics Engineering Numerical analysis Applications of Processing and Computer Vision Signal, Speech Analysis Imaging / Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: Introduction -- Part 1: Inverse Problems -- Tomography -- MR DTI -- Hybrid Methods -- Nonlinear Inverse Problems -- EIT -- Scattering -- Sampling Methods -- Expansion Methods -- Regularization Methods for Ill-Posed Problems -- Iterative Solution Methods -- Wave Phenomena -- Seismic -- Radar -- Ultrasound -- Part 2: Signal and Image Processing -- Morphological Image Processing -- Learning, Classification, Data Mining -- Partial Differential Equations -- Variational Methods for Image Analysis -- Level Set Methods Including Fast Marching Methods -- Segmentation -- Registration, Optical Flow -- Duality and Convex Minimization -- Spline, Statistics -- Wavelets -- Fourier Analysis -- Compressed Sensing -- Geometry Processing -- Compression -- Computational Geometry -- Shape Spaces -- PDEs and Variational Methods on Manifold -- References -- Subject Index En línea: http://dx.doi.org/10.1007/978-0-387-92920-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33084 Handbook of Mathematical Methods in Imaging [documento electrónico] / SpringerLink (Online service) ; Scherzer, Otmar . - New York, NY : Springer New York, 2011 . - eReference : online resource.
ISBN : 978-0-387-92920-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Radiology Image processing Applied mathematics Engineering Numerical analysis Applications of Processing and Computer Vision Signal, Speech Analysis Imaging / Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: Introduction -- Part 1: Inverse Problems -- Tomography -- MR DTI -- Hybrid Methods -- Nonlinear Inverse Problems -- EIT -- Scattering -- Sampling Methods -- Expansion Methods -- Regularization Methods for Ill-Posed Problems -- Iterative Solution Methods -- Wave Phenomena -- Seismic -- Radar -- Ultrasound -- Part 2: Signal and Image Processing -- Morphological Image Processing -- Learning, Classification, Data Mining -- Partial Differential Equations -- Variational Methods for Image Analysis -- Level Set Methods Including Fast Marching Methods -- Segmentation -- Registration, Optical Flow -- Duality and Convex Minimization -- Spline, Statistics -- Wavelets -- Fourier Analysis -- Compressed Sensing -- Geometry Processing -- Compression -- Computational Geometry -- Shape Spaces -- PDEs and Variational Methods on Manifold -- References -- Subject Index En línea: http://dx.doi.org/10.1007/978-0-387-92920-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33084 Ejemplares
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Título : Variational Methods in Imaging Tipo de documento: documento electrónico Autores: Scherzer, Otmar ; SpringerLink (Online service) ; Markus Grasmair ; Harald Grossauer ; Markus Haltmeier ; Frank Lenzen Editorial: New York, NY : Springer New York Fecha de publicación: 2009 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 167 Número de páginas: XIV, 320 p Il.: online resource ISBN/ISSN/DL: 978-0-387-69277-7 Idioma : Inglés (eng) Palabras clave: Mathematics Radiology Image processing Numerical analysis Calculus of variations Variations and Optimal Control; Optimization Processing Computer Vision Signal, Speech Analysis Imaging / Clasificación: 51 Matemáticas Resumen: This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Key Features: - Introduces variational methods with motivation from the deterministic, geometric, and stochastic point of view - Bridges the gap between regularization theory in image analysis and in inverse problems - Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography - Discusses link between non-convex calculus of variations, morphological analysis, and level set methods - Analyses variational methods containing classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations - Uses numerical examples to enhance the theory This book is geared towards graduate students and researchers in applied mathematics. It can serve as a main text for graduate courses in image processing and inverse problems or as a supplemental text for courses on regularization. Researchers and computer scientists in the area of imaging science will also find this book useful Nota de contenido: Fundamentals of Imaging -- Case Examples of Imaging -- Image and Noise Models -- Regularization -- Variational Regularization Methods for the Solution of Inverse Problems -- Convex Regularization Methods for Denoising -- Variational Calculus for Non-convex Regularization -- Semi-group Theory and Scale Spaces -- Inverse Scale Spaces -- Mathematical Foundations -- Functional Analysis -- Weakly Differentiable Functions -- Convex Analysis and Calculus of Variations En línea: http://dx.doi.org/10.1007/978-0-387-69277-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33844 Variational Methods in Imaging [documento electrónico] / Scherzer, Otmar ; SpringerLink (Online service) ; Markus Grasmair ; Harald Grossauer ; Markus Haltmeier ; Frank Lenzen . - New York, NY : Springer New York, 2009 . - XIV, 320 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 167) .
ISBN : 978-0-387-69277-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Radiology Image processing Numerical analysis Calculus of variations Variations and Optimal Control; Optimization Processing Computer Vision Signal, Speech Analysis Imaging / Clasificación: 51 Matemáticas Resumen: This book is devoted to the study of variational methods in imaging. The presentation is mathematically rigorous and covers a detailed treatment of the approach from an inverse problems point of view. Key Features: - Introduces variational methods with motivation from the deterministic, geometric, and stochastic point of view - Bridges the gap between regularization theory in image analysis and in inverse problems - Presents case examples in imaging to illustrate the use of variational methods e.g. denoising, thermoacoustics, computerized tomography - Discusses link between non-convex calculus of variations, morphological analysis, and level set methods - Analyses variational methods containing classical analysis of variational methods, modern analysis such as G-norm properties, and non-convex calculus of variations - Uses numerical examples to enhance the theory This book is geared towards graduate students and researchers in applied mathematics. It can serve as a main text for graduate courses in image processing and inverse problems or as a supplemental text for courses on regularization. Researchers and computer scientists in the area of imaging science will also find this book useful Nota de contenido: Fundamentals of Imaging -- Case Examples of Imaging -- Image and Noise Models -- Regularization -- Variational Regularization Methods for the Solution of Inverse Problems -- Convex Regularization Methods for Denoising -- Variational Calculus for Non-convex Regularization -- Semi-group Theory and Scale Spaces -- Inverse Scale Spaces -- Mathematical Foundations -- Functional Analysis -- Weakly Differentiable Functions -- Convex Analysis and Calculus of Variations En línea: http://dx.doi.org/10.1007/978-0-387-69277-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33844 Ejemplares
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