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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
Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Handbook of Mathematical Methods in Imaging / SpringerLink (Online service) ; Scherzer, Otmar (2011)
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 : 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 : Optimization in Medicine Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Carlos J. S. Alves ; Pardalos, Panos M ; Luis Nunes Vicente Editorial: New York, NY : Springer New York Fecha de publicación: 2008 Colección: Springer Optimization and Its Applications, ISSN 1931-6828 num. 12 Número de páginas: X, 195 p. 60 illus Il.: online resource ISBN/ISSN/DL: 978-0-387-73299-2 Idioma : Inglés (eng) Palabras clave: Medicine Radiology Mathematical optimization Calculus of variations & Public Health Medicine/Public Health, general Optimization Variations and Optimal Control; Imaging / Clasificación: 51 Matemáticas Resumen: Optimization has become an essential tool in addressing the limitation of resources and need for better decision-making in the medical field. Both continuous and discrete mathematical techniques are playing an increasingly important role in understanding several fundamental problems in medicine. This volume presents a wide range of medical applications that can utilize mathematical computing. Examples include using an algorithm for considering the seed reconstruction problem in brachytherapy and using optimization-classification models to assist in the early prediction, diagnosis and detection of diseases. Discrete optimization techniques and measures derived from the theory of nonlinear dynamics, with analysis of multi-electrode electroencephalographic (EEG) data, assist in predicting impending epileptic seizures. Mathematics in medicine can also be found in recent cancer research. Sophisticated mathematical models and optimization algorithms have been used to generate treatment plans for radionuclide implant and external beam radiation therapy. Optimization techniques have also been used to automate the planning process in Gamma Knife treatment, as well as to address a variety of medical image registration problems. This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization Nota de contenido: The influence of dose grid resolution on beam selection strategies in radiotherapy treatment design -- Decomposition of matrices and static multileaf collimators: a survey -- Neuro-dynamic programming for fractionated radiotherapy planning -- Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy -- Global optimization and spatial synchronization changes prior to epileptic seizures -- Optimization-based predictive models in medicine and biology -- Optimal reconstruction kernels in medical imaging -- Optimal control in high intensity focused ultrasound surgery En línea: http://dx.doi.org/10.1007/978-0-387-73299-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34179 Optimization in Medicine [documento electrónico] / SpringerLink (Online service) ; Carlos J. S. Alves ; Pardalos, Panos M ; Luis Nunes Vicente . - New York, NY : Springer New York, 2008 . - X, 195 p. 60 illus : online resource. - (Springer Optimization and Its Applications, ISSN 1931-6828; 12) .
ISBN : 978-0-387-73299-2
Idioma : Inglés (eng)
Palabras clave: Medicine Radiology Mathematical optimization Calculus of variations & Public Health Medicine/Public Health, general Optimization Variations and Optimal Control; Imaging / Clasificación: 51 Matemáticas Resumen: Optimization has become an essential tool in addressing the limitation of resources and need for better decision-making in the medical field. Both continuous and discrete mathematical techniques are playing an increasingly important role in understanding several fundamental problems in medicine. This volume presents a wide range of medical applications that can utilize mathematical computing. Examples include using an algorithm for considering the seed reconstruction problem in brachytherapy and using optimization-classification models to assist in the early prediction, diagnosis and detection of diseases. Discrete optimization techniques and measures derived from the theory of nonlinear dynamics, with analysis of multi-electrode electroencephalographic (EEG) data, assist in predicting impending epileptic seizures. Mathematics in medicine can also be found in recent cancer research. Sophisticated mathematical models and optimization algorithms have been used to generate treatment plans for radionuclide implant and external beam radiation therapy. Optimization techniques have also been used to automate the planning process in Gamma Knife treatment, as well as to address a variety of medical image registration problems. This work grew out of a workshop on optimization which was held during the 2005 CIM Thematic Term on Optimization in Coimbra, Portugal. It provides an overview of the state-of-the-art in optimization in medicine and will serve as an excellent reference for researchers in the medical computing community and for those working in applied mathematics and optimization Nota de contenido: The influence of dose grid resolution on beam selection strategies in radiotherapy treatment design -- Decomposition of matrices and static multileaf collimators: a survey -- Neuro-dynamic programming for fractionated radiotherapy planning -- Randomized algorithms for mixed matching and covering in hypergraphs in 3D seed reconstruction in brachytherapy -- Global optimization and spatial synchronization changes prior to epileptic seizures -- Optimization-based predictive models in medicine and biology -- Optimal reconstruction kernels in medical imaging -- Optimal control in high intensity focused ultrasound surgery En línea: http://dx.doi.org/10.1007/978-0-387-73299-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34179 Ejemplares
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Título : Polarization and Moment Tensors : With Applications to Inverse Problems and Effective Medium Theory Tipo de documento: documento electrónico Autores: Habib Ammari ; SpringerLink (Online service) ; Hyeonbae Kang Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 162 Número de páginas: X, 314 p Il.: online resource ISBN/ISSN/DL: 978-0-387-71566-7 Idioma : Inglés (eng) Palabras clave: Mathematics Radiology Partial differential equations Potential theory (Mathematics) Applied mathematics Engineering Biomedical engineering Applications of Theory Differential Equations Imaging / Clasificación: 51 Matemáticas Resumen: This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors. The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful Nota de contenido: Layer Potentials and Transmission Problems -- Uniqueness for Inverse Conductivity Problems -- Generalized Isotropic and Anisotropic Polarization Tensors -- Full Asymptotic Formula for the Potentials -- Near-Boundary Conductivity Inclusions -- Impedance Imaging of Conductivity Inclusions -- Effective Properties of Electrical Composites -- Transmission Problem for Elastostatics -- Elastic Moment Tensor -- Full Asymptotic Expansions of the Displacement Field -- Imaging of Elastic Inclusions -- Effective Properties of Elastic Composites En línea: http://dx.doi.org/10.1007/978-0-387-71566-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34526 Polarization and Moment Tensors : With Applications to Inverse Problems and Effective Medium Theory [documento electrónico] / Habib Ammari ; SpringerLink (Online service) ; Hyeonbae Kang . - New York, NY : Springer New York, 2007 . - X, 314 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 162) .
ISBN : 978-0-387-71566-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Radiology Partial differential equations Potential theory (Mathematics) Applied mathematics Engineering Biomedical engineering Applications of Theory Differential Equations Imaging / Clasificación: 51 Matemáticas Resumen: This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. The methods involved come from various areas of pure and applied mathematics, such as potential theory, PDEs, complex analysis, and numerical methods. The unifying thread in this book is the use of generalized polarization and moment tensors. The main approach is based on modern layer potential techniques. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. With its extensive list of references and open problems, the book should enhance accessibility to specialized literature and stimulate progress in the fields of impedance imaging and composite materials. Graduate students and researchers in applied mathematics will benefit from this book. Researchers in engineering and physics might also find this book helpful Nota de contenido: Layer Potentials and Transmission Problems -- Uniqueness for Inverse Conductivity Problems -- Generalized Isotropic and Anisotropic Polarization Tensors -- Full Asymptotic Formula for the Potentials -- Near-Boundary Conductivity Inclusions -- Impedance Imaging of Conductivity Inclusions -- Effective Properties of Electrical Composites -- Transmission Problem for Elastostatics -- Elastic Moment Tensor -- Full Asymptotic Expansions of the Displacement Field -- Imaging of Elastic Inclusions -- Effective Properties of Elastic Composites En línea: http://dx.doi.org/10.1007/978-0-387-71566-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34526 Ejemplares
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