Epstein, Charles L.
Overview
Works:  23 works in 92 publications in 2 languages and 2,336 library holdings 

Genres:  Personal narratives Interviews Oral histories Personal narratives‡vJewish Biography 
Roles:  Author 
Publication Timeline
.
Most widely held works by
Charles L Epstein
Degenerate diffusion operators arising in population biology by
Charles L Epstein(
)
14 editions published between 2013 and 2017 in English and held by 1,572 WorldCat member libraries worldwide
"This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hèolder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right halfplane. Epstein and Mazzeo also demonstrate precise asymptotic results for the longtime behavior of solutions to both the forward and backward Kolmogorov equations."
14 editions published between 2013 and 2017 in English and held by 1,572 WorldCat member libraries worldwide
"This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hèolder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right halfplane. Epstein and Mazzeo also demonstrate precise asymptotic results for the longtime behavior of solutions to both the forward and backward Kolmogorov equations."
Introduction to the mathematics of medical imaging by
Charles L Epstein(
Book
)
29 editions published between 2003 and 2008 in English and held by 454 WorldCat member libraries worldwide
"At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts, as well as techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis." "This text uses Xray computed tomography as a "pedagogical machine" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises." "New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI." "The book is appropriate for one or twosemester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis."Jacket
29 editions published between 2003 and 2008 in English and held by 454 WorldCat member libraries worldwide
"At the heart of every medical imaging technology is a sophisticated mathematical model of the measurement process and an algorithm to reconstruct an image from the measured data. This book provides a firm foundation in the mathematical tools used to model the measurements and derive the reconstruction algorithms used in most imaging modalities in current use. In the process, it also covers many important analytic concepts, as well as techniques used in Fourier analysis, integral equations, sampling theory, and noise analysis." "This text uses Xray computed tomography as a "pedagogical machine" to illustrate important ideas and incorporates extensive discussions of background material making the more advanced mathematical topics accessible to readers with a less formal mathematical education. The mathematical concepts are illuminated with over 200 illustrations and numerous exercises." "New to the second edition are a chapter on magnetic resonance imaging (MRI), a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, an improved description of the gridding method, and a new section on noise analysis in MRI." "The book is appropriate for one or twosemester courses at the advanced undergraduate or beginning graduate level on the mathematical foundations of modern medical imaging technologies. The text assumes an understanding of calculus, linear algebra, and basic mathematical analysis."Jacket
The spectral theory of geometrically periodic hyperbolic 3manifolds by
Charles L Epstein(
Book
)
16 editions published in 1985 in English and held by 266 WorldCat member libraries worldwide
16 editions published in 1985 in English and held by 266 WorldCat member libraries worldwide
Advanced real analysis by
Anthony W Knapp(
Book
)
6 editions published in 2005 in English and held by 23 WorldCat member libraries worldwide
Advanced€Real Analysis systematically develops the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established. This work presents a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: . Early chapters treat the fundamentals of real variables, the theory of Fourier series for the Riemann integral, and the theoretical underpinnings of multivariable calculus and differential equations . Subsequent chapters develop measure theory, pointset topology, Fourier series for the Lebesgue integral, and the basics of Banach and Hilbert spaces . Later chapters provide a higherlevel view of the interaction between real analysis and algebra, including functional analysis, partial differential equations, and further topics in Fourier analysis . Throughout the text are problems that develop and illuminate aspects of the theory of probability . Includes many examples and hundreds of problems, and a chapter gives hints or complete solutions for most of the problems It requires of the reader only familiarity with some linear algebra and real variable theory, a few weeks' worth of group theory, and an acquaintance with proofs. Because it focuses on what every young mathematician needs to know about real analysis, this book is ideal both as a course text and for selfstudy, especially for graduate students preparing for qualifying examinations. Its scope and unique approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, math physics, and applied differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician. TOC:Preface * Theory of calculus in one real variable * Metric spaces * Theory of differential calculus in several variables * Theory of ordinary differential equations and systems * Riemann integration in several variables * Abstract measure theory and Lebesgue measure * Measure theory for Euclidean space * Fourier transform in R^N * L^p spaces * Further topics in abstract measure theory * Topological spaces * Integration on locally compact spaces * Haar measure * Hilbert and Banach spaces * Distributions and their application to PDEs * References * Index
6 editions published in 2005 in English and held by 23 WorldCat member libraries worldwide
Advanced€Real Analysis systematically develops the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established. This work presents a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: . Early chapters treat the fundamentals of real variables, the theory of Fourier series for the Riemann integral, and the theoretical underpinnings of multivariable calculus and differential equations . Subsequent chapters develop measure theory, pointset topology, Fourier series for the Lebesgue integral, and the basics of Banach and Hilbert spaces . Later chapters provide a higherlevel view of the interaction between real analysis and algebra, including functional analysis, partial differential equations, and further topics in Fourier analysis . Throughout the text are problems that develop and illuminate aspects of the theory of probability . Includes many examples and hundreds of problems, and a chapter gives hints or complete solutions for most of the problems It requires of the reader only familiarity with some linear algebra and real variable theory, a few weeks' worth of group theory, and an acquaintance with proofs. Because it focuses on what every young mathematician needs to know about real analysis, this book is ideal both as a course text and for selfstudy, especially for graduate students preparing for qualifying examinations. Its scope and unique approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, math physics, and applied differential equations. Indeed, the clarity and breadth of Advanced Real Analysis make it a welcome addition to the personal library of every mathematician. TOC:Preface * Theory of calculus in one real variable * Metric spaces * Theory of differential calculus in several variables * Theory of ordinary differential equations and systems * Riemann integration in several variables * Abstract measure theory and Lebesgue measure * Measure theory for Euclidean space * Fourier transform in R^N * L^p spaces * Further topics in abstract measure theory * Topological spaces * Integration on locally compact spaces * Haar measure * Hilbert and Banach spaces * Distributions and their application to PDEs * References * Index
A relative index on the space of embeddable CRstructures by
Charles L Epstein(
Book
)
3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1995 in English and held by 3 WorldCat member libraries worldwide
Magnetic resonance imaging of shortT₂ tissues with applications for quantifying cortical bone water and myelin by Cheng Li(
Book
)
2 editions published in 2014 in English and held by 2 WorldCat member libraries worldwide
The human body contains a variety of tissue species with short T₂ ranging from a few microseconds to hundreds of microseconds. Detection and quantification of these short T₂ species is of considerable clinical and scientific interest. Cortical bone water and myelin are two of the most important tissue constituents. Quantification of cortical bone water concentration allows for indirect estimation of bone pore volume and noninvasive assessment of bone quality. Myelin is essential for the proper functioning of the central nervous system (CNS). Direct assessment of myelin would reveal CNS abnormalities and enhance our understanding of neurological diseases. However, conventional MRI with echo times of several milliseconds or longer is unable to detect these shortlived MR signals. Recent advances in MRI technology and hardware have enabled development of a number of short T₂ imaging techniques, key among which are ultrashort echo time (UTE) imaging, zero echo time (ZTE) imaging, and sweep imaging with Fourier transform (SWIFT). While these pulse sequences are able to detect short T₂ species, they still suffer from signal interference between different T₂ tissue constituents, image artifacts and excessive scan time. These are primary technical hurdles for application to wholebody clinical scanners. In this thesis research, new MRI techniques for improving short T₂ tissue imaging have been developed to address these challenges with a focus on direct detection and quantification of cortical bone water and myelin on a clinical MRI scanner. The first focus of this research was to optimize long T₂ suppression in UTE imaging. Saturation and adiabatic RF pulses were designed to achieve maximum long T₂ suppression while maximizing the signal from short T₂ species. The imaging protocols were optimized by Bloch equation simulations and were validated using phantom and in vivo experiments. The results show excellent short T₂ contrast with these optimized pulse sequences. The problem of blurring artifacts resulting from the inhomogeneous excitation profile of the rectangular pulses in ZTE imaging was addressed. The proposed approach involves quadratic phasemodulated RF excitation and iterative solution of an inverse problem formulated from the signal model of ZTE imaging and is shown to effectively remove the image artifacts. Subsequently image acquisition efficiency was improved in order to attain clinicallyfeasible scan times. To accelerate the acquisition speed in UTE and ZTE imaging, compressed sensing was applied with a hybrid 3D UTE sequence. Further, the pulse sequence and reconstruction procedure were modified to enable anisotropic fieldofview shape conforming to the geometry of the elongated imaged object. These enhanced acquisition techniques were applied to the detection and quantification of cortical bone water. A new biomarker, the suppression ratio (a ratio image derived from two UTE images, one without and the other with long T₂ suppression), was conceived as a surrogate measure of cortical bone porosity. Experimental data suggest the suppression ratio may be a more direct measure of porosity than previously measured total bone water concentration. Lastly, the feasibility of directly detecting and quantifying spatiallyresolved myelin concentration with a clinical imager was explored, both theoretically and experimentally. Bloch equation simulations were conducted to investigate the intrinsic image resolution and the fraction of detectable myelin signal under current scanner hardware constraints. The feasibility of quantitative ZTE imaging of myelin extract and lamb spinal cord at 3T was demonstrated. The technological advances achieved in this dissertation research may facilitate translation of short T₂ MRI methods from the laboratory to the clinic
2 editions published in 2014 in English and held by 2 WorldCat member libraries worldwide
The human body contains a variety of tissue species with short T₂ ranging from a few microseconds to hundreds of microseconds. Detection and quantification of these short T₂ species is of considerable clinical and scientific interest. Cortical bone water and myelin are two of the most important tissue constituents. Quantification of cortical bone water concentration allows for indirect estimation of bone pore volume and noninvasive assessment of bone quality. Myelin is essential for the proper functioning of the central nervous system (CNS). Direct assessment of myelin would reveal CNS abnormalities and enhance our understanding of neurological diseases. However, conventional MRI with echo times of several milliseconds or longer is unable to detect these shortlived MR signals. Recent advances in MRI technology and hardware have enabled development of a number of short T₂ imaging techniques, key among which are ultrashort echo time (UTE) imaging, zero echo time (ZTE) imaging, and sweep imaging with Fourier transform (SWIFT). While these pulse sequences are able to detect short T₂ species, they still suffer from signal interference between different T₂ tissue constituents, image artifacts and excessive scan time. These are primary technical hurdles for application to wholebody clinical scanners. In this thesis research, new MRI techniques for improving short T₂ tissue imaging have been developed to address these challenges with a focus on direct detection and quantification of cortical bone water and myelin on a clinical MRI scanner. The first focus of this research was to optimize long T₂ suppression in UTE imaging. Saturation and adiabatic RF pulses were designed to achieve maximum long T₂ suppression while maximizing the signal from short T₂ species. The imaging protocols were optimized by Bloch equation simulations and were validated using phantom and in vivo experiments. The results show excellent short T₂ contrast with these optimized pulse sequences. The problem of blurring artifacts resulting from the inhomogeneous excitation profile of the rectangular pulses in ZTE imaging was addressed. The proposed approach involves quadratic phasemodulated RF excitation and iterative solution of an inverse problem formulated from the signal model of ZTE imaging and is shown to effectively remove the image artifacts. Subsequently image acquisition efficiency was improved in order to attain clinicallyfeasible scan times. To accelerate the acquisition speed in UTE and ZTE imaging, compressed sensing was applied with a hybrid 3D UTE sequence. Further, the pulse sequence and reconstruction procedure were modified to enable anisotropic fieldofview shape conforming to the geometry of the elongated imaged object. These enhanced acquisition techniques were applied to the detection and quantification of cortical bone water. A new biomarker, the suppression ratio (a ratio image derived from two UTE images, one without and the other with long T₂ suppression), was conceived as a surrogate measure of cortical bone porosity. Experimental data suggest the suppression ratio may be a more direct measure of porosity than previously measured total bone water concentration. Lastly, the feasibility of directly detecting and quantifying spatiallyresolved myelin concentration with a clinical imager was explored, both theoretically and experimentally. Bloch equation simulations were conducted to investigate the intrinsic image resolution and the fraction of detectable myelin signal under current scanner hardware constraints. The feasibility of quantitative ZTE imaging of myelin extract and lamb spinal cord at 3T was demonstrated. The technological advances achieved in this dissertation research may facilitate translation of short T₂ MRI methods from the laboratory to the clinic
A stable manifold theorem for the curve shortening equation by
Charles L Epstein(
Book
)
1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1986 in English and held by 2 WorldCat member libraries worldwide
The spectral theory of geometrically periodic hyperbolic 3manifolds by
Charles L Epstein(
)
4 editions published in 1983 in English and held by 2 WorldCat member libraries worldwide
4 editions published in 1983 in English and held by 2 WorldCat member libraries worldwide
Optimal neural codes for natural stimuli by Zhuo Wang(
Book
)
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
Under our framework, we can try to answer questions such as what is the objective function the neural code is actually using? Under what constraints can the predicted results provide a better fit for the actual data? Using different combination of objective function and constraints, we tested our analytical predictions against previously measured characteristics of some early visual systems found in biology. We find solutions under the metabolic constraint and low values of p provides a better fit for physiology data on early visual perception systems
2 editions published in 2016 in English and held by 2 WorldCat member libraries worldwide
Under our framework, we can try to answer questions such as what is the objective function the neural code is actually using? Under what constraints can the predicted results provide a better fit for the actual data? Using different combination of objective function and constraints, we tested our analytical predictions against previously measured characteristics of some early visual systems found in biology. We find solutions under the metabolic constraint and low values of p provides a better fit for physiology data on early visual perception systems
Genomic imprinting : a lasting memory of your parents(
Visual
)
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
1 edition published in 1992 in English and held by 1 WorldCat member library worldwide
Gulfwar aftermath : building up to a construction bonanza(
)
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
1 edition published in 1991 in English and held by 1 WorldCat member library worldwide
Mathematics of medical imaging by
Charles L Epstein(
Book
)
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
1 edition published in 2003 in English and held by 1 WorldCat member library worldwide
Degenerate Diffusion Operators Arising in Population Biology (Annals of Mathematics Studies) by
Charles L Epstein(
Book
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Introduction to the mathematics of medical by
Charles L Epstein(
Book
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
Along with a Companion Volume : Basic Algebra by
Charles L Epstein(
Book
)
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra *Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry *Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis *Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forwardlooking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a twosemester firstyear graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra
1 edition published in 2007 in English and held by 1 WorldCat member library worldwide
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and features of Advanced Algebra: *Topics build upon the linear algebra, group theory, factorization of ideals, structure of fields, Galois theory, and elementary theory of modules as developed in Basic Algebra *Chapters treat various topics in commutative and noncommutative algebra, providing introductions to the theory of associative algebras, homological algebra, algebraic number theory, and algebraic geometry *Sections in two chapters relate the theory to the subject of Gröbner bases, the foundation for handling systems of polynomial equations in computer applications *Text emphasizes connections between algebra and other branches of mathematics, particularly topology and complex analysis *Book carries on two prominent themes recurring in Basic Algebra: the analogy between integers and polynomials in one variable over a field, and the relationship between number theory and geometry *Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems *The exposition proceeds from the particular to the general, often providing examples well before a theory that incorporates them; it includes blocks of problems that illuminate aspects of the text and introduce additional topics Advanced Algebra presents its subject matter in a forwardlooking way that takes into account the historical development of the subject. It is suitable as a text for the more advanced parts of a twosemester firstyear graduate sequence in algebra. It requires of the reader only a familiarity with the topics developed in Basic Algebra
Geometric function theory : explorations in complex analysis by
Steven G Krantz(
Book
)
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous CauchyRiemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysisand also to spark the interest of seasoned workers in the fieldthe book imparts a solid education both in complex analysis and in how modern mathematics works
1 edition published in 2006 in English and held by 1 WorldCat member library worldwide
Complex variables is a precise, elegant, and captivating subject. Presented from the point of view of modern work in the field, this new book addresses advanced topics in complex analysis that verge on current areas of research, including invariant geometry, the Bergman metric, the automorphism groups of domains, harmonic measure, boundary regularity of conformal maps, the Poisson kernel, the Hilbert transform, the boundary behavior of harmonic and holomorphic functions, the inhomogeneous CauchyRiemann equations, and the corona problem. The author adroitly weaves these varied topics to reveal a number of delightful interactions. Perhaps more importantly, the topics are presented with an understanding and explanation of their interrelations with other important parts of mathematics: harmonic analysis, differential geometry, partial differential equations, potential theory, abstract algebra, and invariant theory. Although the book examines complex analysis from many different points of view, it uses geometric analysis as its unifying theme. This methodically designed book contains a rich collection of exercises, examples, and illustrations within each individual chapter, concluding with an extensive bibliography of monographs, research papers, and a thorough index. Seeking to capture the imagination of advanced undergraduate and graduate students with a basic background in complex analysisand also to spark the interest of seasoned workers in the fieldthe book imparts a solid education both in complex analysis and in how modern mathematics works
CT CISM team response to Newtown, CT  December 14, 2012 by
Charles L Epstein(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Study of image local scale structure using nonlinear diffusion by Yan Wang(
)
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Multiscale representation and local scale extraction of images are important in computer vision research, as in general , structures within images are unknown. Traditionally, the multiscale analysis is based on the linear diusion (i.e. heat diusion) with known limitation in edge distortions. In addition, the term scale which is used widely in multiscale and local scale analysis does not have a consistent denition and it can pose potential diculties in real image analysis, especially for the proper interpretation of scale as a geometric measure. In this study, in order to overcome limitations of linear diusion, we focus on the multiscale analysis based on total variation minimization model. This model has been used in image denoising with the power that it can preserve edge structures. Based on the total variation model, we construct the multiscale space and propose a denition for image local scale. The new denition of local scale incorporates both pixelwise and orientation information. This denition can be interpreted with a clear geometrical meaning and applied in general image analysis. The potential applications of total variation model in retinal fundus image analysis is explored. The existence of blood vessel and drusen structures within a single fundus image makes the image analysis a challenging problem. A multiscale model based on total variation is used, showing the capabilities in both drusen and blood vessel detections. The performance of vessel detection is compared with publicly available methods, showing the improvements both quantitatively and qualitatively. This study provides a better insight into local scale study and shows the potentials of total variation model in medical image analysis
1 edition published in 2013 in English and held by 1 WorldCat member library worldwide
Multiscale representation and local scale extraction of images are important in computer vision research, as in general , structures within images are unknown. Traditionally, the multiscale analysis is based on the linear diusion (i.e. heat diusion) with known limitation in edge distortions. In addition, the term scale which is used widely in multiscale and local scale analysis does not have a consistent denition and it can pose potential diculties in real image analysis, especially for the proper interpretation of scale as a geometric measure. In this study, in order to overcome limitations of linear diusion, we focus on the multiscale analysis based on total variation minimization model. This model has been used in image denoising with the power that it can preserve edge structures. Based on the total variation model, we construct the multiscale space and propose a denition for image local scale. The new denition of local scale incorporates both pixelwise and orientation information. This denition can be interpreted with a clear geometrical meaning and applied in general image analysis. The potential applications of total variation model in retinal fundus image analysis is explored. The existence of blood vessel and drusen structures within a single fundus image makes the image analysis a challenging problem. A multiscale model based on total variation is used, showing the capabilities in both drusen and blood vessel detections. The performance of vessel detection is compared with publicly available methods, showing the improvements both quantitatively and qualitatively. This study provides a better insight into local scale study and shows the potentials of total variation model in medical image analysis
Charles Epstein oral history (interview code : 14036) by
Charles L Epstein(
Visual
)
1 edition published in 1996 in French and held by 1 WorldCat member library worldwide
Audiovisual testimony of a Holocaust survivor. Includes prewar, wartime, and postwar experiences
1 edition published in 1996 in French and held by 1 WorldCat member library worldwide
Audiovisual testimony of a Holocaust survivor. Includes prewar, wartime, and postwar experiences
Seizures and pseudoseizures(
Visual
)
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 1992 in English and held by 0 WorldCat member libraries worldwide
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Diagnostic imagingMathematics Differential equations, Partial Distribution (Probability theory) Elliptic operators Fourier analysis Functional analysis Functions of complex variables Genomic imprinting Geometric function theory Geometry, Differential Global analysis (Mathematics) Global differential geometry Harmonic analysis Holocaust, Jewish (19391945) Holocaust survivors JewsSocial life and customs Manifolds (Mathematics) Markov processes Mathematical analysis Mathematics Medical physicsMathematics Neurology Population biologyMathematical models Potential theory (Mathematics) Probabilities Searches and seizures Spectral theory (Mathematics) Threemanifolds (Topology) World War (19391945)
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Alternative Names
Charles Epstein Amerikaans wiskundige
Charles Epstein matemático estadounidense
Charles Epstein matematico statunitense
Charles Epstein mathématicien américain, a professé à l'université de Pennsylvanie, Philadelphie.
Epstein, C. 1957
Epstein, C. L. 1957
Epstein, Charles 1957
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