• Mathematics

Oscillating Patterns in Image Processing and Nonlinear Evolution Equations

The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
Author: Yves Meyer
Publisher: American Mathematical Soc.
ISBN: 9780821829202
Category: Mathematics
Page: 122
View: 1365
Image compression, the Navier-Stokes equations, and detection of gravitational waves are three seemingly unrelated scientific problems that, remarkably, can be studied from one perspective. The notion that unifies the three problems is that of ``oscillating patterns'', which are present in many natural images, help to explain nonlinear equations, and are pivotal in studying chirps and frequency-modulated signals. The first chapter of this book considers image processing, more precisely algorithms of image compression and denoising. This research is motivated in particular by the new standard for compression of still images known as JPEG-2000. The second chapter has new results on the Navier-Stokes and other nonlinear evolution equations. Frequency-modulated signals and their use in the detection of gravitational waves are covered in the final chapter. In the book, the author describes both what the oscillating patterns are and the mathematics necessary for their analysis. It turns out that this mathematics involves new properties of various Besov-type function spaces and leads to many deep results, including new generalizations of famous Gagliardo-Nirenberg and Poincare inequalities. This book is based on the ``Dean Jacqueline B. Lewis Memorial Lectures'' given by the author at Rutgers University. It can be used either as a textbook in studying applications of wavelets to image processing or as a supplementary resource for studying nonlinear evolution equations or frequency-modulated signals. Most of the material in the book did not appear previously in monograph literature.

    • Mathematics

Level Set and PDE Based Reconstruction Methods in Imaging

Cetraro, Italy 2008, Editors: Martin Burger, Stanley Osher
Author: Martin Burger,Andrea C.G. Mennucci,Stanley Osher,Martin Rumpf
Publisher: Springer
ISBN: 3319017128
Category: Mathematics
Page: 319
View: 5484
This book takes readers on a tour through modern methods in image analysis and reconstruction based on level set and PDE techniques, the major focus being on morphological and geometric structures in images. The aspects covered include edge-sharpening image reconstruction and denoising, segmentation and shape analysis in images, and image matching. For each, the lecture notes provide insights into the basic analysis of modern variational and PDE-based techniques, as well as computational aspects and applications.

    • Computers

Image Processing Based on Partial Differential Equations

Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse Problems, CMA, Oslo, August 8-12, 2005
Author: Xue-Cheng Tai,Knut-Andreas Lie,Tony F. Chan,Stanley Osher
Publisher: Springer Science & Business Media
ISBN: 3540332677
Category: Computers
Page: 440
View: 7916
This book publishes a collection of original scientific research articles that address the state-of-art in using partial differential equations for image and signal processing. Coverage includes: level set methods for image segmentation and construction, denoising techniques, digital image inpainting, image dejittering, image registration, and fast numerical algorithms for solving these problems.

    • Computers

Scale Space and Variational Methods in Computer Vision

Second International Conference, SSVM 2009, Voss, Norway, June 1-5, 2009. Proceedings
Author: Xue-Cheng Tai,Knut Moerken,Marius Lysaker,Knut-Andreas Lie
Publisher: Springer
ISBN: 3642022561
Category: Computers
Page: 870
View: 4094
This book contains 71 original, scienti?c articles that address state-of-the-art researchrelatedto scale space and variationalmethods for image processing and computer vision. Topics covered in the book range from mathematical analysis of both established and new models, fast numerical methods, image analysis, segmentation, registration, surface and shape construction and processing, to real applications in medical imaging and computer vision. The ideas of scale spaceandvariationalmethodsrelatedtopartialdi?erentialequationsarecentral concepts. The papers re?ect the newest developments in these ?elds and also point to the latest literature. All the papers were submitted to the Second International Conference on Scale Space and Variational Methods in Computer Vision, which took place in Voss, Norway, during June 1–5, 2009. The papers underwent a peer review process similar to that of high-level journals in the ?eld. We thank the authors, the Scienti?c Committee, the Program Committee and the reviewers for their hard work and helpful collaboration. Their contribution has been crucial for the e?cient processing of this book, and for the success of the conference.

    • Mathematics

Proceedings of the International Congress of Mathematicians

Madrid, August 22-30, 2006
Author: Marta Sanz Solé
Publisher: Amer Mathematical Society
ISBN: 9783037190227
Category: Mathematics
Page: 4500
View: 3818
The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Information for our distributors: Distributed within the Americas by the American Mathematical Society. All commerical channel discounts apply.



    • Mathematics

Wavelets and Operators:


Author: Yves Meyer
Publisher: Cambridge University Press
ISBN: 9780521458696
Category: Mathematics
Page: 244
View: 2540
Over the last two years, wavelet methods have shown themselves to be of considerable use to harmonic analysts and, in particular, advances have been made concerning their applications. The strength of wavelet methods lies in their ability to describe local phenomena more accurately than a traditional expansion in sines and cosines can. Thus, wavelets are ideal in many fields where an approach to transient behaviour is needed, for example, in considering acoustic or seismic signals, or in image processing. Yves Meyer stands the theory of wavelets firmly upon solid ground by basing his book on the fundamental work of Calderón, Zygmund and their collaborators. For anyone who would like an introduction to wavelets, this book will prove to be a necessary purchase.

    • Mathematics

Mathematics in Image Processing


Author: Hong-Kai Zhao
Publisher: American Mathematical Soc.
ISBN: 0821898418
Category: Mathematics
Page: 245
View: 1253
The theme of the 2010 PCMI Summer School was Mathematics in Image Processing in a broad sense, including mathematical theory, analysis, computation algorithms and applications. In image processing, information needs to be processed, extracted and analyzed from visual content, such as photographs or videos. These demands include standard tasks such as compression and denoising, as well as high-level understanding and analysis, such as recognition and classification. Centered on the theme of mathematics in image processing, the summer school covered quite a wide spectrum of topics in this field. The summer school is particularly timely and exciting due to the very recent advances and developments in the mathematical theory and computational methods for sparse representation. This volume collects three self-contained lecture series. The topics are multi-resolution based wavelet frames and applications to image processing, sparse and redundant representation modeling of images and simulation of elasticity, biomechanics, and virtual surgery. Recent advances in image processing, compressed sensing and sparse representation are discussed.

    • Mathematics

Mathematical Problems in Image Processing

Partial Differential Equations and the Calculus of Variations
Author: Gilles Aubert,Pierre Kornprobst
Publisher: Springer Science & Business Media
ISBN: 0387217665
Category: Mathematics
Page: 288
View: 7890
Partial differential equations and variational methods were introduced into image processing about 15 years ago, and intensive research has been carried out since then. The main goal of this work is to present the variety of image analysis applications and the precise mathematics involved. It is intended for two audiences. The first is the mathematical community, to show the contribution of mathematics to this domain and to highlight some unresolved theoretical questions. The second is the computer vision community, to present a clear, self-contained, and global overview of the mathematics involved in image processing problems. The book is divided into five main parts. Chapter 1 is a detailed overview. Chapter 2 describes and illustrates most of the mathematical notions found throughout the work. Chapters 3 and 4 examine how PDEs and variational methods can be successfully applied in image restoration and segmentation processes. Chapter 5, which is more applied, describes some challenging computer vision problems, such as sequence analysis or classification. This book will be useful to researchers and graduate students in mathematics and computer vision.

    • Computers

Scale Space and Variational Methods in Computer Vision

5th International Conference, SSVM 2015, Lège-Cap Ferret, France, May 31 - June 4, 2015, Proceedings
Author: Jean-François Aujol,Mila Nikolova,Nicolas Papadakis
Publisher: Springer
ISBN: 331918461X
Category: Computers
Page: 716
View: 5153
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.

    • Computers

Energy Minimization Methods in Computer Vision and Pattern Recognition

5th International Workshop, EMMCVPR 2005, St. Augustine, FL, USA, November 9-11, 2005, Proceedings
Author: Anand Rangarajan,Baba Vemuri,Alan L. Yuille
Publisher: Springer Science & Business Media
ISBN: 3540302875
Category: Computers
Page: 666
View: 9083
This volume consists of the 42 papers presented at the International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recog- tion (EMMCVPR 2005), which was held at the Hilton St. Augustine Historic Bayfront, St. Augustine, Florida, USA, during November9 11,2005.This wo- shop is the ?fth in a series which began with EMMCVPR 1997 held in Venice, Italy, in May 1997 and continued with EMMCVPR 1999 held in York, UK, in July 1999, EMMCVPR 2001 held in Sophia-Antipolis, France, in September 2001 and EMMCVPR 2003 held in Lisbon, Portugal, in July 2003. Many problems in computer vision and pattern recognition (CVPR) are couchedintheframeworkofoptimization.Theminimizationofaglobalquantity, often referred to as the energy, forms the bulwark of most approachesin CVPR. Disparate approaches such as discrete and probabilistic formulations on the one hand and continuous, deterministic strategies on the other often have optimi- tion or energy minimization as a common theme. Instances of energy minimi- tion arise in Gibbs/Markov modeling, Bayesian decision theory, geometric and variational approaches and in areas in CVPR such as object recognition and - trieval, image segmentation, registration, reconstruction, classi?cation and data mining. The aim of this workshop was to bring together researchers with interests in thesedisparateareasofCVPRbutwithanunderlyingcommitmenttosomeform of not only energy minimization but global optimization in general. Although thesubjectistraditionallywellrepresentedinmajorinternationalconferenceson CVPR, recent advances information geometry, Bayesian networks and gra- ical models, Markov chain Monte Carlo, graph algorithms, implicit methods in variational approaches and PDEs deserve an informal and focused hearing in a workshop setting."

    • Mathematics

Wavelets

Calderón-Zygmund and Multilinear Operators
Author: Yves Meyer,Ronald Coifman
Publisher: Cambridge University Press
ISBN: 9780521794732
Category: Mathematics
Page: 336
View: 7434
A classic exposition of the theory of wavelets from two of the subject's leading experts.

    • Science

Handbook of Mathematical Fluid Dynamics


Author: S. Friedlander,D. Serre
Publisher: Elsevier
ISBN: 9780080478302
Category: Science
Page: 724
View: 1520
This is the fourth volume in a series of survey articles covering many aspects of mathematical fluid dynamics, a vital source of open mathematical problems and exciting physics.

    • Mathematics

Free Discontinuity Problems


Author: Nicola Fusco,Aldo Pratelli
Publisher: Springer
ISBN: 8876425934
Category: Mathematics
Page: N.A
View: 2442
This book presents a series of lectures on three of the best known examples of free discontinuity problems: the Mumford-Shah model for image segmentation, a variational model for the epitaxial growth of thin films, and the sharp interface limit of the Ohta-Kawasaki model for pattern formation in dyblock copolymers.

    • Literary Criticism

Susan Sontag

An Annotated Bibliography 1948-1992
Author: Leland Poague,Kathy A. Parsons
Publisher: Routledge
ISBN: 1135575347
Category: Literary Criticism
Page: 672
View: 8384
Susan Sontag: An Annotated Bibliographycatalogues the works of one of America's most prolific and important 20th century authors. Known for her philosophical writings on American culture, topics left untouched by Sontag's writings are few and far between. This volume is an exhaustive collection that includes her novels, essays, reviews, films and interviews. Each entry is accompanied by an annotated bibliography.

    • Mathematics

Wavelets, Vibrations, and Scalings


Author: Yves Meyer
Publisher: American Mathematical Soc.
ISBN: 0821806858
Category: Mathematics
Page: 133
View: 426
Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilations. This book discusses the relevance of wavelet analysis to problems in which self-similarities are important. Among the conclusions drawn are the following: 1) A weak form of self-similarity can be given a simple characterization through size estimates on wavelet coefficients, and 2) Wavelet bases can be tuned in order to provide a sharper characterization of this self-similarity. A pioneer of the wavelet ``saga'', Meyer gives new and as yet unpublished results throughout the book. It is recommended to scientists wishing to apply wavelet analysis to multifractal signal processing.

    • Calculus of variations

Convex Analysis and Variational Problems


Author: Ivar Ekeland,Roger Témam
Publisher: SIAM
ISBN: 9781611971088
Category: Calculus of variations
Page: 402
View: 3546
This book contains different developments of infinite dimensional convex programming in the context of convex analysis, including duality, minmax and Lagrangians, and convexification of nonconvex optimization problems in the calculus of variations (infinite dimension). It also includes the theory of convex duality applied to partial differential equations; no other reference presents this in a systematic way. The minmax theorems contained in this book have many useful applications, in particular the robust control of partial differential equations in finite time horizon. First published in English in 1976, this SIAM Classics in Applied Mathematics edition contains the original text along with a new preface and some additional references.

    • Computers

Image Processing and Analysis with Graphs

Theory and Practice
Author: Olivier Lezoray,Leo Grady
Publisher: CRC Press
ISBN: 1351833170
Category: Computers
Page: 570
View: 2198
Covering the theoretical aspects of image processing and analysis through the use of graphs in the representation and analysis of objects, Image Processing and Analysis with Graphs: Theory and Practice also demonstrates how these concepts are indispensible for the design of cutting-edge solutions for real-world applications. Explores new applications in computational photography, image and video processing, computer graphics, recognition, medical and biomedical imaging With the explosive growth in image production, in everything from digital photographs to medical scans, there has been a drastic increase in the number of applications based on digital images. This book explores how graphs—which are suitable to represent any discrete data by modeling neighborhood relationships—have emerged as the perfect unified tool to represent, process, and analyze images. It also explains why graphs are ideal for defining graph-theoretical algorithms that enable the processing of functions, making it possible to draw on the rich literature of combinatorial optimization to produce highly efficient solutions. Some key subjects covered in the book include: Definition of graph-theoretical algorithms that enable denoising and image enhancement Energy minimization and modeling of pixel-labeling problems with graph cuts and Markov Random Fields Image processing with graphs: targeted segmentation, partial differential equations, mathematical morphology, and wavelets Analysis of the similarity between objects with graph matching Adaptation and use of graph-theoretical algorithms for specific imaging applications in computational photography, computer vision, and medical and biomedical imaging Use of graphs has become very influential in computer science and has led to many applications in denoising, enhancement, restoration, and object extraction. Accounting for the wide variety of problems being solved with graphs in image processing and computer vision, this book is a contributed volume of chapters written by renowned experts who address specific techniques or applications. This state-of-the-art overview provides application examples that illustrate practical application of theoretical algorithms. Useful as a support for graduate courses in image processing and computer vision, it is also perfect as a reference for practicing engineers working on development and implementation of image processing and analysis algorithms.

    • Science

Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics


Author: Roland Glowinski,Patrick Le Tallec
Publisher: SIAM
ISBN: 0898712300
Category: Science
Page: 295
View: 6757
This volume deals with the numerical simulation of the behavior of continuous media by augmented Lagrangian and operator-splitting methods.