mathematical problems in image processing applied mathematical sciences

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Mathematical Problems In Image Processing

Author : Gilles Aubert
ISBN : 9780387217666
Genre : Mathematics
File Size : 31. 92 MB
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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.

Variational Methods In Imaging

Author : Otmar Scherzer
ISBN : 9780387692777
Genre : Mathematics
File Size : 20. 47 MB
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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. Many numerical examples accompany the theory throughout the text. It is geared towards graduate students and researchers in applied mathematics. Researchers in the area of imaging science will also find this book appealing. It can serve as a main text in courses in image processing or as a supplemental text for courses on regularization and inverse problems at the graduate level.

Statistical And Computational Inverse Problems

Author : Jari Kaipio
ISBN : 9780387271323
Genre : Mathematics
File Size : 29. 9 MB
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This book covers the statistical mechanics approach to computational solution of inverse problems, an innovative area of current research with very promising numerical results. The techniques are applied to a number of real world applications such as limited angle tomography, image deblurring, electical impedance tomography, and biomagnetic inverse problems. Contains detailed examples throughout and includes a chapter on case studies where such methods have been implemented in biomedical engineering.

Variational Methods In Image Processing

Author : Luminita A. Vese
ISBN : 9781439849743
Genre : Technology & Engineering
File Size : 68. 22 MB
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Variational Methods in Image Processing presents the principles, techniques, and applications of variational image processing. The text focuses on variational models, their corresponding Euler–Lagrange equations, and numerical implementations for image processing. It balances traditional computational models with more modern techniques that solve the latest challenges introduced by new image acquisition devices. The book addresses the most important problems in image processing along with other related problems and applications. Each chapter presents the problem, discusses its mathematical formulation as a minimization problem, analyzes its mathematical well-posedness, derives the associated Euler–Lagrange equations, describes the numerical approximations and algorithms, explains several numerical results, and includes a list of exercises. MATLAB® codes are available online. Filled with tables, illustrations, and algorithms, this self-contained textbook is primarily for advanced undergraduate and graduate students in applied mathematics, scientific computing, medical imaging, computer vision, computer science, and engineering. It also offers a detailed overview of the relevant variational models for engineers, professionals from academia, and those in the image processing industry.

Level Set Methods And Dynamic Implicit Surfaces

Author : Stanley Osher
ISBN : 9780387227467
Genre : Mathematics
File Size : 87. 44 MB
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Very hot area with a wide range of applications; Gives complete numerical analysis and recipes, which will enable readers to quickly apply the techniques to real problems; Includes two new techniques pioneered by Osher and Fedkiw; Osher and Fedkiw are internationally well-known researchers in this area

Mathematical Methods In Image Reconstruction

Author : Frank Natterer
ISBN : 9780898716221
Genre : Computers
File Size : 69. 92 MB
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This book provides readers with a superior understanding of the mathematical principles behind imaging.

Computational Homology

Author : Tomasz Kaczynski
ISBN : 9780387215976
Genre : Mathematics
File Size : 34. 5 MB
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Homology is a powerful tool used by mathematicians to study the properties of spaces and maps that are insensitive to small perturbations. This book uses a computer to develop a combinatorial computational approach to the subject. The core of the book deals with homology theory and its computation. Following this is a section containing extensions to further developments in algebraic topology, applications to computational dynamics, and applications to image processing. Included are exercises and software that can be used to compute homology groups and maps. The book will appeal to researchers and graduate students in mathematics, computer science, engineering, and nonlinear dynamics.

A First Course In Applied Mathematics

Author : Jorge Rebaza
ISBN : 9781118277157
Genre : Mathematics
File Size : 43. 79 MB
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Explore real-world applications of selected mathematical theory, concepts, and methods Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation for transitioning to more advanced subjects. The author utilizes MATLAB® to showcase the presented theory and illustrate interesting real-world applications to Google's web page ranking algorithm, image compression, cryptography, chaos, and waste management systems. Additional topics covered include: Linear algebra Ranking web pages Matrix factorizations Least squares Image compression Ordinary differential equations Dynamical systems Mathematical models Throughout the book, theoretical and applications-oriented problems and exercises allow readers to test their comprehension of the presented material. An accompanying website features related MATLAB® code and additional resources. A First Course in Applied Mathematics is an ideal book for mathematics, computer science, and engineering courses at the upper-undergraduate level. The book also serves as a valuable reference for practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work.

Digital Picture Processing

Author : Azriel Rosenfeld
ISBN : 9780323139915
Genre : Computers
File Size : 66. 99 MB
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The rapid rate at which the field of digital picture processing has grown in the past five years had necessitated extensive revisions and the introduction of topics not found in the original edition.

Industrial Mathematics

Author : Avner Friedman
ISBN : 1611971543
Genre : Mathematics
File Size : 76. 4 MB
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Industrial mathematics is a fast growing field within the mathematical sciences. It is characterized by the origin of the problems which it engages; they all come from industry: research and development, finances, and communications. The common feature running through this enterprise is the goal of gaining a better understanding of industrial models and processes through mathematical ideas and computations. The authors of this book have undertaken the approach of presenting real industrial problems and their mathematical modeling as a motivation for developing mathematical methods that are needed for solving the problems. With each chapter presenting one important problem that arises in today's industry, and then studying the problem by mathematical analysis and computation, this book introduces the reader to many new ideas and methods from ordinary and partial differential equations, and from integral equations and control theory. It brings the excitement of real industrial problems into the undergraduate mathematical curriculum. The problems selected are accessible to students who have already taken what in many colleges and universities constitutes the first two-year basic Calculus sequence. A working knowledge of Fortran, Pascal, or C language is required.

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