Mathematical Problems In Image Processing

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Mathematical Problems in Image Processing

Gilles Aubert,Pierre Kornprobst
Mathematical Problems in Image Processing Book PDF

Author : Gilles Aubert,Pierre Kornprobst
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 42,9 Mb
Release : 2008-04-06
Category : Mathematics
ISBN : 9780387217666

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Mathematical Problems in Image Processing by Gilles Aubert,Pierre Kornprobst Pdf

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.

Mathematical Image Processing

Kristian Bredies,Dirk Lorenz
Mathematical Image Processing Book PDF

Author : Kristian Bredies,Dirk Lorenz
Publisher : Springer
Page : 473 pages
File Size : 55,9 Mb
Release : 2019-02-06
Category : Mathematics
ISBN : 9783030014582

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Mathematical Image Processing by Kristian Bredies,Dirk Lorenz Pdf

This book addresses the mathematical aspects of modern image processing methods, with a special emphasis on the underlying ideas and concepts. It discusses a range of modern mathematical methods used to accomplish basic imaging tasks such as denoising, deblurring, enhancing, edge detection and inpainting. In addition to elementary methods like point operations, linear and morphological methods, and methods based on multiscale representations, the book also covers more recent methods based on partial differential equations and variational methods. Review of the German Edition: The overwhelming impression of the book is that of a very professional presentation of an appropriately developed and motivated textbook for a course like an introduction to fundamentals and modern theory of mathematical image processing. Additionally, it belongs to the bookcase of any office where someone is doing research/application in image processing. It has the virtues of a good and handy reference manual. (zbMATH, reviewer: Carl H. Rohwer, Stellenbosch)

Mathematical Problems in Image Processing

Gilles Aubert,Pierre Kornprobst
Mathematical Problems in Image Processing Book PDF

Author : Gilles Aubert,Pierre Kornprobst
Publisher : Springer
Page : 0 pages
File Size : 46,6 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0387512136

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Mathematical Problems in Image Processing by Gilles Aubert,Pierre Kornprobst Pdf

The updated 2nd edition of this book presents a variety of image analysis applications, reviews their precise mathematics and shows how to discretize them. For the mathematical community, the book shows the contribution of mathematics to this domain, and highlights unsolved theoretical questions. For the computer vision community, it presents a clear, self-contained and global overview of the mathematics involved in image procesing problems. The second edition offers a review of progress in image processing applications covered by the PDE framework, and updates the existing material. The book also provides programming tools for creating simulations with minimal effort.

Mathematical Methods in Image Processing and Inverse Problems

Xue-Cheng Tai,Suhua Wei,Haiguang Liu
Mathematical Methods in Image Processing and Inverse Problems Book PDF

Author : Xue-Cheng Tai,Suhua Wei,Haiguang Liu
Publisher : Springer Nature
Page : 226 pages
File Size : 42,7 Mb
Release : 2021-09-25
Category : Mathematics
ISBN : 9789811627019

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Mathematical Methods in Image Processing and Inverse Problems by Xue-Cheng Tai,Suhua Wei,Haiguang Liu Pdf

This book contains eleven original and survey scientific research articles arose from presentations given by invited speakers at International Workshop on Image Processing and Inverse Problems, held in Beijing Computational Science Research Center, Beijing, China, April 21–24, 2018. The book was dedicated to Professor Raymond Chan on the occasion of his 60th birthday. The contents of the book cover topics including image reconstruction, image segmentation, image registration, inverse problems and so on. Deep learning, PDE, statistical theory based research methods and techniques were discussed. The state-of-the-art developments on mathematical analysis, advanced modeling, efficient algorithm and applications were presented. The collected papers in this book also give new research trends in deep learning and optimization for imaging science. It should be a good reference for researchers working on related problems, as well as for researchers working on computer vision and visualization, inverse problems, image processing and medical imaging.

Variational Methods in Image Processing

Luminita A. Vese,Carole Le Guyader
Variational Methods in Image Processing Book PDF

Author : Luminita A. Vese,Carole Le Guyader
Publisher : CRC Press
Page : 416 pages
File Size : 44,9 Mb
Release : 2015-11-18
Category : Computers
ISBN : 9781439849743

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Variational Methods in Image Processing by Luminita A. Vese,Carole Le Guyader Pdf

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 t

Mathematical Image Processing

Maïtine Bergounioux
Mathematical Image Processing Book PDF

Author : Maïtine Bergounioux
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 44,7 Mb
Release : 2011-05-12
Category : Mathematics
ISBN : 9783642196041

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Mathematical Image Processing by Maïtine Bergounioux Pdf

The contributions appearing in this volume are a snapshot of the different topics that were discussed during the Second Conference "Mathematics and Image Processing” held at the University of Orléans in 2010. They mainly concern, image reconstruction, texture extraction and image classification and involve a variety of different methods and applications. Therefore it was impossible to split the papers into generic groups which is why they are presented in alphabetic order. However they mainly concern: texture analysis (5 papers) with different techniques (variational analysis, wavelet and morphological component analysis, fractional Brownian fields), geometrical methods (2 papers ) for restoration and invariant feature detection, classification (with multifractal analysis), neurosciences imaging and analysis of Multi-Valued Images.

Image Processing and Analysis

Tony F. Chan,Jianhong (Jackie) Shen
Image Processing and Analysis Book PDF

Author : Tony F. Chan,Jianhong (Jackie) Shen
Publisher : SIAM
Page : 414 pages
File Size : 51,5 Mb
Release : 2005-09-01
Category : Computers
ISBN : 9780898715897

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Image Processing and Analysis by Tony F. Chan,Jianhong (Jackie) Shen Pdf

This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.

Image Processing Based on Partial Differential Equations

Xue-Cheng Tai,Knut-Andreas Lie,Tony F. Chan,Stanley Osher
Image Processing Based on Partial Differential Equations Book PDF

Author : Xue-Cheng Tai,Knut-Andreas Lie,Tony F. Chan,Stanley Osher
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 44,8 Mb
Release : 2006-11-22
Category : Computers
ISBN : 9783540332671

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Image Processing Based on Partial Differential Equations by Xue-Cheng Tai,Knut-Andreas Lie,Tony F. Chan,Stanley Osher Pdf

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.

Mathematical Foundations of Image Processing and Analysis

Jean-Charles Pinoli
Mathematical Foundations of Image Processing and Analysis Book PDF

Author : Jean-Charles Pinoli
Publisher : John Wiley & Sons
Page : 496 pages
File Size : 51,5 Mb
Release : 2014-07-22
Category : Technology & Engineering
ISBN : 9781118984550

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Mathematical Foundations of Image Processing and Analysis by Jean-Charles Pinoli Pdf

Mathematical Imaging is currently a rapidly growing field inapplied mathematics, with an increasing need for theoreticalmathematics. This book, the second of two volumes, emphasizes the role ofmathematics as a rigorous basis for imaging sciences. It provides acomprehensive and convenient overview of the key mathematicalconcepts, notions, tools and frameworks involved in the variousfields of gray-tone and binary image processing and analysis, byproposing a large, but coherent, set of symbols and notations, acomplete list of subjects and a detailed bibliography. Itestablishes a bridge between the pure and applied mathematicaldisciplines, and the processing and analysis of gray-tone andbinary images. It is accessible to readers who have neitherextensive mathematical training, nor peer knowledge in ImageProcessing and Analysis. It is a self-contained book focusing on the mathematicalnotions, concepts, operations, structures, and frameworks that arebeyond or involved in Image Processing and Analysis. The notationsare simplified as far as possible in order to be more explicativeand consistent throughout the book and the mathematical aspects aresystematically discussed in the image processing and analysiscontext, through practical examples or concrete illustrations.Conversely, the discussed applicative issues allow the role ofmathematics to be highlighted. Written for a broad audience – students, mathematicians,image processing and analysis specialists, as well as otherscientists and practitioners – the author hopes that readerswill find their own way of using the book, thus providing amathematical companion that can help mathematicians become morefamiliar with image processing and analysis, and likewise, imageprocessing and image analysis scientists, researchers and engineersgain a deeper understanding of mathematical notions andconcepts.

Mathematics of Shape Description

Pijush K. Ghosh,Koichiro Deguchi
Mathematics of Shape Description Book PDF

Author : Pijush K. Ghosh,Koichiro Deguchi
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 47,8 Mb
Release : 2009-03-04
Category : Technology & Engineering
ISBN : 9780470823088

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Mathematics of Shape Description by Pijush K. Ghosh,Koichiro Deguchi Pdf

Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book. Key Features Explains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approach Promotes interaction of image processing geochronology and mathematics in the field of algebraic geometry Provides a shape description scheme that is a notational system for the shape of objects Offers a thorough and detailed discussion on the mathematical characteristics and significance of the Minkowski operators

Mathematics in Image Processing

Hong-Kai Zhao
Mathematics in Image Processing Book PDF

Author : Hong-Kai Zhao
Publisher : American Mathematical Soc.
Page : 258 pages
File Size : 49,8 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9780821898413

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Mathematics in Image Processing by Hong-Kai Zhao Pdf

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.

Mathematical Methods in Computer Vision

Peter J. Olver
Mathematical Methods in Computer Vision Book PDF

Author : Peter J. Olver
Publisher : Springer Science & Business Media
Page : 176 pages
File Size : 48,7 Mb
Release : 2003-10
Category : Business & Economics
ISBN : 0387004971

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Mathematical Methods in Computer Vision by Peter J. Olver Pdf

"Comprises some of the key work presented at two IMA Wokshops on Computer Vision during fall of 2000."--Pref.

Image Processing

Jonathan M. Blackledge
Image Processing Book PDF

Author : Jonathan M. Blackledge
Publisher : Unknown
Page : 548 pages
File Size : 48,6 Mb
Release : 1997
Category : Computers
ISBN : UOM:39015041344501

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Image Processing by Jonathan M. Blackledge Pdf

Digital image processing technology has developed markedly over the last ten years, and more and more information is being conveyed through its display and analysis. The way in which image data is stored and processed is fundamental to all aspects of information technology. Examples include remote sensing using digital satellites; making diagnoses using conventional X-ray computed tomography; and research into the behavior of the human brain using magnetic resonance imaging. This book consists of twenty-one papers that collectively cover a broad range of image processing problems and the way in which their solutions are used in different areas of science and technology. The papers present details of the ways computers of varying processing power can be programmed to store images efficiently, resolve features and patterns that are either time consuming or impossible for humans to interpret, and develop machines that can "see" like humans. They also discuss a wide range of applications, including the use of lasers for studying dynamic behavior of mechanical components, and fractal geometry for recognizing patterns. The book will be useful to any engineer, scientist, and technologist interested in current research issues in image processing.

Mathematical Nonlinear Image Processing

Edward R. Dougherty,Jaakko Astola
Mathematical Nonlinear Image Processing Book PDF

Author : Edward R. Dougherty,Jaakko Astola
Publisher : Springer Science & Business Media
Page : 173 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9781461531487

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Mathematical Nonlinear Image Processing by Edward R. Dougherty,Jaakko Astola Pdf

Mathematical Nonlinear Image Processing deals with a fast growing research area. The development of the subject springs from two factors: (1) the great expansion of nonlinear methods applied to problems in imaging and vision, and (2) the degree to which nonlinear approaches are both using and fostering new developments in diverse areas of mathematics. Mathematical Nonlinear Image Processing will be of interest to people working in the areas of applied mathematics as well as researchers in computer vision. Mathematical Nonlinear Image Processing is an edited volume of original research. It has also been published as a special issue of the Journal of Mathematical Imaging and Vision. (Volume 2, Issue 2/3).

Image Processing and Mathematical Morphology

Frank Y. Shih
Image Processing and Mathematical Morphology Book PDF

Author : Frank Y. Shih
Publisher : CRC Press
Page : 439 pages
File Size : 46,8 Mb
Release : 2017-07-12
Category : Technology & Engineering
ISBN : 9781351834445

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Image Processing and Mathematical Morphology by Frank Y. Shih Pdf

In the development of digital multimedia, the importance and impact of image processing and mathematical morphology are well documented in areas ranging from automated vision detection and inspection to object recognition, image analysis and pattern recognition. Those working in these ever-evolving fields require a solid grasp of basic fundamentals, theory, and related applications—and few books can provide the unique tools for learning contained in this text. Image Processing and Mathematical Morphology: Fundamentals and Applications is a comprehensive, wide-ranging overview of morphological mechanisms and techniques and their relation to image processing. More than merely a tutorial on vital technical information, the book places this knowledge into a theoretical framework. This helps readers analyze key principles and architectures and then use the author’s novel ideas on implementation of advanced algorithms to formulate a practical and detailed plan to develop and foster their own ideas. The book: Presents the history and state-of-the-art techniques related to image morphological processing, with numerous practical examples Gives readers a clear tutorial on complex technology and other tools that rely on their intuition for a clear understanding of the subject Includes an updated bibliography and useful graphs and illustrations Examines several new algorithms in great detail so that readers can adapt them to derive their own solution approaches This invaluable reference helps readers assess and simplify problems and their essential requirements and complexities, giving them all the necessary data and methodology to master current theoretical developments and applications, as well as create new ones.