Mathematical Problems in Image Processing

2001-11-09

Author: Gilles Aubert

Publisher: Springer Science & Business Media

ISBN: 9780387953267

Category: Mathematics

Page: 303

View: 785

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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.

Mathematical Problems in Image Processing

2008-04-06

Author: Gilles Aubert

Publisher: Springer Science & Business Media

ISBN: 9780387217666

Category: Mathematics

Page: 288

View: 625

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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.

Image Processing Based on Partial Differential Equations

2006-11-22

Author: Xue-Cheng Tai

Publisher: Springer Science & Business Media

ISBN: 9783540332671

Category: Computers

Page: 440

View: 435

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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 Methods in Image Processing and Inverse Problems

2021-09-25

Author: Xue-Cheng Tai

Publisher: Springer Nature

ISBN: 9789811627019

Category: Mathematics

Page: 223

View: 856

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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.

Mathematical Foundations of Image Processing and Analysis

2014-07-22

Author: Jean-Charles Pinoli

Publisher: John Wiley & Sons

ISBN: 9781118984550

Category: Technology & Engineering

Page: 496

View: 664

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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.

Scale Space and Variational Methods in Computer Vision

2009-05-25

Author: Xue-Cheng Tai

Publisher: Springer Science & Business Media

ISBN: 9783642022555

Category: Computers

Page: 882

View: 561

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This book constitutes the refereed proceedings of the Second International Conference on Scale Space Methods and Variational Methods in Computer Vision, SSVM 2009, emanated from the joint edition of the 5th International Workshop on Variational, Geometric and Level Set Methods in Computer Vision, VLSM 2009 and the 7th International Conference on Scale Space and PDE Methods in Computer Vision, Scale-Space 2009, held in Voss, Norway in June 2009. The 71 revised full papers presented were carefully reviewed and selected numerous submissions. The papers are organized in topical sections on segmentation and detection; image enhancement and reconstruction; motion analysis, optical flow, registration and tracking; surfaces and shapes; scale space and feature extraction.

Nonlinear Eigenproblems in Image Processing and Computer Vision

2018-03-29

Author: Guy Gilboa

Publisher: Springer

ISBN: 9783319758473

Category: Computers

Page: 172

View: 278

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This unique text/reference presents a fresh look at nonlinear processing through nonlinear eigenvalue analysis, highlighting how one-homogeneous convex functionals can induce nonlinear operators that can be analyzed within an eigenvalue framework. The text opens with an introduction to the mathematical background, together with a summary of classical variational algorithms for vision. This is followed by a focus on the foundations and applications of the new multi-scale representation based on non-linear eigenproblems. The book then concludes with a discussion of new numerical techniques for finding nonlinear eigenfunctions, and promising research directions beyond the convex case. Topics and features: introduces the classical Fourier transform and its associated operator and energy, and asks how these concepts can be generalized in the nonlinear case; reviews the basic mathematical notion, briefly outlining the use of variational and flow-based methods to solve image-processing and computer vision algorithms; describes the properties of the total variation (TV) functional, and how the concept of nonlinear eigenfunctions relate to convex functionals; provides a spectral framework for one-homogeneous functionals, and applies this framework for denoising, texture processing and image fusion; proposes novel ways to solve the nonlinear eigenvalue problem using special flows that converge to eigenfunctions; examines graph-based and nonlocal methods, for which a TV eigenvalue analysis gives rise to strong segmentation, clustering and classification algorithms; presents an approach to generalizing the nonlinear spectral concept beyond the convex case, based on pixel decay analysis; discusses relations to other branches of image processing, such as wavelets and dictionary based methods. This original work offers fascinating new insights into established signal processing techniques, integrating deep mathematical concepts from a range of different fields, which will be of great interest to all researchers involved with image processing and computer vision applications, as well as computations for more general scientific problems.

Computational Vision and Medical Image Processing V

2015-10-14

Author: Joao Tavares

Publisher: CRC Press

ISBN: 9781315642796

Category: Computers

Page: 374

View: 149

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VipIMAGE 2015 contains invited lectures and full papers presented at VIPIMAGE 2015 - V ECCOMAS Thematic Conference on Computational Vision and Medical Image Processing (Tenerife, Canary Islands, Spain, 19-21 October, 2015). International contributions from 19 countries provide a comprehensive coverage of the current state-of-the-art in the fields o

Parallel Processing and Applied Mathematics

2016-04-05

Author: Roman Wyrzykowski

Publisher: Springer

ISBN: 9783319321523

Category: Computers

Page: 622

View: 540

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This two-volume-set (LNCS 9573 and 9574) constitutes the refereed proceedings of the 11th International Conference of Parallel Processing and Applied Mathematics, PPAM 2015, held in Krakow, Poland, in September 2015. The 111 revised full papers presented in both volumes were carefully reviewed and selected from 196 submissions. The focus of PPAM 2015 was on models, algorithms, and software toolswhich facilitate efficient and convenient utilization of modern parallel and distributed computing architectures, as well as on large-scale applications, including big data problems.

Contemporary Problems in Mathematical Physics

2004-12-08

Author: Jan Govaerts

Publisher: World Scientific

ISBN: 9789814481847

Category: Science

Page: 628

View: 963

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The COPROMAPH Conference series has now evolved into a significant international arena where fundamental concepts in mathematical and theoretical physics and their physics applications can be conceived, developed and disseminated. Basic ideas for addressing a variety of contemporary problems in mathematical and theoretical physics are presented in a nonintimidating atmosphere. Experts provide the reader the fundamentals to predict new possibilities in physics and other fields. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings) • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) • CC Proceedings — Engineering & Physical Sciences Contents:Lectures on Diffeomorphisms Groups in Quantum Physics (G A Goldin)On the Road Towards the Quantum Geometer's Universe: An Introduction to Four-Dimensional Supersymmetric Quantum Field Theory (J Govaerts)Theoretical Methods of Modern Classical and Quantum Physics:A Stochastic Streamflow Model Based on a Minimum Energy Expenditure Concept (A Afouda et al.)Regge Poles Trajectories for Nonsingular Potentials: The Thomas-Fermi Potentials (Z Felfli et al.)Proposed Differential Equation for Spin 1/2 (H V Mweene)Influence of Diseases and Arterial Prostheses on Solitary Blood Waves: Characteristics of an Ideal Prosthesis (S Noubissié & P Woafo)Coherent States, Wavelets and Geometric Methods in Theoretical Physics:Vector Coherent States over Matrix Domains (S T Ali)Wavelet Analysis and Some of Its Applications in Physics (J-P Antoine)Some Variations on the Berezin Quantization Method (M Engliš)Variational Analysis, PDE's and Image Analysis: The Big Picture and a Sampling of Details (N D George & K R Vixie)Functional Analysis Special Functions and Orthogonal Polynomials:On Generalized Continuous D Semi-Classical Orthogonal Polynomials of Class One (E S Azatassou & M N Hounkonnou)and other papers Readership: Researchers and professionals in physics and mathematics. Keywords:Mathematical Physics;Theoretical Physics;Quantum Physics;Coherent States;Supersymmetry

Tensors in Image Processing and Computer Vision

2009-05-21

Author: Santiago Aja-Fernández

Publisher: Springer Science & Business Media

ISBN: 9781848822993

Category: Computers

Page: 470

View: 320

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Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing. This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.

Variational and Level Set Methods in Image Segmentation

2010-10-22

Author: Amar Mitiche

Publisher: Springer Science & Business Media

ISBN: 9783642153525

Category: Technology & Engineering

Page: 192

View: 766

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Image segmentation consists of dividing an image domain into disjoint regions according to a characterization of the image within or in-between the regions. Therefore, segmenting an image is to divide its domain into relevant components. The efficient solution of the key problems in image segmentation promises to enable a rich array of useful applications. The current major application areas include robotics, medical image analysis, remote sensing, scene understanding, and image database retrieval. The subject of this book is image segmentation by variational methods with a focus on formulations which use closed regular plane curves to define the segmentation regions and on a level set implementation of the corresponding active curve evolution algorithms. Each method is developed from an objective functional which embeds constraints on both the image domain partition of the segmentation and the image data within or in-between the partition regions. The necessary conditions to optimize the objective functional are then derived and solved numerically. The book covers, within the active curve and level set formalism, the basic two-region segmentation methods, multiregion extensions, region merging, image modeling, and motion based segmentation. To treat various important classes of images, modeling investigates several parametric distributions such as the Gaussian, Gamma, Weibull, and Wishart. It also investigates non-parametric models. In motion segmentation, both optical flow and the movement of real three-dimensional objects are studied.

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