Variational Methods in Image Segmentation

Variational Methods in Image Segmentation
Author: Jean-Michel Morel
Publisher: Springer Science & Business Media
Total Pages: 257
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468405675

This book contains both a synthesis and mathematical analysis of a wide set of algorithms and theories whose aim is the automatic segmen tation of digital images as well as the understanding of visual perception. A common formalism for these theories and algorithms is obtained in a variational form. Thank to this formalization, mathematical questions about the soundness of algorithms can be raised and answered. Perception theory has to deal with the complex interaction between regions and "edges" (or boundaries) in an image: in the variational seg mentation energies, "edge" terms compete with "region" terms in a way which is supposed to impose regularity on both regions and boundaries. This fact was an experimental guess in perception phenomenology and computer vision until it was proposed as a mathematical conjecture by Mumford and Shah. The third part of the book presents a unified presentation of the evi dences in favour of the conjecture. It is proved that the competition of one-dimensional and two-dimensional energy terms in a variational for mulation cannot create fractal-like behaviour for the edges. The proof of regularity for the edges of a segmentation constantly involves con cepts from geometric measure theory, which proves to be central in im age processing theory. The second part of the book provides a fast and self-contained presentation of the classical theory of rectifiable sets (the "edges") and unrectifiable sets ("fractals").

Variational Methods in Image Processing

Variational Methods in Image Processing
Author: Luminita A. Vese
Publisher: CRC Press
Total Pages: 416
Release: 2015-11-18
Genre: Computers
ISBN: 1439849749

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

Image Processing and Analysis

Image Processing and Analysis
Author: Tony F. Chan
Publisher: SIAM
Total Pages: 414
Release: 2005-09-01
Genre: Computers
ISBN: 089871589X

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.

Variational Methods in Imaging

Variational Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 323
Release: 2008-09-26
Genre: Mathematics
ISBN: 0387692770

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.

Computer Vision Analysis of Image Motion by Variational Methods

Computer Vision Analysis of Image Motion by Variational Methods
Author: Amar Mitiche
Publisher: Springer Science & Business Media
Total Pages: 212
Release: 2013-09-05
Genre: Technology & Engineering
ISBN: 3319007114

This book presents a unified view of image motion analysis under the variational framework. Variational methods, rooted in physics and mechanics, but appearing in many other domains, such as statistics, control, and computer vision, address a problem from an optimization standpoint, i.e., they formulate it as the optimization of an objective function or functional. The methods of image motion analysis described in this book use the calculus of variations to minimize (or maximize) an objective functional which transcribes all of the constraints that characterize the desired motion variables. The book addresses the four core subjects of motion analysis: Motion estimation, detection, tracking, and three-dimensional interpretation. Each topic is covered in a dedicated chapter. The presentation is prefaced by an introductory chapter which discusses the purpose of motion analysis. Further, a chapter is included which gives the basic tools and formulae related to curvature, Euler Lagrange equations, unconstrained descent optimization, and level sets, that the variational image motion processing methods use repeatedly in the book.

Mathematical Image Processing

Mathematical Image Processing
Author: Kristian Bredies
Publisher: Springer
Total Pages: 481
Release: 2019-02-06
Genre: Mathematics
ISBN: 3030014584

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)

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2008

Medical Image Computing and Computer-Assisted Intervention - MICCAI 2008
Author: Dimitris Metaxas
Publisher: Springer
Total Pages: 1161
Release: 2008-10-30
Genre: Computers
ISBN: 354085990X

The 11th International Conference on Medical Imaging and Computer Assisted Intervention, MICCAI 2008, was held at the Helen and Martin Kimmel Center of New York University, New York City, USA on September 6–10, 2008. MICCAI is the premier international conference in this domain, with - depth papers on the multidisciplinary ?elds of biomedical image computing and analysis, computer assisted intervention and medical robotics. The conference brings together biological scientists, clinicians, computer scientists, engineers, mathematicians, physicists and other interested researchers and o?ers them a forum to exchange ideas in these exciting and rapidly growing ?elds. The conference is both very selective and very attractive: this year we - ceived a record number of 700 submissions from 34 countries and 6 continents, fromwhich258papers were selectedfor publication,whichcorrespondsto a s- cess rate of approximately 36%. Some interesting facts about the distribution of submitted and accepted papers are shown graphically at the end of this preface. The paper selection process this year was based on the following procedure, which included the introduction of several novelties over previous years. 1. A ProgramCommittee (PC) of 49 members was recruited by the Program Chairs,to getthenecessarybody ofexpertiseandgeographicalcoverage.All PC members agreed in advance to participate in the ?nal paper selection process. 2. Key words grouped in 7 categories were used to describe the content of the submissions and the expertise of the reviewers.

Handbook of Mathematical Methods in Imaging

Handbook of Mathematical Methods in Imaging
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
Total Pages: 1626
Release: 2010-11-23
Genre: Mathematics
ISBN: 0387929193

The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.

The Variational Bayes Method in Signal Processing

The Variational Bayes Method in Signal Processing
Author: Václav Šmídl
Publisher: Springer Science & Business Media
Total Pages: 241
Release: 2006-03-30
Genre: Technology & Engineering
ISBN: 3540288201

Treating VB approximation in signal processing, this monograph is for academic and industrial research groups in signal processing, data analysis, machine learning and identification. It reviews distributional approximation, showing that tractable algorithms for parametric model identification can be generated in off-line and on-line contexts.