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Author: Jean-Michel Morel
Publisher: Springer Science & Business Media
ISBN: 1468405675
Category : Mathematics
Languages : en
Pages : 257
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Book Description
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").
Author: Jean-Michel Morel
Publisher: Springer Science & Business Media
ISBN: 1468405675
Category : Mathematics
Languages : en
Pages : 257
Get Book Here
Book Description
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").
Author: Luminita A. Vese
Publisher: CRC Press
ISBN: 1439849749
Category : Computers
Languages : en
Pages : 416
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Book Description
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
Author: Tony F. Chan
Publisher: SIAM
ISBN: 089871589X
Category : Computers
Languages : en
Pages : 414
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Book Description
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.
Author: Aly A. Farag
Publisher: Cambridge University Press
ISBN: 0521196795
Category : Computers
Languages : en
Pages : 486
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Book Description
Ideal for classroom use and self-study, this book explains the implementation of the most effective modern methods in image analysis, covering segmentation, registration and visualisation, and focusing on the key theories, algorithms and applications that have emerged from recent progress in computer vision, imaging and computational biomedical science. Structured around five core building blocks - signals, systems, image formation and modality; stochastic models; computational geometry; level set methods; and tools and CAD models - it provides a solid overview of the field. Mathematical and statistical topics are presented in a straightforward manner, enabling the reader to gain a deep understanding of the subject without becoming entangled in mathematical complexities. Theory is connected to practical examples in x-ray, ultrasound, nuclear medicine, MRI and CT imaging, removing the abstract nature of the models and assisting reader understanding.
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
ISBN: 0387692770
Category : Mathematics
Languages : en
Pages : 323
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Book Description
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.
Author: Kristian Bredies
Publisher: Springer
ISBN: 3030014584
Category : Mathematics
Languages : en
Pages : 481
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Book Description
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)
Author: Dimitris Metaxas
Publisher: Springer
ISBN: 354085990X
Category : Computers
Languages : en
Pages : 1161
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Book Description
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.
Author: Otmar Scherzer
Publisher: Springer Science & Business Media
ISBN: 0387929193
Category : Mathematics
Languages : en
Pages : 1626
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Book Description
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.
Author: Maïtine Bergounioux
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110430398
Category : Mathematics
Languages : en
Pages : 538
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Book Description
With a focus on the interplay between mathematics and applications of imaging, the first part covers topics from optimization, inverse problems and shape spaces to computer vision and computational anatomy. The second part is geared towards geometric control and related topics, including Riemannian geometry, celestial mechanics and quantum control. Contents: Part I Second-order decomposition model for image processing: numerical experimentation Optimizing spatial and tonal data for PDE-based inpainting Image registration using phase・amplitude separation Rotation invariance in exemplar-based image inpainting Convective regularization for optical flow A variational method for quantitative photoacoustic tomography with piecewise constant coefficients On optical flow models for variational motion estimation Bilevel approaches for learning of variational imaging models Part II Non-degenerate forms of the generalized Euler・Lagrange condition for state-constrained optimal control problems The Purcell three-link swimmer: some geometric and numerical aspects related to periodic optimal controls Controllability of Keplerian motion with low-thrust control systems Higher variational equation techniques for the integrability of homogeneous potentials Introduction to KAM theory with a view to celestial mechanics Invariants of contact sub-pseudo-Riemannian structures and Einstein・Weyl geometry Time-optimal control for a perturbed Brockett integrator Twist maps and Arnold diffusion for diffeomorphisms A Hamiltonian approach to sufficiency in optimal control with minimal regularity conditions: Part I Index
Author: David Forsyth
Publisher: Springer Science & Business Media
ISBN: 3540886818
Category : Computers
Languages : en
Pages : 833
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Book Description
The four-volume set comprising LNCS volumes 5302/5303/5304/5305 constitutes the refereed proceedings of the 10th European Conference on Computer Vision, ECCV 2008, held in Marseille, France, in October 2008. The 243 revised papers presented were carefully reviewed and selected from a total of 871 papers submitted. The four books cover the entire range of current issues in computer vision. The papers are organized in topical sections on recognition, stereo, people and face recognition, object tracking, matching, learning and features, MRFs, segmentation, computational photography and active reconstruction.
