geometric partial differential equations and image analysis

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Geometric Partial Differential Equations And Image Analysis

Author : Guillermo Sapiro
ISBN : 0521685079
Genre : Computers
File Size : 34. 87 MB
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This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. State-of-the-art practical results in a large number of real problems are achieved with the techniques described in this book. Applications covered include image segmentation, shape analysis, image enhancement, and tracking. This book will be a useful resource for researchers and practioners. It is intened to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.

Author : Guillermo Sapiro
ISBN : 7506259419
Genre : Differential equations, Partial
File Size : 62. 87 MB
Format : PDF, Docs
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责任者译名:萨皮罗。

Numerical Geometry Of Images

Author : Ron Kimmel
ISBN : 9780387216379
Genre : Computers
File Size : 33. 54 MB
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Numerical Geometry of Images examines computational methods and algorithms in image processing. It explores applications like shape from shading, color-image enhancement and segmentation, edge integration, offset curve computation, symmetry axis computation, path planning, minimal geodesic computation, and invariant signature calculation. In addition, it describes and utilizes tools from mathematical morphology, differential geometry, numerical analysis, and calculus of variations. Graduate students, professionals, and researchers with interests in computational geometry, image processing, computer graphics, and algorithms will find this new text / reference an indispensable source of insight of instruction.

Geometric Partial Differential Equations

Author : Antonin Chambolle
ISBN : 9788876424731
Genre : Mathematics
File Size : 41. 34 MB
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This book is the outcome of a conference held at the Centro De Giorgi of the Scuola Normale of Pisa in September 2012. The aim of the conference was to discuss recent results on nonlinear partial differential equations, and more specifically geometric evolutions and reaction-diffusion equations. Particular attention was paid to self-similar solutions, such as solitons and travelling waves, asymptotic behaviour, formation of singularities and qualitative properties of solutions. These problems arise in many models from Physics, Biology, Image Processing and Applied Mathematics in general, and have attracted a lot of attention in recent years.

Hyperbolic Partial Differential Equations And Geometric Optics

Author : Jeffrey Rauch
ISBN : 9780821872918
Genre : Mathematics
File Size : 32. 7 MB
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This book introduces graduate students and researchers in mathematics and the sciences to the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to describe propagation of waves at finite speed. Among the topics carefully presented in the book are nonlinear geometric optics, the asymptotic analysis of short wavelength solutions, and nonlinear interaction of such waves. Studied in detail are the damping of waves, resonance, dispersive decay, and solutions to the compressible Euler equations with dense oscillations created by resonant interactions. Many fundamental results are presented for the first time in a textbook format. In addition to dense oscillations, these include the treatment of precise speed of propagation and the existence and stability questions for the three wave interaction equations. One of the strengths of this book is its careful motivation of ideas and proofs, showing how they evolve from related, simpler cases. This makes the book quite useful to both researchers and graduate students interested in hyperbolic partial differential equations. Numerous exercises encourage active participation of the reader. The author is a professor of mathematics at the University of Michigan. A recognized expert in partial differential equations, he has made important contributions to the transformation of three areas of hyperbolic partial differential equations: nonlinear microlocal analysis, the control of waves, and nonlinear geometric optics.

Image Processing And Analysis

Author : Tony F. Chan
ISBN : 9780898715897
Genre : Computers
File Size : 68. 85 MB
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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

Author : Xue-Cheng Tai
ISBN : 9783540332671
Genre : Computers
File Size : 72. 78 MB
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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.

Function Theory Of Several Complex Variables

Author : Steven George Krantz
ISBN : 9780821827246
Genre : Mathematics
File Size : 49. 5 MB
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The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. The main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. Some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. While due attention is paid to algebraic aspects of several complex variables (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. This book is suitable for a first graduate course in several complex variables.

Elliptic Partial Differential Equations And Quasiconformal Mappings In The Plane Pms 48

Author : Kari Astala
ISBN : 0691137773
Genre : Mathematics
File Size : 85. 25 MB
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This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Mathematical Problems In Image Processing

Author : Gilles Aubert
ISBN : 9780387217666
Genre : Mathematics
File Size : 88. 23 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.

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