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Author: Frédéric Cao
Publisher: Springer Science & Business Media
ISBN: 9783540004028
Category : Mathematics
Languages : en
Pages : 204
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Book Description
In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.
Author: Frédéric Cao
Publisher: Springer Science & Business Media
ISBN: 9783540004028
Category : Mathematics
Languages : en
Pages : 204
Get Book
Book Description
In image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.
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Languages : en
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Book Description
In this digital era of our world, huge amounts of digital image data are being collected on a daily basis. The collected image data is being stored for subsequent processing and use in a wide variety of applications. For this purpose, it is often important to accurately and precisely extract relevant information out of this data. In computer vision applications, for instance, an important goal is to understand the contents of an image and be able to automatically gain an understanding of a scene, implying an extraction and recognition of an object. This task is, however, greatly complicated by the acquired image data being often noisy, and target objects and background bearing textural variations. As a result, there is a strong demand for reliable and automated image processing algorithms, for image smoothing, textured image segmentation, object extraction, tracking, and recognition. The objective of this thesis is to develop image processing algorithms which are efficient, statistically robust and sufficiently general, in order to account for noise and textural variations in images, and which have the ability to extract and provide compact and useful descriptions of target objects in images, for object recognition and tracking purposes. The main contribution of the thesis is the development of image processing algorithms, which are based on the theory of curve evolution with connections to information theory and probability theory. These connections form the basis for extracting a compact object description, in the form of a polygonal contour. One contribution is the development of a new class of curve evolution equations designed to preserve prescribed polygonal structures in an image while removing noise. In conjunction with these flows, a local stochastic formulation of a well-studied curve evolution equation, namely the geometric heat equation, provides an alternative microscopic as well as macroscopic view, which in turn led to our proposal of vanishing at pre.
Author: Guillermo Sapiro
Publisher: Cambridge University Press
ISBN: 1139936514
Category : Mathematics
Languages : en
Pages : 391
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Book Description
This book provides an introduction to the use of geometric partial differential equations in image processing and computer vision. This research area brings a number of new concepts into the field, providing a very fundamental and formal approach to image processing. 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 practitioners. It is intended to provide information for people investigating new solutions to image processing problems as well as for people searching for existent advanced solutions.
Author: Stanley Osher
Publisher: Springer Science & Business Media
ISBN: 0387218106
Category : Computers
Languages : en
Pages : 523
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Book Description
Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.
Author: Ron Kimmel
Publisher: Springer Science & Business Media
ISBN: 0387216375
Category : Computers
Languages : en
Pages : 222
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Book Description
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.
Author: Alain Connes
Publisher: Springer Science & Business Media
ISBN: 9783540203575
Category : Mathematics
Languages : en
Pages : 372
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Book Description
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Author: Michael Cowling
Publisher: Springer
ISBN: 3540768920
Category : Mathematics
Languages : en
Pages : 400
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Book Description
Six leading experts lecture on a wide spectrum of recent results on the subject of the title. They present a survey of various interactions between representation theory and harmonic analysis on semisimple groups and symmetric spaces, and recall the concept of amenability. They further illustrate how representation theory is related to quantum computing; and much more. Taken together, this volume provides both a solid reference and deep insights on current research activity.
Author: Yuliya Mishura
Publisher: Springer
ISBN: 3540758739
Category : Mathematics
Languages : en
Pages : 411
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Book Description
This volume examines the theory of fractional Brownian motion and other long-memory processes. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. It proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.
Author:
Publisher: Springer Science & Business Media
ISBN: 9783540207283
Category : Forms, Pfister
Languages : en
Pages : 212
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Book Description
Author: Andras Telcs
Publisher: Springer
ISBN: 3540330283
Category : Mathematics
Languages : en
Pages : 193
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Book Description
The main aim of this book is to reveal connections between the physical and geometric properties of space and diffusion. This is done in the context of random walks in the absence of algebraic structure, local or global spatial symmetry or self-similarity. The author studies heat diffusion at this general level and discusses the multiplicative Einstein relation; Isoperimetric inequalities; and Heat kernel estimates; Elliptic and parabolic Harnack inequality.
