Vicent Caselles's Books

Geometric Description of Images as Topographic Maps

By: Vicent Caselles,Pascal Monasse

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Geometric Description of Images as Topographic Maps

By: Vicent Caselles,Pascal Monasse

This book discusses the basic geometric contents of an image and presents a treedatastructuretohandleite?ciently.Itanalyzesalsosomemorphological operators that simplify this geometric contents and their implementation in termsofthe datastructuresintroduced.It?nallyreviewsseveralapplications to image comparison and registration, to edge and corner computation, and the selection of features associated to a given scale in images. Let us ?rst say that, to avoid a long list, we shall not give references in this summary; they are obviously contained in this monograph. A gray level image is usually modeled as a function de?ned in a bounded N domain D? R (typically N = 2 for usual snapshots, N=3formedical images or movies) with values in R. The sensors of a camera or a CCD array transform the continuum of light energies to a ?nite interval of values by means of a nonlinear function g. The contrast change g depends on the pr- ertiesofthesensors,butalsoontheilluminationconditionsandthere?ection propertiesofthe objects,andthoseconditionsaregenerallyunknown.Images are thus observed modulo an arbitrary and unknown contrast change.

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Page Count

200

Publisher

Springer

Published Date

ISBN 10

3642046118

ISBN 13

9783642046117

Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

By: Fuensanta Andreu-Vaillo,Vicent Caselles,José M. Mazon

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Parabolic Quasilinear Equations Minimizing Linear Growth Functionals

By: Fuensanta Andreu-Vaillo,Vicent Caselles,José M. Mazon

This book details the mathematical developments in total variation based image restauration. From the reviews: "This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters....The book is written with great care, paying also a lot of attention to the bibliographical and historical notes."-- ZENTRALBLATT MATH

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Page Count

351

Publisher

Birkhäuser

Published Date

ISBN 10

3034879288

ISBN 13

9783034879286

Optimal Transportation Networks

Models and Theory

By: Marc Bernot,Vicent Caselles,Jean-Michel Morel

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Optimal Transportation Networks

Models and Theory

By: Marc Bernot,Vicent Caselles,Jean-Michel Morel

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

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