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Geometric Description of Images as Topographic Maps

  • Book
  • © 2010

Overview

Authors:
  1. Vicent Caselles

    1. Depto. Tecnologia, Universidad Pompeu Fabra, Barcelona, Spain

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  2. Pascal Monasse

    1. IMAGINE, Ecole des Ponts ParisTech, Marne-la-Vallée CX 2, France

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1984)

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Table of contents (8 chapters)

  1. Front Matter

    Pages 1-14
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  2. Introduction

    • Vicent Caselles, Pascal Monasse
    Pages 1-7

  3. The Tree of Shapes of an Image

    • Vicent Caselles, Pascal Monasse
    Pages 9-34

  4. Grain Filters

    • Vicent Caselles, Pascal Monasse
    Pages 35-73

  5. A Topological Description of the Topographic Map

    • Vicent Caselles, Pascal Monasse
    Pages 75-102

  6. Merging the Component Trees

    • Vicent Caselles, Pascal Monasse
    Pages 103-113

  7. Computation of the Tree of Shapes of a Digital Image

    • Vicent Caselles, Pascal Monasse
    Pages 115-140

  8. Computation of the Tree of Bilinear Level Lines

    • Vicent Caselles, Pascal Monasse
    Pages 141-153

  9. Applications

    • Vicent Caselles, Pascal Monasse
    Pages 155-171

  10. Back Matter

    Pages 1-18
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Keywords

About this book

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.

Authors and Affiliations

  • Depto. Tecnologia, Universidad Pompeu Fabra, Barcelona, Spain

    Vicent Caselles

  • IMAGINE, Ecole des Ponts ParisTech, Marne-la-VallĂ©e CX 2, France

    Pascal Monasse

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