Geometric Description of Images as Topographic Maps

  • Vicent Caselles
  • Pascal Monasse

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

Table of contents

  1. Front Matter
    Pages 1-14
  2. Vicent Caselles, Pascal Monasse
    Pages 1-7
  3. Vicent Caselles, Pascal Monasse
    Pages 9-34
  4. Vicent Caselles, Pascal Monasse
    Pages 35-73
  5. Vicent Caselles, Pascal Monasse
    Pages 75-102
  6. Vicent Caselles, Pascal Monasse
    Pages 103-113
  7. Vicent Caselles, Pascal Monasse
    Pages 115-140
  8. Vicent Caselles, Pascal Monasse
    Pages 141-153
  9. Vicent Caselles, Pascal Monasse
    Pages 155-171
  10. Back Matter
    Pages 1-18

About this book


This volume discusses the basic geometric contents of an image and presents a tree data structure to handle those contents efficiently. The nodes of the tree are derived from connected components of level sets of the intensity, while the edges represent inclusion information. Grain filters, morphological operators simplifying these geometric contents, are analyzed and several applications to image comparison and registration, and to edge and corner detection, are presented.
The mathematically inclined reader may be most interested in Chapters 2 to 6, which generalize the topological Morse description to continuous or semicontinuous functions, while mathematical morphologists may more closely consider grain filters in Chapter 3. Computer scientists will find algorithmic considerations in Chapters 6 and 7, the full justification of which may be found in Chapters 2 and 4 respectively. Lastly, all readers can learn more about the motivation for this work in the image processing applications presented in Chapter 8.


Algorithms Graph Node Sim algorithm data structure image processing information

Authors and affiliations

  • Vicent Caselles
    • 1
  • Pascal Monasse
    • 2
  1. 1.Depto. TecnologiaUniversidad Pompeu FabraBarcelonaSpain
  2. 2.IMAGINEEcole des Ponts ParisTechMarne-la-Vallée CX 2France

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-04610-0
  • Online ISBN 978-3-642-04611-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site