Lecture Notes in Mathematics

Geometric Description of Images as Topographic Maps

Authors: Caselles, Vicent, Monasse, Pascal

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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.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Introduction

    Pages 1-7

    Caselles, Vicent (et al.)

  • The Tree of Shapes of an Image

    Pages 9-34

    Caselles, Vicent (et al.)

  • Grain Filters

    Pages 35-73

    Caselles, Vicent (et al.)

  • A Topological Description of the Topographic Map

    Pages 75-102

    Caselles, Vicent (et al.)

  • Merging the Component Trees

    Pages 103-113

    Caselles, Vicent (et al.)

Buy this book

eBook $34.99
price for USA in USD
  • ISBN 978-3-642-04611-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $44.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Description of Images as Topographic Maps
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1984
Copyright
2010
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-04611-7
DOI
10.1007/978-3-642-04611-7
Softcover ISBN
978-3-642-04610-0
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XVII, 192
Topics