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Lecture Notes in Mathematics

Geometric Curve Evolution and Image Processing

Authors: Cao, Frédéric

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  • ISBN 978-3-540-36392-7
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  • ISBN 978-3-540-00402-8
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About this book

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.

Table of contents (10 chapters)

Table of contents (10 chapters)
  • 1. Curve evolution and image processing

    Pages 3-21

    Cao, Frédéric

  • 2. Rudimentary bases of curve geometry

    Pages 23-28

    Cao, Frédéric

  • 3. Geometric curve shortening flow

    Pages 31-53

    Cao, Frédéric

  • 4. Curve evolution and level sets

    Pages 55-103

    Cao, Frédéric

  • 5. Classical numerical methods for curve evolution

    Pages 107-110

    Cao, Frédéric

Buy this book

eBook 28,88 €
price for Spain (gross)
  • The eBook version of this title will be available soon
  • ISBN 978-3-540-36392-7
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,35 €
price for Spain (gross)
  • ISBN 978-3-540-00402-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Curve Evolution and Image Processing
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1805
Copyright
2003
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-36392-7
DOI
10.1007/b10404
Softcover ISBN
978-3-540-00402-8
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 194
Topics