Skip to main content
SpringerLink
Log in

Geometric Curve Evolution and Image Processing

  • Book
  • © 2003

Overview

Authors:
  1. Frédéric Cao
    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Lecture Notes in Mathematics (LNM, volume 1805)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
Softcover Book USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (10 chapters)

  1. Front Matter

    Download chapter PDF

  2. 1. Curve evolution and image processing

    • Frédéric Cao
    Pages 3-21

  3. 2. Rudimentary bases of curve geometry

    • Frédéric Cao
    Pages 23-28

  4. 3. Geometric curve shortening flow

    • Frédéric Cao
    Pages 31-53

  5. 4. Curve evolution and level sets

    • Frédéric Cao
    Pages 55-103

  6. 5. Classical numerical methods for curve evolution

    • Frédéric Cao
    Pages 107-110

  7. 6. A geometrical scheme for curve evolution

    • Frédéric Cao
    Pages 111-166

  8. Conclusion and perspectives

    • Frédéric Cao
    Pages 167-169

  9. A. Proof of Thm. 4.34

    • Frédéric Cao
    Pages 171-176

  10. References

    • Frédéric Cao
    Pages 177-184

  11. Index

    • Frédéric Cao
    Pages 185-187
Back to top

Keywords

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.

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation