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  • © 2003

Geometric Curve Evolution and Image Processing

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

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Table of contents (10 chapters)

  1. Front Matter

  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. 6. A geometrical scheme for curve evolution

    • Frédéric Cao
    Pages 111-166
  7. Conclusion and perspectives

    • Frédéric Cao
    Pages 167-169
  8. A. Proof of Thm. 4.34

    • Frédéric Cao
    Pages 171-176
  9. References

    • Frédéric Cao
    Pages 177-184
  10. Index

    • Frédéric Cao
    Pages 185-187

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.

Keywords

  • Applied Mathematics
  • Numerical Analysis
  • computer vision
  • curvature
  • image processing
  • partial differential equations

Bibliographic Information

  • Book Title: Geometric Curve Evolution and Image Processing

  • Authors: Frédéric Cao

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/b10404

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2003

  • Softcover ISBN: 978-3-540-00402-8Published: 27 February 2003

  • eBook ISBN: 978-3-540-36392-7Published: 01 January 2003

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 194

  • Topics: Differential Equations, Computer Vision, Differential Geometry

Buying options

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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions