Table of contents

  1. Front Matter
  2. Frédéric Cao
    Pages 3-21
  3. Frédéric Cao
    Pages 23-28
  4. Frédéric Cao
    Pages 31-53
  5. Frédéric Cao
    Pages 55-103
  6. Frédéric Cao
    Pages 111-166
  7. Frédéric Cao
    Pages 167-169
  8. Frédéric Cao
    Pages 171-176
  9. Frédéric Cao
    Pages 177-184
  10. 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.


Applied Mathematics Numerical Analysis computer vision curvature image processing

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