# Geometric Curve Evolution and Image Processing

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

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

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

- DOI https://doi.org/10.1007/b10404
- Copyright Information Springer-Verlag Berlin/Heidelberg 2003
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Springer Book Archive
- Print ISBN 978-3-540-00402-8
- Online ISBN 978-3-540-36392-7
- Series Print ISSN 1617-9692
- Series Online ISSN 0075-8434
- About this book