Geometric Curve Evolution and Image Processing

Frédéric Cao

198 pages, parution le 10/03/2003

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Résumé

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.

Contents

Part I. The curve smoothing problem

Curve evolution and image processing
Rudimentary bases of curve geometry

Part II. Theoretical curve evolution

Geometric curve shortening flow
Curve evolution and level sets

Part III. Numerical curve evolution

Classical numerical methods for curve evolution
A geometrical scheme for curve evolution

Conclusion and perspectives
A. Proof of Thm. 4.34

L'auteur - Frédéric Cao

IRISA / INRIA, Rennes, France

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Frédéric Cao
Parution	10/03/2003
Nb. de pages	198
Format	15,5 x 23,5
Couverture	Broché
Poids	301g
Intérieur	Noir et Blanc
EAN13	9783540004028