Geometric curve evolution and image processing /

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Bibliographic Details
Author / Creator:Cao, Frédéric, 1973-
Imprint:Berlin ; New York : Springer, ©2003.
Description:1 online resource (x, 187 pages) : illustrations.
Language:English
Series:Lecture notes in mathematics, 0075-8434 ; 1805
Lecture notes in mathematics (Springer-Verlag) ; 1805.
Subject:Curves on surfaces.
Differential equations, Parabolic -- Numerical solutions.
Image processing.
Curves on surfaces.
Differential equations, Parabolic -- Numerical solutions.
Image processing.
Electronic books.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11065219
Hidden Bibliographic Details
ISBN:9783540363927
3540363920
3540004025
9783540004028
Notes:Includes bibliographical references (pages 177-184) and index.
Summary: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.
Other form:Print version: Cao, Frédéric, 1973- Geometric curve evolution and image processing. Berlin ; New York : Springer, ©2003 3540004025