Book Cover
Author Cao, Frédéric, 1973-

Title Geometric curve evolution and image processing / Frédéric Cao
Published Berlin ; New York : Springer, [2003]


Location Call no. Vol. Availability
 W'PONDS  516.362 Cao/Gce  AVAILABLE
Description x, 187 pages : illustrations ; 24 cm
Series Lecture notes in mathematics, 0075-8434 ; 1805
Lecture notes in mathematics (Springer-Verlag)
Contents Pt. I. The curve smoothing problem -- 1. Curve evolution and image processing -- 2. Rudimentary bases of curve geometry -- Pt. II. Theoretical curve evolution -- 3. Geometric curve shortening flow -- 4. Curve evolution and level sets -- Pt. III. Numerical curve evolution -- 5. Classical numerical methods for curve evolution -- 6. A geometrical scheme for curve evolution -- A Proof of Thm.4.34
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
Bibliography Includes bibliographical references (pages [177]-184) and index
Notes Also available via the World Wide Web. (Restricted to LINK subscribers)
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Mode of access: World Wide Web
Lecture notes in mathematics (Springer-Verlag) no:1805 0075-8434
Subject Mathematics.
Computer vision.
Differential equations, Partial.
Global differential geometry.
Curves, Plane.
Curves on surfaces.
Differential equations, Parabolic -- Numerical solutions.
Image processing.
LC no. 2003041554
ISBN 3540004025 softcover acid-free paper
9783540004028 softcover alkaline paper