Geometric Curve Evolution and Image Processing
Edition: 1 edition
Publisher: Springer
Published: April 28, 2003
Language: eng
Format: Paperback
Number of pages: 187
ISBN-13: 9783540004028
Subjects: Geometry; Mathematics; Geometry - Differential; Science/Mathematics; Numerical solutions; Computer Graphics - Image Processing; Differential Equations; 35K65, 35D05, 53A04, 68U10; Applied Mathematics; Computer Vision; Computers : Computer Graphics - Image Processing; Mathematics / Differential Equations; Mathematics / Geometry / Differential; Mathematics : Differential Equations; Numerical Analysis; Differential equations, Parabolic; Geometry - General; Curves on surfaces; Differential equations, Parabo; Image processing
First sentence: In this volume, we study some theoretical results and the numerical analysis of the motions of plane curves driven by a function of the curvature.
Description: 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.
Notes: Lecture Notes in Mathematics