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Overview"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." Full Product DetailsAuthor: Frédéric CaoPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2003 ed. Volume: 1805 Dimensions: Width: 15.50cm , Height: 1.00cm , Length: 23.50cm Weight: 0.650kg ISBN: 9783540004028ISBN 10: 3540004025 Pages: 194 Publication Date: 27 February 2003 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of print, replaced by POD  We will order this item for you from a manufatured on demand supplier. Table of ContentsPreface.- Part I. The curve smoothing problem: 1. Curve evolution and image processing; 2. Rudimentary bases of curve geometry.- Part II. Theoretical curve evolution: 3. Geometric curve shortening flow; 4. Curve evolution and level sets.- Part III. Numerical curve evolution: 5. Classical numerical methods for curve evolution; 6. A geometrical scheme for curve evolution.- Conclusion and perspectives.- A. Proof of Thm. 4.3.4.- References.- Index.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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