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- catalog abstract "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.".
- catalog contributor b12810045.
- catalog created "c2003.".
- catalog date "2003".
- catalog date "c2003.".
- catalog dateCopyrighted "c2003.".
- catalog 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.".
- catalog description "Includes bibliographical references (p. [177]-184) and index.".
- catalog description "Preface -- 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.".
- catalog extent "x, 187 p. :".
- catalog hasFormat "Also available in an electronic version.".
- catalog identifier "3540004025 (softcover : alk. paper)".
- catalog isFormatOf "Also available in an electronic version.".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1805.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1805".
- catalog issued "2003".
- catalog issued "c2003.".
- catalog language "eng".
- catalog publisher "Berlin ; New York : Springer,".
- catalog relation "Also available in an electronic version.".
- catalog subject "510 s 516.3/62 21".
- catalog subject "Computer vision.".
- catalog subject "Curves on surfaces.".
- catalog subject "Differential equations, Parabolic Numerical solutions.".
- catalog subject "Differential equations, partial.".
- catalog subject "Global differential geometry.".
- catalog subject "Image processing.".
- catalog subject "Mathematics.".
- catalog subject "QA3 .L28 no. 1805 QA643".
- catalog tableOfContents "Preface -- 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.".
- catalog title "Geometric curve evolution and image processing / Frédéric Cao.".
- catalog type "Computer network resources. local".
- catalog type "Electronic books. lcsh".
- catalog type "text".