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024 7 $a10.1007/b10404
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035   $a(DE-He213)978-3-540-36392-7
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100   $a20121227d2003      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aGeometric Curve Evolution and Image Processing$b[electronic resource] /$fby Frédéric Cao
205   $a1st ed. 2003.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2003.
215   $a1 online resource (X, 194 p.) 
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1805
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-00402-5 
327   $aPreface -- 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.
330   $aIn image processing, "motions by curvature" provide an efficient way to smooth curves representing the boundaries of objects. In such a motion, each point of the curve moves, at any instant, with a normal velocity equal to a function of the curvature at this point. This book is a rigorous and self-contained exposition of the techniques of "motion by curvature". The approach is axiomatic and formulated in terms of geometric invariance with respect to the position of the observer. This is translated into mathematical terms, and the author develops the approach of Olver, Sapiro and Tannenbaum, which classifies all curve evolution equations. He then draws a complete parallel with another axiomatic approach using level-set methods: this leads to generalized curvature motions. Finally, novel, and very accurate, numerical schemes are proposed allowing one to compute the solution of highly degenerate evolution equations in a completely invariant way. The convergence of this scheme is also proved.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1805
606   $aPartial differential equations
606   $aOptical data processing
606   $aDifferential geometry
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aImage Processing and Computer Vision$3https://scigraph.springernature.com/ontologies/product-market-codes/I22021
606   $aDifferential Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M21022
615  0$aPartial differential equations.
615  0$aOptical data processing.
615  0$aDifferential geometry.
615 14$aPartial Differential Equations.
615 24$aImage Processing and Computer Vision.
615 24$aDifferential Geometry.
676   $a516.3/62
676   $a510 s
700   $aCao$b Frédéric$4aut$4http://id.loc.gov/vocabulary/relators/aut$067451
906   $aBOOK
912   $a996466594003316
996   $aGeometric curve evolution and image processing$9145369
997   $aUNISA