000 | 03384nam a22005055i 4500 | ||
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001 | 978-3-540-36392-7 | ||
003 | DE-He213 | ||
005 | 20190213151245.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s2003 gw | s |||| 0|eng d | ||
020 |
_a9783540363927 _9978-3-540-36392-7 |
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024 | 7 |
_a10.1007/b10404 _2doi |
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050 | 4 | _aQA370-380 | |
072 | 7 |
_aPBKJ _2bicssc |
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072 | 7 |
_aMAT007000 _2bisacsh |
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072 | 7 |
_aPBKJ _2thema |
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082 | 0 | 4 |
_a515.353 _223 |
100 | 1 |
_aCao, Frédéric. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aGeometric Curve Evolution and Image Processing _h[electronic resource] / _cby Frédéric Cao. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2003. |
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300 |
_aX, 194 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1805 |
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505 | 0 | _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. | |
520 | _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. | ||
650 | 0 | _aDifferential equations, partial. | |
650 | 0 | _aComputer vision. | |
650 | 0 | _aGlobal differential geometry. | |
650 | 1 | 4 |
_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155 |
650 | 2 | 4 |
_aImage Processing and Computer Vision. _0http://scigraph.springernature.com/things/product-market-codes/I22021 |
650 | 2 | 4 |
_aDifferential Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M21022 |
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783540004028 |
776 | 0 | 8 |
_iPrinted edition: _z9783662203408 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1805 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/b10404 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c10052 _d10052 |