000 03384nam a22005055i 4500
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
024 7 _a10.1007/b10404
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
072 7 _aPBKJ
_2thema
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.
300 _aX, 194 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1805
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