Partial differential equations and image smoothing
V. Caselles; B. Coll; J.-M. Morel
Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996)
- page 1-30
Access Full Article
topHow to cite
topCaselles, V., Coll, B., and Morel, J.-M.. "Partial differential equations and image smoothing." Séminaire Équations aux dérivées partielles (Polytechnique) (1995-1996): 1-30. <http://eudml.org/doc/112133>.
@article{Caselles1995-1996,
author = {Caselles, V., Coll, B., Morel, J.-M.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {mean curvature motion; Osher-Sethian equation; local image smoothing; singular points; degenerate partial differential equation},
language = {eng},
pages = {1-30},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Partial differential equations and image smoothing},
url = {http://eudml.org/doc/112133},
year = {1995-1996},
}
TY - JOUR
AU - Caselles, V.
AU - Coll, B.
AU - Morel, J.-M.
TI - Partial differential equations and image smoothing
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1995-1996
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 30
LA - eng
KW - mean curvature motion; Osher-Sethian equation; local image smoothing; singular points; degenerate partial differential equation
UR - http://eudml.org/doc/112133
ER -
References
top- [AGLM1] L. Alvarez, F. Guichard, P.L. Lions and J.M. Morel, Axioms and fundamental equations of image processing Report 9216, 1992 CEREMADE. Université Paris Dauphine. Arch. for Rat. Mech. 16, IX, 200-257, 1993 Zbl0788.68153MR1225209
- [AMI] L. Alvarez and J.M. Morel.Formalization and Computational Aspects of Image Analysis, Acta Numerica, 1994, Cambridge University Press. Zbl0933.68143MR1288095
- [AM] L. Alvarez and Freya Morales.Affine Morphological Multiscale Analysis of Corners and Multiple Junctions. Ref 9402, August 1994, Dept. Informatica y Systemas, Universidad de Las Palmas de Gran Canaria. To appear in International Journal of Computer Vision.
- [BMO] B. Merriman, J. Bence and S. Osher, Motion of multiple junctions: a level set approach, CAM Report 93-19. Depart. of Mathematics. University of California, Los Angeles CA, June 1993. Zbl0805.65090MR1277282
- [CCCD] V. Caselles, F. Catté, T. Coll and F. Dibos.A geometric model for active contours in image processing. Numerische Mathematik, 66, 1-31, 1993. Zbl0804.68159MR1240700
- [CCM] V. Caselles, T. Coll and J.M. Morel.A Kanizsa programme, preprint, Ceremade, 1995. Submitted to Int. Journal of Comp. Vision.
- [CGG] Y.G. Chen, Y. Giga and S. Goto.Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Diff. Geometry, 33, 749-786, 1991. Zbl0696.35087MR1100211
- [CIL] M.G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equation, Bull. Amer. Math. Soc., 27,1-67,1992. Zbl0755.35015MR1118699
- [ES] L.C. Evans and J. Spruck.Motion of level sets by mean curvature. J. Differential Geom., (33): 635-681, 1991. Zbl0726.53029MR1100206
- [F] W. Fuchs.Experimentelle Untersuchungen ueber das simultane Hintereinandersehen auf der selben Sehrichtung, Zeitschrift fuer Psychologie, 91, 154-253, 1923
- [GH] M. Gage and R.S. Hamilton, The heat equation shrinking convex plane curves, J. Differential Geometry23, 69-96, 1986. Zbl0621.53001MR840401
- [GGIS] Y. Giga, S. Goto, H. Ishii and M.M. Sato.Comparison principle and convexity preserving properties for singular degenerate parabolic equations on unbounded domains. Indiana Univ. Math. J., 40, 443-470, 1991. Zbl0836.35009MR1119185
- [Gr] M. Grayson, The heat equation shrinks embedded plane curves to round points, J. Differential Geometry26, 285-314, 1987. Zbl0667.53001MR906392
- [GM] F. Guichard and J.M. Morel.Image Iterative Smoothing and P.D.E.'s. To appear, Cambridge University Press.
- [Ka] G. KanizsaVedere e pensare, Il Mulino, Bologna, 1991.
- [KTZ] B.B. Kimia, A. Tannenbaum, and S.W. Zucker, On the evolution of curves via a function of curvature, 1: the classical case, J. of Math. Analysis and Applications163, No 2, 1992. Zbl0771.53003MR1145840
- [MS] J.M. Morel and S. Solimini.Variational methods in image processing, Birkhäuser, 1994. Zbl0827.68111
- [NM] M. Nitzberg and D. Mumford. "The 2.1 Sketch", in Proceedings of the Third International Conference on Computer Vision, Osaka1990.
- [OS] S. Osher and J. Sethian, Fronts propagating with curvature dependent speed: algorithms based on the Hamilton-Jacobi formulation, J. Comp. Physics79, 12-49, 1988. Zbl0659.65132MR965860
- [ST1] G. Sapiro and A. Tannenbaum.On affine plane curve evolution. Journal of Functional Analysis, 119, 1, 79-120, 1994. Zbl0801.53008MR1255274
- [Wi] A.P. Witkin.Scale-space filtering. Proc. of IJCAI, Karlsruhe1983, 1019-1021.
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.