# Approximation of viscosity solution by morphological filters

ESAIM: Control, Optimisation and Calculus of Variations (1999)

- Volume: 4, page 335-359
- ISSN: 1292-8119

## Access Full Article

top## How to cite

topPasquignon, Denis. "Approximation of viscosity solution by morphological filters." ESAIM: Control, Optimisation and Calculus of Variations 4 (1999): 335-359. <http://eudml.org/doc/90543>.

@article{Pasquignon1999,

author = {Pasquignon, Denis},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {morphological filters; viscosity solution; inf-sup scheme; curvature equation; Matheron operators},

language = {eng},

pages = {335-359},

publisher = {EDP Sciences},

title = {Approximation of viscosity solution by morphological filters},

url = {http://eudml.org/doc/90543},

volume = {4},

year = {1999},

}

TY - JOUR

AU - Pasquignon, Denis

TI - Approximation of viscosity solution by morphological filters

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 1999

PB - EDP Sciences

VL - 4

SP - 335

EP - 359

LA - eng

KW - morphological filters; viscosity solution; inf-sup scheme; curvature equation; Matheron operators

UR - http://eudml.org/doc/90543

ER -

## References

top- [1] L. Alvarez, F. Guichard, P.-L. Lions and J.-M. Morel, Axioms and fundamental equations of image processing. Arch. Rational Mech. 123 ( 1993) 199-257. Zbl0788.68153MR1225209
- [2] G. Barles and P.M. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis 4 ( 1991) 271-283. Zbl0729.65077MR1115933
- [3] F. Cao, Partial Differential Equations and Mathematical Morphology. J. Math. Pures Appl. 77 ( 1998) 909-941. Zbl0920.35040MR1656780
- [4] F. Catte, F. Dibos and G. Koepfler, A Morphological Scheme for Mean Curvature Motion. SIAM J. Numer. Anal. ( 1995) SINUM 32.6. Zbl0841.68124MR1360464
- [5] Y.-G. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations. J. Differential Geom. 33 ( 1991) 749-786 Zbl0696.35087MR1100211
- [6] M. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solution of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.) 27 ( 1992) 1-67. Zbl0755.35015MR1118699
- [7] L.C. Evans and J. Spruck, Motion of level sets by mean curvature I. J. Differential Geom. 33 ( 1991) 635-681. Zbl0726.53029MR1100206
- [8] F. Guichard and J.M. Morel, Partial Differential Equation and image iterative filtering. Tutorial of ICIP 95, Washington D.C. ( 1995).
- [9] H. Ishii and P. Souganidis, Generalized Motion of noncompact hypersurfaces with velocity having arbitrary growth on the curvature tensor. Tohoku Math. J. 47 ( 1995) 227-250. Zbl0837.35066MR1329522
- [10] J.J. Koenderink, The structure of images. Biol. Cybern. 50 ( 1984) 363-370. Zbl0537.92011MR758126
- [11] B.B. Kimia, A. Tannenbaum and S.W. Zucker, Shapes, shocks and deformations. Internat. J. Comput. Vision ( 1994).
- [12] G. Matheron, Random sets and Integral Geometry (John Wiley N.Y., 1975). Zbl0321.60009MR385969
- [13] Pasquignon D., Computation of skeleton by PDE. IEEE-ICIP, Washington D.C. ( 1995).
- [14] J. Serra, Image Analysis and Mathematical Morphology. Vol. 2, Theoretical Advances, Serra Ed. (London Academic Press, 1988). Zbl0565.92001MR949918
- [15] A.P. Witkin, Scale space filtering, in Proc. of IJCAI, Karlsruhe ( 1983) 1019-1021.