Approximation of viscosity solution by morphological filters
ESAIM: Control, Optimisation and Calculus of Variations, Volume 4  (1999), p. 335-359
@article{COCV_1999__4__335_0,
author = {Pasquignon, Denis},
title = {Approximation of viscosity solution by morphological filters},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {4},
year = {1999},
pages = {335-359},
zbl = {0929.65063},
mrnumber = {1693049},
language = {en},
url = {http://www.numdam.org/item/COCV_1999__4__335_0}
}

Pasquignon, Denis. Approximation of viscosity solution by morphological filters. ESAIM: Control, Optimisation and Calculus of Variations, Volume 4 (1999) , pp. 335-359. http://www.numdam.org/item/COCV_1999__4__335_0/

[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. | MR 1225209 | Zbl 0788.68153

[2] G. Barles and P.M. Souganidis, Convergence of approximation schemes for fully nonlinear second order equations. Asymptotic Analysis 4 ( 1991) 271-283. | MR 1115933 | Zbl 0729.65077

[3] F. Cao, Partial Differential Equations and Mathematical Morphology. J. Math. Pures Appl. 77 ( 1998) 909-941. | MR 1656780 | Zbl 0920.35040

[4] F. Catte, F. Dibos and G. Koepfler, A Morphological Scheme for Mean Curvature Motion. SIAM J. Numer. Anal. ( 1995) SINUM 32.6. | MR 1360464 | Zbl 0841.68124

[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 | MR 1100211 | Zbl 0696.35087

[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. | MR 1118699 | Zbl 0755.35015

[7] L.C. Evans and J. Spruck, Motion of level sets by mean curvature I. J. Differential Geom. 33 ( 1991) 635-681. | MR 1100206 | Zbl 0726.53029

[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. | MR 1329522 | Zbl 0837.35066

[10] J.J. Koenderink, The structure of images. Biol. Cybern. 50 ( 1984) 363-370. | MR 758126 | Zbl 0537.92011

[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). | MR 385969 | Zbl 0321.60009

[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). | MR 949918 | Zbl 0565.92001

[15] A.P. Witkin, Scale space filtering, in Proc. of IJCAI, Karlsruhe ( 1983) 1019-1021.