L. Alvarez and L. Mazorra, Signal and Image Restoration Using Shock Filters and Anisotropic Diffusion, SIAM Journal on Numerical Analysis, vol.31, issue.2, pp.590-605, 1994.
DOI : 10.1137/0731032

A. Baudes, B. Coll, and J. Morel, A Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.490-530, 2005.
DOI : 10.1137/040616024

C. Boncelet, Image noise models Handbook of image and video processing, pp.325-335, 2000.

A. Buades, B. Coll, and J. M. Morel, A Review of Image Denoising Algorithms, with a New One, Multiscale Modeling & Simulation, vol.4, issue.2, pp.490-530, 2005.
DOI : 10.1137/040616024
URL : https://hal.archives-ouvertes.fr/hal-00271141

R. Chan, H. Chung-wa, and M. Nikolova, Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization, IEEE Transactions on Image Processing, vol.14, issue.10, pp.1479-1485, 2005.
DOI : 10.1109/TIP.2005.852196

P. Chatterjee and P. Milanfar, Is Denoising Dead?, IEEE Transactions on Image Processing, vol.19, issue.4, pp.895-911, 2010.
DOI : 10.1109/TIP.2009.2037087

E. Diop and J. Angulo, Spatially adaptive PDEs for robust image sharpening, 2012 19th IEEE International Conference on Image Processing, pp.949-952, 2012.
DOI : 10.1109/ICIP.2012.6467018
URL : https://hal.archives-ouvertes.fr/hal-00834439

J. Elder and S. Zucker, Local scale control for edge detection and blur estimation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.7, pp.699-716, 1998.
DOI : 10.1109/34.689301

G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove et al., A Compendium of Continuous Lattices, 1980.
DOI : 10.1007/978-3-642-67678-9

G. Gilboa, N. Sochen, and Y. Zeevi, Image enhancement and denoising by complex diffusion processes, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.26, issue.8, pp.1020-1034, 2004.
DOI : 10.1109/TPAMI.2004.47

G. Gilboa, N. A. Sochen, and Y. Y. Zeevi, Regularized Shock Filters and Complex Diffusion, Proceeding of the 7th European Conference on Computer Vision-Part I, ECCV '02, pp.399-413, 2002.
DOI : 10.1007/3-540-47969-4_27

R. Gonzalez and R. Woods, Digital image processing, 2008.

J. Gower and G. Ross, Minimum Spanning Trees and Single Linkage Cluster Analysis, Applied Statistics, vol.18, issue.1, pp.54-64, 1969.
DOI : 10.2307/2346439

J. Grazzini and P. Soille, Edge-preserving smoothing using a similarity measure in adaptive geodesic neighbourhoods, Pattern Recognition, vol.42, issue.10, pp.2306-2316, 2009.
DOI : 10.1016/j.patcog.2008.11.004

H. J. Heijmans, Composing morphological filters, IEEE Transactions on Image Processing, vol.6, issue.5, pp.713-724, 1997.
DOI : 10.1109/83.568928

H. J. Heijmans, P. Nacken, A. Toet, and L. Vincent, Graph morphology, Journal of Visual Communication and Image Representation, vol.3, issue.1, pp.24-38, 1992.
DOI : 10.1016/1047-3203(92)90028-R

H. J. Heijmans and C. Ronse, The algebraic basis of mathematical morphology I. Dilations and erosions, Computer Vision, Graphics, and Image Processing, vol.50, issue.3, pp.245-295, 1990.
DOI : 10.1016/0734-189X(90)90148-O

H. Hwang and R. A. Haddad, Adaptive median filters: new algorithms and results, IEEE Transactions on Image Processing, vol.4, issue.4, pp.499-502, 1995.
DOI : 10.1109/83.370679

T. Jochems, Morphologie mathématique appliquée au contrôle industriel depì eces coulées, 1997.

R. Keshet and H. J. Heijmans, Adjunctions in pyramids, curve evolution and scalespaces, International Journal of Computer Vision, vol.52, pp.139-151, 2003.

H. P. Kramer and J. B. Bruckner, Iterations of a non-linear transformation for enhancement of digital images, Pattern Recognition, vol.7, issue.1-2, pp.53-58, 1975.
DOI : 10.1016/0031-3203(75)90013-8

R. Lukac, B. Smolka, K. Martin, K. Plataniotis, and A. Venetsanopoulos, Vector filtering for color imaging, IEEE Signal Processing Magazine, vol.22, issue.1, pp.74-86, 2005.
DOI : 10.1109/MSP.2005.1407717

S. Mallat, A wavelet tour of signal processing, 2008.

P. Maragos, Lattice Image Processing: A Unification of Morphological and Fuzzy Algebraic Systems, Journal of Mathematical Imaging and Vision, vol.8, issue.3, pp.333-353, 2005.
DOI : 10.1007/s10851-005-4897-z

F. Meyer, The levelings, Proc. of the ISMM'98, pp.199-206, 1998.

F. Meyer and J. Serra, Contrasts and activity lattice, Signal Processing, vol.16, issue.4, pp.303-3170165, 1989.
DOI : 10.1016/0165-1684(89)90028-5

G. Motta, E. Ordentlich, I. Ramírez, G. Seroussi, and M. J. Weinberger, The iDUDE Framework for Grayscale Image Denoising, IEEE Transactions on Image Processing, vol.20, issue.1, pp.1-21, 2011.
DOI : 10.1109/TIP.2010.2053939

S. Osher and L. Rudin, Feature-Oriented Image Enhancement Using Shock Filters, SIAM Journal on Numerical Analysis, vol.27, issue.4, pp.919-940, 1990.
DOI : 10.1137/0727053

S. Osher and L. Rudin, Shocks and other nonlinear filtering applied to image processing, Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, pp.414-431, 1991.

J. F. Rivest, P. Soille, and S. Beucher, Morphological gradients, Nonlinear Image Processing III, pp.326-336, 1993.
DOI : 10.1117/12.58373

J. B. Roerdink, Adaptivity and group invariance in mathematical morphology, 2009 16th IEEE International Conference on Image Processing (ICIP), pp.2253-22565413983, 2009.
DOI : 10.1109/ICIP.2009.5413983

J. Schavemaker, M. J. Reinders, J. J. Gerbrands, and E. Backer, Image sharpening by morphological filtering, Pattern Recognition, vol.33, issue.6, pp.997-1012, 2000.
DOI : 10.1016/S0031-3203(99)00160-0

J. Serra, Toggle mappings In: From Pixels to Features, pp.61-72, 1989.

J. Serra and L. Vincent, An overview of morphological filtering, Circuits Systems and Signal Processing, vol.34, issue.No. 4, pp.47-108, 1992.
DOI : 10.1007/BF01189221

P. Soille, Beyond self-duality in morphological image analysis, Image and Vision Computing, vol.23, issue.2, pp.249-257, 2005.
DOI : 10.1016/j.imavis.2004.06.002

P. Soille, Constrained connectivity for hierarchical image partitioning and simplification, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.30, issue.7, pp.1132-1145, 2008.
DOI : 10.1109/TPAMI.2007.70817

P. Soille, Constrained connectivity for the processing of very-high-resolution satellite images, International Journal of Remote Sensing, vol.31, issue.22, pp.5879-5893, 2010.
DOI : 10.1109/TGRS.2002.804618

P. Soille, Preventing Chaining through Transitions While Favouring It within Homogeneous Regions, Lecture Notes in Computer Science, vol.6671, pp.96-107, 2011.
DOI : 10.1007/978-3-642-21569-8_9

P. Soille and J. Grazzini, Constrained Connectivity and Transition Regions, Proc. of the ISMM'09, pp.59-69, 2009.
DOI : 10.1016/j.patcog.2008.11.004
URL : https://commerce.metapress.com/content/g6h8mk8447041532/resource-secured/?target=fulltext.pdf&sid=iiot13nznlhqylrqczxwal55&sh=www.springerlink.com

K. Srinivasan and D. Ebenezer, A New Fast and Efficient Decision-Based Algorithm for Removal of High-Density Impulse Noises, IEEE Signal Processing Letters, vol.14, issue.3, pp.189-192, 2007.
DOI : 10.1109/LSP.2006.884018

A. Taguchi and T. Matsumoto, <title>Removal of impulse noise from highly corrupted images by using noise position information and directional information of image</title>, Nonlinear Image Processing and Pattern Analysis XII, pp.188-196, 2001.
DOI : 10.1117/12.424974

H. Takeda, S. Farsiu, and P. Milanfar, Robust Kernel Regression for Restoration and Reconstruction of Images from Sparse Noisy Data, 2006 International Conference on Image Processing, pp.1257-1260, 2006.
DOI : 10.1109/ICIP.2006.312573

H. Takeda, S. Farsiu, and P. Milanfar, Kernel Regression for Image Processing and Reconstruction, IEEE Transactions on Image Processing, vol.16, issue.2, pp.349-366, 2007.
DOI : 10.1109/TIP.2006.888330

C. Tomasi and R. Manduchi, Bilateral filtering for gray and color images, Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), pp.839-846, 1998.
DOI : 10.1109/ICCV.1998.710815

S. Velasco-forero and J. Angulo, Supervised Ordering in <formula formulatype="inline"> <tex Notation="TeX">${\rm I}\!{\rm R}^p$</tex></formula>: Application to Morphological Processing of Hyperspectral Images, IEEE Transactions on Image Processing, vol.20, issue.11, pp.3301-3308, 2011.
DOI : 10.1109/TIP.2011.2144611

S. Velasco-forero and J. Angulo, Random Projection Depth for Multivariate Mathematical Morphology, IEEE Journal of Selected Topics in Signal Processing, vol.6, issue.7, pp.753-763, 2012.
DOI : 10.1109/JSTSP.2012.2211336
URL : https://hal.archives-ouvertes.fr/hal-00751347

L. Van-vliet, I. Young, and G. Beckers, A nonlinear laplace operator as edge detector in noisy images, Computer Vision, Graphics, and Image Processing, vol.45, issue.2, pp.167-195, 1989.
DOI : 10.1016/0734-189X(89)90131-X

Z. Wang and D. Zhang, Progressive switching median filter for the removal of impulse noise from highly corrupted images, IEEE Trans. Circuits and Systems II: Analog and Digital Signal Processing, vol.46, issue.1, pp.78-80, 1999.

J. Weickert, Coherence-Enhancing Shock Filters, In: Lecture Notes in Computer Science, pp.1-8, 2003.
DOI : 10.1007/978-3-540-45243-0_1

M. Welk, J. Weickert, and I. Gal´cgal´c, Theoretical foundations for spatially discrete 1-D shock filtering, Image and Vision Computing, vol.25, issue.4, pp.455-463, 2007.
DOI : 10.1016/j.imavis.2006.06.001

H. Xu, G. Zhu, H. Peng, and D. Wang, Adaptive fuzzy switching filter for images corrupted by impulse noise, Pattern Recognition Letters, vol.25, issue.15, pp.1657-1663, 2004.
DOI : 10.1016/j.patrec.2004.05.025

S. Zhang and M. Karim, A new impulse detector for switching median filters, IEEE Signal Processing Letters, vol.9, issue.11, pp.360-363, 2002.
DOI : 10.1109/LSP.2002.805310