). Fas and . Fo, 4 (f ) (j) FAS. FO f 5,7 (f ) (k) FAS. FO f 5, ) (l) S(FAS. FO f 5,4 (f )) (m) S(FAS. FO f 5,7 (f )) (n) S(FAS. FO f 5, p.10

@. J. Debayle and J. Pinoli, General Adaptive Neighborhood Image Processing, Journal of Mathematical Imaging and Vision, vol.13, issue.6, 2005.
DOI : 10.1007/s10851-006-7452-7

URL : https://hal.archives-ouvertes.fr/hal-00128123

. Catte, Scale-space par diffusion anisotrope régularisée, p.38, 1992.

. Alvarez, Scale-space par diffusion anisotrope généralisée, p.38, 1992.

L. Alvarez, P. L. Lions, and J. M. Morel, Image selective smoothing and edge detection by nonlimear diffusion : (ii), SIAM Journal of Applied Mathematics, vol.29, issue.38, pp.845-866, 1992.
DOI : 10.1137/0729052

M. Amattouch, Théorie de la mesure appliquée à l'analyse d'image. Master's thesis, p.119, 2005.

J. P. Antoine, P. Carrette, R. Murenzi, and B. Piette, Image analysis with two-dimensional continuous wavelet transform, Signal Processing, vol.31, issue.3, pp.241-272, 1993.
DOI : 10.1016/0165-1684(93)90085-O

R. Ash and C. Doleans-dade, Probability and measure theory, p.116, 2000.

B. R. Bakshi, Multiscale analysis and modeling using wavelets, Journal of Chemometrics, vol.38, issue.3-4, pp.415-434, 1999.
DOI : 10.1002/(SICI)1099-128X(199905/08)13:3/4<415::AID-CEM544>3.0.CO;2-8

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.38.5404

J. A. Bangham, P. Chardaire, C. J. Pye, L. , and P. D. , Multiscale nonlinear decomposition: the sieve decomposition theorem, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.5, pp.529-539, 1996.
DOI : 10.1109/34.494642

J. A. Bangham, P. Ling, Y. , and R. , Multiscale recursive medians, scale-space, and transforms with applications to image processing, IEEE Transactions on Image Processing, vol.5, issue.6, pp.1043-1048, 1996.
DOI : 10.1109/83.503918

J. A. Bangham, P. D. Ling, H. , and R. , Scale-space from nonlinear filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.5, pp.520-528, 1996.
DOI : 10.1109/34.494641

Z. Belmandt, Manuel de prétopologie et ses applications, p.187, 1993.

P. Bertolino, Contributions des pyramides irrégulières en segmentation d'images multirésolution, pp.29-191, 1995.

P. Bertolino and A. Montanvert, Multiresolution segmentation using the irregular pyramid, Proceedings of 3rd IEEE International Conference on Image Processing, pp.257-260, 1996.
DOI : 10.1109/ICIP.1996.559482

S. Beucher, Segmentation d'images et morphologie mathématique, p.44, 1990.

S. Beucher and C. Lantuejoul, Use of watersheds in contour detection In International Workshop on image processing, real-time edge and motion detection/estimation, 1979.

A. Cech, Topological Spaces, p.187, 1966.

M. Charif-chefchaouni and D. Schonfeld, Spatially-variant mathematical morphology, Proceedings of 1st International Conference on Image Processing, pp.555-559, 1994.
DOI : 10.1109/ICIP.1994.413632

J. M. Chassery and A. Montanvert, Géométrie discrète en analyse d'images. Hermès, p.28, 1991.

L. Chazallon and J. C. Pinoli, An Automatic Morphological Method for Aluminium Grain Segmentation in Complex Grey Level Images, Acta Stereologica, vol.16, issue.2, pp.119-130, 1997.

F. Cheng and A. N. Venetsanopoulos, Adaptive morphological operators, fast algorithms and their applications, Pattern Recognition, vol.33, issue.6, pp.917-933, 2000.
DOI : 10.1016/S0031-3203(99)00155-7

G. Choquet, Theory of capacities. Annales de l'Institut Fourier, pp.131-295, 1953.

G. Choquet, Topology, 1966.

G. Choquet, Cours de topologie, chapter Espaces topologiques et espaces métriques, Dunod, vol.76, pp.45-51, 2000.

C. K. Chui, Wavelet analysis and its applications An introduction to wavelets, 1992.

C. K. Chui, Wavelet analysis and its applications Wavelets -A tutorial in theory and applications, 1992.

C. K. Chui and J. Lian, A study of orthonormal multi-wavelets, Applied Numerical Mathematics, vol.20, issue.3, pp.273-298, 1996.
DOI : 10.1016/0168-9274(95)00111-5

M. Ciuc, R. M. Rangayyan, T. Zaharia, and V. Buzuloiu, Filtering noise in color images using adaptive-neighborhood statistics, Journal of Electronic Imaging, vol.9, issue.4, pp.484-494, 2000.
DOI : 10.1117/1.1289772

J. P. Cocquerez and S. Philipp, Analyse d'images : Filtrage et segmentation, p.40, 1995.
URL : https://hal.archives-ouvertes.fr/hal-00706168

A. Cohen, I. Daubechies, and J. Feauveau, Biorthogonal bases of compactly supported wavelets, Communications on Pure and Applied Mathematics, vol.10, issue.5, pp.485-560, 1992.
DOI : 10.1002/cpa.3160450502

R. Coifman and Y. Meyer, Remarque sur l'analyse de Fourier à fenêtres, Comptes Rendus de l'Académie des Sciences, pp.259-261, 1991.

T. N. Cornsweet, Visual Perception, 1970.

M. Coster and J. L. Chermant, Précis d'analyse d'image. Hermès, p.129, 1985.

G. Cottet and L. Germain, Image processing through reaction combined with non-linear diffusion, Mathematics of Computation, issue.204, pp.61659-673, 1993.

R. Bibliographiques-coulibaly and M. , Analyse par ondelettes : quelques aspects numériques et applications à des signaux océaniques simulés et à l'estimation de densité de probabilité, p.32, 1992.

J. Crespo, J. Serra, and R. W. Schafer, Theoretical aspects of morphological filters by reconstruction, Signal Processing, vol.47, issue.2, pp.201-225, 1995.
DOI : 10.1016/0165-1684(95)00108-5

O. Cuisenaire, Locally adaptable mathematical morphology, IEEE International Conference on Image Processing 2005, pp.125-128, 2005.
DOI : 10.1109/ICIP.2005.1530007

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.505.4910

J. C. Dainty and R. Shaw, Image Science, p.45, 1974.

I. Daubechies, Orthonormal bases of compactly supported wavelets, Commun. Pure Appl. Math, vol.31, pp.901-996, 1988.

I. Daubechies, Ten Lectures on Wavelets, SIAM. Notes for the CBMS Conference, pp.31-32, 1992.

J. Debayle and J. C. Pinoli, Adaptive-Neighborhood Mathematical Morphology and its Applications to Image Filtering and Segmentation, 9th European Congress on Stereology and Image Analysis, pp.10-13, 2005.

J. Debayle and J. C. Pinoli, General Adaptive Neighborhood Image Processing:, Journal of Mathematical Imaging and Vision, vol.13, issue.6, p.185, 2005.
DOI : 10.1007/s10851-006-7451-8

URL : https://hal.archives-ouvertes.fr/hal-00128123

J. Debayle and J. C. Pinoli, General Adaptive Neighborhood Image Processing, Journal of Mathematical Imaging and Vision, vol.13, issue.6, p.185, 2005.
DOI : 10.1007/s10851-006-7452-7

URL : https://hal.archives-ouvertes.fr/hal-00128123

J. Debayle and J. C. Pinoli, Multiscale image filtering and segmentation by means of adaptive neighborhood mathematical morphology, IEEE International Conference on Image Processing 2005, pp.537-540, 2005.
DOI : 10.1109/ICIP.2005.1530447

J. Debayle and J. C. Pinoli, SPATIALLY ADAPTIVE MORPHOLOGICAL IMAGE FILTERING USING INTRINSIC STRUCTURING ELEMENTS, Image Analysis & Stereology, vol.23, issue.3, pp.145-158, 2005.
DOI : 10.5566/ias.v24.p145-158

URL : https://doaj.org/article/f8aeac3aab904e5e8deee587700fca16

B. Delaunay, Sur la sphère vide. Izvestia Akademia Nauk SSSR, VII Seria, Otdelenie Matematicheskii i Estestvennyka Nauk, vol.7, pp.793-800, 1934.

G. Deng and L. W. Cahill, Multiscale image enhancement using the logarithmic image processing model, Electronics Letters, vol.29, issue.9, pp.803-804, 1993.
DOI : 10.1049/el:19930536

G. Deng, L. W. Cahill, T. , and J. R. , The study of logarithmic image processing model and its application to image enhancement, IEEE Transactions on Image Processing, vol.4, issue.4, pp.506-512, 1995.
DOI : 10.1109/83.370681

G. Deng and J. C. Pinoli, Differentiation-Based Detection Using the Logarithmic Image Processing Model, Journal of Mathematical Imaging and Vision, vol.8, issue.2, pp.161-180, 1998.
DOI : 10.1023/A:1008277328822

G. Deng, J. C. Pinoli, W. Y. Ng, L. W. Cahill, and M. Jourlin, A comparative study of the Log-ratio image processing approach and the logarithmic image processing model, p.57, 1994.

A. Dias and R. M. Rangayyan, Adaptive region-based filtering of multiplicative noise, Nonlinear Image Processing VIII, volume 3026 of Proc. SPIE, pp.338-348, 1997.

J. Dieudonné, Pour l'honneur de l'esprit humain, Hachette, issue.11, 1987.

N. Dunford and J. T. Schwartz, Linear Operators, Part I, General Theory, p.57, 1988.

G. Eichmann, C. Lu, J. Zhu, L. , and Y. , Pyramidal Image Processing using Morphology, Proceedings of The SPIE Applications of Digital Image Processing XI, pp.30-37, 1988.

S. Fejes and F. Vajda, An Efficient Implementation Technique of Adaptive Morphological Operations, Mathematical Morphology and its Applications to Image Processing. Proceedings of The International Society for Mathematical Morphoogy of Computational Imaging and Vision, p.42, 1994.
DOI : 10.1007/978-94-011-1040-2_35

S. Fejes and F. Vajda, Simplified adaptive approach to efficient morphological image analysis, Proceedings of the 12th IAPR International Conference on Pattern Recognition (Cat. No.94CH3440-5), pp.257-261, 1994.
DOI : 10.1109/ICPR.1994.577172

L. M. Florack and A. Ku?per, The Topological Structure of Scale-Space Images, Journal of Mathematical Imaging and Vision, vol.12, issue.1, pp.65-79, 2000.
DOI : 10.1023/A:1008304909717

L. M. Florack, A. H. Salden, B. M. Romeny, J. J. Koenderink, and M. A. Viergever, Nonlinear scale-space, Image and Vision Computing, vol.13, issue.4, pp.279-294, 1995.
DOI : 10.1016/0262-8856(95)99716-E

G. Flouzat, O. Amram, F. Laporterie, C. , and S. , Multiresolution analysis and reconstruction by a morphological pyramid in the remote sensing of terrestrial surfaces, Signal Processing, vol.81, issue.10, pp.812171-2185, 2001.
DOI : 10.1016/S0165-1684(01)00114-1

D. Gabor, Theory of communication, Journal of the Institution of Electrical Engineers - Part I: General, vol.94, issue.73, pp.429-457, 1946.
DOI : 10.1049/ji-1.1947.0015

R. C. Gonzalez and R. C. Woods, Digital Image Processing, p.40, 1992.

R. Gordon and R. M. Rangayyan, Feature enhancement of film mammograms using fixed and adaptive neighborhoods, Applied Optics, vol.23, issue.4, pp.560-564, 1984.
DOI : 10.1364/AO.23.000560

R. Bibliographiques-goupillaud, P. Grossmann, A. Morlet, and J. , Cycle-octave and related transforms in seismic signal analysis, Geoexploration, vol.23, issue.1, pp.85-102, 1984.
DOI : 10.1016/0016-7142(84)90025-5

J. Goutsias and H. J. He?mans, Nonlinear multiresolution signal decomposition schemes. I. Morphological pyramids, IEEE Transactions on Image Processing, vol.9, issue.11, pp.1862-1876, 2000.
DOI : 10.1109/83.877209

M. Grabisch, Fuzzy integrals as a generalized class of order filters, Proceedings of European Symposium on Satellite Remote Sensing, p.117, 1994.

D. J. Granrath, The role of human visual models in image processing, Proceedings of the IEEE, pp.552-561, 1981.
DOI : 10.1109/PROC.1981.12024

P. Gremillet, M. Jourlin, and J. C. Pinoli, LIP-model-based three-dimensional reconstruction and visualization of HIV-infected entire cells, Journal of Microscopy, vol.60, issue.1, pp.31-38, 1994.
DOI : 10.1111/j.1365-2818.1994.tb04321.x

M. Grimaud, La géodésie numérique en morphologie mathématique Application à la détection automatique de microcalcifications en mammographie numérique, p.44, 1991.

A. Grossman and J. Morlet, Decomposition of Hardy Functions into Square Integrable Wavelets of Constant Shape, SIAM Journal on Mathematical Analysis, vol.15, issue.4, pp.723-736, 1984.
DOI : 10.1137/0515056

J. E. Hafstrom, Introduction to Analysis and Abstract Algebra, W.B. Saunders, 1967.

P. Halmos, Measure Theory. D. van Nostrand and Co, p.116, 1950.

P. Hawkes, Image Algebra and Rank-Order Filters, Scanning Microscopy, vol.11, pp.479-482, 1997.

H. J. He?mans and R. V. Boomgaard, Algebraic Framework for Linear and Morphological Scale-Spaces, Journal of Visual Communication and Image Representation, vol.13, issue.1-2, pp.269-301, 2000.
DOI : 10.1006/jvci.2001.0480

H. J. He?mans and J. Goutsias, Morphological Pyramids and Wavelets Based on the Quincunx Lattice, Mathematical Morphology and Its Applications to Image and Signal Processing, pp.273-281, 2000.
DOI : 10.1007/0-306-47025-X_30

H. J. He?mans and J. Goutsias, Nonlinear multiresolution signal decomposition schemes. II. Morphological wavelets, IEEE Transactions on Image Processing, vol.9, issue.11, pp.1897-1913, 2000.
DOI : 10.1109/83.877211

C. L. Hendriks and L. J. Vliet, Morphological Scale-Space to Differentiate Microstructures of food products, Proceedings of The 6th Annual Conference of the Advanced School for Computing and Imaging, pp.289-293, 2000.

J. L. Horowitz and T. Pavlidis, Picture segmentation by a direct split-and-merge procedure, Proceedings of the 2nd ICPR, pp.424-433, 1974.

P. T. Jackway, Morphological scale-space The Hague, The Netherlands, Proceedings of The 11th IAPR International Conference on Pattern Recognition, p.35, 1992.

P. T. Jackway, Scale-Space Properties of the Multiscale Morphological Closing-Opening Filter, Proceedings of The 2nd Singapore International Conference on Image Processing, pp.278-281, 1992.

P. T. Jackway and M. Deriche, Scale-Space Properties of the Multiscale Morphological Dilatation-Erosion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.36, pp.33-51, 1996.

A. K. Jain, Advances in mathematical models for image processing, Proceedings of the IEEE, pp.502-528, 1981.
DOI : 10.1109/PROC.1981.12021

A. K. Jain, Fundamentals of Digital Image Processing, p.40, 1989.

J. M. Jolion, Analyse d'image : le modèle pyramidal, Traitement du Signal, vol.7, issue.1, pp.5-17, 1990.

J. M. Jolion and A. Montanvert, The adapted pyramid : a framework for 2d image analysis. Computer Vision Graphics and Image Processing, pp.339-348, 1992.

M. Jourlin and J. C. Pinoli, Logarithmic image processing, Acta Stereologica, vol.6, issue.46, pp.651-656, 1987.
DOI : 10.1016/S1076-5670(01)80095-1

URL : https://hal.archives-ouvertes.fr/hal-00986490

M. Jourlin and J. C. Pinoli, A model for logarithmic image processing, Journal of Microscopy, vol.60, issue.7, pp.21-35, 1988.
DOI : 10.1111/j.1365-2818.1988.tb04559.x

M. Jourlin and J. C. Pinoli, Image dynamic range enhancement and stabilization in the context of the logarithmic image processing model, Signal Processing, vol.41, issue.2, pp.225-237, 1995.
DOI : 10.1016/0165-1684(94)00102-6

M. Jourlin and J. C. Pinoli, Logarithmic image processing, Advances in Imaging and Electron Physics, pp.129-196, 2001.
DOI : 10.1016/S1076-5670(01)80095-1

URL : https://hal.archives-ouvertes.fr/hal-00986490

M. Jourlin, J. C. Pinoli, and R. Zeboudj, Contrast definition and contour detection for logarithmic images, Journal of Microscopy, vol.60, issue.1, pp.33-40, 1988.
DOI : 10.1111/j.1365-2818.1989.tb02904.x

L. Kantorovitch and G. Akilov, Analyse Fonctionnelle, Editions Mir, vol.47, p.55, 1981.

J. L. Kelley, General Topology. D. Van Nostrand, 1955.

M. D. Kelly, Edge detection in pictures by computer using planning, Machine Intelligence, pp.397-409, 1971.

V. Klee, On the complexity ofd- dimensional Voronoi diagrams, Archiv der Mathematik, vol.8, issue.1, pp.75-80, 1980.
DOI : 10.1007/BF01224932

J. J. Koenderink, The structure of images, Biological Cybernetics, vol.27, issue.269, pp.363-370, 1984.
DOI : 10.1007/BF00336961

K. Krissian, Traitement multi-échelle : applications à l'imagerie médicale et à la détection tridimensionnelle de vaisseaux, p.39, 2000.

W. G. Kropatsch and H. Macho, Finding the structure of connected components using dual irregular pyramids, Cinquième Colloque DGCI, pp.147-158, 1995.

P. Kyeong-ryeol and L. Chung-nim, Scale-space using mathematical morphology, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.11, pp.1121-1126, 1996.
DOI : 10.1109/34.544083

S. Lang, Linear Algebra, p.46, 1966.
DOI : 10.1007/978-1-4757-1949-9

C. Lantuéjoul and S. Beucher, Geodesic distance and image analysis, Mikroskopie, vol.37, pp.138-142, 1980.

C. Lantuéjoul and S. Beucher, On the use of the geodesic metric in image analysis, Journal of Microscopy, vol.121, issue.1, pp.39-49, 1981.
DOI : 10.1111/j.1365-2818.1981.tb01197.x

F. Laporterie, G. Flouzat, and O. Amram, The Morphological Pyramid and its Applications to Remote Sensing : Multiresolution Data Analysis and Features Extraction, Image Analysis and Stereology, vol.21, issue.1, pp.49-53, 2002.

L. Pennec, E. Mallat, and S. , Sparse geometric image representations with bandelets, IEEE Transactions on Image Processing, vol.14, issue.4, pp.423-438, 2004.
DOI : 10.1109/TIP.2005.843753

D. T. Lee and B. J. Schachter, Two algorithms for constructing a Delaunay triangulation, International Journal of Computer & Information Sciences, vol.134, issue.3, 1980.
DOI : 10.1007/BF00977785

J. S. Lee, Refined filtering of image noise using local statistics, Computer Graphics and Image Processing, vol.15, issue.4, pp.380-389, 1981.
DOI : 10.1016/S0146-664X(81)80018-4

J. S. Lee, A simple speckle smoothing algorithm for synthetic aperture radar images, IEEE Transactions on Systems, Man, and Cybernetics, vol.13, issue.1, pp.85-89, 1983.
DOI : 10.1109/TSMC.1983.6313036

Y. H. Lee and S. A. Kassam, Generalized median filtering and related nonlinear filtering techniques, IEEE Transaction on Acoustics, Speech and Signal Processing, vol.33, pp.673-683, 1985.

P. G. Lemarié, Ondelettes à localisation exponentielle, J. Math. Pures Appl, vol.67, issue.3, pp.227-236, 1988.

R. Lerallut, E. Decencière, M. , and F. , Image filtering using morphological amoebas, Proceedings of the 7th International Symposium on Mathematical Morphology, pp.13-22, 2005.
DOI : 10.1007/1-4020-3443-1_2

URL : https://hal.archives-ouvertes.fr/hal-01431825

J. S. Lim, Two-Dimensional Signal and Image Processing, 1990.

T. Lindeberg, Scale-space for discrete signals, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.3, pp.234-245, 1990.
DOI : 10.1109/34.49051

T. Lindeberg, Scale-space theory: a basic tool for analyzing structures at different scales, Supplement on Advances in Applied Statistics : Statistics and Images, pp.225-270, 1994.
DOI : 10.1080/757582976

T. Lindeberg, Scale-Space Theory in Computer Vision, p.23, 1994.
DOI : 10.1007/978-1-4757-6465-9

T. Lindeberg, Scale-Space, Proceedings of The CERN School of Computing Egmond aan Zee, p.34, 1996.
DOI : 10.1002/9780470050118.ecse609

T. Lindeberg and J. Garding, Shape-adapted smoothing in estimation of 3-D depth cues from affine distortions of local 2-D brightness structure, Proceedings of The Third European Conference on Computer Vision, pp.389-400, 1994.
DOI : 10.1007/3-540-57956-7_42

W. A. Luxemburg and A. C. Zaanen, Riesz Spaces, p.55, 1971.

B. Mahesh, W. J. Song, and W. A. Pearlman, Adaptive estimators for filtering noisy images, Optical Engineering, vol.29, pp.489-494, 1990.

S. Mallat, A Theory for Multiresolution Signal Decomposition: The Wavelet Representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.33, pp.674-693, 1989.
DOI : 10.1515/9781400827268.494

S. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.7, pp.674-693, 1989.
DOI : 10.1109/34.192463

S. Mallat, Multifrequency channel decompositions of images and wavelet models, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.37, issue.12, pp.2091-2110, 1989.
DOI : 10.1109/29.45554

S. Mallat, Multiresolution Approximations and Wavelet Orthonormal Bases of L 2 (R), Transactions of the American Mathematical Society, vol.315, issue.1, 1989.
DOI : 10.2307/2001373

H. Malvar, Lapped transforms for efficient transform/subband coding, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.38, issue.6, pp.966-978, 1990.
DOI : 10.1109/29.56057

P. Maragos, Morphology-based symbolic image modeling, multi-scale nonlinear smoothing, and pattern spectrum, Proceedings CVPR '88: The Computer Society Conference on Computer Vision and Pattern Recognition, pp.766-773, 1988.
DOI : 10.1109/CVPR.1988.196321

URL : http://dspace.lib.ntua.gr/handle/123456789/33377

D. Marr, Vision : A Computational Investigation into the Human Representation and Processing of Visual Information, p.45, 1982.
DOI : 10.7551/mitpress/9780262514620.001.0001

D. Marr and E. Hildreth, Theory of Edge Detection, Proceedings of R. Soc. London, volume B, pp.187-217, 1980.
DOI : 10.1098/rspb.1980.0020

G. Matheron, Eléments pour une théorie des milieux poreux, p.61, 1967.

F. Mayet, J. C. Pinoli, and M. Jourlin, Justifications physiques et applications du modèle LIP pour le traitement des images obtenues en lumière transmise, pp.251-262, 1996.

K. R. Mecke, Morphological characterization of patterns in reaction-diffusion systems, Physical Review E, vol.53, issue.5, pp.4794-4800, 1996.
DOI : 10.1103/PhysRevE.53.4794

P. Meer, Stochastic image pyramids. Computer Vision Graphics and Image Processing, pp.269-294, 1989.
DOI : 10.1016/0734-189x(88)90134-x

F. Meyer, Minimum Spanning Forests for Morphological Segmentation, Mathematical Morphology and its Applications to Image Processing, pp.77-84, 1994.
DOI : 10.1007/978-94-011-1040-2_11

F. Meyer, Flooding and Segmentation, Mathematical Morphology and its Applications to Image and Signal Processing, pp.189-198, 2000.
DOI : 10.1007/0-306-47025-X_21

F. Meyer and S. Beucher, Morphological segmentation, Journal of Visual Communication and Image Representation, vol.1, issue.1, pp.21-46, 1990.
DOI : 10.1016/1047-3203(90)90014-M

F. Meyer, P. Maragos, M. Nielsen, P. Johansen, O. F. Olsen et al., Morphological Scale-Space Representation with Levelings, Scale-Space Theories in Computer Vision. Proceedings of The Second International Conference, Scale-Space'99, pp.187-198, 1999.
DOI : 10.1007/3-540-48236-9_17

Y. Meyer, Ondelettes, fonctions splines et analyse graduée, Cahiers du Cérémade, p.32, 1987.

Y. Meyer, Ondelettes et opérateurs, Hermann, pp.31-32, 1990.

Y. Meyer, Wavelets and applications, p.31, 1992.

H. Minkowski, Volumen und Oberfl???che, Mathematische Annalen, vol.57, issue.4, pp.447-495, 1903.
DOI : 10.1007/BF01445180

A. Montanvert, P. Meer, and A. Rosenfeld, Hierarchical image analysis using irregular tessellations, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.4, pp.307-316, 1991.
DOI : 10.1109/34.88566

A. Morales, Morphological pyramids with alternating sequential filters, IEEE Transactions on Image Processing, vol.4, issue.7, pp.965-977, 1995.
DOI : 10.1109/83.392337

J. Morlet, G. Arens, E. Fourgeau, and D. Girard, Wave propagation and sampling theory???Part I: Complex signal and scattering in multilayered media, GEOPHYSICS, vol.47, issue.2, pp.203-221, 1982.
DOI : 10.1190/1.1441328

J. Morlet, G. Arens, E. Fourgeau, and D. Girard, Wave propagation and sampling theory???Part II: Sampling theory and complex waves, GEOPHYSICS, vol.47, issue.2, pp.222-236, 1982.
DOI : 10.1190/1.1441329

R. Murenzi, Ondelettes multidimensionnelles et applications à l'analyse d'images, p.33, 1990.

M. Nagao and T. Matsuyama, Edge preserving smoothing, Computer Graphics and Image Processing, vol.9, issue.4, pp.394-407, 1979.
DOI : 10.1016/0146-664X(79)90102-3

M. Nitzberg and T. Shiota, Nonlinear image filtering with edge and corner enhancement, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.8, pp.826-833, 1992.
DOI : 10.1109/34.149593

A. Okabe, B. Boots, and K. Sugihara, Spatial Tessellations : Concepts and Applications of Voronoi Diagrams, 2000.

A. V. Oppenheim, Superposition in a class of nonlinear systems, p.57, 1965.

A. V. Oppenheim, Generalized superposition, Information and Control, vol.11, issue.5-6, pp.528-536, 1967.
DOI : 10.1016/S0019-9958(67)90739-5

A. V. Oppenheim, Nonlinear filtering of Multiplied and Convolved Signals, Proceedings of the IEEE, p.56, 1968.

R. B. Paranjape, W. M. Morrow, and R. M. And-rangayyan, Adaptive-neighborhood histogram equalization for image enhancement, CVGIP: Graphical Models and Image Processing, vol.54, issue.3, pp.259-267, 1992.
DOI : 10.1016/1049-9652(92)90056-4

R. B. Paranjape, T. F. Rabie, and R. M. And-rangayyan, Image restoration by adaptive-neighborhood noise subtraction, Applied Optics, vol.33, issue.14, pp.1861-1869, 1994.
DOI : 10.1364/AO.33.002861

R. B. Paranjape, R. M. Rangayyan, and W. M. Morrow, Adaptive Neighbourhood Mean and Median Image Filtering, Electronic Imaging, vol.3, issue.44, pp.360-367, 1994.

J. M. Park, W. J. Song, and W. A. Pearlman, Speckle filtering of SAR images based on adaptive windowing, IEEE Proceedings of Vision, Image and Signal Processing, pp.191-197, 1999.
DOI : 10.1049/ip-vis:19990550

R. Bibliographiques-perona, P. Malik, and J. , Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

J. C. Pinoli, Contribution à la modélisation, au traitement et à l'analyse d'image, p.57, 1987.

J. C. Pinoli, A contrast definition for logarithmic images in the continuous setting, Acta Stereologica, vol.10, issue.77, pp.85-96, 1991.

J. C. Pinoli, Metrics, scalar product and correlation adapted to logarithmic images, Acta Stereologica, vol.11, pp.157-168, 1992.

J. C. Pinoli, Modélisation et traitement des images logarithmiques : Théorie et applications fondamentales of Saint- Etienne. (this report is a revised and expanded synthesis of the theoretical basis and several fundamental applications of the LIP approach published from 1984 to 1992. It has been reviewed by international referees and presented in December 1992 for passing the, p.150, 1992.

J. C. Pinoli, A general comparative study of the multiplicative homomorphic, log-ratio and logarithmic image processing approaches, Signal Processing, vol.58, issue.1, pp.11-45, 1997.
DOI : 10.1016/S0165-1684(97)00011-X

J. C. Pinoli, The Logarithmic Image Processing Model : Connections with Human Brightness Perception and Contrast Estimators, Journal of Mathematical Imaging and Vision, vol.7, issue.4, pp.341-358, 1997.
DOI : 10.1023/A:1008259212169

I. Pitas and A. N. Venetsanopoulos, Nonlinear Digital Filters : Principles and Applications, p.40, 1990.
DOI : 10.1007/978-1-4757-6017-0

W. K. Pratt, Digital Image Processing, p.58, 1991.

F. R. Preparata and M. I. Shamos, Computational Geometry : An Introduction, p.29, 1985.
DOI : 10.1007/978-1-4612-1098-6

T. F. Rabie, R. M. Rangayyan, and R. B. Paranjape, Adaptive-Neighborhood Image Deblurring, Electronic Imaging, vol.3, issue.4, pp.368-378, 1994.

R. M. Rangayyan, M. Ciuc, and F. Faghih, Adaptive-neighborhood filtering of images corrupted by signal-dependent noise, Applied Optics, vol.37, issue.20, pp.4477-4487, 1998.
DOI : 10.1364/AO.37.004477

R. M. Rangayyan and A. Das, Filtering multiplicative noise in images using adaptive region-based statistics, Journal of Electronic Imaging, vol.7, issue.1, pp.222-230, 1998.
DOI : 10.1117/1.482640

R. M. Rangayyan, L. Shen, J. E. Desaultes, H. Bryant, T. J. Terry et al., Improvement of sensitivity of breast cancer diagnosis with adaptive neighborhood contrast enhancement of mammograms, IEEE Transactions on Information Technology in Biomedicine, vol.1, issue.3, pp.161-170, 1997.
DOI : 10.1109/4233.654859

G. X. Ritter, Recent Developments in Image Algebra, Advances in Electronics and Electron Physics, pp.243-308, 1991.
DOI : 10.1016/S0065-2539(08)60610-1

G. X. Ritter and J. N. Wilson, Handbook of Computer Vision Algorithms in Image Algebra, 1996.
DOI : 10.1201/9781420042382

G. X. Ritter, J. N. Wilson, D. , and J. L. , Image algebra: An overview, Computer Vision, Graphics, and Image Processing, vol.49, issue.3, pp.297-331, 1990.
DOI : 10.1016/0734-189X(90)90106-6

B. M. Romeny, Scale-Space Theory for Multiscale Geometric Image Analysis, p.35, 1999.

A. Rosenfeld, Picture Processing by Computer, ACM Computing Surveys, vol.1, issue.3, 1969.
DOI : 10.1145/356551.356554

P. Salembier, Structuring element adaptation for morphological filters, Journal of Visual Communication and Image Representation, vol.3, issue.2, pp.115-136, 1992.
DOI : 10.1016/1047-3203(92)90010-Q

P. Salembier and J. Serra, Flat zones filtering, connected operators, and filters by reconstruction, IEEE Transactions on Image Processing, vol.4, issue.8, pp.1153-1159, 1995.
DOI : 10.1109/83.403422

H. Samet, Region representation: Quadtrees from binary arrays, Computer Graphics and Image Processing, vol.13, issue.1, pp.88-93, 1980.
DOI : 10.1016/0146-664X(80)90118-5

M. Schmitt and J. Mattioli, Morphologie mathématique, Masson, vol.62, p.63, 1994.

A. C. Segall, W. Chen, and S. T. Acton, Nonlinear pyramids for object identification, Conference Record of The Thirtieth Asilomar Conference on Signals, Systems and Computers, p.31, 1996.
DOI : 10.1109/ACSSC.1996.599095

J. Serra, Image Analysis and Mathematical Morphology, 1982.

J. Serra, Image Analysis and Mathematical Morphology, chapter Size Criteria, pp.318-372, 1982.

J. Serra, Image Analysis and Mathematical Morphology, Theoretical Advances, chapter Mathematical Morphology for Complete Lattices, pp.13-35, 1988.

J. Serra, Image Analysis and Mathematical Morphology Theoretical Advances, chapter Introduction to Morphological Filters, pp.101-114, 1988.

R. Bibliographiques-serra and J. , Image Analysis and Mathematical Morphology, Theoretical Advances, chapter Mathematical Morphology fo Boolean Lattices, pp.37-58, 1988.

J. Serra, Image Analysis and Mathematical Morphology Theoretical Advances, chapter Examples of Structuring Functions and Their Uses, pp.71-99, 1988.

J. Serra, Image Analysis and Mathematical Morphology, Theoretical Advances, chapter Filters and Lattices, pp.115-140, 1988.

J. Serra, Image Analysis and Mathematical Morphology, Theoretical Advances, chapter Alternating Sequential Filters, pp.203-216, 1988.

J. Serra and P. Salembier, Connected Operators and Pyramids, Proceedings of The SPIE Conference on Visual Communication and Image Processing, pp.65-76, 1993.
DOI : 10.1117/12.146672

J. Sethian, Level Sets Methods, p.35, 1996.

H. Shvayster and S. Peleg, Pictures as elements in a vector space, Proceedings of the IEEE International Conference on Computer Vision and Pattern Recognition, pp.442-446, 1983.

H. Shvayster and S. Peleg, Inversion of picture operators, Pattern Recognition Letters, vol.5, issue.1, pp.49-61, 1987.
DOI : 10.1016/0167-8655(87)90025-0

M. B. Smyth, Semi-metrics, closure spaces and digital topology, Theoretical Computer Science, vol.151, issue.1, pp.257-276, 1995.
DOI : 10.1016/0304-3975(95)00053-Y

URL : http://doi.org/10.1016/0304-3975(95)00053-y

P. Soille, Morphological Image Analysis. Principles and Applications, p.63, 2003.

P. Soille, Morphological Image Analysis. Principles and Applications, chapter Filtering, pp.241-265, 2003.

W. J. Song and W. A. Pearlman, Restoration of Noisy Images with Adaptive Windowing and Nonlinear Filtering, Visual Communication and Image Processing, pp.198-206, 1986.

T. G. Stockham, The application of generalized linearity to automatic gain control, IEEE Transactions on Audio and Electroacoustics, vol.16, issue.2, pp.267-270, 1968.
DOI : 10.1109/TAU.1968.1161976

T. G. Stockham, Image processing in the context of a visual model, Proceedings of the IEEE, pp.825-842, 1972.
DOI : 10.1109/PROC.1972.8782

G. Strang, Linear Algebra and its Applications, 1976.

M. Sugeno, Theory of fuzzy integrals and its applications, p.115, 1974.

F. K. Sun and P. Maragos, Experiments on Image Compression using Morphological Pyramids, Proceedings of The SPIE Visual Communications and Image Processing IV, pp.1303-1312, 1989.

W. Sweldens, The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets, Applied and Computational Harmonic Analysis, vol.3, issue.2, pp.186-200, 1999.
DOI : 10.1006/acha.1996.0015

M. Tabiza, Filtres Lp : étude des propriétés et application en traitement d'images, p.40, 1998.

S. Tanimoto, Image transmission with gross information first, Computer Graphics and Image Processing, vol.9, issue.1, pp.72-76, 1979.
DOI : 10.1016/0146-664X(79)90083-2

S. Tanimoto and T. Pavlidis, A hierarchical data structure for picture processing, Computer Graphics and Image Processing, vol.4, issue.2, pp.104-119, 1975.
DOI : 10.1016/S0146-664X(75)80003-7

B. Ter-haar-romeny, Geometry-Driven Diffusion in Computer Vision, p.23, 1994.
DOI : 10.1007/978-94-017-1699-4

A. Toët, A morphological pyramidal image decomposition, Pattern Recognition Letters, vol.9, issue.4, pp.255-261, 1989.
DOI : 10.1016/0167-8655(89)90004-4

C. Vachier, Morphological scale-space analysis and feature extraction, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205), pp.676-679, 2001.
DOI : 10.1109/ICIP.2001.958209

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.103.4420

F. A. Valentine, Convex Sets, 1964.

J. G. Verly and R. L. Delanoy, Some principles and applications of adaptive mathematical morphology for range imagery, Optical Engineering, vol.32, issue.12, pp.3295-3306, 1993.
DOI : 10.1117/12.151299

L. Vincent and P. Soille, Watersheds in digital spaces: an efficient algorithm based on immersion simulations, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.6, pp.583-589, 1991.
DOI : 10.1109/34.87344

R. C. Vogt, A Spatially Variant, Locally Adaptive, Background Normalization Operator, Mathematical Morphology and its Applications to Image Processing, pp.45-52, 1994.
DOI : 10.1007/978-94-011-1040-2_7

G. Voronoï, Nouvelles applications de paramètres continus à la théorie des formes quadratiques Deuxième mémoire : recherches sur les paralléloèdres primitifs, Journal für die reine and angewandte Mathematik, pp.198-287, 1908.

J. Weickert, Scale-Space Properties of Non-Linear Diffusion Filtering with a Diffusion Tensor, p.195, 1994.

J. Weickert, Anisotropic Diffusion in Image Processing, European Consortium for Mathematics in Industry. B.G. Teubner Stuttgart, vol.23, issue.25, p.39, 1998.

F. M. Whal, Digital Image Signal processing, Artech House, 1987.

R. Whitaker and S. Pizer, A multi-scale approach to nonuniform diffusion, CVGIP : Image Understanding, vol.57, issue.1, pp.99-110, 1993.

D. Willersinn, Dual irregular pyramids, p.30, 1995.

A. P. Witkin, SCALE-SPACE FILTERING, Proceedings of The International Joint Conference on Artificial Intelligence, pp.1019-1023, 1983.
DOI : 10.1016/B978-0-08-051581-6.50036-2

A. S. Wright and S. T. Acton, Watershed pyramids for edge detection, Proceedings of International Conference on Image Processing, pp.578-581, 1997.
DOI : 10.1109/ICIP.1997.638837

Y. Wu and H. Maître, Smoothing speckled synthetic aperture radar images by using maximum homgeneous region filters, Optical Engineering, vol.31, issue.8, pp.1785-1792, 1992.
DOI : 10.1117/12.59897

V. Orientation-À, 128 (définition 2), p.132

.. Pyramide-d-'opérateurs, 157 S Section d'une image à tons de gris, p.66