Y. Bertrand, C. Fiorio, and Y. Pennaneach, Border Map: A Topological Representation for nD Image Analysis, 8th International Conference on Discrete Geometry for Computer Imagery (DGCI'1999), num. 1568 de LNCS, pp.242-257
DOI : 10.1007/3-540-49126-0_19
URL : https://hal.archives-ouvertes.fr/lirmm-01168382

F. Marne-la-vallée, Disponible depuis http, 1999.

D. Blostein and N. , Ahuja : A multiscale region detector Computer Vision, Graphics, and Image Processing, pp.22-41, 1989.

J. Braquelaire and L. Brun, Image Segmentation with Topological Maps and Inter-pixel Representation, Journal of Visual Communication and Image Representation, vol.9, issue.1, pp.62-79, 1998.
DOI : 10.1006/jvci.1998.0374

J. Braquelaire and J. Domenger, Representation of segmented images with discrete geometric maps, Image and Vision Computing, vol.17, issue.10, pp.715-73510, 1999.
DOI : 10.1016/S0262-8856(98)00152-8
URL : https://hal.archives-ouvertes.fr/hal-01465410

J. Braquelaire and A. Vialard, Euclidean Paths: A New Representation of Boundary of Discrete Regions, Graphical Models and Image Processing, vol.61, issue.1, pp.16-43, 1999.
DOI : 10.1006/gmip.1999.0488

J. Bresenham, S. Fourey, T. Y. Kong, and G. T. Herman, Generic axiomatized digital surfacestructures, IBM Systems Journal Discrete Applied Mathematics, vol.4, issue.1391-3, pp.25-30, 1965.

J. Françon, On recent trends in discrete geometry in computer science
DOI : 10.1007/3-540-62005-2_1

H. Freeman, On the encoding of arbitrary geometric configurations. Electronic Computers, IEEE Transactions, issue.10, pp.260-268, 1961.

H. Freeman, Computer Processing of Line-Drawing Images, ACM Computing Surveys, vol.6, issue.1, pp.57-97, 1974.
DOI : 10.1145/356625.356627

H. N. Gabow and R. E. , A linear-time algorithm for a special case of disjoint set union, Journal of Computer and System Sciences, vol.30, issue.2, pp.209-221, 1984.
DOI : 10.1016/0022-0000(85)90014-5

Z. Galil and G. F. , Data structures and algorithms for disjoint set union problems, ACM Computing Surveys, vol.23, issue.3, pp.319-344, 1991.
DOI : 10.1145/116873.116878

A. Galton, A generalized topological view of motion in discrete space, Theoretical Computer Science, vol.305, issue.1-3, pp.111-134, 2003.
DOI : 10.1016/S0304-3975(02)00701-6

J. Gambotto, A new approach to combining region growing and edge detection, Pattern Recognition Letters, vol.14, issue.11, pp.869-87510, 1993.
DOI : 10.1016/0167-8655(93)90150-C

M. Gangnet, J. Hervé, T. Pudet, and J. , Thong : Incremental computation of planar maps, p.65, 1989.

Y. Gerard, Local Configurations of Digital Hyperplanes, 8th International Conference on Discrete Geometry for Computer Imagery (DGCI'99), p.1568
DOI : 10.1007/3-540-49126-0_6

E. H. Kronheimer, The topology of digital images, Topology and its Applications, vol.46, issue.3, pp.279-30390019, 1992.
DOI : 10.1016/0166-8641(92)90019-V

W. Kropatsch and S. B. Yacoub, A revision of pyramid segmentation, Proceedings of 13th International Conference on Pattern Recognition, pp.477-73, 1996.
DOI : 10.1109/ICPR.1996.546871

W. G. Kropatsch, Building irregular pyramids by dual graph contraction. Rap. tech. PRIP-TR-35, Dept. for Pattern Recognition and Image Processing, p.73, 1994.

W. G. Kropatsch and H. Macho, Finding the structure of connected components using dual irregular pyramids, 5th International Conference on Discrete Geometry for Computer Imagery (DGCI'05), pp.147-158, 1995.

Z. Kulpa, On the properties of discrete circles, rings, and disks, Computer Graphics and Image Processing, vol.10, issue.4, pp.348-365, 1979.
DOI : 10.1016/S0146-664X(79)80043-X

J. Lachaud, Coding cells of digital spaces : a framework to write generic digital topology algorithms, Electronic Notes in Discrete Mathematics, 9th International Workshop on Combinatorial Image Analysis, vol.12, issue.04, pp.337-34810, 2003.
URL : https://hal.archives-ouvertes.fr/hal-00308202

J. Lamy, Integrating digital topology in image-processing libraries, Computer Methods and Programs in Biomedicine, vol.85, issue.1, pp.51-58, 2007.
DOI : 10.1016/j.cmpb.2006.08.006

L. Latecki, Topological connectedness and 8-connectedness in digital pictures CVGIP : Image Understanding, pp.261-262

L. Latecki, Multicolor well-composed pictures, Pattern Recognition Letters, vol.16, issue.4, pp.425-431, 1995.
DOI : 10.1016/0167-8655(94)00104-B

L. Latecki, U. Eckhardt, and A. Rosenfeld, Well-Composed Sets, Computer Vision and Image Understanding, vol.61, issue.1, pp.70-83, 1995.
DOI : 10.1006/cviu.1995.1006

M. Ledoux and M. Talagrand, Probability in Banach spaces, Isoperimetry and processes, p.62, 1991.

P. Lienhardt, Topological models for boundary representation : A survey. research report R 90-02, rue Ren 'e Descartes, p.65, 1990.

P. Lienhardt, Topological models for boundary representation: a comparison with n-dimensional generalized maps, Computer-Aided Design, vol.23, issue.11, pp.59-8210, 1991.
DOI : 10.1016/0010-4485(91)90100-B

P. Lienhardt, Extensions de la notion de carte et modélisation géométrique 'a base topologique Habilitation à diriger des recherches, p.65, 1992.

P. Lienhardt, Aspects in topology-based geometric modeling Possible tools for discrete geometry?, Lecture Notes in Computer Science, vol.1347, pp.33-48, 1997.
DOI : 10.1007/BFb0024828

R. Malgouyres, There is no local characterization of separating and thin objects in Z3, Theoretical Computer Science, vol.163, issue.1-2, pp.303-30810, 1996.
DOI : 10.1016/0304-3975(96)00021-7

J. Marchadier, D. Arqués, and S. Michelin, Thinning grayscale well-composed images, Pattern Recognition Letters, vol.25, issue.5, pp.581-590, 2004.
DOI : 10.1016/j.patrec.2003.12.005

C. and M. Diarmid, Ramirez-Alfonsin et Reed, éds : Probabilistic methods for algorithmic discrete mathematics, pp.195-248, 1998.

M. D. Mcilroy, Best approximate circles on integer grids, ACM Transactions on Graphics, vol.2, issue.4, pp.237-263, 1983.
DOI : 10.1145/245.246

K. Mehlhorn, Data Structures and Algorithms : Sorting and Searching, p.51, 1984.

A. Me?ster and M. Wilkinson, A comparison of algorithms for connected set openings and closings. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.24, issue.4, pp.484-494

M. M. Mesmoudi, A Simplified Recognition Algorithm of Digital Planes Pieces, 10th International Conference on Discrete Geometry for Computer Imagery : (DGCI'02), pp.404-416, 2002.
DOI : 10.1007/3-540-45986-3_36

O. Monga, AN OPTIMAL REGION GROWING ALGORITHM FOR IMAGE SEGMENTATION, International Journal of Pattern Recognition and Artificial Intelligence, vol.01, issue.03n04, pp.351-375, 1987.
DOI : 10.1142/S0218001487000242

E. F. Moore, Machines models of self-reproduction, Symposia in Applied Mathematics , Proceedings of, pp.17-33, 1962.
DOI : 10.1090/psapm/014/9961

D. Morgenthaler and A. Rosenfeld, Surfaces in three-dimensional digital images, Information and Control, vol.51, issue.3, pp.227-247, 1981.
DOI : 10.1016/S0019-9958(81)90290-4

J. Muerle and D. Allen, Experimental evaluation of techniques for automatic segmentation of objects in a complex scene, éds : Pictorial Pattern Recognition, pp.3-13, 1968.

X. Muñoz, J. Freixenet, X. Cufí, and J. Martí, Strategies for image segmentation combining region and boundary information, Pattern Recognition Letters, vol.24, issue.1-3, pp.375-39200262, 2003.
DOI : 10.1016/S0167-8655(02)00262-3

J. P. Mylopoulos, On the Topological Properties of Quantized Spaces, I. The Notion of Dimension, Journal of the ACM, vol.18, issue.2, pp.239-246, 1971.
DOI : 10.1145/321637.321644

J. P. Mylopoulos, On the Topological Properties of Quantized Spaces, II. Connectivity and Order of Connectivity, Journal of the ACM, vol.18, issue.2, pp.247-254, 1971.
DOI : 10.1145/321637.321645

L. Najman and M. Couprie, Building the Component Tree in Quasi-Linear Time, IEEE Transactions on Image Processing, vol.15, issue.11, pp.3531-3539, 2006.
DOI : 10.1109/TIP.2006.877518
URL : https://hal.archives-ouvertes.fr/hal-00622110

J. V. Neumann, Theory of Self-Reproducing Automata, p.22, 1966.

F. Nielsen and R. Nock, On region merging: the statistical soundness of fast sorting, with applications, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings., pp.19-26, 2003.
DOI : 10.1109/CVPR.2003.1211447

R. Nock, R. Nock, and F. Nielsen, Fast and reliable color region merging inspired by decision tree pruning Statistical region merging, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.271-276, 2001.

R. Nock and F. Nielsen, Semi-supervised statistical region refinement for color image segmentation Pattern Recognition : Image Understanding for Photographs, pp.835-846, 2005.

N. R. Pal and S. K. , A review on image segmentation techniques, Pattern Recognition, vol.26, issue.9, pp.1277-129410, 1993.
DOI : 10.1016/0031-3203(93)90135-J

T. Pavlidis, Segmentation of pictures and maps through functional approximation, Computer Graphics and Image Processing, vol.1, issue.4, pp.360-372, 1972.
DOI : 10.1016/0146-664X(72)90021-4

T. Pavlidis, Structural Pattern Recognition, p.64, 1977.
DOI : 10.1007/978-3-642-88304-0

J. C. Pichel, D. E. Singh, and F. F. Rivera, Image segmentation based on merging of sub-optimal segmentations, Pattern Recognition Letters, vol.27, issue.10, pp.1105-1116, 2006.
DOI : 10.1016/j.patrec.2005.12.012

M. Popovic, F. Chantemargue, R. Canals, and P. Bonton, Several approaches to implement the merging step of the split and merge region segmentation, pp.399-412, 1991.

T. Quiger, P. Miché, and R. Debrie, Segmentation by auto-adaptative thresholding, 6th Internaitonal Conference on Image Analysis and Processing (ICIAP'91) Progress in Image Analysis and Processing II, pp.34-42, 1991.

J. Reveillès, Géométrie discrète, Calcul en nombres entiers et algorithmique, Thèse de doctorat, pp.7-80, 1991.

J. Rodrigues, W. Puech, and C. Fiorio, Lossless crypto-data hiding in medical images without increasing the original image size, 2nd International Conference on Advances in Medical Image and Signal Processing, pp.358-365, 2004.
URL : https://hal.archives-ouvertes.fr/lirmm-00108969

A. Rosenfeld, Connectivity in Digital Pictures, Journal of the ACM, vol.17, issue.1, pp.146-156, 1970.
DOI : 10.1145/321556.321570

A. Rosenfeld, Adjacency in digital pictures, Information and Control, vol.26, issue.1, pp.24-3390696, 1974.
DOI : 10.1016/S0019-9958(74)90696-2

A. Rosenfeld, Digital Topology, The American Mathematical Monthly, vol.86, issue.8, pp.621-630, 1979.
DOI : 10.2307/2321290

A. Rosenfeld, Three-dimensional digital topology Information and Control, pp.119-127, 1981.

A. Rosenfeld, R. Hummel, and S. Zucker, Scene labelling by relaxation operations . Systems, Man, and Cybernetics, IEEE Transactions on, vol.6, pp.420-453, 1976.

A. Rosenfeld and J. L. , Pfaltz : Sequential operations in digital picture processing, J. of the Association for Computing Machinery, vol.13, issue.4, pp.471-494, 1966.

A. Rosenfeld and J. , Strong : A grammar for maps, J. Tou, éd. : Software Engineering, vol.2, p.49, 1971.

V. Rosenthal and Y. Visetti, Sens et temps de la gestalt Disponible depuis http, Intellectica, vol.1, issue.28, pp.147-227, 1999.

P. K. Saha, D. D. Majumder, and A. Rosenfeld, Local Topological Parameters in a Tetrahedral Representation, Graphical Models and Image Processing, vol.60, issue.6, pp.423-436, 1998.
DOI : 10.1006/gmip.1998.0481

P. K. Saha and A. Rosenfeld, Strongly normal sets of convex polygons or polyhedra, Pattern Recognition Letters, vol.19, issue.12, pp.1119-1124, 1998.
DOI : 10.1016/S0167-8655(98)00088-9

P. K. Saha and A. Rosenfeld, The Digital Topology of Sets of Convex Voxels, Graphical Models, vol.62, issue.5, pp.343-352, 2000.
DOI : 10.1006/gmod.2000.0527

M. Salotti and C. Garbay, Cooperation between edge detection and region growing : the problem of control, Image Processing : Theory and Applications, pp.95-98, 1993.

J. Shi and J. Malik, Normalized cuts and image segmentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.22, issue.8, pp.888-905, 2000.

C. Simon and G. Damiand, D generalized map pyramids: Definition, representations and basic operations, Pattern Recognition, vol.39, issue.4, pp.527-538, 2006.
DOI : 10.1016/j.patcog.2005.10.004

I. Sivignon, F. Dupont, and J. Chassery, Decomposition of a Three-Dimensional Discrete Object Surface into Discrete Plane Pieces, Algorithmica, vol.38, issue.1, pp.25-4310, 2003.
DOI : 10.1007/s00453-003-1041-6

I. Sivignon, F. Dupont, and J. Chassery, Digital Intersections: minimal carrier, connectivity, and periodicity properties, Graphical Models, vol.66, issue.4, pp.226-244, 2004.
DOI : 10.1016/j.gmod.2004.05.002
URL : https://hal.archives-ouvertes.fr/hal-00185082

M. B. Smyth, Semi-metrics, closure spaces and digital topology. Theoretical Computer Science, Selected Papers of the Workshop on Topology and Completion in Semantics, pp.257-27610, 1995.
DOI : 10.1016/0304-3975(95)00053-y
URL : http://doi.org/10.1016/0304-3975(95)00053-y

M. B. Smyth, Region-based discrete geometry Disponible depuis http, Journal of Universal Computer Science, vol.6, issue.4, pp.447-459, 2000.

J. S. Stahl and S. Wang, Globally optimal grouping for symmetric closed boundaries by combining boundary and region information. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.30, issue.3, pp.395-411, 2008.

K. Suzuki and I. Horiba, Linear-time connected-component labeling based on sequential local operations, Computer Vision and Image Understanding, vol.89, issue.1, pp.1-2310, 2003.
DOI : 10.1016/S1077-3142(02)00030-9

R. E. Tarjan, Efficiency of a Good But Not Linear Set Union Algorithm, Journal of the ACM, vol.22, issue.2, pp.215-225, 1975.
DOI : 10.1145/321879.321884

R. E. Tarjan and J. Van-leeuwen, Worst-case Analysis of Set Union Algorithms, Journal of the ACM, vol.31, issue.2, pp.245-281, 1984.
DOI : 10.1145/62.2160

A. Torsello and E. R. Hancock, Graph embedding using tree edit-union, Pattern Recognition, vol.40, issue.5, pp.1393-1405, 2007.
DOI : 10.1016/j.patcog.2006.09.006

J. Toutant, W. Puech, and C. Fiorio, Minimizing data-hiding noise in color jpeg images by adapting the quantization, European Conference on Colour in Graphics, Imaging, and Vision, p.8, 2006.
URL : https://hal.archives-ouvertes.fr/lirmm-00102863

J. Toutant, W. Puech, and C. Fiorio, Amélioration de l'invisibilité par adaptation de la quantification aux données à insérer, GRETSI'05 : 20eme Colloque sur le Traitement du Signal et des Images, pp.1193-1196, 2005.

J. Toutant, W. Puech, and C. Fiorio, Asynchroneous dct-based data-hiding robust to cropping, 5th International Workshop on Image Analysis for Multimedia Interactive Services (WIAMIS'05), p.8, 2005.

J. Vittone, Caractéristaion et reconnaissance de droites et plans en géométrie discrète, Thèse de doctorat, p.90, 1999.

J. Vittone and J. , Chassery : Coexistence of tricubes in digital naive plane, International Conference on Discrete Geometry for Computer Imagery (DGCI'97, pp.99-110, 1997.

J. Vittone and J. , (n, m)-Cubes and Farey Nets for Naive Planes Understanding, 8th International Conference on Discrete Geometry for Computer Imagery (DGCI'99), pp.76-87, 1999.
DOI : 10.1007/3-540-49126-0_7

J. Vittone and J. Chassery, Recognition of Digital Naive Planes and Polyhedrization, 9th International Conference on Discrete Geometry for Computer Imagery (DGCI'00), pp.296-307, 1953.
DOI : 10.1007/3-540-44438-6_25

Y. Wang and P. Bhattacharya, A theory of parameter-dependent connected components of gray images and segmentation, Proceedings., International Conference on Image Processing, pp.69-72, 1995.
DOI : 10.1109/ICIP.1995.537582

Y. Wang and P. Bhattacharya, On parameter-dependent connected components of gray images, Pattern Recognition, vol.29, issue.8, pp.1359-136810, 1996.
DOI : 10.1016/0031-3203(95)00159-X

Y. Wang and P. Bhattacharya, Digital Connectivity and Extended Well-Composed Sets for Gray Images, Computer Vision and Image Understanding, vol.68, issue.3, pp.330-345, 1997.
DOI : 10.1006/cviu.1997.0551

R. Watzel, K. Braun, A. Hess, W. Zuschratter, and H. Scheich, Restoration of dendrites and spines with the objective of topologically correct segmentation, Proceedings of 13th International Conference on Pattern Recognition, pp.472-57, 1996.
DOI : 10.1109/ICPR.1996.546870

M. Wilkinson and J. Roerdink, Fast morphological attribute operations using tarjan 's union-find algorithm, Mathematical Morphology and its Applications to Image and Signal Processing, pp.311-320, 2000.

G. Windreich and N. Kiryati, Voxel-based surface area estimation: from theory to practice, Pattern Recognition, vol.36, issue.11, pp.2531-254110, 2003.
DOI : 10.1016/S0031-3203(03)00173-0

R. Yapa and K. Harada, A connected component labelling algorithm for greyscale mammography image processing as a pre-processing tool. Machine Graphics and Vision, pp.305-327, 2007.

Y. Zeng, D. Samaras, W. Chen, and Q. Peng, Topology cuts: A novel min-cut/max-flow algorithm for topology preserving segmentation in N???D images, Computer Vision and Image Understanding, vol.112, issue.1, pp.81-90, 2008.
DOI : 10.1016/j.cviu.2008.07.008

H. Zhang, J. E. Fritts, and S. A. Goldman, Image segmentation evaluation: A survey of unsupervised methods, Computer Vision and Image Understanding, vol.110, issue.2, pp.260-280, 2008.
DOI : 10.1016/j.cviu.2007.08.003

S. C. Zhu and A. Yuille, Region competition : unifying snakes, region growing, and bayes/mdl for multiband image segmentation. Pattern Analysis and Machine Intelligence, IEEE Transactions on, vol.18, issue.9, pp.884-90010, 1996.

J. Zunic, On the Number of Digital Discs, Journal of Mathematical Imaging and Vision, vol.21, issue.3, pp.199-204, 1023.
DOI : 10.1023/B:JMIV.0000043736.15525.ed

R. E. Tarjan, A class of algorithms which require nonlinear time to maintain disjoint sets, Journal of Computer and System Sciences, vol.18, issue.2, pp.110-127, 1979.
DOI : 10.1016/0022-0000(79)90042-4

R. E. Tarjan and J. Van-leeuwen, Worst-case Analysis of Set Union Algorithms, Journal of the ACM, vol.31, issue.2, pp.245-281, 1984.
DOI : 10.1145/62.2160

S. Zucker, Region growing: Childhood and adolescence, Computer Graphics and Image Processing, vol.5, issue.3, pp.382-399, 1976.
DOI : 10.1016/S0146-664X(76)80014-7

]. S. Dugelay, J. Graffigne, and . Augustin, Segmentation of multibeam acoustic imagery in the exploration of the deep sea-bottom, Proceedings of 13th International Conference on Pattern Recognition, pp.437-446, 1996.
DOI : 10.1109/ICPR.1996.546864

P. F. Felzenszwalb and D. P. Huttenlocher, Image segmentation using local variation, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231), pp.98-104, 1998.
DOI : 10.1109/CVPR.1998.698594

C. Fiorio and J. Gustedt, Two linear time Union-Find strategies for image processing, Theoretical Computer Science, vol.154, issue.2, pp.165-181, 1996.
DOI : 10.1016/0304-3975(94)00262-2
URL : https://hal.archives-ouvertes.fr/inria-00549539

W. G. Kropatsch and S. B. Yacoub, A revision of pyramid segmentation, Proceedings of 13th International Conference on Pattern Recognition, pp.477-481, 1996.
DOI : 10.1109/ICPR.1996.546871

S. C. Zhu and A. Yuille, Region competition: unifying snakes, region growing, energy/Bayes/MDL for multi-band image segmentation, Proceedings of IEEE International Conference on Computer Vision, pp.884-900, 1996.
DOI : 10.1109/ICCV.1995.466909

S. Dugelay, J. Graffigne, and . Augustin, Segmentation of multibeam acoustic imagery in the exploration of the deep sea-bottom, Proceedings of 13th International Conference on Pattern Recognition, pp.437-446, 1996.
DOI : 10.1109/ICPR.1996.546864

W. G. Kropatsch and S. B. Yacoub, A revision of pyramid segmentation, Proceedings of 13th International Conference on Pattern Recognition, pp.477-481, 1996.
DOI : 10.1109/ICPR.1996.546871

C. Fiorio and R. Nock, A Statistical Approach to Region Merging of Optimal Complexity, 1999.

C. Mcdiarmid, Concentration, Probabilistic Methods for Algorithmic Discrete Mathematics, pp.1-54, 1998.
DOI : 10.1007/978-3-662-12788-9_6

K. Mehlhorn, ]. E. Ahronovitz, C. Fiorio, and S. Glaize, Data Structures and Algorithms 1: Sorting and Searching References Topological operators on the topological graph of frontiers, in: Discrete Geometry for Computer Imagery, Lecture Notes in Computer Science, vol.1568, issue.1, pp.207-217, 1984.
DOI : 10.1007/978-3-642-69672-5

Y. Bertrand, G. Damiand, and C. Fiorio, Topological Encoding of 3D Segmented Images, Lecture Notes in Computer Science, vol.1953, pp.311-324, 2000.
DOI : 10.1007/3-540-44438-6_26
URL : https://hal.archives-ouvertes.fr/lirmm-01168508

Y. Bertrand, G. Damiand, and C. Fiorio, Topological map: minimal encoding of 3d segmented images, Graph Based Representations, pp.64-73, 2001.
URL : https://hal.archives-ouvertes.fr/lirmm-01168509

Y. Bertrand and J. F. Dufourd, Algebraic Specification of a 3D-Modeler Based on Hypermaps, CVGIP: Graphical Models and Image Processing, vol.56, issue.1, pp.29-60, 1994.
DOI : 10.1006/cgip.1994.1005

Y. Bertrand, C. Fiorio, and Y. Pennaneach, Border Map: A Topological Representation for nD Image Analysis, Lecture Notes in Computer Science, vol.1568, pp.242-257, 1999.
DOI : 10.1007/3-540-49126-0_19
URL : https://hal.archives-ouvertes.fr/lirmm-01168382

P. Bourdon, O. Alata, G. Damiand, C. Olivier, and Y. Bertrand, Geometrical and topological informations for image segmentation with Monte Carlo Markov chain implementation, in: Vision Interface, pp.413-420, 2002.

J. Braquelaire, P. Desbarats, and J. , Domenger, 3d split and merge with 3-maps, in: Workshop on Graph Based Representations, pp.32-43, 2001.

J. Braquelaire, P. Desbarats, J. Domenger, C. A. W?, and . Uthrich, A topological structuring for aggregates of 3d discrete objects, in: Workshop on Graph Based Representations, Austria, pp.193-202, 1999.

J. Braquelaire and J. Domenger, Representation of segmented images with discrete geometric maps, Image and Vision Computing, vol.17, issue.10, pp.715-735, 1999.
DOI : 10.1016/S0262-8856(98)00152-8
URL : https://hal.archives-ouvertes.fr/hal-01465410

L. Brun and J. Domenger, A new split and merge algorithm with topological maps and inter-pixel boundaries, The Fifth International Conference in Central Europe on Computer Graphics and Visualization, 1997.

L. Brun, J. Domenger, and J. Braquelaire, Discrete Maps: a Framework for Region Segmentation Algorithms, IAPR-TC15, published in Advances in Computing, 1997.
DOI : 10.1007/978-3-7091-6487-7_9

P. Charnier, Outils algorithmiques pour le codage interpixel et ses applications, 1995.

R. Cori, Un code pour les graphes planaires et ses applications, 1973.

R. Cori, Un code pour les graphes planaires et ses applications, Ast e erisque, 1975.

G. Damiand, D e efinition et e etude dÕun mod e ele topologique minimal de repr e esentation dÕimages 2D et 3D, Th e ese de doctorat, 2001.

G. Damiand and P. Lienhardt, Removal and Contraction for n-Dimensional Generalized Maps, pp.208-221, 2002.
DOI : 10.1007/978-3-540-39966-7_39

G. Damiand and P. Resch, Topological Map Based Algorithms for 3D Image Segmentation, Lecture Notes in Computer Science, vol.2301, pp.220-231, 2002.
DOI : 10.1007/3-540-45986-3_20

J. P. Domenger, Conception et impl e ementation du noyeau graphique dÕun environnement 2D1=2 dÕ e edition dÕimages discr e etes, Th e ese de doctorat, 1992.

J. Edmonds, A combinatorial representation for polyhedral surfaces, Notices Am, Math. Soc, vol.7, 1960.

C. Fiorio, Approche interpixel en analyse dÕimages: une topologie et des algorithmes de segmentation, Th e ese de doctorat, 1995.
URL : https://hal.archives-ouvertes.fr/tel-01168523

C. Fiorio, A topologically consistent representation for image analysis: The Frontiers Topological Graph, Lecture Notes in Computer Science, vol.1176, pp.151-162, 1996.
DOI : 10.1007/3-540-62005-2_13
URL : https://hal.archives-ouvertes.fr/lirmm-01168321

J. Franc-ßon, Topologie de khalimsi et kovalevski et algorithmique graphique Rapport de recherche 91-10, 1991.

A. Jacques, Constellations et graphes topologiques, Combinatorial Theory and Applications, pp.657-673, 1970.

E. Khalimsky, R. Kopperman, and P. R. Meyer, Boundaries in digital planes, Journal of Applied Mathematics and Stochastic Analysis, vol.3, issue.1, pp.27-55, 1990.
DOI : 10.1155/S1048953390000041

T. Y. Kong, R. Kopperman, and P. R. Meyer, A Topological Approach to Digital Topology, The American Mathematical Monthly, vol.98, issue.10, pp.901-917, 1991.
DOI : 10.2307/2324147

T. Y. Kong and A. Rosenfeld, Digital Topology, pp.357-393, 1989.
DOI : 10.1007/978-1-4615-1529-6_3

V. A. Kovalevsky, Finite topology as applied to image analysis, Comput. Vision, Graph., Image Process, pp.141-161, 1989.

W. G. Kropatsch, Building irregular pyramids by dual-graph contraction, Vision, Image Signal Process, pp.366-374, 1995.

W. G. Kropatsch, Abstraction Pyramids on Discrete Representations, LNCS, vol.2301, pp.1-21, 2002.
DOI : 10.1007/3-540-45986-3_1

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

P. Lienhardt, -dimensional generalized maps, Proceedings of the fifth annual symposium on Computational geometry , SCG '89, pp.228-236, 1989.
DOI : 10.1145/73833.73859
URL : https://hal.archives-ouvertes.fr/hal-00909382

P. Lienhardt, Topological models for boundary representation: a comparison with n-dimensional generalized maps, Computer-Aided Design, vol.23, issue.11, 1991.
DOI : 10.1016/0010-4485(91)90100-B

P. Lienhardt, N-DIMENSIONAL GENERALIZED COMBINATORIAL MAPS AND CELLULAR QUASI-MANIFOLDS, International Journal of Computational Geometry & Applications, vol.04, issue.03, pp.275-324, 1994.
DOI : 10.1142/S0218195994000173

J. Pailloncy and J. Jolion, The Frontier-Region Graph, Computing Supplementum, vol.12, pp.123-134, 1997.
DOI : 10.1007/978-3-7091-6487-7_13

A. Rosenfeld, Adjacency in digital pictures, Information and Control, vol.26, issue.1, pp.24-33, 1974.
DOI : 10.1016/S0019-9958(74)90696-2

W. T. Tutte, A census of planar maps, Canad, J. Math, vol.15, pp.249-271, 1963.

G. Damiand, Topological model for two-dimensional image representation: definition and optimal extraction algorithm, Computer Vision and Image Understanding, vol.93, issue.2, pp.111-154, 2004.
DOI : 10.1016/j.cviu.2003.09.001
URL : https://hal.archives-ouvertes.fr/lirmm-00137917

]. E. Andres, R. Acharya, and C. Sibata, Discrete Analytical Hyperplanes, Graphical Models and Image Processing, vol.59, issue.5, pp.302-309, 1997.
DOI : 10.1006/gmip.1997.0427

P. Arnoux, V. Berthé, and A. Siegel, Two-dimensional iterated morphisms and discrete planes, Theoretical Computer Science, vol.319, issue.1-3, pp.319-145, 2004.
DOI : 10.1016/j.tcs.2004.02.017
URL : https://hal.archives-ouvertes.fr/lirmm-00108555

R. P. Barneva, V. E. Brimkov, and P. Nehlig, Thin discrete triangular meshes, Theoretical Computer Science, vol.246, issue.1-2, pp.1-2, 2000.
DOI : 10.1016/S0304-3975(98)00346-6

V. Berthé and B. , Density of symbols in discretized rotation configurations, Words 2005 ? 5th International Conference on Words of Publications du LaCIM, pp.163-173, 2005.

V. Berthé and L. Vuillon, Tilings and rotations on the torus: a twodimensional generalization of sturmian sequences, Discrete Math, pp.27-53, 2000.

V. Berthé and L. Vuillon, Palindromes and two-dimensional sturmian sequences, J. Autom. Lang. Comb, vol.6, issue.2, pp.121-138, 2001.

V. Berthé, C. Fiorio, and D. Jamet, Generalized Functionality for Arithmetic Discrete Planes, DGCI 2005, 12th International Conference, pp.276-286, 2005.
DOI : 10.1007/978-3-540-31965-8_26

V. E. Brimkov, E. Andres, and R. P. Barneva, Object discretizations in higher dimensions, Pattern Recogn, Lett, vol.23, issue.6, pp.623-636, 2002.

V. E. Brimkov and R. P. Barneva, Graceful Planes and Thin Tunnel-Free Meshes, DGCI, 8th International Conference, pp.53-64, 1999.
DOI : 10.1007/3-540-49126-0_5

V. E. Brimkov, R. P. Barneva, and P. Nehlig, Minimally Thin Discrete Triangulation, pp.51-70, 2000.
DOI : 10.1007/978-1-4471-0737-8_3

V. E. Brimkov and R. P. Barneva, Graceful planes and lines, Theoretical Computer Science, vol.283, issue.1, pp.151-170, 2002.
DOI : 10.1016/S0304-3975(01)00061-5
URL : http://doi.org/10.1016/s0304-3975(01)00061-5

V. E. Brimkov and R. Klette, Curves, Hypersurfaces, and Good Pairs of Adjacency Relations, Lecture Notes in Computer Science, vol.3322, pp.270-284, 2004.
DOI : 10.1007/978-3-540-30503-3_21

M. A. Jacob-da and . Col, About local configurations in arithmetic planes, Theoretical Computer Science, vol.283, issue.1, pp.183-201, 2002.
DOI : 10.1016/S0304-3975(01)00064-0

I. Debled-rennesson, J. Rémy, and J. Rouyer-degli, Segmentation of Discrete Curves into Fuzzy Segments, 9th International Workshop on Combinatorial Image Analysis ? Electronic Notes in Discrete Mathematics, p.12, 2003.
DOI : 10.1016/S1571-0653(04)00500-1
URL : https://hal.archives-ouvertes.fr/inria-00107709

I. Debled-renesson, Reconnaissance des Droites et Plans Discrets, Thèse de doctorat, 1995.

I. Debled-renesson and J. Reveillès, A New Approach to Digital Planes, in: Vision geometry III, Proc. SPIE, 1994.

J. Françon, Sur la topologie d'un plan arithm??tique, Theoretical Computer Science, vol.156, issue.1-2, pp.1-2, 1996.
DOI : 10.1016/0304-3975(95)00059-3

J. Françon and L. Papier, Polyhedrization of the Boundary of a Voxel Object, DGCI, 8th International Conference, pp.425-434, 1999.
DOI : 10.1007/3-540-49126-0_33

J. Françon, J. Schramm, and M. Tajine, Recognizing arithmetic straight lines and planes, Lecture Notes Computer Science, pp.141-150, 1996.
DOI : 10.1007/3-540-62005-2_12

Y. Gérard, Local Configurations of Digital Hyperplanes, DGCI, 8th International Conference, pp.65-75, 1999.
DOI : 10.1007/3-540-49126-0_6

Y. Kenmochi and A. Imiya, Naive Planes as Discrete Combinatorial Surfaces, Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery, pp.249-261, 2000.
DOI : 10.1007/3-540-44438-6_21
URL : https://hal.archives-ouvertes.fr/hal-00622087

Y. Kenmochi and A. Imiya, Combinatorial Topologies for Discrete Planes, DGCI, 11th International Conference, DGCI 2003, pp.144-153, 2003.
DOI : 10.1007/978-3-540-39966-7_13
URL : https://hal.archives-ouvertes.fr/hal-00622084

L. Kuipers and H. Niederreiter, Uniform distribution of sequences. (Ravnomernoe raspredelenie posledovatel'nostej), Moskva: Nauka. Glavnaya Redaktsiya Fiziko-Matematicheskoj Literatury (Transl. from the English. Transl.), 1985.

R. Malgouyres and G. Bertrand, COMPLETE LOCAL CHARACTERIZATION OF STRONG 26-SURFACES: CONTINUOUS ANALOGS FOR STRONG 26-SURFACES, International Journal of Pattern Recognition and Artificial Intelligence, vol.13, issue.04, pp.465-484, 1999.
DOI : 10.1142/S0218001499000288

D. G. Morgenthaler and A. Rosenfeld, Surfaces in three-dimensional digital images, Information and Control, vol.51, issue.3, pp.227-247, 1981.
DOI : 10.1016/S0019-9958(81)90290-4

N. and P. Fogg, Substitutions in dynamics, arithmetics and combinatorics, Lecture Notes in Mathematics, vol.1794, 2002.
DOI : 10.1007/b13861

J. Reveillès, Calcul en Nombres Entiers et Algorithmique, Thèse d'e ´tat, 1991.

J. Reveillès, Combinatorial pieces in digital lines and planes, in: Vision geometry IV, Proc. SPIE, 2573, pp.23-24, 1995.

G. Rote, Sequences With Subword Complexity 2n, Journal of Number Theory, vol.46, issue.2, pp.196-213, 1994.
DOI : 10.1006/jnth.1994.1012

J. Schramm, Coplanar tricubes, Lecture Notes in Computer Science, vol.1347, pp.87-98, 1997.
DOI : 10.1007/BFb0024832

J. Vittone and J. Chassery, Coexistence of tricubes in digital naive plane, DGCI, 7th International Workshop, pp.99-110, 1997.
DOI : 10.1007/BFb0024833

J. Vittone and J. Chassery, (n, m)-Cubes and Farey Nets for Naive Planes Understanding, DGCI, 8th International Conference, pp.76-87, 1999.
DOI : 10.1007/3-540-49126-0_7

J. Vittone and J. Chassery, Recognition of Digital Naive Planes and Polyhedrization, DGCI, 9th International Conference, pp.296-307, 2000.
DOI : 10.1007/3-540-44438-6_25

L. Vuillon, Local configurations in a discrete plane, Bull. Belgian Math. Soc, vol.6, pp.625-636, 1999.

V. Berthé, On some applications of generalized functionality for arithmetic discrete planes, Image and Vision Computing, vol.25, issue.10, pp.1671-1684, 2007.
DOI : 10.1016/j.imavis.2006.06.023