Références

[AFG99]: E. Ahronovitz, C. Fiorio, and S. Glaize. Topological operators on the topological graph of frontiers. In Proceedings of International Conference Discrete Geometry for Computer Imagery, volume 1568 of Lecture Notes in Computer Science, pages 207–217, Marne-la-Vallée, France, 1999.
[Ago76]: M. Agoston. Algebraic topology: a first course. Lecture Notes in Pure and Applied Mathematics. Marcel Dekker, New York, 1976.
[AK88]: D. Arques and P. Koch. Définition et implémentation de pavages dans l’espace. Technical Report 46, Laboratoire d’Informatique, UFR Sciences et Techniques, Besançon, France, août 1988.
[AK89]: D. Arques and P. Koch. Modélisation de solides par les pavages. In Proceedings of Pixim 89, pages 47–61, Paris, 1989.
[Ala05]: S. Alayrangues. Modèles et invariants topologiques en imagerie numérique. Thèse de doctorat, Université Bordeaux 1, Juillet 2005.
[APDL09]: S. Alayrangues, S. Peltier, G. Damiand, and P. Lienhardt. Border operator for generalized maps. In Proc. of 15th International Conference on Discrete Geometry for Computer Imagery, volume 5810 of Lecture Notes in Computer Science, pages 300–312, Montréal, Canada, September 2009. Springer Berlin/Heidelberg.
[BAD⁺02]: 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 Proc. of 15th IAPR International Conference on Vision Interface, pages 413–420, Calgary, Alberta, Canada, May 2002.
[Bal09]: F. Baldacci. Graphe de Surface Orientée : un modèle opérationnel de segmentation d’image 3D. Thèse de doctorat, Université Bordeaux 1, december 2009.
[Bau74]: B. Baumgart. Geometric modelling for computer vision. Technical Report STAN-CS-74-463, Computer Science Department, Stanford University, 1974.
[Bau75]: B. Baumgart. A polyhedron representation for computer vision. In Proceedings of AFIPS National Computer Conference, volume 44, pages 589–596, 1975.
[BB98]: J.P. Braquelaire and L. Brun. Image segmentation with topological maps and inter-pixel representation. Journal of Visual Communication and Image Representation, 9(1):62–79, march 1998.
[BBD09]: F. Baldacci, A. Braquelaire, and G. Damiand. 3d topological map extraction from oriented boundary graph. In Proc. of 7th Workshop on Graph-Based Representations in Pattern Recognition, volume 5534 of Lecture Notes in Computer Science, pages 283–292, Venice, Italy, May 2009. Springer Berlin/Heidelberg.
[BBDD08]: F. Baldacci, A. Braquelaire, P. Desbarats, and J.P. Domenger. 3d image topological structuring with an oriented boundary graph for split and merge segmentation. In Proc. of 14th International Conference on Discrete Geometry for Computer Imagery, volume 4992 of Lecture Notes in Computer Science, pages 541–552, Lyon, France, April 2008. Springer Berlin/Heidelberg.
[BD97]: L. Brun and J.P. Domenger. A new split and merge algorithm with topological maps and inter-pixel boundaries. In Proceedings of The fifth International Conference in Central Europe on Computer Graphics and Visualization, pages 21–30, february 1997.
[BD99]: J.P. Braquelaire and J.P. Domenger. Representation of segmented images with discrete geometric maps. Image and Vision Computing, 17(10):715–735, 1999.
[BDB97]: L. Brun, J.P. Domenger, and J.P. Braquelaire. Discrete maps : a framework for region segmentation algorithms. In Proceedings of International Workshop on Graph based representations, pages 83–92, Lyon, april 1997. IAPR-TC15. published in Advances in Computing (Springer).
[BDD01]: J.P. Braquelaire, P. Desbarats, and J.P. Domenger. 3d split and merge with 3-maps. In Proceedings of International Workshop on Graph based representations, pages 32–43, Ischia, Italy, may 2001. IAPR-TC15.
[BDDV03]: A. Braquelaire, G. Damiand, J.-P. Domenger, and F. Vidil. Comparison and convergence of two topological models for 3d image segmentation. In Proc. of 4th Workshop on Graph-Based Representations in Pattern Recognition, volume 2726 of Lecture Notes in Computer Science, pages 59–70, York, England, July 2003. Springer Berlin/Heidelberg.
[BDDW99]: J.P. Braquelaire, P. Desbarats, J.P. Domenger, and C.A. Wüthrich. A topological structuring for aggregates of 3d discrete objects. In Proceedings of International Workshop on Graph based representations, pages 193–202, Austria, may 1999. IAPR-TC15.
[BDF00]: Y. Bertrand, G. Damiand, and C. Fiorio. Topological encoding of 3d segmented images. In Proc. of 9th International Conference on Discrete Geometry for Computer Imagery, volume 1953 of Lecture Notes in Computer Science, pages 311–324, Uppsala, Sweden, December 2000. Springer Berlin/Heidelberg.
[BDF01]: Y. Bertrand, G. Damiand, and C. Fiorio. Topological map: Minimal encoding of 3d segmented images. In Proc. of 3rd Workshop on Graph-Based Representation in Pattern Recognition, pages 64–73, Ischia, Italy, May 2001.
[BDM03]: L. Brun, J.P. Domenger, and M. Mokhtari. Incremental modifications of segmented image defined by discrete maps. Journal of Visual Communication and Image Representation, 14(3):251–290, 2003.
[BDSM08]: M. Baba-Ali, G. Damiand, X. Skapin, and D. Marcheix. Insertion and expansion operations for n -dimensional generalized maps. In Proc. of 14th International Conference on Discrete Geometry for Computer Imagery, volume 4992 of Lecture Notes in Computer Science, pages 141–152, Lyon, France, April 2008. Springer Berlin/Heidelberg.
[BG88]: J.P. Braquelaire and P. Guitton. A model for image structuration. In Proceedings of Computer Graphics International, pages 426–435, 1988.
[BG89]: P. Baudelaire and M. Gangnet. Planar maps: an interaction paradigm for graphic design. In Proceedings of SIGCHI’89, volume 20, pages 313––318. ACM, 1989.
[BG91]: J.P. Braquelaire and P. Guitton. 2d1/2 scene update by insertion of contour. Computer and Graphics, 15(1):41–48, 1991.
[BHS80]: I.C. Braid, R.C. Hillyard, and I.A. Stroud. Mathematical Methods in Computer Graphics and Design, chapter Stepwise Construction of Polyhedra in Geometric Modelling, pages 123–141. Academic Press, brodlie, k.w. edition, 1980.
[BK01]: L. Brun and W.G. Kropatsch. Contraction kernels and combinatorial maps. In Proceedings of International Workshop on Graph based representations, pages 12–21, Ischia, Italy, may 2001. IAPR-TC15.
[BK02]: L Brun and W.G. Kropatsch. Receptive fields within the combinatorial pyramid framework. In Proceedings of International Conference Discrete Geometry for Computer Imagery, number 2301 in Lecture Notes in Computer Science, pages 92–101, Bordeaux, France, april 2002.
[BK03a]: L. Brun and W.G Kropatsch. Combinatorial pyramids. In Suvisoft, editor, IEEE International Conference on Image Processing, volume II, pages 33–37, Barcelona, Spain, September 2003. IEEE.
[BK03b]: L. Brun and W.G. Kropatsch. Receptive fields within the combinatorial pyramid framework. Graphical Models, 65:23–42, 2003.
[BK06]: L. Brun and W.G Kropatsch. Contains and inside relationships within combinatorial pyramids. Pattern Recognition, 39(4):515–526, April 2006.
[BMSB07]: M. Baba-Ali, D. Marcheix, X. Skapin, and Y. Bertrand. Generic computation of bulletin boards into geometric kernels. In Proceedings of the 5th international conference on Computer graphics, virtual reality, visualisation and interaction in Africa, AFRIGRAPH ’07, pages 85–93, New York, NY, USA, 2007. ACM.
[Bra22]: H.R. Brahana. Systems of circuits on two-dimensional manifolds. Annals of Math., 23:144–168, 1922.
[Bri89]: E. Brisson. Representing geometric structures in d dimensions: topology and order. In Proceedings of 5^th Annual ACM Symposium on Computational Geometry, pages 218–227, Saarbrücken, Germany, 1989.
[Bri93]: E. Brisson. Representing geometric structures in d dimensions: topology and order. Discrete & Computational Geometry, 9(1):387–426, 1993.
[Bru96]: L. Brun. Segmentation d’images couleur à base topologique. Thèse de doctorat, Université Bordeaux 1, décembre 1996.
[BSP⁺04]: B. Brandel, S. Schneider, M. Perrin, N. Guiard, J.-F. Rainaud, P. Lienhardt, and Y. Bertrand. Automatic building of structured geological models. In Proceedings of the ninth ACM symposium on Solid modeling and applications, SM ’04, pages 59–69. Eurographics Association, june 2004.
[Cor73]: R. Cori. Un code pour les graphes planaires et ses applications. PhD thesis, Université Paris VII, 1973.
[Cor75]: R. Cori. Un code pour les graphes planaires et ses applications. In Astérisque, volume 27. Soc. Math. de France, Paris, France, 1975.
[Cro78]: F. Croom. Basic Concepts of Algebraic Topology. Graduate Texts in Mathematics. Springer-Verlag, New York, 1978.
[DA07]: G. Damiand and D. Arrivault. A new contour filling algorithm based on 2d topological map. In Proc. of 6th Workshop on Graph-Based Representations in Pattern Recognition, volume 4538 of Lecture Notes in Computer Science, pages 319–329, Alicante, Spain, June 2007. Springer Berlin/Heidelberg.
[DA08]: G. Damiand and S. Alayrangues. Computing canonical polygonal schemata with generalized maps. In Proc. of International Conference on Topological & Geometric Graph Theory, volume 31 of Electronic Notes in Discrete Mathematics, pages 287–292, Paris, France, August 2008. Elsevier.
[DAB03]: G. Damiand, O. Alata, and C. Bihoreau. Using 2d topological map information in a markovian image segmentation. In Proc. of 11th International Conference on Discrete Geometry for Computer Imagery, volume 2886 of Lecture Notes in Computer Science, pages 288–297, Naples, Italy, November 2003. Springer Berlin/Heidelberg.
[Dam01]: G. Damiand. Définition et étude d’un modèle topologique minimal de représentation d’images 2d et 3d. Thèse de doctorat, Université Montpellier II, décembre 2001.
[Dam08]: G. Damiand. Topological model for 3d image representation: Definition and incremental extraction algorithm. Computer Vision and Image Understanding, 109(3):260–289, March 2008.
[DB07]: G. Damiand and L. Brun. Géométrie discrète et images numériques, chapitre 4. Cartes combinatoires pour l’analyse d’images, chapter 4, pages 103–120. Traité IC2, Signal et Image. Hermès Paris, France, Août 2007.
[DBF04]: G. Damiand, Y. Bertrand, and C. Fiorio. Topological model for two-dimensional image representation: Definition and optimal extraction algorithm. Computer Vision and Image Understanding, 93(2):111–154, February 2004.
[dBvKOS00]: M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, January 2000.
[DC08]: G. Damiand and D. Coeurjolly. A generic and parallel algorithm for 2d image discrete contour reconstruction. In Proc. of 4th International Symposium on Visual Computing, volume 5359 of Lecture Notes in Computer Science, pages 792–801, Las vegas, Nevada, USA, December 2008. Springer Berlin/Heidelberg.
[DD08a]: A. Dupas and G. Damiand. Comparison of local and global region merging in the topological map. In Proc. of 12th International Workshop on Combinatorial Image Analysis, volume 4958 of Lecture Notes in Computer Science, pages 420–431, Buffalo, NY, USA, April 2008. Springer Berlin/Heidelberg.
[DD08b]: A. Dupas and G. Damiand. First results for 3d image segmentation with topological map. In Proc. of 14th International Conference on Discrete Geometry for Computer Imagery, volume 4992 of Lecture Notes in Computer Science, pages 507–518, Lyon, France, April 2008. Springer Berlin/Heidelberg.
[DD09]: A. Dupas and G. Damiand. Region merging with topological control. Discrete Applied Mathematics, 157(16):3435–3446, August 2009.
[DDL09]: A. Dupas, G. Damiand, and J.-O. Lachaud. Multi-label simple points definition for 3d images digital deformable model. In Proc. of 15th International Conference on Discrete Geometry for Computer Imagery, volume 5810 of Lecture Notes in Computer Science, pages 156–167, Montréal, Canada, September 2009. Springer Berlin/Heidelberg.
[DDL10]: G. Damiand, A. Dupas, and J.-O. Lachaud. Fully deformable 3d digital partition model with topological control. Pattern Recognition Letter, 2010. to appear.
[DDLA05]: G. Damiand, M. Dexet-Guiard, P. Lienhardt, and E. Andres. Removal and contraction operations to define combinatorial pyramids: Application to the design of a spatial modeler. Image and Vision Computing, 23(2):259–269, February 2005.
[DdlHJ⁺09a]: G. Damiand, C. de la Higuera, J.-C. Janodet, E. Samuel, and C. Solnon. A polynomial algorithm for subisomorphism of holey plane graphs. In Proc. of 7th International Workshop on Mining and Learning with Graphs, Leuven, Belgium, July 2009.
[DdlHJ⁺09b]: G. Damiand, C. de la Higuera, J.-C. Janodet, E. Samuel, and C. Solnon. Polynomial algorithm for submap isomorphism: Application to searching patterns in images. In Proc. of 7th Workshop on Graph-Based Representation in Pattern Recognition, volume 5534 of Lecture Notes in Computer Science, pages 102–112, Venice, Italy, May 2009. Springer Berlin/Heidelberg.
[Des01]: P. Desbarats. Structuration des images segmentées 3D discrètes. Thèse de doctorat, Université Bordeaux 1, décembre 2001.
[dFPM97]: L. de Floriani, E. Puppo, and P. Magillo. A formal approach to multiresolution hypersurface modeling. In Geometric Modeling: Theory and Pratice, pages 302–323. Springer-Verlag, 1997.
[DG98]: T.K. Dey and S. Guha. Computing homology groups of simplicial complexes in ℝ³. Journal of the ACM, 45(2):266–287, 1998.
[DL03]: G. Damiand and P. Lienhardt. Removal and contraction for n-dimensional generalized maps. In Proc. of 11th International Conference on Discrete Geometry for Computer Imagery, volume 2886 of Lecture Notes in Computer Science, pages 408–419, Naples, Italy, November 2003. Springer Berlin/Heidelberg.
[Dom92]: J.P. Domenger. Conception et implémentation du noyau graphique d’un environnement 2D1/2 d’édition d’images discrètes. Thèse de doctorat, Université Bordeaux 1, avril 1992.
[DPF06]: G. Damiand, S. Peltier, and L. Fuchs. Computing homology for surfaces with generalized maps: Application to 3d images. In Proc. of 2nd International Symposium on Visual Computing, volume 4292 of Lecture Notes in Computer Science, pages 235–244, Lake Tahoe, Nevada, USA, November 2006. Springer Berlin/Heidelberg.
[DPF08]: G. Damiand, S. Peltier, and L. Fuchs. Computing homology generators for volumes using minimal generalized maps. In Proc. of 12th International Workshop on Combinatorial Image Analysis, volume 4958 of Lecture Notes in Computer Science, pages 63–74, Buffalo, NY, USA, April 2008. Springer Berlin/Heidelberg.
[DPFL06]: G. Damiand, P. Peltier, L. Fuchs, and P. Lienhardt. Topological map: An efficient tool to compute incrementally topological features on 3d images. In Proc. of 11th International Workshop on Combinatorial Image Analysis, volume 4040 of Lecture Notes in Computer Science, pages 1–15, Berlin, Germany, June 2006. Springer Berlin/Heidelberg.
[DR02]: G. Damiand and P. Resch. Topological map based algorithms for 3d image segmentation. In Proc. of 10th International Conference on Discrete Geometry for Computer Imagery, volume 2301 of Lecture Notes in Computer Science, pages 220–231, Bordeaux, France, April 2002. Springer Berlin/Heidelberg.
[DR03]: G. Damiand and P. Resch. Split and merge algorithms defined on topological maps for 3d image segmentation. Graphical Models, 65(1-3):149–167, May 2003.
[Dup09]: A. Dupas. Opérations et Algorithmes pour la Segmentation Topologique d’Images 3D. Thèse de doctorat, Université de Poitiers, Novembre 2009.
[Edm60]: J. Edmonds. A combinatorial representation for polyhedral surfaces. Notices of the American Mathematical Society, 7, 1960.
[EGS90]: H. Edelsbrunner, L. J. Guibas, and M. Sharir. The complexity and construction of many faces in arrangements of lines and of segments. Discrete & Computational Geometry, 5(2):161–196, 1990.
[EL93]: H. Elter and P. Lienhardt. Different combinatorial models based on the map concept for the representation of different types of cellular complexes. In Proceedings of IFIP TC 5/WG II Working Conference on Geometric Modeling in Computer Graphics, Genova, Italy, 1993. Springer.
[EL94]: H. Elter and P. Lienhardt. Cellular complexes as structured semi-simplicial sets. International Journal of Shape Modeling, 1(2):191–217, December 1994.
[EL03]: U. Eckhardt and L. J. Latecki. Topologies for the digital spaces z2 and z3. Computer Vision and Image Understanding, 90:295–312, June 2003.
[Elt94]: H. Elter. Étude de structures combinatoires pour la représentation de complexes cellulaires. Thèse de doctorat, Université Louis-Pasteur de Strasbourg, septembre 1994.
[EW79]: C. Eastman and K. Weiler. Geometric modeling using Euler operators. In Proceedings of the First Annual Conference on Computer Graphics in CAD/CAM Systems, pages 248–259, May 1979.
[Fav09]: J.-M. Favreau. Outils pour le pavage de surfaces. Thèse de doctorat, Université Blaise Pascal Clermont-Ferrand II, Octobre 2009.
[FB09a]: S. Fourey and L. Brun. Connecting walks and connecting dart sequences for n-d combinatorial pyramids. In Proc. of 13th International Workshop on Combinatorial Image Analysis, Research Publishing Services, pages 109–122, Cancun, Mexico, November 2009. RPS, Singapore.
[FB09b]: S. Fourey and L. Brun. A first step toward combinatorial pyramids in n-d spaces. In Proc. of 7th Workshop on Graph-Based Representation in Pattern Recognition, volume 5534 of Lecture Notes in Computer Science, pages 304–313, Venice, Italy, May 2009. Springer Berlin/Heidelberg.
[FH98]: P.F. Felzenszwalb and D.P. Huttenlocher. Image segmentation using local variation. In Proc. of Computer Vision and Pattern Recognition, pages 98–104, June 1998.
[FH04]: P.F. Felzenszwalb and D.P. Huttenlocher. Efficient graph-based image segmentation. International Journal of Computer Vision, 59(2):167–181, 2004.
[Fio95]: C. Fiorio. Approche interpixel en analyse d’images : une topologie et des algorithmes de segmentation. Thèse de doctorat, Université Montpellier II, 24 novembre 1995.
[Fio96]: C. Fiorio. A topologically consistent representation for image analysis: the frontiers topological graph. In Proceedings of International Conference Discrete Geometry for Computer Imagery, volume 1176 of Lecture Notes in Computer Science, pages 151–162, Lyon, France, november 1996.
[FK97]: A.T. Fomenko and T.L. Kunii. Topological Modeling for Visualization. Springer, 1997.
[FML06]: D. Fradin, D. Meneveaux, and P. Lienhardt. A hierarchical topology-based model for handling complex indoor scenes. Computer Graphics Forum, 25(2):149–162, June 2006.
[FP90]: F. Fritsch and R.A. Piccinini. Cellular Structures in Topology. Cambridge University Press, 1990.
[Fra04]: D. Fradin. Modélisation et simulation d’éclairage à base topologique : application aux environnements architecturaux complexes. Thèse de doctorat, Université de Poitiers, Décembre 2004.
[GBD09]: R. Goffe, L. Brun, and G. Damiand. A top-down construction scheme for irregular pyramids. In Proc. of 4th International Conference On Computer Vision Theory And Applications, pages 163–170, Lisboa, Portugal, February 2009.
[GBD10]: R. Goffe, L. Brun, and G. Damiand. Tiled top-down combinatorial pyramids for large images representation. International Journal of Imaging Systems and Technology, 2010. to appear.
[GDB09]: R. Goffe, G. Damiand, and L. Brun. Extraction of tiled top-down irregular pyramids from large images. In Proc. of 13th International Workshop on Combinatorial Image Analysis, Research Publishing Services, pages 123–137, Cancun, Mexico, November 2009. RPS, Singapore.
[GDB10]: R. Goffe, G. Damiand, and L. Brun. A causal extraction scheme in top-down pyramids for large images segmentation. In Proc. of 13th International Workshop on Structural and Syntactic Pattern Recognition, Lecture Notes in Computer Science, Cesme, Izmir, Turkey, August 2010. Springer Berlin/Heidelberg. to appear.
[GDS09]: S. Gosselin, G. Damiand, and C. Solnon. Signatures of combinatorial maps. In Proc. of 13th International Workshop on Combinatorial Image Analysis, volume 5852 of Lecture Notes in Computer Science, pages 370–382, Cancun, Mexico, November 2009. Springer Berlin/Heidelberg.
[GHPVT89]: M. Gangnet, J.C. Herve, T. Pudet, and J.M. Van Thong. Incremental computation of planar maps. ACM Computer Graphics, 23(3):345–354, 1989.
[Gib81]: P.J. Giblin. Graphs, Surfaces, and Homology: An Introduction to Algebraic Topology. Mathematics Series. Chapman and Hall, New-York, 2^nd edition, 1981. 329 pages.
[GS85]: L. Guibas and J. Stolfi. Primitives for the manipulation of general subdivisions and the computation of voronoi diagrams. ACM Trans. Graph., 4(2):74–123, 1985.
[Gui00]: O. Guilbert. Un modèle hiérarchique pour la modélisation géométrique à base toplogique. Thèse de doctorat, Université Louis Pasteur de Strasbourg, janvier 2000.
[Hat02]: A. Hatcher. Algebraic Topology. Cambridge University Press, 2002. disponible sur http://www.math.cornell.edu/∼hatcher/AT/ATpage.html.
[Hav05]: S. Havemann. Generative Mesh Modeling. PhD thesis, Technische Universität Braunschweig, November 2005.
[HDMB07]: S. Horna, G. Damiand, D. Meneveaux, and Y. Bertrand. Building 3d indoor scenes topology from 2d architectural plans. In Proc. of 2nd International Conference on Computer Graphics Theory and Applications, pages 37–44, Barcelona, Spain, March 2007.
[Her98]: G.T. Herman. Geometry of Digital Spaces. Birkhäuser Boston, 1998.
[HMDB09]: S. Horna, D. Meneveaux, G. Damiand, and Y. Bertrand. Consistency constraints and 3d building reconstruction. Computer-Aided Design, 41(1):13–27, January 2009.
[Hor08]: S. Horna. Reconstruction géométrique et topologique de complexes architecturaux 3D à partir de plans numériques 2D. Thèse de doctorat, Université de Poitiers, Novembre 2008.
[HW83]: G.T. Herman and D. Webster. A topological proof of a surface tracking algorithm. Computer Vision, Graphics, and Image Processing, 23:162–177, 1983.
[Jac70]: A. Jacques. Constellations et graphes topologiques. In Proceedings of Combinatorial Theory and Applications, volume 2, pages 657–673, Budapest, Hungary, 1970.
[JM92]: J.M. Jolion and A. Montanvert. The adaptative pyramid: a framework for 2d image analysis. Computer Vision, Graphics, and Image Processing: Image Understanding, 55(3):339–348, 1992.
[Jol03]: J.M. Jolion. Stochastic pyramid revisited. Pattern Recognition Letter, 24(8):1035–1042, 2003.
[KCB09]: P. Kraemer, D. Cazier, and D. Bechmann. Extension of half-edges for the representation of multiresolution subdivision surfaces. The Visual Computer, 25(2):149–163, 2009.
[KKM90a]: E. Khalimsky, R. Kopperman, and P.R. Meyer. Boundaries in digital planes. Journal of Applied Mathematics and Stochastic Analysis, 3(1):27–55, 1990.
[KKM90b]: E. Khalimsky, R. Kopperman, and P.R. Meyer. Computer graphics and connected topologies on finite ordered sets. Topology and its Applications, 36:1–17, 1990.
[KKM91]: T.Y. Kong, R. Kopperman, and P.R. Meyer. A topological approach to digital topology. American Mathematical Monthly, 98(10):901–917, 1991.
[Kle00]: R Klette. Cell complexes through time. In Proc. Vision Geometry IX, pages 134–145, San Diego, CA, USA, 2000.
[KM95]: W.G. Kropatsch and H. Macho. Finding the structure of connected components using dual irregular pyramids. In Proceedings of International Conference Discrete Geometry for Computer Imagery, pages 147–158, september 1995.
[KMS98]: T. Kaczynski, M. Mrozek, and M. Slusarek. Homology computation by reduction of chain complexes. Computers & Math. Appl., 34(4):59–70, 1998.
[Kon02]: T. Y. Kong. Topological adjacency relations on zⁿ. Theoretical Computer Science, 283:3–68, June 2002.
[Köt02]: U. Köthe. Xpmaps and topological segmentation - a unified approach to finite topologies in the plane. In Proceedings of International Conference Discrete Geometry for Computer Imagery, volume 2301 of Lecture Notes in Computer Science, pages 22–33, Bordeaux, France, april 2002.
[Kov84]: V.A. Kovalevsky. Discrete topology and contour definition. Pattern Recognition Letters, 2(5):281–288, 1984.
[Kov89]: V.A. Kovalevsky. Finite topology as applied to image analysis. Computer Vision, Graphics, and Image Processing, 46:141–161, 1989.
[Kov08]: V.A. Kovalevsky. Geometry of Locally Finite Spaces. Publishing House, Berlin, Germany, 2008.
[KR89]: T.Y. Kong and A. Rosenfeld. Digital topology: introduction and survey. Computer Vision, Graphics, and Image Processing, 48(3):357–393, 1989.
[KR04]: R. Klette and A. Rosenfeld. Digital Geometry: Geometric Methods for Digital Picture Analysis. Morgan Kaufmann Publishers, 2004.
[Kro95]: W.G. Kropatsch. Building irregular pyramids by dual-graph contraction. Vision, Image and Signal Processing, 142(6):366–374, december 1995.
[KU92]: T.Y. Kong and J.K. Udupa. A justification of a fast surface tracking algorithm. Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, 54:162–170, 1992.
[Lac03]: J.-O. Lachaud. Coding cells of digital spaces: a framework to write generic digital topology algorithms. Electronic Notes in Discrete Mathematics, 12:337–348, 2003.
[Lan95]: V. Lang. Une étude de l’utilisation des ensembles simpliciaux en modélisation géométrique interactive. Thèse de doctorat, Université Louis Pasteur de Strasbourg, Strasbourg, France, 1995.
[Lee00]: J. M. Lee. Introduction to Topological Manifolds. Graduate Texts in Mathematics. Springer, May 2000.
[Lev99]: B. Levy. Topologie algorithmique : combinatoire et plongement. Thèse de doctorat, Institut National Polytechnique de Lorraine, Octobre 1999.
[LFB07]: P. Lienhardt, L. Fuchs, and Y. Bertrand. Informatique graphique, modélisation géométrique et animation., chapter Modèles topologiques, pages 49–93. Traitement du Signal et de l’Image. Hermès, 2007. sous la direction de D. Bechmann et B. Péroche.
[Lie88]: P. Lienhardt. Extension of the notion of map and subdivisions of a three-dimensional space. In Proceedings of 5^th Symposium on the Theoretical Aspects of Computer Science, volume 294 of Lecture Notes in Computer Science, pages 301–311, Bordeaux, France, february 1988.
[Lie89]: P. Lienhardt. Subdivision of n-dimensional spaces and n-dimensional generalized maps. In Proceedings of 5^th Annual ACM Symposium on Computational Geometry, pages 228–236, Saarbrücken, Germany, 1989.
[Lie91]: P. Lienhardt. Topological models for boundary representation: a comparison with n-dimensional generalized maps. Commputer Aided Design, 23(1):59–82, 1991.
[Lie93]: P. Lienhardt. N-dimensional generalized combinatorial maps and cellular quasi-manitolds. Research Report R 93-04, Université Louis Pasteur, département d’informatique, Strasbourg, France, mars 1993.
[Lie94]: P. Lienhardt. N-dimensional generalized combinatorial maps and cellular quasi-manifolds. International Journal of Computational Geometry and Applications, 4(3):275–324, 1994.
[LL95]: V. Lang and P. Lienhardt. Geometric modeling with simplicial sets. In Proceedings of Pacific Graphics’95, Seoul, Korea, 1995.
[LSM08]: P.-F. Léon, X. Skapin, and P. Meseure. A topology-based animation model for the description of 2d models with a dynamic structure. In Virtual Reality Interactions and Physical Simulations VRIPHYS. EG, Novembre 2008.
[LSM09]: P.-F. Léon, X. Skapin, and P. Meseure. Modèle générateur d’évolutions géologiques par animation basée sur la topologie. Revue Électronique Francophone d’Informatique Graphique, 3(1):31–50, Janvier 2009.
[Män84]: M. Mäntylä. A note on the modeling space of euler operators. Computer Vision, Graphics, and Image Processing, 26(1):45–60, April 1984.
[Män88]: M. Mäntylä. An Introduction to Solid Modeling. Principles Computer Science. Computer Science Press, Rockville, MD, 1988.
[May67]: J. P. May. Simplicial Objects in Algebraic Topology. Van Nostrand, 1967.
[Mee89]: P. Meer. Stochastic image pyramids. Computer Vision, Graphics, and Image Processing, 45:269–294, 1989.
[MMR91]: A. Montanvert, P. Meer, and A. Rosenfeld. Hierarchical image analysis using irregular tesselations. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(4):307–316, 1991.
[MP78]: D.E. Muller and F.P. Preparata. Finding the intersection of two convex polyhedra. Theoretical Computer Science, 7(217-236), 1978.
[Mun84]: J.R. Munkres. Elements of Algebraic Topology. Perseus Books, 1984.
[Nov55]: P.S. Novikov. On the algorithmic unsolvability of the word problem in group theory. Proceedings of Steklov Mathematical Institute, 44:1–145, 1955.
[PABL07]: M. Poudret, A. Arnould, Y. Bertrand, and P. Lienhardt. Cartes combinatoires ouvertes. Research Notes 2007-1, Laboratoire SIC E.A. 4103, F-86962 Futuroscope Cedex, France, October 2007.
[PBCF93]: A. Paoluzzi, F. Bernardini, C. Cattani, and V. Ferruci. Dimension-independent modeling with simplicial complexes. A.C.M. Transactions on Graphics, 12(1):56–102, 1993.
[Pel06]: S. Peltier. Calcul de groupes d’homologie sur des structures simpliciales, simploïdales et cellulaires. Thèse de doctorat, Université de Poitiers, Juin 2006.
[PIH⁺07]: S. Peltier, A. Ion, Y. Haxhimusa, W.g. Kropatsch, and G. Damiand. Computing homology group generators of images using irregular graph pyramids. In Proc. of 6th Workshop on Graph-Based Representations in Pattern Recognition, volume 4538 of Lecture Notes in Computer Science, pages 283–294, Alicante, Spain, June 2007. Springer Berlin/Heidelberg.
[PIK⁺09]: S. Peltier, A. Ion, W.g. Kropatsch, G. Damiand, and Y. Haxhimusa. Directly computing the generators of image homology using graph pyramids. Image and Vision Computing, 27(7):846–853, June 2009.
[Ros74]: A. Rosenfeld. Adjacency in digital pictures. Information and Control, 26(1):24–33, 1974.
[SD06]: C. Simon and G. Damiand. Generalized map pyramid for multi-level 3d image segmentation. In Proc. of 13th International Conference on Discrete Geometry for Computer Imagery, volume 4245 of Lecture Notes in Computer Science, pages 530–541, Szeged, Hungary, October 2006. Springer Berlin/Heidelberg.
[SDL05a]: C. Simon, G. Damiand, and P. Lienhardt. Pyramids of n-dimensional generalized maps. In Proc. of 5th Workshop on Graph-Based Representations in Pattern Recognition, volume 3434 of Lecture Notes in Computer Science, pages 142–152, Poitiers, France, April 2005. Springer Berlin/Heidelberg.
[SDL05b]: C. Simon, G. Damiand, and P. Lienhardt. Receptive fields for generalized map pyramids: The notion of generalized orbit. In Proc. of 12th International Conference on Discrete Geometry for Computer Imagery, volume 3429 of Lecture Notes in Computer Science, pages 56–67, Poitiers, France, April 2005. Springer Berlin/Heidelberg.
[SDL06]: C. Simon, G. Damiand, and P. Lienhardt. nd generalized map pyramids: Definition, representations and basic operations. Pattern Recognition, 39(4):527–538, April 2006.
[Sim06]: C Simon. Définition et étude des pyramides généralisées nD : application pour la segmentation multi-échelle d’images 3D. Thèse de doctorat, Université de Poitiers, Décembre 2006.
[Spa66]: E. H. Spanier. Algebraic topology. Springer, 1966.
[Spe91]: J.C. Spehner. Merging in maps and in pavings. Theoretical Computer Science, 86(2):205–232, September 1991.
[SSG89]: D. Salesin, J Stolfi, and L. Guibas. Epsilon geometry: building robust algorithms from imprecise computations. In SCG ’89: Proceedings of the fifth annual symposium on Computational geometry, pages 208–217, New York, NY, USA, 1989. ACM.
[Sti80]: J. Stillwell. Classical topology and combinatorial group theory. Graduate Texts in Mathematics. Springer-Verlag, New York, 1980.
[Str06]: I.A. Stroud. Boundary Representation Modelling Techniques. Springer, 2006.
[Tak91]: T. Takala. A taxonomy on geometric and topological models. In C.Pienovi B.Falcidieno, I.Herman, editor, Proceedings of Computer Graphics and Mathematics, pages 147–171. Springer-Verlag, 1991.
[Tar75]: R. Tarjan. Efficiency of a good but not linear set union algorithm. Journal of the ACM, 22(2):215–225, 1975.
[Tut63]: W.T. Tutte. A census of planar maps. Canad. J. Math., 15:249–271, 1963.
[Udu94]: J.K. Udupa. Multidimensional digital boundaries. Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, 56(4):311–323, July 1994.
[VY90]: G. Vegter and C.K. Yap. Computational complexity of combinatorial surfaces. In Proceedings of SCG ’90: the sixth annual symposium on Computational geometry, pages 102–111, New York, NY, USA, 1990. ACM.
[Wei85]: K. Weiler. Edge-based data structures for solid modeling in curved-surface environments. IEEE Computer Graphics and Applications, 5(1):21–40, 1985.
[Wei88]: K. Weiler. The radial edge structure: a topological representation for non-manifold geometric boundary modeling. In M.J. Wozny, H.W. McLaughlin, and J.L. Encarnacao, editors, Geometric Modeling for CAD Applications, pages 217–254. Elsevier Science, 1988.
[Whi49]: J.H.C. Whitehead. Combinatorial homotopy ii. Bull. Amer. Math. Soc., 55(5):453–496, 1949.
[WK94]: D. Willersinn and W.G. Kropatsch. Dual graph contraction for irregular pyramids. In Proceedings of 12th IAPR International Conference on Signal Processing, volume 3, pages 251–256, Jerusalem, Israel, 1994.
[Yap04]: Chee K. Yap. Robust geometric computation. In Jacob E. Goodman and Joseph O’Rourke, editors, Handbook of Discrete and Computational Geometry, chapter 41, pages 927–952. Chapmen & Hall/CRC, Boca Raton, FL, 2nd edition, 2004. Revised and expanded from 1997 version.