, Equivalence between closed connected n-g-maps without multi-incidence and n-surfaces, J. Math. Imaging Vis, vol.32, issue.1, pp.1-22, 2008.
, A boundary operator for computing the homology of cellular structures Algebraic Topology, a first course. Pure and applied mathematics Conversion between chains of maps and chains of surfaces; application to the computation of incidence graphs homology, 1976.
, Border operator for generalized maps References References editors, Discrete Geometry for Computer Imagery A polyhedron representation for computer vision, Srecko Brlek, Christophe Reutenauer, and Xavier Provençal Proc. AFIPS Nat. Conf., volume, pp.300-312, 1975.
, Comparison and convergence of two topological models for 3d image segmentation Topological encoding of 3d segmented images, Proceedings of 4th IAPR-TC15 Workshop on Graph-Based Representations in Pattern Recognition Proceedings of 9th Discrete Geometry for Computer Imagery Braquelaire and P. Guitton. A model for image structuration Proc. Computer Graphics International'88, pp.59-70, 1988.
, Designing a Topological Modeler Kernel: A Rule-Based Approach, 2010 Shape Modeling International Conference, pp.387-426, 1993.
DOI : 10.1109/SMI.2010.31
URL : https://hal.archives-ouvertes.fr/hal-00488171
, Automatic building of structured geological models Non-manifold modeling : an approach based on spatial subdivisions, Journal of Computing and Information Science in Ingeneering Computer-Aided Design, vol.5, issue.23, pp.29299-320, 1997.
, Representing topological structures using cell-chains Geometric Modeling and Processing -GMP Topological model for two-dimensional image representation: definition and optimal extraction algorithm First results for 3d image segmentation with topological map, Proceedings of 14th International Conference on Discrete Geometry for Computer Imagery, pp.248-266111, 1995.
, Coreduction homology algorithm for regular cw-complexes Primitives for the manipulation of three-dimensional subdivisions Computing Homology Generators for Volumes Using Minimal Generalized Maps On efficient sparse integer matrix smith normal form computations, International Workshop on Combinatorial Image Analysis International Workshop on Combinatorial Image Analysis, pp.361-3883, 1960.
, CELLULAR COMPLEXES AS STRUCTURED SEMI-SIMPLICIAL SETS, International Journal of Shape Modeling, vol.01, issue.02, pp.191-217511, 1990.
DOI : 10.1142/S021865439400013X
, Chain homotopies for object topological representations, Discrete Applied Mathematics, vol.157, issue.3, pp.490-499, 2009.
DOI : 10.1016/j.dam.2008.05.029
, Probabilistic computation of the smith normal form of a sparse integer matrix, Proceedings of the Second Int. Symp. on Algorithmic Number Theory, pp.173-186, 1996.
, Vertex-based representation of nonmanifolds boundaries Primitives for the manipulation of general subdivisions and the computation of voronoi diagrams Algebraic Topology On the realizability of homotopy groups and their operations, Geometric Modeling for Product EngineeringJac70] A. Jacque. Constellations et graphes topologiques Colloque Math. Soc. Janos BolyaiKB79] R. Kannan and A. Bachem. Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix. SIAM Journal on Computing, pp.107-13074, 1951.
, Computational Homology Homology computation by reduction of chain complexes Topological models for boundary representation: a comparison with n-dimensional generalized maps N-dimensional generalized combinatorial maps and cellular quasimanifolds Simplicial sets and triangular patches Partial entity structure : a fast and compact non-manifold boundary representation based on partial topological entities Holes and Genus of 2D and 3D Digital Images. CVGIP: Graphical Models and Image Processing Cartesian product of simplicial and cellular structures Simplicial objects in algebraic topology, Proceedings of CGI'96 6th A.C.M. Symposium on Solid Modeling and ApplicationsMas91] W. S. Massey. A Basic Course in Algebraic Topology. Graduate Texts in Mathematics Proc. IAPR Graph-based representations in pattern recognition, pp.59-7059, 1967.
, The GeoMap: A Unified Representation for Topology and Geometry, GbRPR, pp.132-141, 1975.
DOI : 10.1007/978-3-540-31988-7_12
, Analysis of blood vessel topology by cubical homology, Proceedings. International Conference on Image Processing, pp.969-972, 2002.
DOI : 10.1109/ICIP.2002.1040114
, Computation of homology groups and generators, Computers & Graphics, vol.30, issue.1, pp.62-69, 2006.
DOI : 10.1016/j.cag.2005.10.011
URL : https://hal.archives-ouvertes.fr/hal-00308012
, Computation of Homology Groups and Generators. computer & graphics Simploidals sets: Definitions, operations and comparison with simplicial sets. Discrete App References References Homologie singuliere des espaces fibres Merging in maps and pavings Near optimal algorithms for computing smith normal forms of integer matrices, Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation, pp.62-69542, 1951.
, 3gmap l-systems: an application to the modelling of wood. The Visual Computer [UCB13] Lionel Untereiner, David Cazier, and Dominique Bechmann. n-dimensional multiresolution representation of subdivision meshes with arbitrary topology Optimal pants decompositions and shortest homotopic cycles on an orientable surface The radial-edge data structure: A topological representation for nonmanifold geometry boundary modeling, Proc. IFIP WG 5.2 Working Conference, pp.165-180231, 1983.