Computing homology for surfaces with generalized maps: Application to 3D images

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4292 LNCS - II, Issue , 2006, Pages 235-244

  Damiand, Guillaume ^a   Peltier, Samuel ^b   Fuchs, Laurent ^a  

^a SIC Laboratory   (France)

^b VIENNA UNIVERSITY OF TECHNOLOGY   (Austria)

Author keywords

Generalized maps; Homology generators; Minimal subdivision; Topological features

Indexed keywords

ALGORITHMS; COMPUTATION THEORY; THREE DIMENSIONAL;

GENERALIZED MAPS; HOMOLOGY GENERATORS; MINIMAL SUBDIVISION; TOPOLOGICAL FEATURES;

IMAGE ANALYSIS;

EID: 33845415698     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11919629_25     Document Type: Conference Paper

References (14)

1. Lienhardt, P.: Topological models for boundary representation: a comparison with n-dimensional generalized maps. Commputer Aided Design 23 (1991)
2. Lienhardt, P.: N-dimensional generalized combinatorial maps and cellular quasi-manifolds. International Journal of Computational Geometry and Applications 4 (1994) 275-324
3. Kaczynski, T., Mrozek, M., Slusarek, M.: Homology computation by reduction of chain complexes. Computers & Math. Appl. 34 (1998) 59-70
4. Damiand, G., Lienhardt, P.: Removal and contraction for n-dimensional generalized maps. In: Discrete Geometry for Computer Imagery. Number 2886 in Lecture Notes in Computer Science, Naples, Italy (2003) 408-419
5. Hatcher, A.: Algebraic Topology. Cambridge University Press (2002) available on http://www.math.cornell.edu/~hatcher/AT/ATpage.html.
6. Taxjan, R.: Efficiency of a good but not linear set union algorithm. Journal of the ACM 22 (1975) 215-225
7. Braquelaire, J.P., Desbarats, P., Domenger, J.P., Wüthrich, C.: A topological structuring for aggregates of 3d discrete objects. In: Workshop on Graph-Based Representations in Pattern Recognition, Austria, IAPR-TC15 (1999) 193-202
8. Bertrand, Y., Damiand, G., Fiorio, C.: Topological map: Minimal encoding of 3d segmented images. In: Workshop on Graph-Based Representations in Pattern Recognition, Ischia, Italy, IAPR-TC15 (2001) 64-73
9. Domenger, J.: Conception et implementation du noyeau graphique d'un environnement 2D1/2 d'édition d'images discrètes. Thèse de doctorat, Université Bordeaux I (1992)
10. Fiorio, C.: A topologically consistent representation for image analysis: the frontiers topological graph, In: Discrete Geometry for Computer Imagery. Number 1176 in Lecture Notes in Computer Science, Lyon, France (1996) 151-162
11. Braquelaire, J.P., Brun, L.: Image segmentation with topological maps and inter-pixel representation. Journal of Visual Communication and Image Representation 9 (1998) 62-79
12. Damiand, G., Resch, P.: Topological map based algorithms for 3d image segmentation. In: Discrete Geometry for Computer Imagery. Number 2301 in Lecture Notes in Computer Science, Bordeaux, France (2002) 220-231
13. Bourdon, P., Alata, O., Damiand, G., Olivier, C., Bertrand, Y.: Geometrical and topological informations for image segmentation with monte carlo markov chain implementation. In: Vision Interface, Calgary, Canada (2002) 413-420
14. Bertrand, Y., Damiand, G., Fiorio, C.: Topological encoding of 3d segmented images. In: Discrete Geometry for Computer Imagery. Number 1953 in Lecture Notes in Computer Science, Uppsala, Sweden (2000) 311-324