Removal Operations in nD Generalized Maps for Efficient Homology Computation

Damiand G., Gonzalez-Diaz R., Peltier S.

Proc. of 4th International Workshop on Computational Topology in Image Context (CTIC)
Lecture Notes in Computer Science 7309, pages 20-29, May 2012, Bertinoro, Italy

Abstract: In this paper, we present an efficient way for computing homology generators of nD generalized maps. The algorithm proceeds in two steps: (1) cell removals reduces the number of cells while preserving homology; (2) homology generator computation is performed on the reduced object by reducing incidence matrices into their Smith-Agoston normal form. In this paper, we provide a definition of cells that can be removed while preserving homology. Some results on 2D and 3D homology generators computation are presented.

Keywords: nD Generalized Maps; Cellular Homology; Homology Generators; Removal Operations.

BibTex references

@InProceedings{DGP12,
      author = {Damiand, G. and Gonzalez-Diaz, R. and Peltier, S.},
      title = {Removal Operations in nD Generalized Maps for Efficient Homology Computation},
      booktitle = {Proc. of 4th International Workshop on Computational Topology in Image Context (CTIC)},
      series = {Lecture Notes in Computer Science},
      publisher = {Springer Berlin/Heidelberg},
      volume = {7309},
      pages = {20-29},
      month = {May},
      year = {2012},
      address = {Bertinoro, Italy},
      keywords = {nD Generalized Maps; Cellular Homology; Homology Generators; Removal Operations.},
      url = {https://doi.org/10.1007/978-3-642-30238-1_3}
}

Guillaume Damiand

Removal Operations in nD Generalized Maps for Efficient Homology Computation

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BibTex references

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