Computing Homology for Surfaces with Generalized Maps: Application to 3D Images

Damiand G., Peltier S., Fuchs L.

Proc. of 2nd International Symposium on Visual Computing (ISVC)
Lecture Notes in Computer Science 4292, pages 235-244, November 2006, Lake Tahoe, Nevada, USA

Abstract: In this paper, we present an algorithm which allows to compute efficiently generators of the first homology group of a closed surface, orientable or not. Starting with an initial subdivision of a surface, we simplify it to its minimal form (minimal refers to the number of cells), while preserving its homology. Homology generators can thus be directly deduced from the minimal representation of the initial surface. Finally, we show how this algorithm can be used in a 3D labelled image in order to compute homology of each region described by its boundary.

Keywords: Topological features; Homology generators; Generalized maps; Minimal subdivision.

BibTex references

@InProceedings{DPF06,
      author = {Damiand, G. and Peltier, S. and Fuchs, L.},
      title = {Computing Homology for Surfaces with Generalized Maps: Application to 3D Images},
      booktitle = {Proc. of 2nd International Symposium on Visual Computing (ISVC)},
      series = {Lecture Notes in Computer Science},
      publisher = {Springer Berlin/Heidelberg},
      volume = {4292},
      pages = {235-244},
      month = {November},
      year = {2006},
      address = {Lake Tahoe, Nevada, USA},
      keywords = {Topological features; Homology generators; Generalized maps; Minimal subdivision.},
      url = {https://doi.org/10.1007/11919629_25}
}

Guillaume Damiand

Computing Homology for Surfaces with Generalized Maps: Application to 3D Images

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BibTex references

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