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

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.
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International Symposium on Visual Computing, Nov 2006, Lake Tahoe, Nevada, United States. Springer Berlin/Heidelberg, Lecture Notes in Computer Science, 4292, pp.235-244, 2006, Advances in Visual Computing. 〈10.1007/11919629_25〉
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Guillaume Damiand, Samuel Peltier, Laurent Fuchs. Computing Homology for Surfaces with Generalized Maps: Application to 3D Images. International Symposium on Visual Computing, Nov 2006, Lake Tahoe, Nevada, United States. Springer Berlin/Heidelberg, Lecture Notes in Computer Science, 4292, pp.235-244, 2006, Advances in Visual Computing. 〈10.1007/11919629_25〉. 〈hal-00366105〉

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