Homological Reconstruction and Simplification in R3
Résumé
We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H*(X) of some complex X with L contained in X and X contained in K. We show that this problem is NP-complete even if K is embedded in R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.
Domaines
Géométrie algorithmique [cs.CG]
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2014-cgta-NP-hardness.pdf (1.09 Mo)
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| Origine | Fichiers produits par l'(les) auteur(s) |
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| Format | Figure, Image |
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| Origine | Fichiers produits par l'(les) auteur(s) |
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