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Journal articles
Homological Reconstruction and Simplification in R3
Abstract : 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.
Cited literature [21 references]
https://hal.archives-ouvertes.fr/hal-01132440
Contributor : Olivier Devillers <>
Submitted on : Tuesday, April 21, 2015 - 5:31:28 PM
Last modification on : Monday, December 14, 2020 - 5:02:54 PM
Long-term archiving on: : Wednesday, April 19, 2017 - 2:25:22 AM
Contributor : Olivier Devillers <>
Submitted on : Tuesday, April 21, 2015 - 5:31:28 PM
Last modification on : Monday, December 14, 2020 - 5:02:54 PM
Long-term archiving on: : Wednesday, April 19, 2017 - 2:25:22 AM
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2014-cgta-NP-hardness.pdf
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