Homological Reconstruction and Simplification in R3 - Archive ouverte HAL Access content directly
Journal Articles Computational Geometry Year : 2015

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.
Fichier principal
Vignette du fichier
2014-cgta-NP-hardness.pdf (1.09 Mo) Télécharger le fichier
Vignette du fichier
vignette.jpg (8.87 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Format Figure, Image
Origin Files produced by the author(s)
Loading...

Dates and versions

hal-01132440 , version 1 (21-04-2015)

Identifiers

Cite

Dominique Attali, Ulrich Bauer, Olivier Devillers, Marc Glisse, André Lieutier. Homological Reconstruction and Simplification in R3. Computational Geometry, 2015, 48 (8), pp.606-621. ⟨10.1016/j.comgeo.2014.08.010⟩. ⟨hal-01132440⟩
659 View
526 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More