TY - CONF
AB - 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 ⊂ X ⊂ 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.
AU - Attali, Dominique
AU - Bauer, Ulrich
AU - Devillers, Olivier
AU - Glisse, Marc
AU - Lieutier, André
ID - 2812
T2 - Proceedings of the 29th annual symposium on Computational Geometry
TI - Homological reconstruction and simplification in R3
ER -