{"corr_author":"1","quality_controlled":"1","ddc":["500"],"publication":"Computational Geometry: Theory and Applications","date_published":"2015-06-03T00:00:00Z","OA_place":"publisher","publisher":"Elsevier","intvolume":"        48","abstract":[{"text":"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 double-struck R3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on double-struck 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.","lang":"eng"}],"author":[{"last_name":"Attali","full_name":"Attali, Dominique","first_name":"Dominique"},{"full_name":"Bauer, Ulrich","first_name":"Ulrich","orcid":"0000-0002-9683-0724","last_name":"Bauer","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Devillers, Olivier","first_name":"Olivier","last_name":"Devillers"},{"last_name":"Glisse","full_name":"Glisse, Marc","first_name":"Marc"},{"last_name":"Lieutier","full_name":"Lieutier, André","first_name":"André"}],"date_updated":"2026-06-18T17:57:28Z","year":"2015","isi":1,"main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.comgeo.2014.08.010"}],"volume":48,"department":[{"_id":"HeEd"}],"related_material":{"record":[{"id":"2812","status":"public","relation":"earlier_version"}]},"scopus_import":"1","type":"journal_article","article_processing_charge":"No","month":"06","issue":"8","status":"public","publist_id":"5305","date_created":"2018-12-11T11:54:06Z","language":[{"iso":"eng"}],"article_type":"original","doi":"10.1016/j.comgeo.2014.08.010","project":[{"name":"Topological Complex Systems","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"318493"}],"oa":1,"external_id":{"isi":["000357353200006"]},"page":"606 - 621","oa_version":"Published Version","publication_status":"published","OA_type":"free access","_id":"1805","fulldoi":"https://doi.org/10.1016/j.comgeo.2014.08.010","title":"Homological reconstruction and simplification in R3","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"citation":{"ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 8. Elsevier, pp. 606–621, 2015.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., &#38; Lieutier, A. (2015). Homological reconstruction and simplification in R3. <i>Computational Geometry: Theory and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">https://doi.org/10.1016/j.comgeo.2014.08.010</a>","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” <i>Computational Geometry: Theory and Applications</i>, vol. 48, no. 8, Elsevier, 2015, pp. 606–21, doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">10.1016/j.comgeo.2014.08.010</a>.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, Computational Geometry: Theory and Applications 48 (2015) 606–621.","ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2015. Homological reconstruction and simplification in R3. Computational Geometry: Theory and Applications. 48(8), 606–621.","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. <i>Computational Geometry: Theory and Applications</i>. 2015;48(8):606-621. doi:<a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">10.1016/j.comgeo.2014.08.010</a>","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” <i>Computational Geometry: Theory and Applications</i>. Elsevier, 2015. <a href=\"https://doi.org/10.1016/j.comgeo.2014.08.010\">https://doi.org/10.1016/j.comgeo.2014.08.010</a>."},"day":"03"}