[{"article_type":"original","date_published":"2015-06-03T00:00:00Z","OA_type":"free access","doi":"10.1016/j.comgeo.2014.08.010","article_processing_charge":"No","project":[{"grant_number":"318493","_id":"255D761E-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Topological Complex Systems"}],"citation":{"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>.","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.","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>","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.","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>.","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>"},"department":[{"_id":"HeEd"}],"page":"606 - 621","day":"03","month":"06","ec_funded":1,"publication":"Computational Geometry: Theory and Applications","_id":"1805","quality_controlled":"1","corr_author":"1","volume":48,"OA_place":"publisher","issue":"8","date_updated":"2025-09-23T09:18:30Z","intvolume":"        48","year":"2015","oa_version":"Published Version","publication_status":"published","scopus_import":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","date_created":"2018-12-11T11:54:06Z","language":[{"iso":"eng"}],"external_id":{"isi":["000357353200006"]},"author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"last_name":"Bauer","first_name":"Ulrich","orcid":"0000-0002-9683-0724","id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","full_name":"Bauer, Ulrich"},{"full_name":"Devillers, Olivier","first_name":"Olivier","last_name":"Devillers"},{"full_name":"Glisse, Marc","last_name":"Glisse","first_name":"Marc"},{"full_name":"Lieutier, André","last_name":"Lieutier","first_name":"André"}],"status":"public","isi":1,"type":"journal_article","publist_id":"5305","publisher":"Elsevier","related_material":{"record":[{"status":"public","id":"2812","relation":"earlier_version"}]},"title":"Homological reconstruction and simplification in R3","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1016/j.comgeo.2014.08.010"}],"oa":1,"abstract":[{"lang":"eng","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."}]}]