{"page":"117 - 125","year":"2013","publisher":"ACM","status":"public","day":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_published":"2013-06-01T00:00:00Z","oa":1,"acknowledgement":"Some of the authors were partially supported by the GIGA ANR grant (contract ANR-09-BLAN-0331-01) and the European project CG-Learning (contract 255827).","department":[{"_id":"HeEd"}],"citation":{"ista":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. 2013. Homological reconstruction and simplification in R3. Proceedings of the 29th annual symposium on Computational Geometry. SoCG: Symposium on Computational Geometry, 117–125.","chicago":"Attali, Dominique, Ulrich Bauer, Olivier Devillers, Marc Glisse, and André Lieutier. “Homological Reconstruction and Simplification in R3.” In <i>Proceedings of the 29th Annual Symposium on Computational Geometry</i>, 117–25. ACM, 2013. <a href=\"https://doi.org/10.1145/2462356.2462373\">https://doi.org/10.1145/2462356.2462373</a>.","apa":"Attali, D., Bauer, U., Devillers, O., Glisse, M., &#38; Lieutier, A. (2013). Homological reconstruction and simplification in R3. In <i>Proceedings of the 29th annual symposium on Computational Geometry</i> (pp. 117–125). Rio de Janeiro, Brazil: ACM. <a href=\"https://doi.org/10.1145/2462356.2462373\">https://doi.org/10.1145/2462356.2462373</a>","ama":"Attali D, Bauer U, Devillers O, Glisse M, Lieutier A. Homological reconstruction and simplification in R3. In: <i>Proceedings of the 29th Annual Symposium on Computational Geometry</i>. ACM; 2013:117-125. doi:<a href=\"https://doi.org/10.1145/2462356.2462373\">10.1145/2462356.2462373</a>","mla":"Attali, Dominique, et al. “Homological Reconstruction and Simplification in R3.” <i>Proceedings of the 29th Annual Symposium on Computational Geometry</i>, ACM, 2013, pp. 117–25, doi:<a href=\"https://doi.org/10.1145/2462356.2462373\">10.1145/2462356.2462373</a>.","short":"D. Attali, U. Bauer, O. Devillers, M. Glisse, A. Lieutier, in:, Proceedings of the 29th Annual Symposium on Computational Geometry, ACM, 2013, pp. 117–125.","ieee":"D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier, “Homological reconstruction and simplification in R3,” in <i>Proceedings of the 29th annual symposium on Computational Geometry</i>, Rio de Janeiro, Brazil, 2013, pp. 117–125."},"date_created":"2018-12-11T11:59:44Z","month":"06","doi":"10.1145/2462356.2462373","conference":{"start_date":"2013-06-17","end_date":"2013-06-20","location":"Rio de Janeiro, Brazil","name":"SoCG: Symposium on Computational Geometry"},"author":[{"last_name":"Attali","first_name":"Dominique","full_name":"Attali, Dominique"},{"id":"2ADD483A-F248-11E8-B48F-1D18A9856A87","last_name":"Bauer","orcid":"0000-0002-9683-0724","full_name":"Bauer, Ulrich","first_name":"Ulrich"},{"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"}],"main_file_link":[{"open_access":"1","url":"http://hal.archives-ouvertes.fr/hal-00833791/"}],"_id":"2812","title":"Homological reconstruction and simplification in R3","related_material":{"record":[{"status":"public","id":"1805","relation":"later_version"}]},"quality_controlled":"1","scopus_import":1,"publication_status":"published","publication":"Proceedings of the 29th annual symposium on Computational Geometry","oa_version":"Submitted Version","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 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.","lang":"eng"}],"date_updated":"2023-02-23T10:15:15Z","publist_id":"4072","type":"conference","language":[{"iso":"eng"}]}