{"quality_controlled":"1","scopus_import":1,"abstract":[{"lang":"eng","text":"We are interested in 3-dimensional images given as arrays of voxels with intensity values. Extending these values to acontinuous function, we study the robustness of homology classes in its level and interlevel sets, that is, the amount of perturbationneeded to destroy these classes. The structure of the homology classes and their robustness, over all level and interlevel sets, can bevisualized by a triangular diagram of dots obtained by computing the extended persistence of the function. We give a fast hierarchicalalgorithm using the dual complexes of oct-tree approximations of the function. In addition, we show that for balanced oct-trees, thedual complexes are geometrically realized in $R^3$ and can thus be used to construct level and interlevel sets. We apply these tools tostudy 3-dimensional images of plant root systems."}],"citation":{"mla":"Bendich, Paul, et al. “Computing Robustness and Persistence for Images.” <i>IEEE Transactions of Visualization and Computer Graphics</i>, vol. 16, no. 6, IEEE, 2010, pp. 1251–60, doi:<a href=\"https://doi.org/10.1109/TVCG.2010.139\">10.1109/TVCG.2010.139</a>.","apa":"Bendich, P., Edelsbrunner, H., &#38; Kerber, M. (2010). Computing robustness and persistence for images. <i>IEEE Transactions of Visualization and Computer Graphics</i>. IEEE. <a href=\"https://doi.org/10.1109/TVCG.2010.139\">https://doi.org/10.1109/TVCG.2010.139</a>","ieee":"P. Bendich, H. Edelsbrunner, and M. Kerber, “Computing robustness and persistence for images,” <i>IEEE Transactions of Visualization and Computer Graphics</i>, vol. 16, no. 6. IEEE, pp. 1251–1260, 2010.","chicago":"Bendich, Paul, Herbert Edelsbrunner, and Michael Kerber. “Computing Robustness and Persistence for Images.” <i>IEEE Transactions of Visualization and Computer Graphics</i>. IEEE, 2010. <a href=\"https://doi.org/10.1109/TVCG.2010.139\">https://doi.org/10.1109/TVCG.2010.139</a>.","ama":"Bendich P, Edelsbrunner H, Kerber M. Computing robustness and persistence for images. <i>IEEE Transactions of Visualization and Computer Graphics</i>. 2010;16(6):1251-1260. doi:<a href=\"https://doi.org/10.1109/TVCG.2010.139\">10.1109/TVCG.2010.139</a>","short":"P. Bendich, H. Edelsbrunner, M. Kerber, IEEE Transactions of Visualization and Computer Graphics 16 (2010) 1251–1260.","ista":"Bendich P, Edelsbrunner H, Kerber M. 2010. Computing robustness and persistence for images. IEEE Transactions of Visualization and Computer Graphics. 16(6), 1251–1260."},"intvolume":"        16","author":[{"last_name":"Bendich","full_name":"Bendich, Paul","id":"43F6EC54-F248-11E8-B48F-1D18A9856A87","first_name":"Paul"},{"full_name":"Edelsbrunner, Herbert","last_name":"Edelsbrunner","first_name":"Herbert","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"},{"orcid":"0000-0002-8030-9299","id":"36E4574A-F248-11E8-B48F-1D18A9856A87","first_name":"Michael","last_name":"Kerber","full_name":"Kerber, Michael"}],"department":[{"_id":"HeEd"}],"title":"Computing robustness and persistence for images","status":"public","ddc":["000"],"month":"10","type":"journal_article","has_accepted_license":"1","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","file_date_updated":"2020-07-14T12:46:21Z","date_published":"2010-10-28T00:00:00Z","oa_version":"Submitted Version","date_created":"2018-12-11T12:05:47Z","date_updated":"2021-01-12T07:53:04Z","_id":"3901","publication":"IEEE Transactions of Visualization and Computer Graphics","publist_id":"2253","doi":"10.1109/TVCG.2010.139","issue":"6","file":[{"access_level":"open_access","file_name":"IST-2016-536-v1+1_2010-J-02-PersistenceforImages.pdf","creator":"system","date_updated":"2020-07-14T12:46:21Z","checksum":"f6d813c04f4b46023cec6b9a17f15472","relation":"main_file","file_id":"5262","content_type":"application/pdf","date_created":"2018-12-12T10:17:10Z","file_size":721994}],"page":"1251 - 1260","publication_status":"published","pubrep_id":"536","day":"28","volume":16,"publisher":"IEEE","year":"2010","oa":1,"language":[{"iso":"eng"}]}