{"publisher":"Society for Industrial and Applied Mathematics ","issue":"2","year":"2016","abstract":[{"lang":"eng","text":"We consider the problem of minimizing the continuous valued total variation subject to different unary terms on trees and propose fast direct algorithms based on dynamic programming to solve these problems. We treat both the convex and the nonconvex case and derive worst-case complexities that are equal to or better than existing methods. We show applications to total variation based two dimensional image processing and computer vision problems based on a Lagrangian decomposition approach. The resulting algorithms are very effcient, offer a high degree of parallelism, and come along with memory requirements which are only in the order of the number of image pixels."}],"department":[{"_id":"VlKo"}],"oa_version":"Preprint","ec_funded":1,"status":"public","date_created":"2018-12-11T11:51:40Z","type":"journal_article","citation":{"mla":"Kolmogorov, Vladimir, et al. “Total Variation on a Tree.” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 2, Society for Industrial and Applied Mathematics , 2016, pp. 605–36, doi:<a href=\"https://doi.org/10.1137/15M1010257\">10.1137/15M1010257</a>.","ama":"Kolmogorov V, Pock T, Rolinek M. Total variation on a tree. <i>SIAM Journal on Imaging Sciences</i>. 2016;9(2):605-636. doi:<a href=\"https://doi.org/10.1137/15M1010257\">10.1137/15M1010257</a>","ieee":"V. Kolmogorov, T. Pock, and M. Rolinek, “Total variation on a tree,” <i>SIAM Journal on Imaging Sciences</i>, vol. 9, no. 2. Society for Industrial and Applied Mathematics , pp. 605–636, 2016.","short":"V. Kolmogorov, T. Pock, M. Rolinek, SIAM Journal on Imaging Sciences 9 (2016) 605–636.","ista":"Kolmogorov V, Pock T, Rolinek M. 2016. Total variation on a tree. SIAM Journal on Imaging Sciences. 9(2), 605–636.","apa":"Kolmogorov, V., Pock, T., &#38; Rolinek, M. (2016). Total variation on a tree. <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial and Applied Mathematics . <a href=\"https://doi.org/10.1137/15M1010257\">https://doi.org/10.1137/15M1010257</a>","chicago":"Kolmogorov, Vladimir, Thomas Pock, and Michal Rolinek. “Total Variation on a Tree.” <i>SIAM Journal on Imaging Sciences</i>. Society for Industrial and Applied Mathematics , 2016. <a href=\"https://doi.org/10.1137/15M1010257\">https://doi.org/10.1137/15M1010257</a>."},"title":"Total variation on a tree","month":"05","date_updated":"2021-01-12T06:50:15Z","scopus_import":1,"quality_controlled":"1","language":[{"iso":"eng"}],"publist_id":"5834","intvolume":"         9","main_file_link":[{"url":"http://arxiv.org/abs/1502.07770","open_access":"1"}],"oa":1,"page":"605 - 636","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication":"SIAM Journal on Imaging Sciences","day":"03","publication_status":"published","date_published":"2016-05-03T00:00:00Z","volume":9,"_id":"1377","doi":"10.1137/15M1010257","author":[{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","last_name":"Kolmogorov","full_name":"Kolmogorov, Vladimir","first_name":"Vladimir"},{"last_name":"Pock","full_name":"Pock, Thomas","first_name":"Thomas"},{"id":"3CB3BC06-F248-11E8-B48F-1D18A9856A87","full_name":"Rolinek, Michal","last_name":"Rolinek","first_name":"Michal"}],"project":[{"call_identifier":"FP7","grant_number":"616160","name":"Discrete Optimization in Computer Vision: Theory and Practice","_id":"25FBA906-B435-11E9-9278-68D0E5697425"}]}