{"quality_controlled":"1","day":"01","date_updated":"2021-01-12T06:56:28Z","abstract":[{"text":"The problem of minimizing the Potts energy function frequently occurs in computer vision applications. One way to tackle this NP-hard problem was proposed by Kovtun [19, 20]. It identifies a part of an optimal solution by running k maxflow computations, where k is the number of labels. The number of “labeled” pixels can be significant in some applications, e.g. 50-93% in our tests for stereo. We show how to reduce the runtime to O (log k) maxflow computations (or one parametric maxflow computation). Furthermore, the output of our algorithm allows to speed-up the subsequent alpha expansion for the unlabeled part, or can be used as it is for time-critical applications. To derive our technique, we generalize the algorithm of Felzenszwalb et al. [7] for Tree Metrics . We also show a connection to k-submodular functions from combinatorial optimization, and discuss k-submodular relaxations for general energy functions.","lang":"eng"}],"external_id":{"arxiv":["1310.1771"]},"date_created":"2018-12-11T11:56:43Z","page":"2320 - 2327","_id":"2276","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.1771"}],"oa_version":"Preprint","title":"Potts model, parametric maxflow and k-submodular functions","oa":1,"language":[{"iso":"eng"}],"publication_status":"published","department":[{"_id":"JoCs"},{"_id":"VlKo"}],"author":[{"full_name":"Gridchyn, Igor","id":"4B60654C-F248-11E8-B48F-1D18A9856A87","first_name":"Igor","last_name":"Gridchyn"},{"id":"3D50B0BA-F248-11E8-B48F-1D18A9856A87","full_name":"Kolmogorov, Vladimir","last_name":"Kolmogorov","first_name":"Vladimir"}],"citation":{"short":"I. Gridchyn, V. Kolmogorov, in:, IEEE, 2013, pp. 2320–2327.","chicago":"Gridchyn, Igor, and Vladimir Kolmogorov. “Potts Model, Parametric Maxflow and k-Submodular Functions,” 2320–27. IEEE, 2013. <a href=\"https://doi.org/10.1109/ICCV.2013.288\">https://doi.org/10.1109/ICCV.2013.288</a>.","ama":"Gridchyn I, Kolmogorov V. Potts model, parametric maxflow and k-submodular functions. In: IEEE; 2013:2320-2327. doi:<a href=\"https://doi.org/10.1109/ICCV.2013.288\">10.1109/ICCV.2013.288</a>","ista":"Gridchyn I, Kolmogorov V. 2013. Potts model, parametric maxflow and k-submodular functions. ICCV: International Conference on Computer Vision, 2320–2327.","ieee":"I. Gridchyn and V. Kolmogorov, “Potts model, parametric maxflow and k-submodular functions,” presented at the ICCV: International Conference on Computer Vision, Sydney, Australia, 2013, pp. 2320–2327.","mla":"Gridchyn, Igor, and Vladimir Kolmogorov. <i>Potts Model, Parametric Maxflow and k-Submodular Functions</i>. IEEE, 2013, pp. 2320–27, doi:<a href=\"https://doi.org/10.1109/ICCV.2013.288\">10.1109/ICCV.2013.288</a>.","apa":"Gridchyn, I., &#38; Kolmogorov, V. (2013). Potts model, parametric maxflow and k-submodular functions (pp. 2320–2327). Presented at the ICCV: International Conference on Computer Vision, Sydney, Australia: IEEE. <a href=\"https://doi.org/10.1109/ICCV.2013.288\">https://doi.org/10.1109/ICCV.2013.288</a>"},"date_published":"2013-12-01T00:00:00Z","type":"conference","month":"12","year":"2013","publist_id":"4668","status":"public","conference":{"end_date":"2013-12-08","name":"ICCV: International Conference on Computer Vision","start_date":"2013-12-01","location":"Sydney, Australia"},"doi":"10.1109/ICCV.2013.288","publisher":"IEEE","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"}