{"paper":{"title":"Structured learning of sum-of-submodular higher order energy functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","stat.ML"],"primary_cat":"cs.CV","authors_text":"Alexander Fix, Ramin Zabih, Sam Park, Thorsten Joachims","submitted_at":"2013-09-28T23:55:01Z","abstract_excerpt":"Submodular functions can be exactly minimized in polynomial time, and the special case that graph cuts solve with max flow \\cite{KZ:PAMI04} has had significant impact in computer vision \\cite{BVZ:PAMI01,Kwatra:SIGGRAPH03,Rother:GrabCut04}. In this paper we address the important class of sum-of-submodular (SoS) functions \\cite{Arora:ECCV12,Kolmogorov:DAM12}, which can be efficiently minimized via a variant of max flow called submodular flow \\cite{Edmonds:ADM77}. SoS functions can naturally express higher order priors involving, e.g., local image patches; however, it is difficult to fully exploi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7512","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}