Show simple item record

dc.contributor.authorLellmann, Jan
dc.contributor.authorLenzen, Frank
dc.contributor.authorSchnörr, Christoph
dc.date.accessioned2016-02-25T13:52:49Z
dc.date.available2016-02-25T13:52:49Z
dc.date.issued2012-11-09
dc.identifier.citationLellmann J, Lenzen F, Schnörr C (2012) Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem. J Math Imaging Vis 47: 239–257. Available: http://dx.doi.org/10.1007/s10851-012-0390-7.
dc.identifier.issn0924-9907
dc.identifier.issn1573-7683
dc.identifier.doi10.1007/s10851-012-0390-7
dc.identifier.urihttp://hdl.handle.net/10754/599097
dc.description.abstractWe consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation methods for finite-dimensional problems. While for the latter several optimality bounds are known, to our knowledge no such bounds exist in the infinite-dimensional setting. We provide such a bound by analyzing a probabilistic rounding method, showing that it is possible to obtain an integral solution of the original partitioning problem from a solution of the relaxed problem with an a priori upper bound on the objective. The approach has a natural interpretation as an approximate, multiclass variant of the celebrated coarea formula. © 2012 Springer Science+Business Media New York.
dc.description.sponsorshipThis publication is partly based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).
dc.publisherSpringer Nature
dc.subjectApproximation bound
dc.subjectCombinatorial optimization
dc.subjectConvex relaxation
dc.subjectLinear programming relaxation
dc.subjectMulticlass labeling
dc.subjectTotal variation
dc.titleOptimality Bounds for a Variational Relaxation of the Image Partitioning Problem
dc.typeArticle
dc.identifier.journalJournal of Mathematical Imaging and Vision
dc.contributor.institutionUniversitat Heidelberg, Heidelberg, Germany
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdom
kaust.grant.numberKUK-I1-007-43
dc.date.published-online2012-11-09
dc.date.published-print2013-11


This item appears in the following Collection(s)

Show simple item record