Handle URI:
http://hdl.handle.net/10754/597994
Title:
Discrete and Continuous Models for Partitioning Problems
Authors:
Lellmann, Jan; Lellmann, Björn; Widmann, Florian; Schnörr, Christoph
Abstract:
Recently, variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention, since they introduce significantly less artifacts than established graph cut-based techniques. This work is concerned with the sources of such artifacts. We discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples. Moreover, we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method. Since the employed regularizer is quite tight, the considered relaxation generally involves a large computational cost. We propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics, thus generalizing a method recently proposed by Strekalovskiy and Cremers (IEEE conference on computer vision and pattern recognition, pp. 1905-1911, 2011). © 2013 Springer Science+Business Media New York.
Citation:
Lellmann J, Lellmann B, Widmann F, Schnörr C (2013) Discrete and Continuous Models for Partitioning Problems. Int J Comput Vis 104: 241–269. Available: http://dx.doi.org/10.1007/s11263-013-0621-4.
Publisher:
Springer Nature
Journal:
International Journal of Computer Vision
KAUST Grant Number:
KUK-I1- 007-43
Issue Date:
11-Apr-2013
DOI:
10.1007/s11263-013-0621-4
Type:
Article
ISSN:
0920-5691; 1573-1405
Sponsors:
The second and third author were supported by Engineering and Physical Sciences Research Council (EPSRC)-Project EP/H016317/1. This publication is partly based on work supported by Award No. KUK-I1- 007-43, made by King Abdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorLellmann, Janen
dc.contributor.authorLellmann, Björnen
dc.contributor.authorWidmann, Florianen
dc.contributor.authorSchnörr, Christophen
dc.date.accessioned2016-02-25T13:10:34Zen
dc.date.available2016-02-25T13:10:34Zen
dc.date.issued2013-04-11en
dc.identifier.citationLellmann J, Lellmann B, Widmann F, Schnörr C (2013) Discrete and Continuous Models for Partitioning Problems. Int J Comput Vis 104: 241–269. Available: http://dx.doi.org/10.1007/s11263-013-0621-4.en
dc.identifier.issn0920-5691en
dc.identifier.issn1573-1405en
dc.identifier.doi10.1007/s11263-013-0621-4en
dc.identifier.urihttp://hdl.handle.net/10754/597994en
dc.description.abstractRecently, variational relaxation techniques for approximating solutions of partitioning problems on continuous image domains have received considerable attention, since they introduce significantly less artifacts than established graph cut-based techniques. This work is concerned with the sources of such artifacts. We discuss the importance of differentiating between artifacts caused by discretization and those caused by relaxation and provide supporting numerical examples. Moreover, we consider in depth the consequences of a recent theoretical result concerning the optimality of solutions obtained using a particular relaxation method. Since the employed regularizer is quite tight, the considered relaxation generally involves a large computational cost. We propose a method to significantly reduce these costs in a fully automatic way for a large class of metrics including tree metrics, thus generalizing a method recently proposed by Strekalovskiy and Cremers (IEEE conference on computer vision and pattern recognition, pp. 1905-1911, 2011). © 2013 Springer Science+Business Media New York.en
dc.description.sponsorshipThe second and third author were supported by Engineering and Physical Sciences Research Council (EPSRC)-Project EP/H016317/1. This publication is partly based on work supported by Award No. KUK-I1- 007-43, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherSpringer Natureen
dc.subjectConvex relaxationen
dc.subjectGraph cuten
dc.subjectMulti-class labelingen
dc.subjectPartitioning problemen
dc.subjectSegmentationen
dc.subjectVariational methodsen
dc.titleDiscrete and Continuous Models for Partitioning Problemsen
dc.typeArticleen
dc.identifier.journalInternational Journal of Computer Visionen
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdomen
dc.contributor.institutionImperial College London, London, United Kingdomen
dc.contributor.institutionUniversitat Heidelberg, Heidelberg, Germanyen
kaust.grant.numberKUK-I1- 007-43en
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