title: Continuous Multiclass Labeling Approaches and Algorithms
creator: Lellmann, Jan
creator: Schnörr, Christoph
subject: 510
subject: 510 Mathematics
description: We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity – one can be used to tightly relax any metric interaction potential, while the other one only covers Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent Douglas-Rachford scheme, and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other first-order methods, the approach shows competitive performance on synthetical and real-world images. By combining the method with an improved binarization technique for nonstandard potentials, we were able to routinely recover discrete solutions within 1%–5% of the global optimum for the combinatorial image labeling problem.
date: 2010
type: Other
type: info:eu-repo/semantics/report
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/10460/1/manuscript_preprint.pdf
identifier: DOI:10.11588/heidok.00010460
identifier: urn:nbn:de:bsz:16-opus-104603
identifier:   Lellmann, Jan ; Schnörr, Christoph  (2010) Continuous Multiclass Labeling Approaches and Algorithms.  [Other]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/10460/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: ger