Continuous multiclass labeling approaches and algorithms

• Verfasst von: Lellmann, Jan [VerfasserIn]
• Verfasst von: Schnörr, Christoph [VerfasserIn]
• Titel: Continuous multiclass labeling approaches and algorithms
• Verf.angabe: J. Lellmann and C. Schnörr
• E-Jahr: 2011
• Jahr: November 22, 2011
• Umfang: 48 S.
• Fussnoten: Gesehen am 29.08.2018
• Titel Quelle: Enthalten in: Society for Industrial and Applied MathematicsSIAM journal on imaging sciences
• Ort Quelle: Philadelphia, Pa. : SIAM, 2008
• Jahr Quelle: 2011
• Band/Heft Quelle: 4(2011), 4, Seite 1049-1096
• ISSN Quelle: 1936-4954
• DOI: doi:10.1137/100805844
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 158052267X

Abstract

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 original 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 covers only 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 synthetic and real-world images. By combining the method with an improved rounding technique for nonstandard potentials, we were able to routinely recover integral solutions within 1%-5% of the global optimum for the combinatorial image labeling problem.