Image labeling and grouping by minimizing linear functionals over cones


Schellewald, Christian ; Keuchel, Jens ; Schnörr, Christoph


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URL: http://ub-madoc.bib.uni-mannheim.de/1849
URN: urn:nbn:de:bsz:180-madoc-18498
Dokumenttyp: Arbeitspapier
Erscheinungsjahr: 2001
Sprache der Veröffentlichung: Englisch
Einrichtung: Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik > Sonstige - Fakultät für Mathematik und Informatik
MADOC-Schriftenreihe: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Informatik > Technical Reports
Fachgebiet: 004 Informatik
Fachklassifikation: MSC: 68U99 68T10 68T45 ,
Normierte Schlagwörter (SWD): Mustererkennung , Maschinelles Sehen
Abstract: We consider energy minimization problems related to image labeling, partitioning, and grouping, which typically show up at mid-level stages of computer vision systems. A common feature of these problems is their intrinsic combinatorial complexity from an optimization pointof-view. Rather than trying to compute the global minimum - a goal we consider as elusive in these cases - we wish to design optimization approaches which exhibit two relevant properties: First, in each application a solution with guaranteed degree of suboptimality can be computed. Secondly, the computations are based on clearly defined algorithms which do not comprise any (hidden) tuning parameters. In this paper, we focus on the second property and introduce a novel and general optimization technique to the field of computer vision which amounts to compute a sub optimal solution by just solving a convex optimization problem. As representative examples, we consider two binary quadratic energy functionals related to image labeling and perceptual grouping. Both problems can be considered as instances of a general quadratic functional in binary variables, which is embedded into a higher-dimensional space such that sub optimal solutions can be computed as minima of linear functionals over cones in that space (semidefinite programs). Extensive numerical results reveal that, on the average, sub optimal solutions can be computed which yield a gap below 5% with respect to the global optimum in case where this is known.
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Schellewald, Christian und Keuchel, Jens und Schnörr, Christoph (2001) Image labeling and grouping by minimizing linear functionals over cones. [Arbeitspapier]
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