Image labeling by assignment

• Verfasst von: Åström, Freddie [VerfasserIn]
• Verfasst von: Petra, Stefania [VerfasserIn]
• Verfasst von: Schmitzer, Bernhard [VerfasserIn]
• Verfasst von: Schnörr, Christoph [VerfasserIn]
• Titel: Image labeling by assignment
• Verf.angabe: Freddie Åström, Stefania Petra, Bernhard Schmitzer, Christoph Schnörr
• Umfang: 28 S.
• Fussnoten: Gesehen am 08.03.2018
• Titel Quelle: Enthalten in: Journal of mathematical imaging and vision
• Jahr Quelle: 2017
• Band/Heft Quelle: 58(2017), 2, S. 211-238
• ISSN Quelle: 1573-7683
• DOI: doi:10.1007/s10851-016-0702-4
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1570624453

Abstract

We introduce a novel geometric approach to the image labeling problem. Abstracting from specific labeling applications, a general objective function is defined on a manifold of stochastic matrices, whose elements assign prior data that are given in any metric space, to observed image measurements. The corresponding Riemannian gradient flow entails a set of replicator equations, one for each data point, that are spatially coupled by geometric averaging on the manifold. Starting from uniform assignments at the barycenter as natural initialization, the flow terminates at some global maximum, each of which corresponds to an image labeling that uniquely assigns the prior data. Our geometric variational approach constitutes a smooth non-convex inner approximation of the general image labeling problem, implemented with sparse interior-point numerics in terms of parallel multiplicative updates that converge efficiently.