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Image labeling by assignment

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. T...

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Bibliographic Details
Main Authors: Åström, Freddie (Author) , Petra, Stefania (Author) , Schmitzer, Bernhard (Author) , Schnörr, Christoph (Author)
Format: Article (Journal)
Language:English
Published: 12 January 2017
In: Journal of mathematical imaging and vision
Year: 2017, Volume: 58, Issue: 2, Pages: 211-238
ISSN:1573-7683
DOI:10.1007/s10851-016-0702-4
Online Access:Verlag, Volltext: http://dx.doi.org/10.1007/s10851-016-0702-4
Verlag, Volltext: https://link.springer.com/article/10.1007/s10851-016-0702-4
Verlag, Volltext: https://link.springer.com/content/pdf/10.1007%2Fs10851-016-0702-4.pdf
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Author Notes:Freddie Åström, Stefania Petra, Bernhard Schmitzer, Christoph Schnörr
Description
Summary: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.
Item Description:Gesehen am 08.03.2018
Physical Description:Online Resource
ISSN:1573-7683
DOI:10.1007/s10851-016-0702-4

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