Generalized roof duality for multi-label optimization: optimal lower bounds and persistency

Authors:
Thomas Windheuser;Hiroshi Ishikawa;Daniel Cremers
Affiliations:
Department of Computer Science, Technische Universität München, Munich, Germany, Department of Computer Science and Engineering, Waseda University, Tokyo, Japan;Department of Computer Science and Engineering, Waseda University, Tokyo, Japan;Department of Computer Science, Technische Universität München, Munich, Germany
Venue:
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Year:
2012

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Abstract

We extend the concept of generalized roof duality from pseudo-boolean functions to real-valued functions over multi-label variables. In particular, we prove that an analogue of the persistency property holds for energies of any order with any number of linearly ordered labels. Moreover, we show how the optimal submodular relaxation can be constructed in the first-order case.