Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem
KAUST Grant NumberKUK-I1-007-43
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AbstractWe consider a variational convex relaxation of a class of optimal partitioning and multiclass labeling problems, which has recently proven quite successful and can be seen as a continuous analogue of Linear Programming (LP) relaxation methods for finite-dimensional problems. While for the latter several optimality bounds are known, to our knowledge no such bounds exist in the infinite-dimensional setting. We provide such a bound by analyzing a probabilistic rounding method, showing that it is possible to obtain an integral solution of the original partitioning problem from a solution of the relaxed problem with an a priori upper bound on the objective. The approach has a natural interpretation as an approximate, multiclass variant of the celebrated coarea formula. © 2012 Springer Science+Business Media New York.
CitationLellmann J, Lenzen F, Schnörr C (2012) Optimality Bounds for a Variational Relaxation of the Image Partitioning Problem. J Math Imaging Vis 47: 239–257. Available: http://dx.doi.org/10.1007/s10851-012-0390-7.
SponsorsThis publication is partly based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST).