### Abstract

Original language | English |
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Journal | arXiv.org e-Print archive |

Publication status | Published - 2019 |

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### Cite this

*arXiv.org e-Print archive*.

**Fast Decomposable Submodular Function Minimization using Constrained Total Variation.** / Kumar, KS; Bach, Francis; Pock, Thomas.

Research output: Contribution to journal › Article › Research › peer-review

*arXiv.org e-Print archive*.

}

TY - JOUR

T1 - Fast Decomposable Submodular Function Minimization using Constrained Total Variation

AU - Kumar, KS

AU - Bach, Francis

AU - Pock, Thomas

PY - 2019

Y1 - 2019

N2 - We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding Lovász extensions and the squared Euclidean norm, leading to algorithms requiring total variation oracles of the summand functions; without further assumptions, these more complex oracles require many calls to the simpler minimization oracles often available in practice. In this paper, we consider a modified convex problem requiring constrained version of the total variation oracles that can be solved with significantly fewer calls to the simple minimization oracles. We support our claims by showing results on graph cuts for 2D and 3D graphs

AB - We consider the problem of minimizing the sum of submodular set functions assuming minimization oracles of each summand function. Most existing approaches reformulate the problem as the convex minimization of the sum of the corresponding Lovász extensions and the squared Euclidean norm, leading to algorithms requiring total variation oracles of the summand functions; without further assumptions, these more complex oracles require many calls to the simpler minimization oracles often available in practice. In this paper, we consider a modified convex problem requiring constrained version of the total variation oracles that can be solved with significantly fewer calls to the simple minimization oracles. We support our claims by showing results on graph cuts for 2D and 3D graphs

M3 - Article

JO - arXiv.org e-Print archive

JF - arXiv.org e-Print archive

ER -