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Journal of Mathematical Imaging and Vision

, Volume 52, Issue 3, pp 414–435 | Cite as

Global Binary Optimization on Graphs for Classification of High-Dimensional Data

  • Ekaterina Merkurjev
  • Egil BaeEmail author
  • Andrea L. Bertozzi
  • Xue-Cheng Tai
Article

Abstract

This work develops a global minimization framework for segmentation of high-dimensional data into two classes. It combines recent convex optimization methods from imaging with recent graph- based variational models for data segmentation. Two convex splitting algorithms are proposed, where graph-based PDE techniques are used to solve some of the subproblems. It is shown that global minimizers can be guaranteed for semi-supervised segmentation with two regions. If constraints on the volume of the regions are incorporated, global minimizers cannot be guaranteed, but can often be obtained in practice and otherwise be closely approximated. Experiments on benchmark data sets show that our models produce segmentation results that are comparable with or outperform the state-of-the-art algorithms. In particular, we perform a thorough comparison to recent MBO (Merriman–Bence–Osher, AMS-Selected Lectures in Mathematics Series: Computational Crystal Growers Workshop, 1992) and phase field methods, and show the advantage of the algorithms proposed in this paper.

Keywords

Classification Graphs Combinatorial optimization  Convex optimization 

Notes

Acknowledgments

E. Bae is supported by the Norwegian Research Council eVita Project 214889. E. Merkurjev is supported by the National Science Foundation Graduate Fellowship (NSF). X.-C. Tai is supported by the Christian Michelsen Research (CMR), Bergen. This work was supported by AFOSR MURI Grant FA9550-10-1-0569, NSF Grant DMS-111897, ONR Grants N000141210040 and N000141210838, and the W. M. Keck Foundation.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Ekaterina Merkurjev
    • 1
  • Egil Bae
    • 1
    Email author
  • Andrea L. Bertozzi
    • 1
  • Xue-Cheng Tai
    • 2
  1. 1.University of CaliforniaLos AngelesUSA
  2. 2.University of BergenBergenNorway

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