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International Journal of Computer Vision

, Volume 127, Issue 5, pp 477–511 | Cite as

Kernel Cuts: Kernel and Spectral Clustering Meet Regularization

  • Meng TangEmail author
  • Dmitrii Marin
  • Ismail Ben Ayed
  • Yuri Boykov
Article
  • 373 Downloads

Abstract

This work bridges the gap between two popular methodologies for data partitioning: kernel clustering and regularization-based segmentation. While addressing closely related practical problems, these general methodologies may seem very different based on how they are covered in the literature. The differences may show up in motivation, formulation, and optimization, e.g. spectral relaxation versus max-flow. We explain how regularization and kernel clustering can work together and why this is useful. Our joint energy combines standard regularization, e.g. MRF potentials, and kernel clustering criteria like normalized cut. Complementarity of such terms is demonstrated in many applications using our bound optimization Kernel Cut algorithm for the joint energy (code is publicly available). While detailing combinatorial move-making, our main focus are new linear kernel and spectral bounds for kernel clustering criteria allowing their integration with any regularization objectives with existing discrete or continuous solvers.

Keywords

Segmentation Markov random fields Spectral clustering Kernel methods Bound optimization 

Notes

Acknowledgements

We greatly thank Carl Olsson (Lund University, Sweden) for hours of stimulating discussions, as well as for detailed feedback and valuable recommendations at different stages of our work. We appreciate his tremendous patience when our thoughts were much more confusing than they might be now. Ivan Stelmakh (PhysTech, Russia) also gave helpful feedback on our draft and caught several errors. Anders Eriksson (Lund University, Sweden) helped with related work on NC with constraints. We also thank Jianbo Shi (UPenn, USA) for his excellent spectral-relaxation optimization code for NC.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Meng Tang
    • 1
    Email author
  • Dmitrii Marin
    • 1
    • 2
  • Ismail Ben Ayed
    • 3
  • Yuri Boykov
    • 1
  1. 1.Computer ScienceUniversity of WaterlooWaterlooCanada
  2. 2.Computer ScienceWestern UniversityLondonCanada
  3. 3.ETS MontrealMontrealCanada

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