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Combining Contrast Invariant L1 Data Fidelities with Nonlinear Spectral Image Decomposition

  • Leonie ZeuneEmail author
  • Stephan A. van Gils
  • Leon W. M. M. Terstappen
  • Christoph Brune
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)

Abstract

This paper focuses on multi-scale approaches for variational methods and corresponding gradient flows. Recently, for convex regularization functionals such as total variation, new theory and algorithms for nonlinear eigenvalue problems via nonlinear spectral decompositions have been developed. Those methods open new directions for advanced image filtering. However, for an effective use in image segmentation and shape decomposition, a clear interpretation of the spectral response regarding size and intensity scales is needed but lacking in current approaches. In this context, \(L^1\) data fidelities are particularly helpful due to their interesting multi-scale properties such as contrast invariance. Hence, the novelty of this work is the combination of \(L^1\)-based multi-scale methods with nonlinear spectral decompositions. We compare \(L^1\) with \(L^2\) scale-space methods in view of spectral image representation and decomposition. We show that the contrast invariant multi-scale behavior of \(L^1-TV\) promotes sparsity in the spectral response providing more informative decompositions. We provide a numerical method and analyze synthetic and biomedical images at which decomposition leads to improved segmentation.

Keywords

\(L^{1}\)-TV Denoising Scale-spaces Nonlinear spectral decomposition Multiscale segmentation Eigenfunctions Calibrable sets 

Notes

Acknowledgements

LZ, LT, CB acknowledge support by the EUFP7 program #305341 CTCTrap and the IMI EU program #115749 CANCER-ID. CB acknowledges support for his TT position by the NWO via Veni grant 613.009.032 within the NDNS+ cluster.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Leonie Zeune
    • 1
    • 2
    Email author
  • Stephan A. van Gils
    • 1
  • Leon W. M. M. Terstappen
    • 2
  • Christoph Brune
    • 1
  1. 1.Department of Applied MathematicsUniversity of TwenteEnschedeThe Netherlands
  2. 2.Department of Medical Cell BioPhysicsUniversity of TwenteEnschedeThe Netherlands

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