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International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition

EMMCVPR 2015: Energy Minimization Methods in Computer Vision and Pattern Recognition pp 197–208Cite as

Two-Dimensional Variational Mode Decomposition

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Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8932))

Abstract

In this paper we propose a variational method to adaptively decompose an image into few different modes of separate spectral bands, which are unknown before. A popular method for recursive one dimensional signal decomposition is the Empirical Mode Decomposition algorithm, introduced by Huang in the nineties. This algorithm, as well as its 2D extension, though extensively used, suffers from a lack of exact mathematical model, interpolation choice, and sensitivity to both noise and sampling. Other state-of-the-art models include synchrosqueezing, the empirical wavelet transform, and recursive variational decomposition into smooth signals and residuals. Here, we have created an entirely non-recursive 2D variational mode decomposition (2D-VMD) model, where the modes are extracted concurrently. The model looks for a number of 2D modes and their respective center frequencies, such that the bandlimited modes reproduce the input image (exactly or in least-squares sense). Preliminary results show excellent performance on both synthetic and real images. Running this algorithm on a peptide microscopy image yields accurate, timely, and autonomous segmentation - pertinent in the fields of biochemistry and nanoscience.

This work is supported by the National Science Foundation (NSF) under grant DMS-1118971, UC Lab Fees Research grant 12-LR-236660, the Swiss National Science Foundation (SNF) grant P300P2_147778, and the W. M. Keck Foundation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California,Los Angeles, 520 Portola Plaza, Box 951555, Los Angeles, CA, 90095-1555, USA

    Konstantin Dragomiretskiy & Dominique Zosso

Authors
  1. Konstantin Dragomiretskiy
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  2. Dominique Zosso
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Bergen, 7800, Bergen, Norway

    Xue-Cheng Tai

  2. Department of Mathematics, University of California, Los Angeles, CA, USA

    Egil Bae

  3. The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, S.A.R.

    Tony F. Chan

  4. Telemark University College, Postboks 203, 3901, Porsgrunn, Norway

    Marius Lysaker

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© 2015 Springer International Publishing Switzerland

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Dragomiretskiy, K., Zosso, D. (2015). Two-Dimensional Variational Mode Decomposition. In: Tai, XC., Bae, E., Chan, T.F., Lysaker, M. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2015. Lecture Notes in Computer Science, vol 8932. Springer, Cham. https://doi.org/10.1007/978-3-319-14612-6_15

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  • DOI: https://doi.org/10.1007/978-3-319-14612-6_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14611-9

  • Online ISBN: 978-3-319-14612-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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