WIAS Preprint No. 405, (1998)

Adaptive weights smoothing with applications to image segmentation


  • Polzehl, Jörg
    ORCID: 0000-0001-7471-2658
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62G25 62P10


  • locally constant approximation, adaptive weights, edge restoration, image segmentation, magnetic resonance imaging




We propose a new method of nonparametric estimation which is based on locally constant smoothing with an adaptive choice of weights for every pair of data-points. Some theoretical properties of the procedure are investigated. Then we demonstrate the performance of the method on some simulated univariate and bivariate examples and compare it with other nonparametric methods. Finally we discuss applications of this procedure to Magnetic Resonance Imaging.

Appeared in

  • J. of Royal Stat. Soc., Sers B, 335-354. under the title: Adaptive weights smooting with applications to image restoration.

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