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Nonparametric Regression Based Image Analysis

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Topics in Nonparametric Statistics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 74))

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Abstract

Multivariate nonparametric smoothers are adversely impacted by the sparseness of data in higher dimension, also known as the curse of dimensionality. Adaptive smoothers, that can exploit the underlying smoothness of the regression function, may partially mitigate this effect. We present an iterative procedure based on traditional kernel smoothers, thin plate spline smoothers or Duchon spline smoother that can be used when the number of covariates is important. However the method is limited to small sample sizes (n < 2, 000) and we will propose some thoughts to circumvent that problem using, for example, pre-clustering of the data. Applications considered here are image denoising.

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Author information

Authors and Affiliations

  1. Université Rennes 2, 35043, Rennes, France

    P.-A. Cornillon & E. Matzner-Løber

  2. Los Alamos National laboratory, Los Alamos, NM, USA

    N. Hengartner

  3. Data Knowledge, 75008, Paris, France

    B. Thieurmel

Authors
  1. P.-A. Cornillon
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  2. N. Hengartner
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  3. E. Matzner-Løber
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  4. B. Thieurmel
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Corresponding author

Correspondence to P.-A. Cornillon .

Editor information

Editors and Affiliations

  1. Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania, USA

    Michael G. Akritas

  2. Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA

    S. N. Lahiri

  3. Department of Mathematics, University of California, San Diego, California, USA

    Dimitris N. Politis

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Cornillon, PA., Hengartner, N., Matzner-Løber, E., Thieurmel, B. (2014). Nonparametric Regression Based Image Analysis. In: Akritas, M., Lahiri, S., Politis, D. (eds) Topics in Nonparametric Statistics. Springer Proceedings in Mathematics & Statistics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0569-0_17

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