Nonparametric regression based image analysis

P. A. Cornillon; N. Hengartner; E. Matzner-Løber; B. Thieurmel

doi:10.1007/978-1-4939-0569-0_17

Nonparametric regression based image analysis

P. A. Cornillon
, N. Hengartner
, E. Matzner-Løber
, B. Thieurmel

Université de Rennes 2
MST-8, Los Alamos National Laboratory
Data Knowledge

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Topics in Nonparametric Statistics - Proceedings of the 1st Conference of the International Society for Nonparametric Statistics
Editors	Dimitris N. Politis, Michael G. Akritas, Soumendra N. Lahiri
Publisher	Springer New York LLC
Pages	185-195
Number of pages	11
ISBN (Electronic)	9781493905683
DOIs	https://doi.org/10.1007/978-1-4939-0569-0_17
Publication status	Published - 1 Jan 2014
Externally published	Yes
Event	1st Conference of the International Society of Nonparametric Statistics, ISNPS 2012 - Chalkidiki, Greece Duration: 15 Jun 2012 → 19 Jun 2012

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	74
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Conference

Conference	1st Conference of the International Society of Nonparametric Statistics, ISNPS 2012
Country/Territory	Greece
City	Chalkidiki
Period	15/06/12 → 19/06/12

Keywords

Duchon splines
Image sequence denoising
Iterative bias reduction
Kernel smoother

Access to Document

10.1007/978-1-4939-0569-0_17

Cite this

Cornillon, P. A., Hengartner, N., Matzner-Løber, E., & Thieurmel, B. (2014). Nonparametric regression based image analysis. In D. N. Politis, M. G. Akritas, & S. N. Lahiri (Eds.), Topics in Nonparametric Statistics - Proceedings of the 1st Conference of the International Society for Nonparametric Statistics (pp. 185-195). (Springer Proceedings in Mathematics and Statistics; Vol. 74). Springer New York LLC. https://doi.org/10.1007/978-1-4939-0569-0_17

Cornillon, P. A. ; Hengartner, N. ; Matzner-Løber, E. et al. / Nonparametric regression based image analysis. Topics in Nonparametric Statistics - Proceedings of the 1st Conference of the International Society for Nonparametric Statistics. editor / Dimitris N. Politis ; Michael G. Akritas ; Soumendra N. Lahiri. Springer New York LLC, 2014. pp. 185-195 (Springer Proceedings in Mathematics and Statistics).

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title = "Nonparametric regression based image analysis",

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 = "Cornillon, \{P. A.\} and N. Hengartner and E. Matzner-L{\o}ber and B. Thieurmel",

note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media New York 2014.; 1st Conference of the International Society of Nonparametric Statistics, ISNPS 2012 ; Conference date: 15-06-2012 Through 19-06-2012",

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language = "English",

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Cornillon, PA, Hengartner, N, Matzner-Løber, E & Thieurmel, B 2014, Nonparametric regression based image analysis. in DN Politis, MG Akritas & SN Lahiri (eds), Topics in Nonparametric Statistics - Proceedings of the 1st Conference of the International Society for Nonparametric Statistics. Springer Proceedings in Mathematics and Statistics, vol. 74, Springer New York LLC, pp. 185-195, 1st Conference of the International Society of Nonparametric Statistics, ISNPS 2012, Chalkidiki, Greece, 15/06/12. https://doi.org/10.1007/978-1-4939-0569-0_17

Nonparametric regression based image analysis. / Cornillon, P. A.; Hengartner, N.; Matzner-Løber, E. et al.
Topics in Nonparametric Statistics - Proceedings of the 1st Conference of the International Society for Nonparametric Statistics. ed. / Dimitris N. Politis; Michael G. Akritas; Soumendra N. Lahiri. Springer New York LLC, 2014. p. 185-195 (Springer Proceedings in Mathematics and Statistics; Vol. 74).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Hengartner, N.

AU - Matzner-Løber, E.

AU - Thieurmel, B.

N1 - Publisher Copyright: © Springer Science+Business Media New York 2014.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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.

AB - 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.

KW - Duchon splines

KW - Image sequence denoising

KW - Iterative bias reduction

KW - Kernel smoother

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Cornillon PA, Hengartner N, Matzner-Løber E, Thieurmel B. Nonparametric regression based image analysis. In Politis DN, Akritas MG, Lahiri SN, editors, Topics in Nonparametric Statistics - Proceedings of the 1st Conference of the International Society for Nonparametric Statistics. Springer New York LLC. 2014. p. 185-195. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-1-4939-0569-0_17

Nonparametric regression based image analysis

Abstract

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Keywords

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