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Semiparametric estimation of shifts on compact Lie groups for image registration
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  • Published: 18 November 2010

Semiparametric estimation of shifts on compact Lie groups for image registration

  • Jérémie Bigot1,
  • Jean-Michel Loubes1 &
  • Myriam Vimond2 

Probability Theory and Related Fields volume 152, pages 425–473 (2012)Cite this article

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Abstract

In this paper we focus on estimating the deformations that may exist between similar images in the presence of additive noise when a reference template is unknown. The deformations are modeled as parameters lying in a finite dimensional compact Lie group. A general matching criterion based on the Fourier transform and its well known shift property on compact Lie groups is introduced. M-estimation and semiparametric theory are then used to study the consistency and asymptotic normality of the resulting estimators. As Lie groups are typically nonlinear spaces, our tools rely on statistical estimation for parameters lying in a manifold and take into account the geometrical aspects of the problem. Some simulations are used to illustrate the usefulness of our approach and applications to various areas in image processing are discussed.

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Author information

Authors and Affiliations

  1. Institut de Mathématiques de Toulouse, Université de Toulouse, 31062, Toulouse Cedex 9, France

    Jérémie Bigot & Jean-Michel Loubes

  2. CREST-ENSAI, ENSAI, Ker-Lann, 35172, Bruz, France

    Myriam Vimond

Authors
  1. Jérémie Bigot
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  2. Jean-Michel Loubes
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  3. Myriam Vimond
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Corresponding author

Correspondence to Jean-Michel Loubes.

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Bigot, J., Loubes, JM. & Vimond, M. Semiparametric estimation of shifts on compact Lie groups for image registration. Probab. Theory Relat. Fields 152, 425–473 (2012). https://doi.org/10.1007/s00440-010-0327-2

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  • Received: 09 September 2008

  • Revised: 29 August 2010

  • Published: 18 November 2010

  • Issue Date: April 2012

  • DOI: https://doi.org/10.1007/s00440-010-0327-2

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Keywords

  • Image registration
  • Lie group
  • Semi-parametric estimation
  • M-estimation
  • Fourier transform
  • Statistical inference on manifolds
  • White noise model

Mathematics Subject Classification (2000)

  • Primary 62F12
  • Secondary 65Hxx
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