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Semiparametric estimation of shifts on compact Lie groups for image registration

Bigot, Jérémie and Loubes, Jean-Michel and Vimond, Myriam Semiparametric estimation of shifts on compact Lie groups for image registration. (2012) Probability Theory and Related Fields, 152 (3-4). 425-473. ISSN 0178-8051

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Official URL: http://dx.doi.org/10.1007/s00440-010-0327-2

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 aremodeled as parameters lying in a finite dimensional compact Lie group. A generalmatching criterion based on the Fourier transformand itswell 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.

Item Type:Article
Additional Information:Thanks to Springer editor. The definitive version is available at http://www.springerlink.com The original PDF of the article can be found at Probability Theory and Related Fields website: http://link.springer.com/journal/440
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National des Sciences Appliquées de Toulouse - INSA (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
Statistics:download
Deposited By: Jérémie Bigot
Deposited On:10 Jan 2013 14:30

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