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Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping

Bigot, Jérémie and Gadat, Sébastien and Loubes, Jean-Michel Statistical M-Estimation and Consistency in Large Deformable Models for Image Warping. (2009) Journal of Mathematical Imaging and Vision, 34 (3). 270-290. ISSN 0924-9907

(Document in English)

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Official URL: http://dx.doi.org/10.1007/s10851-009-0146-1


The problem of defining appropriate distances between shapes or images and modeling the variability of natural images by group transformations is at the heart of modern image analysis. A current trend is the study of probabilistic and statistical aspects of deformation models, and the development of consistent statistical procedure for the estimation of template images. In this paper, we consider a set of images randomly warped from a mean template which has to be recovered. For this, we define an appropriate statistical parametric model to generate random diffeomorphic deformations in two-dimensions. Then, we focus on the problem of estimating the mean pattern when the images are observed with noise. This problem is challenging both from a theoretical and a practical point of view. M-estimation theory enables us to build an estimator defined as a minimizer of a well-tailored empirical criterion. We prove the convergence of this estimator and propose a gradient descent algorithm to compute this M-estimator in practice. Simulations of template extraction and an application to image clustering and classification are also provided.

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 Journal of Mathematical Imaging and Vision website: http://link.springer.com/journal/10851
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 > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Laboratory name:
Deposited On:22 Mar 2013 10:45

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