Inconsistency of Template Estimation with the Fréchet mean in Quotient Space

Abstract : We tackle the problem of template estimation when data have been randomly transformed under an isometric group action in the presence of noise. In order to estimate the template, one often minimizes the variance when the influence of the transformations have been removed (computation of the Fréchet mean in quotient space). The consistency bias is defined as the distance (possibly zero) between the orbit of the template and the orbit of one element which minimizes the variance. In this article we establish an asymptotic behavior of the consistency bias with respect to the noise level. This behavior is linear with respect to the noise level. As a result the inconsistency is unavoidable as soon as the noise is large enough. In practice, the template estimation with a finite sample is often done with an algorithm called max-max. We show the convergence of this algorithm to an empirical Karcher mean. Finally, our numerical experiments show that the bias observed in practice cannot be attributed to the small sample size or to a convergence problem but is indeed due to the previously studied inconsistency.
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Communication dans un congrès
Information Processing in Medical Imaging 2017, Jun 2017, Boone, United States. pp.12, 2017, Information Processing in Medical Imaging: 25th International Conference, IPMI 2017, Boone, NC, USA, June 25-30, 2017, Proceedings. <http://www.ipmi2017.org>. <10.1007/978-3-319-59050-9_2>
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Contributeur : Loic Devilliers <>
Soumis le : jeudi 2 mars 2017 - 18:51:55
Dernière modification le : jeudi 22 juin 2017 - 11:15:30
Document(s) archivé(s) le : mercredi 31 mai 2017 - 15:57:53

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Loïc Devilliers, Xavier Pennec, Stéphanie Allassonnière. Inconsistency of Template Estimation with the Fréchet mean in Quotient Space. Information Processing in Medical Imaging 2017, Jun 2017, Boone, United States. pp.12, 2017, Information Processing in Medical Imaging: 25th International Conference, IPMI 2017, Boone, NC, USA, June 25-30, 2017, Proceedings. <http://www.ipmi2017.org>. <10.1007/978-3-319-59050-9_2>. <hal-01481074v2>

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