Publications of Loïc Devilliers

1. Loïc Devilliers. Consistency of statistics in infinite dimensional quotient spaces. Theses, COMUE Université Côte d'Azur (2015 - 2019), November 2017. Keyword(s): Frechet mean, Quotient space, Template estimation, Moyenne de Fréchet, Espace quotient, Estimation de template. [bibtex-entry]

1. Nina Miolane, Loïc Devilliers, and Xavier Pennec. Bias on estimation in quotient space and correction methods: Applications to statistics on organ shapes. In Riemannian Geometric Statistics in Medical Image Analysis, number Chap. 9, pages 343-376. Elsevier, 2020. [bibtex-entry]



2. Loïc Devilliers, Stéphanie Allassonnière, Alain Trouvé, and Xavier Pennec. Inconsistency of template estimation by minimizing of the variance/pre-variance in the quotient space. Entropy, 19(6):article 288, June 2017. Keyword(s): quotient space, Fréchet mean, Hilbert space, deformable model, regularization, template estimation, inconsistency. [bibtex-entry]



3. Loïc Devilliers, Stéphanie Allassonnière, Alain Trouvé, and Xavier Pennec. Template estimation in computational anatomy: Fréchet means in top and quotient spaces are not consistent. SIAM Journal on Imaging Sciences, 10(3):1139-1169, August 2017. Keyword(s): Fréchet mean, Hilbert space, quotient space, Template, manifold, empirical Fréchet mean, inconsistency, group action, consistency bias. [bibtex-entry]

1. Loïc Devilliers, Xavier Pennec, and Stéphanie Allassonnière. Inconsistency of Template Estimation with the Fréchet mean in Quotient Space. In Information Processing in Medical Imaging. IPMI 2017., volume 10265 of LNCS, Boone, United States, pages 16-27, June 2017. Martin Styner and Marc Niethammer and Dinggang Shen and Stephen Aylward and Ipek Oguz and Hongtu Zhu. [bibtex-entry]



2. Stéphanie Allassonnière, Loïc Devilliers, and Xavier Pennec. Estimating the Template in the Total Space with the Fréchet Mean on Quotient Spaces may have a Bias: a Case Study on Vector Spaces Quotiented by the Group of Translations. In Mathematical Foundations of Computational Anatomy (MFCA'15), Proceedings of the fifth international workshop on Mathematical Foundation sof Computational Anatomy (MFCA'15), Munich, Germany, pages 131-142, October 2015. [bibtex-entry]

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