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 - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2015

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

Abstract

When we have a deformation group acting on a vector space of observations, these data are not anymore elements of our space but rather orbits for the group action we consider. If the data are generated from an unknown template with noise, to estimate this template, one may want to minimize the variance in the quotient set. In this article we study statistics on a particular quotient space. We prove that the expected value of a random variable in our vector space mapped in the quotient space is different from the Fréchet mean in the quotient space when the observations are noisy.
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Dates and versions

hal-01203816 , version 1 (25-09-2015)

Identifiers

  • HAL Id : hal-01203816 , version 1

Cite

Stéphanie Allassonnière, Loïc Devilliers, 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. Mathematical Foundations of Computational Anatomy (MFCA'15), Oct 2015, Munich, Germany. pp.131-142. ⟨hal-01203816⟩
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