Statistics on Diffeomorphisms in a Log-Euclidean Framework

Vincent Arsigny 1 Olivier Commowick 1, 2 Xavier Pennec 1 Nicholas Ayache 1
1 EPIDAURE - Medical imaging and robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this article, we focus on the computation of statistics of invertible geometrical deformations (i.e., diffeomorphisms), based on the generalization to this type of data of the notion of principal logarithm. Remarkably, this logarithm is a simple 3D vector field, and can be used for diffeomorphisms close enough to the identity. This allows to perform vectorial statistics on diffeomorphisms, while preserving the invertibility constraint, contrary to Euclidean statistics on displacement fields.
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Vincent Arsigny, Olivier Commowick, Xavier Pennec, Nicholas Ayache. Statistics on Diffeomorphisms in a Log-Euclidean Framework. 1st MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability, Oct 2006, Copenhagen, Denmark. pp.14-15. ⟨inria-00635671⟩

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