Skip to Main content Skip to Navigation
New interface
Conference papers

Left-Invariant Riemannian Elasticity: a distance on shape diffeomorphisms ?

Xavier Pennec 1 
1 ASCLEPIOS - Analysis and Simulation of Biomedical Images
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In inter-subject registration, one often lacks a good model of the transformation variability to choose the optimal regularization. Some works attempt to model the variability in a statistical way, but the re-introduction in a registration algorithm is not easy. In [1], we interpreted the elastic energy as the distance of the Green-St Venant strain tensor to the identity. By changing the Euclidean metric for a more suitable Riemannian one, we defined a consistent statistical framework to quantify the amount of deformation. In particular, the mean and the covariance matrix of the strain tensor could be efficiently computed from a population of non-linear transformations and introduced as parameters in a Mahalanobis distance to measure the statistical deviation from the observed variability. This statistical Riemannian elasticity was able to handle anisotropic deformations but its isotropic stationary version was locally inverse-consistent. In this paper, we investigate how to modify the Riemannian elasticity to make it globally inverse consistent. This allows to define a left-invariant "distance" between shape diffeomorphisms that we call the left-invariant Riemannian elasticity. Such a closed form energy on diffeomorphisms can optimize it directly without relying on a time and memory consuming numerical optimization of the geodesic path.
Document type :
Conference papers
Complete list of metadata

Cited literature [29 references]  Display  Hide  Download
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s Connect in order to contact the contributor
Submitted on : Thursday, October 20, 2011 - 11:31:54 AM
Last modification on : Saturday, June 25, 2022 - 11:06:50 PM
Long-term archiving on: : Saturday, January 21, 2012 - 2:26:26 AM


Files produced by the author(s)


  • HAL Id : inria-00634098, version 1



Xavier Pennec. Left-Invariant Riemannian Elasticity: a distance on shape diffeomorphisms ?. 1st MICCAI Workshop on Mathematical Foundations of Computational Anatomy: Geometrical, Statistical and Registration Methods for Modeling Biological Shape Variability, Oct 2006, Copenhagen, Denmark. pp.1-13. ⟨inria-00634098⟩



Record views


Files downloads