A Log-Euclidean Framework for Statistics on Diffeomorphisms

  • Vincent Arsigny
  • Olivier Commowick
  • Xavier Pennec
  • Nicholas Ayache
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4190)


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 is well-defined 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. We also present here two efficient algorithms to compute logarithms of diffeomorphisms and exponentials of vector fields, whose accuracy is studied on synthetic data. Finally, we apply these tools to compute the mean of a set of diffeomorphisms, in the context of a registration experiment between an atlas an a database of 9 T1 MR images of the human brain.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Vincent Arsigny
    • 1
  • Olivier Commowick
    • 1
    • 2
  • Xavier Pennec
    • 1
  • Nicholas Ayache
    • 1
  1. 1.INRIA Sophia – Epidaure ProjectSophia AntipolisFrance
  2. 2.DOSISoft S.A.CachanFrance

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