A Log-Euclidean Polyaffine Framework for Locally Rigid or Affine Registration

  • Vincent Arsigny
  • Olivier Commowick
  • Xavier Pennec
  • Nicholas Ayache
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4057)


In this article, we focus on the parameterization of non-rigid geometrical deformations with a small number of flexible degrees of freedom . In previous work, we proposed a general framework called polyaffine to parameterize deformations with a small number of rigid or affine components, while guaranteeing the invertibility of global deformations. However, this framework lacks some important properties: the inverse of a polyaffine transformation is not polyaffine in general, and the polyaffine fusion of affine components is not invariant with respect to a change of coordinate system. We present here a novel general framework, called Log-Euclidean polyaffine, which overcomes these defects. We also detail a simple algorithm, the Fast Polyaffine Transform, which allows to compute very efficiently Log-Euclidean polyaffine transformations and their inverses on a regular grid. The results presented here on real 3D locally affine registration suggest that our novel framework provides a general and efficient way of fusing local rigid or affine deformations into a global invertible transformation without introducing artifacts, independently of the way local deformations are first estimated.


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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. 1.2004 Route des LuciolesINRIA Sophia – Epidaure ProjectSophia AntipolisFrance
  2. 2.DOSISoft S.A.CachanFrance

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