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Journal of Mathematical Imaging and Vision

, Volume 33, Issue 2, pp 222–238 | Cite as

A Fast and Log-Euclidean Polyaffine Framework for Locally Linear Registration

  • Vincent Arsigny
  • Olivier Commowick
  • Nicholas Ayache
  • Xavier Pennec
Article

Abstract

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 finite 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 regular grids. 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.

Keywords

Locally affine transformations Medical imaging ODE Diffeomorphisms Polyaffine transformations Log-Euclidean Non-rigid registration 

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Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Vincent Arsigny
    • 1
  • Olivier Commowick
    • 1
  • Nicholas Ayache
    • 1
  • Xavier Pennec
    • 1
  1. 1.Asclepios Project-TeamINRIA Sophia-Antipolis MediterraneeSophia Antipolis CedexFrance

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