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

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Part of the book series:Lecture Notes in Computer Science ((LNIP,volume 4057))

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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 calledpolyaffine 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, calledLog-Euclidean polyaffine, which overcomes these defects. We also detail a simple algorithm, theFast 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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Author information

Authors and Affiliations

  1. 2004 Route des Lucioles, INRIA Sophia – Epidaure Project, BP 93, 06902 Cedex, Sophia Antipolis, France

    Vincent Arsigny, Olivier Commowick, Xavier Pennec & Nicholas Ayache

  2. DOSISoft S.A., 45 Avenue Carnot, 94 230, Cachan, France

    Olivier Commowick

Authors
  1. Vincent Arsigny

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  2. Olivier Commowick

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  3. Xavier Pennec

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  4. Nicholas Ayache

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Editor information

Editors and Affiliations

  1. Image Sciences Institute, University Medical Center Utrecht, Q0S.459, P.O. Box 85500, 3508, Utrecht, GA, The Netherlands

    Josien P. W. Pluim

  2. Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000, Ljubljana, Slovenia

    Boštjan Likar

  3. Advanced Development, Healthcare Informatics, Philips Medical Systems, Best, The Netherlands

    Frans A. Gerritsen

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© 2006 Springer-Verlag Berlin Heidelberg

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Arsigny, V., Commowick, O., Pennec, X., Ayache, N. (2006). A Log-Euclidean Polyaffine Framework for Locally Rigid or Affine Registration. In: Pluim, J.P.W., Likar, B., Gerritsen, F.A. (eds) Biomedical Image Registration. WBIR 2006. Lecture Notes in Computer Science, vol 4057. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11784012_15

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