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 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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References
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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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DOI: https://doi.org/10.1007/11784012_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35648-6
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