A Log-Euclidean Polyaffine Framework for Locally Rigid or Affine Registration
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.
Unable to display preview. Download preview PDF.
- 1.Arsigny, V., Commowick, O., Pennec, X., Ayache, N.: A fast and Log-Euclidean polyaffine framework for locally affine registration. Research report RR-5865, INRIA (March 2006)Google Scholar
- 5.Commowick, O., Arsigny, V., Costa, J., Malandain, G., Ayache, N.: An efficient multi-affine framework for the registration of anatomical structures. In: Proceedings of ISBI 2006. IEEE, Los Alamitos (to appear, 2006)Google Scholar
- 8.Little, J.A., Hill, D.L.G., Hawkes, D.J.: Deformations incorpotationg rigid structures. CVIU 66(2), 223–232 (1996)Google Scholar
- 12.Pitiot, A., Bardinet, E., Thompson, P.M., Malandain, G.: Piecewise affine registration of biological images for volume reconstruction. Med. Im. Anal.(accepted for publication, 2005)Google Scholar
- 14.Sheppard, D.: A two-dimensionnal interpolation function for irregularly spaced data. In: 23rd National Conference of the ACM, pp. 517–524 (1968)Google Scholar
- 16.Tenenbaum, M., Pollard, H.: Ordinary Differential Equations. Dover (1985)Google Scholar