EPFL | Biomedical Imaging Group | Geometric Transformations

Efficient Geometric Transformations and 3-D Image Registration

P. Thévenaz, M. Unser

Proceedings of the Twentieth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'95), Detroit MI, USA, May 8-12, 1995, vol. V, pp. 2919–2922.

We present a general framework for the fast, high quality implementation of geometric affine transformations of images (p = 2) or volumes (p = 3), including rotations and scaling. The method uses a factorization of the p × p transformation matrix into p + 1 elementary matrices, each affecting one dimension of the data only. This yields a separable implementation through an appropriate sequence of 1-D affine transformations (scaling + translation). Each elementary transformation is implemented in an optimal least-squares sense using a polynomial spline signal model. We consider various matrix factorizations and compare our method with the conventional non-separable interpolation approach. The new method provides essentially the same quality results and at the same time offers significant speed improvement.

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