Efficient geometric transformations and 3-D image registration

Presents 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. The authors consider various matrix factorizations and compare their method with the conventional nonseparable interpolation approach. The new method provides essentially the same quality results and at the same time offers significant speed improvement