Pyramidal implementation of deformable kernels

In computer vision and, increasingly, in rendering and image processing, it is useful to lter images with continuous rotated and scaled families of l-ters. For practical implementations, one can think of using a discrete family of lters, and then to interpolate from their outputs to produce the desired ltered version of the image. We propose a multirate implementation of de-formable kernels, capable to further reduce the computational weight. The \basis" lters are applied to the diierent levels of a pyramidal decomposition. The new system is not shift-invariant { it suuers from \aliasing". We introduce a new quadratic error criterion which keeps into account the ineherent system aliasing. By using hypermatrix and Kronecker algebra, we are able to cast the global optimization task into a multilinear problem. An iterative procedure (\pseudo{SVD") is used to minimize the overall quadratic approximation error.