Pyramidal Implementation of Deformable Kernels

Abstract

In computer vision and increasingly, in rendering and image processing, it is useful to filter images with continuous rotated and scaled families of filters. For practical implementations, one can think of using a discrete family of filters, and then to interpolate from their outputs to produce the desired filtered version of the image. We propose a multirate implementation of deformable kernels, capable to further reduce the computational weight. The “basis” filters are applied to the different levels of a pyramidal decomposition. The new system is not shift-invariant-it suffers from “aliasing”. We introduce a new quadratic error criterion which keeps into account the inherent 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.