Multirate separable implementation of steerable filter banks

This paper describes efficient schemes for the computation of a large number of differently scaled/oriented filtered versions of an image. Previous work has generalized the well-known steerable/scalable (“deformable”) filter bank structure by imposing X-Y separability on the basis filters. These systems, designed by an iterative projections technique, were shown to achieve substantial reduction of the computational cost. To reduce the memory requirement, we adopt a multirate implementation. The resulting structure, however, is not shift-invariant-it gives rise to “aliasing”. We introduce a design criterion for multirate deformable structures that jointly controls the approximation error and the shift-variance