Efficient deformable filter banks

This article describes efficient schemes for the computation of a large number of differently scaled/oriented filtered versions of an image. We generalize the well-known steerable/scalable ("deformable") filter bank structure by imposing X-Y separability on the basis filters. The resulting systems, designed by an iterative projections technique, achieve substantial reduction of the computational cost. To reduce the memory requirement, we adopt a multirate implementation. Due to the inner sampling rate alteration, the resulting structure is not shift invariant. We introduce a design criterion for multirate deformable structures that jointly controls the approximation error and the shift variance.