Nonuniform Directional Filter Banks With Arbitrary Frequency Partitioning

Directional filter banks (DFBs) are highly desired in directional representation of images. In this correspondence, we propose a 2-D nonsubsampled nonuniform directional filter bank (NUDFB) and its design method. The proposed NUDFB has nonuniform wedge-shaped subbands and allows arbitrary frequency partitioning schemes. It can extract directional information according to the directional distribution of images. This attractive advantage cannot be achieved by the existing directional transforms. The design method of the proposed NUDFB is based upon the pseudopolar Fourier transform. By utilizing the geometry property of the pseudopolar grid, we employ a 1-D nonsubsampled nonuniform filter bank to obtain a set of nonuniform wedge-shaped subbands. During the design process, only 1-D operations are involved and, thus, the difficulty encountered in the design of 2-D fan filters is avoided. To demonstrate the potential of the proposed NUDFB, an example on image directional decomposition is given.