Design of Directional Filter Banks With Arbitrary Number of Subbands

This correspondence proposes a novel method for designing directional filter banks (DFBs) with arbitrary number of subbands. Its key feature is the ability to decompose images into arbitrary directionally oriented subbands. The proposed approach is based on the pseudo-polar Fourier transform (PPFT) and one-dimensional (1-D) filter banks (FBs). We take some modifications on the PPFT and then employ 1-D FBs to the modified PPFT. With these operations, the two-dimensional (2-D) DFBs are obtained and the design of them is converted to that of 1-D FBs plus a modified PPFT. Since the number of channels of 1-D FBs can be arbitrary, the 2-D DFBs with arbitrary number of subbands can be achieved which is highly expected for directional representations of images. Two examples on directional feature extractions illustrate that the proposed non-$2^{n}$ channel DFBs can capture directional information more flexibly than the existing methods.