Low-complexity implementation of non-subsampled directional filter banks using polyphase representations and generalized separable processing

In this paper we present efficient filtering methods for the directional decomposition of images and extraction of directional cues. The design and implementation framework proposed in our paper is based on a non-subsampled tree structure, which allows for redundancy capturing some image characteristics for detection. We examine structures for analysis using 2
^M
filters, M > 3, with narrow wedge-shaped passbands. Our structures are derived from the decimation of two-dimensional impulse responses composed of configurations of one-dimensional building blocks. In the implementation, we reconfigure transfer functions of the filters with decimated impulse responses by exploiting appropriate polyphase structure of one-dimensional building blocks to retain the property of generalized separability along directions determined by the passband orientations of the directional filters. The reconfiguration depends on the value of M, and in this paper we provide general rules for choosing the integer factors for polyphase decomposition that help re-cast the expressions for the transfer functions of the analysis bank of filters into forms that allow efficient implementation. The proposed implementation is shown to provide significant improvement compared with conventional two-dimensional implementation. Simulations show that the filtering structure provides good frequency selectivity on airborne surveillance images.