Arbitrarily Directional-Selective Filter Banks For Image Representation

It is well known that the contours and textures of images play an important role inmany image processing applications. Since natural images typically contain abundantcontours and textures, how to analyze and represent the complicated directionalinformation efficiently has become one target of the researchers at home and abroad.Recently, the two-dimensional (2-D) directional filter banks (DFBs) with wedge-shapedfrequency partition and dual-tree transforms with checkerboard-shaped frequencypartition have received much attention, for their ability to extract the directionalinformation of images. The former can extract the locally spatial edges and contoursefficiently, while the latter is more tailored for the process of locally spectral texturesand details. The theory, construction and design of the two type filter banks arecurrently being developed and perfected, and cut a figure in many fields of applications,such as computer vision, pattern recognition, remote sensing data analysis andearthquake prediction. Centering on the problem of how to represent the abundantcontours and textures of images, this dissertation makes deep analysis and research onthe2-D DFBs and dual-tree transforms. The main research results of this dissertationare summarized as follows:1. Studying the one-dimensional (1-D) multi-channel nonuniform filter banks(NUFBs). The2-D wedge-shaped DFBs and dual-tree transforms considered in thisdissertation are proposed based on1-D filter banks. Therefore, starting from the1-Dfilter banks, we analyze the problem of frequency support selection of analysis filters in1-D rationally-sampled NUFBs. The derived necessary and sufficient condition canprovide a guideline for the design of NUFBs. Based on the analysis, an efficient methodfor the design of linear-phase NUFBs with arbitrary integer decimation factors isproposed. These studies on1-D filter banks are the important foundation for the furtherresearch of2-D wedge-shaped DFBs and checkerboard-shaped dual-tree transforms.2. Proposing a new structure and method for the design of2-D wedge-shapedDFBs with arbitrary number of subbands. Since the existing2-D wedge-shaped DFBsare constructed based on tree-structure, their number of subbands is limited to2nandtheir frequency partition schemes are also fixed. Therefore, they cannot extract thecomplicated edges and contours of images efficiently. To solve this problem, we utilizethe affine characteristic of pseudo-polar Fourier transform (PPFT), and apply a1-Dfilter bank to the PPFT of image along the slope direction, constructing the new structure for the design of2-D wedge-shaped DFBs. Since the number of subbands of1-D filter banks is arbitrary, the obtained wedge-shaped DFB can accordingly havearbitrary number of directional subbands. It overcomes the limitation imposed on thenumber of subbands by traditional tree-structure, and can decompose images intoarbitrary number of directional subbands. Besides, the design of the proposed DFB doesnot involve the direct design of2-D directional filters, leadig to low design complexity.3. Based on Research2, we further study the2-D wedge-shaped DFB which isbased on1-D filter banks and PPFT, and propose the2-D nonuniform DFBs which hasarbitrary wedge-shaped frequency partition. Firstly, we adjust the pseudo-polar grid ofPPFT; and then we apply a1-D NUFB with arbitrary frequency partition to the adjustedPPFT, performing the desired wedge-shaped nonuniform frequency partition. As a result,the proposed nonuniform DFBs can capture the image directional information accordingto its characteristic of directional distribution, and has the ability to extract thearbitrarily-orientated edges and contours of images. These cannot be performed by theexisting directional transforms. Several simulation results demonstrate that the proposednonuniform DFB is tailored to process the images with complicated and nonuniformedges and contours.4. Proposing the shift-invariant and flexibly directional-selective dual-treecosine-modulated filter bank (DTCMFB).2-D wedge-shaped DFBs generally involvenonseparable operations. To solve the problems of poor directional-selectivity andshift-variance of wavelet transform while preserving its simple1-D operations, wefurther study the dual-tree transforms, which have the properties of shift-invariance andcheckerboard-shaped directional frequency partition. Based on the fact that the cosineand sine functions are a pair of Hilbert transform, the cosine-modulation technique isintroduced into the design of dual-tree transforms, developing the DTCMFB. It isobtained by cosine-modulating a linear-phase prototype filter, and thus avoids thefractional-delay constraints that have to be faced in traditional dual-tree transforms.Meanwhile, the derived modulation technique ensures each analysis/synthesis filterhaving linear-phase property. More importantly, the DTCMFB can be extended totwo-dimensions via separable operations. The resulting2-D DTCMFB can providemore flexible directional-selectivity and finer checkerboard-shaped frequency partitionthan traditional dual-tree transforms. Unlike the2-D wedge-shaped DFBs, thecheckerboard-shaped directional frequency partition makes the2-D DTCMFB moresuitable to process locally spectral textures and details of images. 5. We further study the cosine-modulation based dual-tree transform, and proposethe dual-tree nonuniform filter bank (DTNUFB) with arbitrary integer decimationfactors. Its two parallel NUFBs are respectively obtained by arbitrarily combining theconsecutive channels of the cosine-and sine-modulated filter banks, and thus canperform the flexible decomposition of signals. Since the cosine-and sine-modulatedfilter banks are obtained by modulating only one prototype filter, the design ofDTNUFB not only avoids the fractional-delay constraints, but also reduced to that ofone prototype filter, leading to low design complexity. By using separable operations,the resulting2-D DTNUFB has checkerboard-shaped nonuniform frequency partitionand arbitrary directional-selectivity. These are highly expected in directionalrepresentation of images with abundant and nonuniform textures and details. Severalsimulation results demonstrate its potential.6. Constructing the non-redundant checkerboard-shaped multiresolution DFB.The above2-D wedge-shaped DFBs and dual-tree transforms are redundant. For theimage processing applications that require economical representations, such as imagecompression, the non-redundancy is required. In order to slove the problem of poordirectional-selectivity of wavelet while preserving its properties of non-redundancy andseparable operations, we construct the non-redundant checkerboard-shapedmultiresolution DFB. It is achieved by combining a non-redundant1-D M-channel filterbank and a non-redundant2-D quadrant filter bank. Firstly, the1-D M-channel filterbank decomposes image into one lowpass subband andM21bandpass subbands viaseparable operations. Then, the2-D quadrant filter bank is applied to each bandpasssubband and decomposes it into two directional subbands with checkerboard-shapedfrequency supports. Since M is an arbitrary integer, the proposed DFB can providearbitrary directional-selectivity and can sparsely represent the images full of directionalinformation. Iterating this procedure on the lowpass subband can perform themultiresolution arbitrarily-directional image decomposition. Experimental resultsillustrate that, this DFB has better nonlinear approximation performance than waveletand contourlet, especially for the images with abundant textures and details.