Study On Filterbank-based Directional Bases

Image becomes an important source of acquiring information, and image edge andtexture information is an important image feature. In recent years, it has been a focus ofresearch in the field of image processing that the idea of using direction transformconstitutes directional bases to represent image, reflecting edge and texture informationof image and applying the directional information to subsequent image processingalgorithm.In recent years, the generation and development of multi-resolution analysis basedon Wavelet theory as the representative has broken through the restriction of tranditionalFourier analysis and brought the revolutionary change. The two-dimensional separableWavelet base is consist of one dimensional Wavelet base in two-dimensional spacetensor product, and one dimensional Wavelet transform has the capability of pointsingularities sparse representation, so it can detect horizontal, vertical and diagonalthree direction information at the field of two-dimensional image processing. However,the traditional Wavelet method is very effective only for singular point by point, but notwork well in the case of multidimensional signal. The smooth edge of actual objectsmakes the natural image discontinuity often embody the singular curve, so Wavelet basecan not effectively deal with the signal, thus how to capture the curve singular of imageis a hot, also a difficulty spot. According to this problem, many scholars put forwarddifferent solutions, such as directional filter banks and the multiscale geometric methodsappearing in recent years, including Ridgelet, Curvelet, Contourlet and other kinds oftransformations.In consideration of the directional bases constituted by the directional filter banks,this thesis carries on the further research and puts forward a new method of constitutingdirectional bases. Major works can be summarized as follows:(1) The theoretical derivation of the directional bases consisted of directional filterbanks is given. From the point of view of the filter, different types and parameters of thefilter how to influence the directional bases, and the different directional bases how toinfluence the properties of image representation are been study.(2) A new method of constituting directional bases is put forward. Based on theimage information characteristics in different scales, the new method can nimbly selectfilter used in direction decomposition of the scale, and can be corresponding to chooseto different filter to complete certain scale direction decomposition according to the image information distribution in different scales.(3) The parabolic scaling will be studied in depth, and the sufficient theoreticalresearch and contrast experiment are given. Thus follow-up work of constituting newdirectional base has a solid theoretical basis. In addition, the cascade redundantdictionary structure based on Contourlet orthogonal bases is presented and verified itsadvantages in image representation.