Study Of A Number Of Issues In The Design Of Filter Banks And Segmentation Algorithm

This paper consists of two topics: filter banks design and subdivision scheme.M-band wavelets have been widely applied to sound coding, image analysis, image compression, etc. Especially, the symmetry and high rank vanishing moments of wavelets are very important for subband coding. The symmetry of wavelets can reduce phase and amplitude distortion. The high rank vanishing moments of wavelets can eliminate the correlation of pixels. M-band wavelets are applied to engineering through their own filter banks. And cosine modulated wavelets filter banks are very important, whose analysis and synthesis filers are gotten by two low-pass prototype filters. The cosine modulated wavelets filter banks have the virtues of simple structure, easy designing, high efficient implement and low resource consuming. Wavelets also can be used to computer graphics. Especially, the idea of multi-resolution of surface modeling is in accord with wavelets'. So wavelets are applied to computer graphics and computer aided geometry design widely. Moreover, subdivision scheme is in accord with wavelets' cascade algorithm. Recent years subdivision scheme has become the important tool of computer graphics, and it is one of the hotspot of computer aided geometry design. The basic idea of subdivision scheme is to get smooth surface modeling from coarse and simple surface modeling through adding new vertices. Subdivision scheme can control arbitary topology meshes. It not only can keep whole smoothness of surface, but also can reserve some local characters. It has become the bridge of surface's continuous modeling and discrete rendering.This paper is organized as follows.In chapter 1, multirate filter banks and wavelets are introduced. At the same time, the relationship of surface's subdivision scheme with wavelets' subdivision function is pointed out, and some characters of subdivision are indicated.In chapter 2, a method for the design of the lowest-delay arbitrary length M-band cosine-modulated perfect reconstruction wavelet filter banks is deduced. The stopband error of prototype filter is used to be the objective function for optimization. Instead of the method of least square approximation, this paper introduce the method of best uniformity approximation.