A DCT multiresolution analysis for image decomposition and texture segmentation

Variants of the discrete cosine transforms have been used for interpolation and extrapolation in applied mathematics and for data compression and image analysis/synthesis in digital signal processing (DSP). Recent years have seen a revival of interest in using DCT transforms for designing hierarchical interpolation wavelets bases.; This thesis proposes novel approaches to solving the problems associated with texture segmentation and image decomposition using interpolation wavelets having Chebyshev polynomial as basis functions. A new image model called the Generalized Discrete Cosine Transform Wavelet Model (GDCTWM) is presented. Compared with traditional multiresolution methods based on 2-channel filter banks, the proposed model offers the following advantages for dealing with image decomposition and texture segmentation: (1) MRA is carried out using fast DCT algorithms; (2) The number of basis functions used equals MAX(N,M), where the image size is {dollar}Ntimes M{dollar} and MAX(N,M) is the maximum of N and M; (3) A large class of signals can be compressed to near theoretical optimum ratios since DCTs are used exclusively.; The existence of fast DCT algorithms makes practical real time implementation of GDCTWM applications feasible. Moreover, unlike 2-channel filter where the basis functions are scale-shifted copies of a single scaling function, the GDCTWM has a number of basis functions depending upon the dimension of the analyzed signal. The GDCTWM has been shown to possess better energy compaction properties than the class of Daubechies' filters widely used for image decomposition.