Complex Directional Wavelet Transforms : Representation , Statistical Modeling

COMPLEX DIRECTIONAL WAVELET TRANSFORMS: REPRESENTATION, STATISTICAL MODELING AND APPLICATIONS AN PHUOC NHU VO, Ph.D. The University of Texas at Arlington, 2008 Supervising Professor: Soontorn Oraintara The thesis presents an new image decomposition for feature extraction, which is called the pyramidal dual-tree directional filter bank (PDTDFB). The image representation has an overcomplete ratio of less than 8/3 and uses a separable filter bank implementation structure. We discuss how to utilize both magnitude and phase information obtained from the PDTDFB for the purpose of texture image retrieval. The relative phase, which is the difference of phases between two adjacent complex coefficients, has a linear relationship with the angle of dominant orientation within a subband. This information is incorporated to form a new feature vector called CDFB-RP. Another application of PDTDFB is texture segmentation. A new feature extraction method is proposed for texture segmentation. The approach is based on incorporating the phase information obtained from complex filter banks. The PDTDFB is used to decompose a texture image in order to provide complex subband coefficients. The local mean direction, extracted from the phases of the coefficients, is defined as additional features for classification and segmentation. We proposed a modified version of the PDTDFB for image denoising. Unlike the previous approach, the new FB provides an approximately tight-frame decomposition. Then we proposed the complex Gaussian scale mixture (CGSM) for modeling the distribution of