Research On Direction-Based Transforms And Filters For Images And Their Applications

Directional information is usually one of the most important and intrinsic image features. People always expect a variety of transforms or filters are capable of representing abundant edge's directional information contained in images, and utilize it to specified algorithms for image processing. Therefore presented direction-based transforms or filters are significant for the applications associated with edges such as image denoising, segmentation, etc.The multistage median filter (MMF) presented in early years is a classical directional approach for denoising with sub-windows with multidirections. Although it is an intuitive local structure-based filter, it achieves a good performance in noise removal and edge preserving. Since the 1980's, the originality and development of multiresolutional analysis represented by wavelet theory break through the limitations of conventional Fourier analysis, and it has brought a revolutionary influence on signal processing. Images are handled by two-dimensional wavelet transform whose basis is spanned from the two one-dimensional ones. As one-dimensional wavelet transform is capable of capturing point-wise singularities, the two-dimensional can only detect edges along three directions: horizontal, vertical, and diagonal. The directional wavelet transform have more directions compared to two-dimensional transform, but they both describe line or sphere singularities in point-wise manner, i.e. they can not achieve a sparse representation for two or high dimensional data. In recent years, the Multiscale Geometric Analysis (GMA) has been developed to overcome the drawback of wavelet transform, which includes a series of transforms such as Curvelet, Ridgelet, Contourlet, etc. Almost within the same period of wavelet's popularity, the PDE-based image processing techniques have risen that consists of anisotropic diffusion and level set mainly. This type of methods employs one or a group of Partial Differential Equations (PDEs) with some boundary conditions to evolve image intensity or contour, and the PDEs can be derived from local structural features. Except for the mentioned approaches, Gabor transform is another efficient tool for representing direction information.It has shown that the direction-based transforms and filters can be categorized into two types: the ones belonging to spatial domain such as MMF and PDE-based approaches, and the other belonging to transform domain such as MGA, wavelet transform and Gabor transform. In this thesis we focus on the Curvelet transform, PDE-based approaches and MMF, and carry out some research theoretically and practically. This work includes as follows.(1) We simulate the Curvelet framework, which includes LP-based subband decomposition and Pseudo-Polar FFT-based Ridgelet transform. As the latter transform is the key step in digital realization of Curvelet transform, we give a description on the numerical algorithm of its forward and inverse transforms, and present Fractional Fourier transform related to Pseudo-Polar FFT;(2) We review the history briefly of PDE-based anisotropic diffusion for images. In particular, we investigate the classical anisotropic diffusion, the Perona-Malik model mathematically and theoretically, and explain some intrinsic relationship between the local structure-based evolution for image intensity or contour and the P-M and TV diffusion models. This deepens our understanding on anisotropic diffusion and the mechanism of PDEs in image processing.(3) Considering the faults of pyramid-based subband decomposition applied to Curvelet transform, we take advantage of the properties of TV models, and use the digital TV filter to substitute subband decomposition procedure. Simultaneously, we improve the digital TV filter to speed up its detail extraction. Then we combine this new filter to Ridgelet transform to achieve image denoising, and experimental results have shown its effectiveness;(4) We improve multistage median filter by adding directions of sub-windows to a directional adaptive algorithm, and it is better in edge preserving and noise removal.(5) We construct a novel set of features for image edges, i.e. local orientation estimation and local intensity contrast. The multilevel local intensity contrast features are then to be fused into a single image which is to be optimized by direction information. Finally we utilize the region-based level set approach to evolve the feature image and obtain segmentation result. Our experiments have shown its effectiveness compared to Gabor approach.