Color Image Filtering And Quaternion-based Color Image Processing Methods

With the rapid development of science and technology and the related hardware devices, color image processing techniques have obtained more and more applications and color image processing has become one important branch of signal processing study. However, since strong spectral relation exists between three color channels, the inherent relation present in three color components should be considered when studing color image processing, which makes color image processing much sophisticated and difficult than gray-level image processing.Due to the imperfection of imaging devices, channel transmission errors and environmental disturbance, images are usually inevitably contaminated by various kinds of noise. Therefore, image filtering and denoising are necessary or even indispensable for any image processing system. Apart from suppressing and removing noise, color image filtering techniques also can be applied to other many situations such as television image enhancement, virtual restoration of artworks, color image enhancement and sharpening, color edge detection, color image interpolation, and so on. So color image filtering is not only one of the fundamental researches in color image processing but also necessary to any image application system. However, there are very small amount of literature to systematically summarize and analyze the theories, methods, and the state-of-the-art of color image filtering researches. To this purpose, this thesis aims to study the new theories and methods of color image filtering, and at the same time, to summarize the related techniques published to date.First, the theories and methods published to date about color image filtering are systematically summarized and classified. Then, a series of the author's researches about this field are introduced and analyzed in detail. Successively, as one of the applications of color image filtering techniques, a novel color image interpolation method that is based on vector filtering solutions is presented. Finally, two efficient color image filtering algorithms that are based on quaternion theories are proposed and the applications of the QSVD (Quaternion Singular Value Decomposition) and QPCA (Quaternion Principal Component Analysis) to color images are analyzed.In order to effectively detect impulsive noise, this thesis presents four directional operators and the method about how to utilize these operators to detect color impulsive noise. It is shown experimentally that the proposed method outperforms almost all the currently popular algorithms both in filtering performance and in computational cost. Combining this impulse detection mechanism with other color image processing techniques, some excellent color image filtering algorithms are developed. According to the human vision perception, the pixels with different distances to the central pixel should have different influences on the central pixel, even though they have the same pixel value. Based on this fact, this thesis proposes a new distance-weighted algorithm that can quantify these influences. By combining this weighting algorithm and the classic vector filtering techniques, three distance- weighted based vector filtering solutions are developed.Since images are highly nonstationary due to the edges and fine details, and it is difficult to differentiate between noise and edge pixels, the fuzzy restoration techniques are proved to be highly appropriate for image filtering tasks. Therefore, this thesis also proposes a novel idea about impulsive noise removal, i.e., the frame- work of combining switching mechanism and adaptive weighted filtering techniques.By using this framework, several high performance filtering algorithms are designed. As an application of color image filtering techniques, this thesis yet utilizes vector filtering techniques to develop a novel color image interpolation algorithm that significantly improves the interpolation performance compared to the conventional color image interpolation methods.A good mathematic theory is an important tool to research color image. How to choose a mathematic tool to effectively represent a color image, which makes the three color components be considered simultaneously as a whole without loss of the spectral relation that is present in them, is a challenging problem. In this aspect, the quaternion theories and methods perhaps are appropriate. Although quaternion was discovered as early as in 1843, its theories and methods were not applied to image processing until the 1990s. In the last two chapters, this thesis first develops two quaternion-based color image filtering methods that are based on the quaternion rotation theory and quaternion unit transform, respectively, then analyzes the fulfillment algorithm of the QSVD (Quaternion Singular Value Decomposition) and its applications to color image processing, and expands the real number-valued PCA (Principal Component Analysis) to quaternion-valued PCA (QPCA).