Research On The Application Of Digital Image Processing Based On Continued Fraction Methods

The purpose of image processing is to effectively transfer vision information, and achieve the aim of extending human eyespot Because the objectivity of image and humans vision peculiarity is nonlinear, the nonlinear image processing algorithms are important. In recent years, nonlinear methods have attracted more and more attention and there have been some successful cases, such as median filter, mathematical morphology, etc. As a preferred way to inverstigate nonlinear numerical problems, the continued fractions method can effectively express the gradually changing data or abrupt data, so it is meaningful to study image processing by means of the continued fractions theory and algorithms.With the review of digital image properties and continued fractions theory, this dissertation focuses on the study of the image interpolation and image reconstruction; the main contributions are as fallows:First of all, the methods of solving the problem of inverse difference being infinite are successfully found while constructing the Thiele-type continued fractions. In this case it is proposed to reorder the set of interpolating points and then construct a Thiele-Newton blending continued fraction. This method is useful to the scattered data interpolation for image reconstruction or image compression.Secondly, a new adaptive osculatory rational interpolation kernel function is constructed from the point of approximating the ideal interpolating function, the function's characteristics, i.e., the space properties, the spectral properties, and the efficiency are analyzed, and the comparision it with other interpolation methods is made.Thirdly, a new method of resizing color image is presented, where the processing of color image data is carried out by using bivariate (vector valued) blending rational interpolation. This method is more effective on color image processing, because of the inherent correlation that exists between the image channels, and the nonlinearity among image pixels.Finally, a novel adaptive interpolation magnification algorithm is proposed for color image to obtain a higher resolution image from its low resolution version. It adopts the basic idea of the adaptive interpolation schemes: local analysis to classify pixels into different categories and choose different interpolation algorithms by means of rational-linear vector valued interpolation over rectangular or triangular grids. The comparison results with classical linear interpolation schemes are alse provided.What fellows are the main results achieved in this dissertation.1. (Vector valued) continued fractions are adopted for the first time to process digital images. Though the rational fractions based on one-variable (vector valued) continued fractions have been used in other engineering fields, its application in the field of digital image processing hasn't yet been reported in the literature so far.2. A new osculatory rational interpolation kernel function is established, which is different from the classical linear interpolation kernel functions. Generally, it is a more accurate approximation for the ideal interpolation function than other linear polynomial interpolants functions. Simulation results are also presented to demonstrate the superior performance of this new interpolation kernel function.3. According to the basic idea of the adaptive interpolation schemes, a novel adaptive rational-linear algorithm is worked out to enhance the resolution of an image. In this approach, the interpolation functions are adaptively selected according to the local image analysis and classification. Our algorithm significantly outperforms the classical bilinear and bicubic interpolation methods in terms of edge sharpness and artifact reduction.4. The applications of the continued fractions are extended, which will further push forward the study of the continued fractions.