Research On The Applications Of The Continued Fractions Methods In Impulse Noise Removal, Time Series Data Compression And Video Shot Detection

Recently the nonlinear method has attracted more and more attention in many application researches. In numerical analysis, the most significant nonlinear analysis method is the continued fractions interpolation and approximation. Compared with other interpolation methods, the continued fractions interpolation has better approximation and smaller error, especially it is suitable to approximate abrupt data fluctuation. Due to excellent nonlinear approximation performance of the continued fractions interpolation, it has been widely applied to solving actual engineering problems. This thesis mainly studies three engineering problems based on continued fractions interpolation, which are detection and removal of impulse noises, compression and reconstruction of time series data and boundary detection of video shot and scene. The main contents can be summarized as follows:· A novel algorithm for impulse removal using Thiele’s continued fractions interpolation is proposed. At first we indicate that there are four aspects of problems in existing methods, which are getting prior knowledge, preserving image edge, automatically detecting noisy image and differentiating unipolar impulse and bipolar impulse. Through the analysis and experiments, we present a novel denoising algorithm, in which the weighted mean of four-direction continued fractions interpolation is computed to estimate the corrupted pixel value. The proposed algorithm can overcome prior knowledge problem and preserving image edge problem.·Through the review of existing impulse detection methods, we indicate that state-of-the-art methods cannot judge automatically whether an image is corrupted or not. In order to overcome this drawback, an automatic detector based on local mean and variance (LMVD) is presented, which can automatically pick out noisy image from massive images and output corrupted gray levels. The detector utilizes local mean and variance of the neighborhood of corrupted pixels to simulate the cognitive processes of human observing noisy image. Based on LMVD, the Newton-Thiele filter (NTF) instead of median filter is applied to remove impulse noise. The process to construct NTF can be divided into two steps:setting up the grid and constructing the Newton-Thiele’s rational interpolation on the grid. First, eight adjacent pixels of the corrupted center pixel are used to construct the two dimensional grid. Second, the corrupted center pixel value will be updated by Newton-Thiele’s rational interpolation on the grid. The NTF has better robustness than existing filters because it does not need to adjust parameters.·Anovel method is proposed to compress time series data based on interpolation of vector valued continued fraction. The proposed method first gets a raw series of compression data points by using Douglas-Peucker method, then the raw series is divided into some segments by using continued fraction interpolation. Finally, some compression points on segments are deleted. Compared with straight segments method, proposed method is suitable to not only linear data compression and reconstructing but also nonlinear data. Moreover, it also has better compression rate.·A method for shot boundary detection based on SURF Features is proposed. The method detect cut transitions by variable step matching algorithm. Gradual transitions are detected based on SVM. The idea of detecting is to distinguish between gradual transition and camera movement. The SURF features are fed to two SVM classifiers to get gradual transition.·Through the analysis of existing shot boundary detection methods, based on decision function (DF), a novel universal detection model of shot boundary is proposed. The model is independent of any features and can be applied to any cases by adjusting and combining various features according to different requirements. The decision function (DF) is constructed by means of Thiele’s continued fractions interpolation, which can be moved on frame sequence to lock the cut and gradual boundary.·Based on shot boundary detection, an indistinct segmentation method is proposed to detect scene boundary. The method indicates that sometimes the scene boundary is indistinct and a fuzzy function Fuz should be used to describe the indistinct degree of scene boundary. The method first constructs shot temporal directed graph and splits graph into sub-graphs, then indistinct degree of scene boundary can be computed by means of the instance-based learning algorithm and fuzzy function fuz...