Images are liable to being corrupted by noise when they are processed for many applications such as sampling, storage and transmission. In this thesis, we propose a method of image restoration for image corrupted by a white Gaussian noise. This method is based upon Gauss-Markov random field model combined with a technique of image segmentation. As a result, the image can be restored by MAP estimation. In the approach of Gauss-Markov random field model, the image is restored by MAP estimation implemented by simulated annealing or deterministic search methods. By image segmentation, the region parameters and the power of generating noise can be obtained for every region. The above parameters are important for MAP estimation of the Gauss-Markov Random field model. As a summary, we first segment the image to find the important region parameters and then restore the image by MAP estimation with using the above region parameters. Finally, the intermediate image is restored again by the conventional Gauss-Markov random field model method. The advantage of our method is the clear edges by the first restoration and deblured images by the second restoration.

The restoration of degraded images is one important application of image processing. The classical approach of image restoration, such as low-pass filter method, is usually stressed on the numerical error but with a disadvantage in visual quality of blurred texture. Therefore, a new method of image restoration, based upon image model by Compound Gauss-Markov(CGM) Random Fields, using MAP(maximum a posteriori probability) approach focused on image texture effect has been proved to be helpful. However, the contour of the restored image and numerical error for the method is poor because the conventional CGM model uses fixed global parameters for the whole image. To improve these disadvantages, we adopt the adjustable parameters method to estimate model parameters and restore the image. But the parameter estimation for the CGM model is difficult since the CGM model has 80 interdependent parameters. Therefore, we first adopt the parameter reduction approach to reduce the complexity of parameter estimation. Finally, the initial value set of the parameters is important. The different initial value might produce different results. The experiment results show that the proposed method using adjustable parameters has good numerical error and visual quality than the conventional methods using fixed parameters.

This Compound Gauss-Markov image model has been proven helpful in image restoration. In this model, a pixel in the image random field is determined by the surrounding pixels according to a predetermined line field. In this thesis, we restored the noisy image based upon the traditional Compound Gauss-Markov image field without the constraint of the model parameters introduced in the original work. The image is restored in two steps iteratively: restoring the line field by the assumed image field and restoring the image field by the just computed line field. Two methods are proposed to replace the traditional method in solving for the line field. They are probability method and vector method. In probability method, we break away from the limitation of the energy function Vcl(L) and the mystical system parameters Ckll(m,n) and£mw2. In vector method, the line field appears more reasonable than the original method. The image restored by our methods has a similar visual quality but a better numerical value than the original method.

This thesis provides an analytical and two numerical methods for solving a parabolic equation of two-dimensional mean curvature flow with some applications. In analytical method, this equation is solved by Lie group analysis method, and in numerical method, two algorithms are implemented in MATLAB for solving this equation. A geometric algorithm and a step-wise algorithm; both are based on a deterministic game theoretic representation for parabolic partial differential equations, originally proposed in the genial work of Kohn-Serfaty [1]. / +46-767165881

The central purpose of this study is the integration of modem philosophical thinking with different chaos theory principles and definitions to form relational perspectives. Relations are used in different contexts to base the causes of deterministic chaos (chaost) in the laws of nature which constitutes order. The chaost-attractor is used as subjective conception to investigate the possibilities of hidden order in a seemingly chaotic state of the objective reality. Relevant definitions of the chaos theory were analysed methodically and transcendentally with the aid of concepts of order and relations. Attention is given to the broad associations and analogies from philosophy and other disciplines which relate to the connectivity of objects to form systems. Subjective model development was done which is used to consequentially analyse some statements from published research which applied principles of chaost. It is argued that: the intrinsic properties of objects determine the causality of forces which bind objects to compose systems; a web of interactive bonds functions subjective to laws of nature which determine whether a system is in a state of order, chaost or real chaos; a dynamical transfer of many intrinsic and asymmetric properties via internal bonds constitutes non-linear connectivity which causes a sensitivity for initial conditions. It is found that the chaost of the chaos theory is not the same as real, objective chaos. The random-like evolution of a dynamic system is determined by the occurrence of irregularities and uncertainties in its internal order. A web of interactive bonds distribute small changes self-similar and scale-relevant. The difficulty in describing and explaining the complex behaviour of composed entities is simplified by the proposed web-chaost model. / Thesis (M.A. (Philosophy))--North-West University, Potchefstroom Campus, 2006.

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The general area of developing, applying and studying new and parallel models of computation is motivated by a need to overcome the limits of current Von Neumann based architectures. A key area of research in understanding how new technology can be applied to Al problem solving is through using logic languages. Logic programming languages provide a procedural interpretation for sentences of first order logic, mainly using a class of sentence called Horn clauses. Horn clauses are open to a wide variety of parallel evaluation models, giving possible speed-ups and alternative parallel models of execution. The research in this thesis is concerned with investigating one class of parallel logic language known as Committed Choice Non-Deterministic languages. The investigation considers the inherent parallel behaviour of Al programs implemented in the CCND languages and the effect of various alternatives open to language implementors and designers. This is achieved by considering how various Al programming techniques map to alternative language designs and the behaviour of these Al programs on alternative implementations of these languages. The aim of this work is to investigate how Al programming techniques are affected (qualitatively and quantitatively) by particular language features. The qualitative evaluation is a consideration of how Al programs can be mapped to the various CCND languages. The applications considered are general search algorithms (which focuses on the committed choice nature of the languages); chart parsing (which focuses on the differences between safe and unsafe languages); and meta-level inference (which focuses on the difference between deep and flat languages). The quantitative evaluation considers the inherent parallel behaviour of the resulting programs and the effect of possible implementation alternatives on this inherent behaviour. To carry out this quantitative evaluation we have implemented a system which improves on the current interpreter based evaluation systems. The new system has an improved model of execution and allows several

The central purpose of this study is the integration of modem philosophical thinking with different chaos theory principles and definitions to form relational perspectives. Relations are used in different contexts to base the causes of deterministic chaos (chaost) in the laws of nature which constitutes order. The chaost-attractor is used as subjective conception to investigate the possibilities of hidden order in a seemingly chaotic state of the objective reality. Relevant definitions of the chaos theory were analysed methodically and transcendentally with the aid of concepts of order and relations. Attention is given to the broad associations and analogies from philosophy and other disciplines which relate to the connectivity of objects to form systems. Subjective model development was done which is used to consequentially analyse some statements from published research which applied principles of chaost. It is argued that: the intrinsic properties of objects determine the causality of forces which bind objects to compose systems; a web of interactive bonds functions subjective to laws of nature which determine whether a system is in a state of order, chaost or real chaos; a dynamical transfer of many intrinsic and asymmetric properties via internal bonds constitutes non-linear connectivity which causes a sensitivity for initial conditions. It is found that the chaost of the chaos theory is not the same as real, objective chaos. The random-like evolution of a dynamic system is determined by the occurrence of irregularities and uncertainties in its internal order. A web of interactive bonds distribute small changes self-similar and scale-relevant. The difficulty in describing and explaining the complex behaviour of composed entities is simplified by the proposed web-chaost model. / Thesis (M.A. (Philosophy))--North-West University, Potchefstroom Campus, 2006.

Geostatistics and more specifically stochastic modeling of reservoir heterogeneities are being increasingly considered by reservoir analysts and engineers for their potential in generating more accurate reservoir models together with usable measures of spatial uncertainty. Geostatistics provides a probabilistic framework and a toolbox for data analysis with early integration of information. The uncertainty about the spatial distribution of critical reservoir parameters is modeled and transferred all the way to a risk conscious reservoir management. The stochastic imaging (modeling) algorithms allow the generation of multiple, equiprobable, unsmoothed reservoir models yet all honoring the data available. This thesis presents stochastic reserve estimation methods as related to the various stages of development of an oil field. Advances in technology are leading to better deterministic estimates as well as stochastic estimates with narrower ranges. Practices in the industry vary from complete dedication to deterministic or stochastic to a choice of the method depending on the stage of the development. In this study, reserves are calculated from the data available in Southeastern Turkey by using stochastic methods. Probability density functions, number of iterations are important statistical concepts. Increasing number of iterations leads to a normal distribution of histogram.

The work in this thesis can be divided into two different parts. In the first part, we suggest an approximate edge 3-coloring polynomial time algorithm for cubic graphs. For any cubic graph with n vertices, using this coloring algorithm, we get an edge 3-coloring with at most n/3 error vertices. In the second part, we study Jim Propp's Rotor-Router model on some non-bipartite graph. We find the difference between the number of chips at vertices after performing a walk on this graph using Propp model and the expected number of chips after a random walk. It is known that for line of integers and d-dimenional grid, this deviation is constant. However, it is also proved that for k-ary infinite trees, for some initial configuration the deviation is no longer a constant and say it is D. We present a similar study on some non-bipartite graph constructed from k-ary infinite trees and conclude that for this graph with the same initial configuration, the deviation is almost (k²)D.