The Design, Based On The Nonlinear Equations Of Image Processing Algorithms

The present dissertation has applied nonlinear equations from the viewpoint of scale-space in the research of image filtering, segmentation and video tracking. The main contributions of the dissertation are itemized as follows: (1) An improved image filtering algorithm based on fourth order partial differential equation (PDE) is put forth. The algorithm could simultaneously suppress mixing Gaussian and salt and pepper type noises while eliminate the blocking effect derived from low order PDEs; (2) To get rid of noises with large variance, a nonlinear adaptive diffusion iterative filter is imposed on high-frequency coefficients of images after wavelet decomposition, which has achieved satisfactory results; (3) An image shock filtering algorithm employing nonlinear complex equations is proposed, which can effectively smooth noises while enhance image edges; (4) Further more, the CGL equation that used to describe the superconductor in its critical phase has been incorporated into complex diffusion equation to form a shock filtering model that has the ability of enhancing edges in the process of noise elimination; (5) A color image filtering algorithm based on Beltrami Flow has been imporved. By using entropy conservation discretization method, the algorithm has anisotropic diffusing speed in gradient direction and contour direction so that mixing noise with Gaussian and Salt and Pepper type could be efficiently suppressed in only a few rounds of iterations; (6) After image segmentation algorithms based on spatial scale-space is summarized, one fast edge detection method using complex diffusion equation has been provided whose localization precision and operation speed are both improved; (7) One feasible segmentation algorithm with good segmentation result but low operation speed is also brought out in the thesis. The level set method in the complex nonlinear scale-space has been used in the algorithm; (8) One active contour video tracking method blending chaos, genetic algorithm and greedy algorithm is proposed, whose segmentation result has exceeded that of the methods just uses greedy algorithm in terms of single frame segmentation.Finally, after analyzing the disadvantages as well as merits of image processing approaches using nonlinear equations, the thesis has pointed out several open problems and further research directions.