Based On Image Processing Technology And The Applications Of The Anisotropic Diffusion

In the field of image processing, anisotropic diffusion technique (in a narrow sense it is to simplify a signal or an image in a way that only interesting features are preserved while unimportant data is considered as noise and gradually removed for both scalar-valued images (namely grayscale images) and vector-valued images (namely multiple-channel images such as RGB images and hyper-spectral images)), is a constituent part of scale space theory, specifically, is a particular instance of nonlinear scale space. On the other hand, the mathematical formulation of anisotropic diffusion technique is of partial differential equation (PDE), resulting that in image processing field this technique is the main content in applications of PDE.However, the existing method of scalar valued anisotropic diffusion has difficulty in locating (or defining) edges accurately and suppressing prominent noise points, due to solitary usage of gradient information (in short the existing method has an ambiguous definition for both edge points and prominent noise points). In this thesis, we define a newly pixel attribute in the procedure of the proposed four-step algorithm, by which prominent noise points and edges are significantly distinguished. Experiments confirm that combining gradient and "length" information in anisotropic diffusion equation, a better diffusion performance is achieved at the expense of moderate computational complexity increment.Generalization from scalar-valued anisotropic diffusion to vector valued anisotropic diffusion is also investigated in the thesis, due to their essential relevance (the former is the special case of the latter). There exists three methods to realize the generalization:functional minimization (variational), divergence expression and oriented Laplacians. Considering their close relationships, when introducing or illustrating them respectively for revealing corresponding features, we also pay attention on their differences and relationships. Based on these preparations, according to literature we introduce a common framework with its instance for boosting the fusion of the three approaches. In the process of generalization, we arrange existing researches. We also study the one to one mapping between trace tensor of oriented Laplacians and the ellipse Gaussian kernel which varies with both space locations and time, and consequently reveals the essence that diffusion strengths controlled by two parameters, exactly equal to squares of major and minor semi-axes of the ellipse Gaussian kernel. Because of this we establish explicit physical meaning for abstract mathematical expressions, and concludes the natural relevancy among oriented Laplacians, circular Gaussian with varying radius (namely pseudo-anisotropic diffusion) and circular Gaussian with constant radius (namely isotropic diffusion, traditional Gaussian kernel). Moreover, we reveal correspondences between two expressions in scalar-valued anisotropic diffusion and expressions in vector-valued anisotropic diffusion (oriented Laplacians and divergence expression respectively) by separating interference item out, as a valuable result. Finally, the algorithm flowchart unifies both scalar-valued and vector-valued anisotropic diffusions.Experiment results shows that the new regularization PDE is available for various applications such as color image restoration, improvement of lossy compressed images, image inpainting and flow visualization.