Some Applications of Nonlinear Reaction-Diffusion Equations to Image Processing
|Keywords||Reaction - diffusion equation (s) Denoising Image decomposition Image Segmentation|
This paper studies the nonlinear reaction diffusion equations in image restoration. Decomposition and segmentation in the first chapter, we propose two reaction-diffusion equations model for image denoising and decomposition in the first part, H-1 model-based image restoration and decomposition of the functional model inspired by Osher et al, we propose a model of coupled reaction-diffusion equations. new model contains two main parts of the equation: One of the main section for the whole while variation diffusion, used to remove noise; another main part is the thermal diffusivity, to amend the denoising equation source term, to protect the image texture effect interaction of two equations, and ultimately achieve denoising good to keep the borders and textures In the second part, in the framework of the above equations model, we introduce p (x)-Laplace flow instead of Total Variation flow to new denoising equation combined with Gaussian heat equation the isotropic diffusion and total variation anisotropic diffusion flow characteristics, to achieve the effect of adaptive regularization method and Galerkin method we obtain two models POSEDNESS in theoretical research, for value calculate the necessary preparations. Unlike the original model, the new model based on reaction-diffusion equations framework. addition, the new model to remove the ladder effect, maintain boundary and denoising have a good effect, especially in maintaining the texture aspects significant effect in the second chapter, we propose hybrid diffusion equation for image denoising model through the analysis of image boundary with the image of the location and structure of dependencies, constructed an anti-noise ability boundary mapping function, corresponding diffusion equation not only has the characteristics of anisotropic diffusion, and in the area of ??the image internally homogeneous Gaussian thermal diffusion, mean curvature diffusion in the near-boundary region, and ultimately achieve adaptive denoising effect. theoretical research, we first use of fixed point method to prove posedness of the new model, and then study the asymptotic state when t → ∞, the conclusions show that the new model recovery results for a long time the limit state of the local mean of the initial image. Finally, we propose a method of calculating format analyze the convergence of numerical experiments, and a series of images. compared with the TV model, the new model in the internal homogeneous region the Gaussian thermal diffusion, effective way to avoid the staircase effect; compared with the PM model, the new model is posed which solution is more stable, and because of the diffusion model and the diffusion speed of the new model depends on the location and structure of the image information, the model adaptive capabilities, better denoising internally homogeneous region close to the boundary more fine to maintain boundary in the third chapter, we create two image segmentation model based on the active contour method first model is mainly used to speed up the level set segmentation algorithm based on the active contour through the analysis of the CV borderless active contour level set segmentation algorithm on the smoothness of the image segmentation results, we propose a new fast algorithm for image segmentation. regularization term new algorithm to remove the original model, discrete gray level set functional energy calculation, the computational complexity is O (N), the computation time is very short, and the segmentation results similar to the original model. second model improved color image segmentation based on partial differential equations of the color image denoising model, we propose a convex energy functional to measure image segmentation model, and constructed according to the principle of duality, algorithms to solve the new model. Numerical experiments show that the new algorithm segmentation results more in line with actual requirements, and the new algorithm is relatively fast and stable.