Advanced numerical methods for image denoising and segmentation

Image denoising is one of the most major steps in current image processing. It is a pre-processing step which aims to remove certain unknown, random noise from an image and obtain an image free of noise for further image processing, such as image segmentation. Image segmentation, as another branch of image processing, plays a significant role in connecting low-level image processing and high-level image processing. Its goal is to segment an image into different parts and extract meaningful information for image analysis and understanding. In recent years, methods based on PDEs and variational functional became very popular in both image denoising and image segmentation. These two branches of methods are presented and investigated in this thesis. In this thesis, several typical methods based on PDE are reviewed and examined. These include the isotropic diffusion model, the anisotropic diffusion model (the P-M model), the fourth-order PDE model (the Y-K model), and the active contour model in image segmentation. Based on the analysis of behaviours of each model, some improvements are proposed. First, a new coefficient is provided for the P-M model to obtain a well-posed model and reduce the “block effect”. Second, a weighted sum operator is used to replace the Laplacian operator in the Y-K model. Such replacement can relieve the creation of the speckles which is brought in by the Y-K model and preserve more details. Third, an adaptive relaxation method with a discontinuity treatment is proposed to improve the numerical solution of the Y-K model. Fourth, an active contour model coupling with the anisotropic diffusion model is proposed to build a noise-resistance segmentation method. Finally, in this thesis, three ways of deriving PDE are developed and summarised. The issue of PSNR is also discussed at the end of the thesis