Study On Image Segmentation And Denoising Based On Partial Differential Equations

Partial differential equations(PDEs, the Partial Differential Equation) have amaturity and a wide range of applications in physics, especially effective for thediffusion model. From around1990s, PDEs image processing and image analysisbecame an active topic in related research area. Typical applications of PDEs in imageprocessing are image segmentation and image denoising.The work traced the development in PDE’s image processing, focuses on imagesegmentation and image denoising, and implemented several classical algorithms in thistrend.The main results are summarized as follows:In study of image segmentation, Chan-Vese model(referred to the C-Vmodel)divide the image into two parts, the background and the objective. The gray values mustclose to constant in each of the parts, which lead to the C-V model can’t segmentationmultiphase image. According to the C-V model, Chan and Vese proposed the multiphaseC-V model, the multi-phase extension of the Chan-Vese model is able to deal withmulti-phase; however, it is computationally expensive and sensitive to the initial curve.In order to address these problems, this paper proposes a new active contour model thatintegrates region gradients. Experiments show that our model can segment multi-phaseimages quickly, while it allows for flexible initialization.In study of image denoising, Gaussian filter is a commonly denoising method,while the Gaussian filter is the solution of the isotropic diffusion. The isotropicdiffusion can effectively remove the noise, but it can’t maintain the edge. Perona-Malik(P-M) model, a well-known anisotropic diffusion denoising model, can effectivelyremove noise while preserving image boundaries. However, its diffusion coefficientonly associates with the gradient of each pixel, but not with the local region informationof the image, thus this model isn’t able to effectively preserve the important details ofthe image. To address this problem, our paper proposes an improved P-M model basedon local entropy. The diffusion coefficient of the new model not only depends on thegradient of image, but also on the local region information described by local entropy.Experimental results show that the proposed model not only can effectively remove noise while preserving the boundaries better, but also can maintain important details ofthe image very well.