Research And Application Of Image Decomposition Based On PDE

In recent years partial differential equation (PDE) becomes a new method to solve problems in the field of image processing. In this dissertation, image decomposition methods which are based on PDE model were studied. PDE-based methods can decompose an image into the homogeneous component composing of structure information and oscillatory component composing of texture. In the process of image decomposition, how to describe the texture component and to preserve the structural feature information are major issues for researchers. This dissertation is the work carried out on these issues.At first we introduce the methods to derive PDE in image processing in this paper. Then we analyzed several image decomposition models including ROF model, TV-G model, VO model, TV-L~1 model and anisotropic model etc., which are all based on PDE. The mechanism and properties of these models were studied. Based on the advantages of these models, we present a new image decomposition model based on PDE which is able to decompose the image to homogenous component and oscillatory texture component. We use variational method to derive the corresponding PDE.The new decomposition model can also be applied to vector-valued(color) images. Numerical experiments show that new method can overcome staircasing and loss of contrast which are major disadvantages of original methods. Furthermore, the new method is more efficient than original methods.Finally we study the application of image decomposition based on PDE in image multiscale analysis, texture feature extraction and image inpainting. Corresponding experimental results are presented in this dissertation. The new image decomposition method is introduced in image inpainting and improves the results.