Region Filling By Digital Image Inpainting

The use of PDE in image processing is a new research topic. Its mathematical model can represent image accurately and can solve many complicated problems. Now, PDEs have been widely used in many aspects of image processing.In this thesis we give some precise information about what we mean by degradation or noise. This is actually a difficult question, and we focus on a simple model with additive noise and convolution by a linear operator for the blur. First, we present restoration through the minimization of a functional involving two terms: a fidelity term to the data plus a regularization term. We discuss some qualitative properties of the restored image; Then, a PDE-Based model is proposed. We develop the model and its mathematical justification in detail.For gray level image, we transform this problem to a variational problem. We use a simple discrete implementation of the Laplacian: ΔI = I_xx + I_yy to be an image smoothness estimator, and use the isophotes directions to be the propagation direction: (N|â†') = â–½I^⊥ , that is, we estimate a variation of the smoothness, given by a descretization of 2D Laplacian, and project this variation into the isophotes direction. This projection is used to update the value of the image inside the region to be inpainted, then we get the inpainting equation.To ensure a correct evolution of the direction field, a diffusion process is interleaved with the image inpainting process described above. That is, every few steps, we apply a few iterations of image diffusion. This diffusion corresponds to the periodical curving of lines to avoid them from crossing each other. We use anisotropic diffusion, in order to achieve this goal without losing sharpness in the reconstruction, then we get the anisotropic diffusion equation.In contract with previous approaches, this technique does not require the user to specify where the novel information comes from. This is automatically done (and in a fast way), thereby allowing to simultaneously fill-in numerous regions containing completely different structures and surrounding backgrounds. In addition, no limitations are imposed on the topology of the region to be inpainted. Applications of this technique include the restoration of old photographs and damaged film; removal of superimposed text like dates, subtitles or publicity; and the removal of entire objects from the image like microphones or wires in special effects.For color image, we consider it as a set of three images, and the above described technique is applied independently to each one.