Image Inpainting And Image Editing By Solving Partial Differential Equations

Accompanying with the popular use of digital camera and image editing software, people's need for image processing is increasing. At present, compared with the traditional image processing techniques, such as filtering and denoising, image processing techniques for special purposes, for example: repairing the damaged parts of images, seamless inserting objects from different images, replacement of image background and image colorization etc are under more widely research and development in academe and industry.Recently PDE-based method plays the important role in the field of image processing due to its advantages. In this dissertation, we mainly focus on the problems of image inpainting and editing using PDE-based methods, and propose several new methods in order to contribute to the development of the attractive and useful areas in image processing.First, we propose an anisotropic heat transfer model to repair the structure information in damaged images. This is achieved by making the propagation direction and intensity relate to the image contents. In the inpainting process, the two components of propagation are the isophote direction and its orthogonal direction. The propagation intensity along the isophote direction is unchanged while intensity along the orthogonal direction of isophote is inversely proportional to the magnitude of gradient. The method can reconstruct the image structure information and avoid edge blurring. In numerical implementation, we adaptively choose the step size of the finite difference according to the curvature. In this way, the proposed method can produce satisfactory image quality and reduce computational complexity.Second, we develop a partial differential equation model for image inpainting which can propagate texture information. We give an additional term representing texture information using the parameters of periodicity and direction, and add it into the PDE. So it can solve the problem of lacking texture information in most PDE-based methods. The method does not need to decompose the image into different layers, and inpaint both image structure and texture simultaneously with high efficiency.We also deal with the high complexity problem of searching for similar neighborhood in textural image repairing. By using nearest neighbor searching algorithm with dynamic space partitioning, we propose a fast texture synthesis method. The input sample texture image can be seen as searching space composed by multi-dimension vectors, and we partition the space by establishing data structure and update the candidate list to find the most similar neighborhood. Compared with other typical accelerating algorithms such as TSVQ, our method is faster and has better visual synthesized results which are closer to the results of exhaustive searching.Third, we propose an improved image editing method without color inconsistency using modified Poisson equation and apply it in image cloning. By adding an additional inner Dirichlet boundary condition and magnify large Laplace values corresponding to the object's true contour in the edited region, the method can insert objects into background of the target image seamlessly, and solve the color inconsistency problem caused by boundary influence. This method does not require precise definition of the object contour, but only needs to choose a rough region of the inserted object and the target location for automatic processing.We also realize the detection and authentication for standard Poisson editing. By rough and refined matching the regions which satisfy the Poisson equation, the corresponding two cloning regions and their exact boundaries are located and acquired. We sum the Laplace values on these two boundaries and differentiate the original region and cloned region according to the analysis of discontinuity on boundary regions. The method can not only detect the cloning manipulation, but also infer original appearance of the suspicious images.We have carried out inpainting and editing experiments on the large number of images and various types of damages. Experimental results show the effectiveness and veracity of the proposed methods.