Towards unifying diffusion and exemplar-based inpainting

A novel framework for image inpainting is proposed, relying on graph-based diffusion processes. Depending on the construction of the graph, both flow-based and exemplar-based inpainting methods can be implemented by the same equations, hence providing a unique framework for geometry and texture-based approaches to inpainting. Furthermore, the use of a variational framework allows to overcome the usual sensitivity of exemplar-based methods to the heuristic issues by providing an evolution criterion. The use of graphs also makes our framework more flexible than former non-local variational formulations, allowing for example to mix spatial and non-local constraints and to use a data term to provide smoother blending between the initial image and the result

Graph-based Image Inpainting

The project goal was to explore the applications of spectral graph theory to address the inpainting problem of large missing chunks. We used a non-local patch graph representation of the image and proposed a structure detector which leverages the graph representation and influences the fill-order of our exemplar-based algorithm. Our method achieved state-of-the-art performances

Patch-based methods for variational image processing problems

Image Processing problems are notoriously difficult. To name a few of these difficulties, they are usually ill-posed, involve a huge number of unknowns (from one to several per pixel!), and images cannot be considered as the linear superposition of a few physical sources as they contain many different scales and non-linearities. However, if one considers instead of images as a whole small blocks (or patches) inside the pictures, many of these hurdles vanish and problems become much easier to solve, at the cost of increasing again the dimensionality of the data to process. Following the seminal NL-means algorithm in 2005-2006, methods that consider only the visual correlation between patches and ignore their spatial relationship are called non-local methods. While powerful, it is an arduous task to define non-local methods without using heuristic formulations or complex mathematical frameworks. On the other hand, another powerful property has brought global image processing algorithms one step further: it is the sparsity of images in well chosen representation basis. However, this property is difficult to embed naturally in non-local methods, yielding algorithms that are usually inefficient or circonvoluted. In this thesis, we explore alternative approaches to non-locality, with the goals of i) developing universal approaches that can handle local and non-local constraints and ii) leveraging the qualities of both non-locality and sparsity. For the first point, we will see that embedding the patches of an image into a graph-based framework can yield a simple algorithm that can switch from local to non-local diffusion, which we will apply to the problem of large area image inpainting. For the second point, we will first study a fast patch preselection process that is able to group patches according to their visual content. This preselection operator will then serve as input to a social sparsity enforcing operator that will create sparse groups of jointly sparse patches, thus exploiting all the redundancies present in the data, in a simple mathematical framework. Finally, we will study the problem of reconstructing plausible patches from a few binarized measurements. We will show that this task can be achieved in the case of popular binarized image keypoints descriptors, thus demonstrating a potential privacy issue in mobile visual recognition applications, but also opening a promising way to the design and the construction of a new generation of smart cameras