FULLY NON-LOCAL SUPER-RESOLUTION VIA SPECTRAL HASHING

Super-resolution is the task of creating an high resolution image from a low resolution input sequence. To overcome the difficul- ties of fine image registration, several methods have been proposed exploiting the non-local intuition, i.e. any datapoint can contribute to the final result if it is relevant. These algorithms however limit in practice the search region for relevant points in order to lower the corresponding computational cost. Furthermore, they define the non-local relations in the high resolution space, where the true im- ages are unknown. In this work, we introduce the use of spectral hashing to effi- ciently compute fully non-local neighbors. We also restate the super- resolution functional using fixed weights in the low resolution space, allowing us to use resolution schemes that avoid many artifacts

Composite Correlation Quantization for Efficient Multimodal Retrieval

Efficient similarity retrieval from large-scale multimodal database is pervasive in modern search engines and social networks. To support queries across content modalities, the system should enable cross-modal correlation and computation-efficient indexing. While hashing methods have shown great potential in achieving this goal, current attempts generally fail to learn isomorphic hash codes in a seamless scheme, that is, they embed multiple modalities in a continuous isomorphic space and separately threshold embeddings into binary codes, which incurs substantial loss of retrieval accuracy. In this paper, we approach seamless multimodal hashing by proposing a novel Composite Correlation Quantization (CCQ) model. Specifically, CCQ jointly finds correlation-maximal mappings that transform different modalities into isomorphic latent space, and learns composite quantizers that convert the isomorphic latent features into compact binary codes. An optimization framework is devised to preserve both intra-modal similarity and inter-modal correlation through minimizing both reconstruction and quantization errors, which can be trained from both paired and partially paired data in linear time. A comprehensive set of experiments clearly show the superior effectiveness and efficiency of CCQ against the state of the art hashing methods for both unimodal and cross-modal retrieval

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas

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