Consistent Image Decoding from Multiple Lossy Versions

With the recent development of tools for data sharing in social networks and peer to peer networks, the same information is often stored in different nodes. Peer-to-peer protocols usually allow one user to collect portions of the same file from different nodes in the network, substantially improving the rate at which data are received by the end user. In some cases, however, the same multimedia document is available in different lossy versions on the network nodes. In such situations, one may be interested in collecting all available versions of the same document and jointly decoding them to obtain a better reconstruction of the original. In this paper we study some methods to jointly decode different versions of the same image. We compare different uses of the method of Projections Onto Convex Sets (POCS) with some Convex Optimization techniques in order to reconstruct an image for which JPEG and JPEG2000 lossy versions are available

Continuous Multiclass Labeling Approaches and Algorithms

We study convex relaxations of the image labeling problem on a continuous domain with regularizers based on metric interaction potentials. The generic framework ensures existence of minimizers and covers a wide range of relaxations of the originally combinatorial problem. We focus on two specific relaxations that differ in flexibility and simplicity -- one can be used to tightly relax any metric interaction potential, while the other one only covers Euclidean metrics but requires less computational effort. For solving the nonsmooth discretized problem, we propose a globally convergent Douglas-Rachford scheme, and show that a sequence of dual iterates can be recovered in order to provide a posteriori optimality bounds. In a quantitative comparison to two other first-order methods, the approach shows competitive performance on synthetical and real-world images. By combining the method with an improved binarization technique for nonstandard potentials, we were able to routinely recover discrete solutions within 1%--5% of the global optimum for the combinatorial image labeling problem

Sparse Modeling for Image and Vision Processing

In recent years, a large amount of multi-disciplinary research has been conducted on sparse models and their applications. In statistics and machine learning, the sparsity principle is used to perform model selection---that is, automatically selecting a simple model among a large collection of them. In signal processing, sparse coding consists of representing data with linear combinations of a few dictionary elements. Subsequently, the corresponding tools have been widely adopted by several scientific communities such as neuroscience, bioinformatics, or computer vision. The goal of this monograph is to offer a self-contained view of sparse modeling for visual recognition and image processing. More specifically, we focus on applications where the dictionary is learned and adapted to data, yielding a compact representation that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics and Visio