Recently, considerable research efforts have been devoted to the design of methods to learn from data overcomplete dictionaries for sparse coding. However, learned dictionaries require the solution of an optimization problem for coding new data. In order to overcome this drawback, we propose an algorithm aimed at learning both a dictionary and its dual: a linear mapping directly performing the coding. By leveraging on proximal methods, our algorithm jointly minimizes the reconstruction error of the dictionary and the coding error of its dual; the sparsity of the representation is induced by an $\ell_1$-based penalty on its coefficients. The results obtained on synthetic data and real images show that the algorithm is capable of recovering the expected dictionaries. Furthermore, on a benchmark dataset, we show that the image features obtained from the dual matrix yield state-of-the-art classification performance while being much less computational intensive.

In multimedia information retrieval, where a document may contain both textual and visual content features, the ranking of documents is often computed by heuristically combining the feature spaces of different media types or combining the ranking scores computed independently from different feature spaces. In this paper, we propose a principled approach inspired by quantum theory. Specifically, we propose a tensor product based model aiming to represent textual and visual content features of an image as a non-separable composite system. The ranking scores of the images are then computed in the form of a quantum measurement. In addition, the correlations between features of different media types are incorporated in the framework. Experiments on ImageClef2007 show a promising performance of the tensor based approach.

We propose a simple kernel based nearest neighbor approach for handwritten digit classification. The "distance" here is actually a kernel defining the similarity between two images. We carefully study the effects of different number of neighbors and weight schemes and report the results. With only a few nearest neighbors (or most similar images) to vote, the test set error rate on MNIST database could reach about 1.5%-2.0%, which is very close to many advanced models.

Many problems of low-level computer vision and image processing, such as denoising, deconvolution, tomographic reconstruction or super-resolution, can be addressed by maximizing the posterior distribution of a sparse linear model (SLM). We show how higher-order Bayesian decision-making problems, such as optimizing image acquisition in magnetic resonance scanners, can be addressed by querying the SLM posterior covariance, unrelated to the density's mode. We propose a scalable algorithmic framework, with which SLM posteriors over full, high-resolution images can be approximated for the first time, solving a variational optimization problem which is convex iff posterior mode finding is convex. These methods successfully drive the optimization of sampling trajectories for real-world magnetic resonance imaging through Bayesian experimental design, which has not been attempted before. Our methodology provides new insight into similarities and differences between sparse reconstruction and approximate Bayesian inference, and has important implications for compressive sensing of real-world images.

Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many signal and image processing tasks. It is now well understood that the choice of the sparsity regularization term is critical in the success of such models. Based on a codelength minimization interpretation of sparse coding, and using tools from universal coding theory, we propose a framework for designing sparsity regularization terms which have theoretical and practical advantages when compared to the more standard l0 or l1 ones. The presentation of the framework and theoretical foundations is complemented with examples that show its practical advantages in image denoising, zooming and classification.

We present an on-line decentralised algorithm for coordinating mobile sensors for a broad class of information gathering tasks. These sensors can be deployed in unknown and possibly hostile environments, where uncertainty and dynamism are endemic. Such environments are common in the areas of disaster response and military surveillance. Our coordination approach itself is based on work by Stranders et al. (2009), that uses the max-sum algorithm to coordinate mobile sensors for monitoring spatial phenomena. In particular, we generalise and extend their approach to any domain where measurements can be valued. Also, we introduce a clustering approach that allows sensors to negotiate over paths to the most relevant locations, as opposed to a set of fixed directions, which results in a significantly improved performance. We demonstrate our algorithm by applying it to two challenging and distinct information gathering tasks. In the first–pursuit-evasion (PE)–sensors need to capture a target whose movement might be unknown. In the second–patrolling (P)–sensors need to minimise loss from intrusions that occur within their environment. In doing so, we obtain the first decentralised coordination algorithms for these domains. Finally, in each domain, we empirically evaluate our approach in a simulated environment, and show that it outperforms two state of the art greedy algorithms by 30% (PE) and 44% (P), and an existing approach based on the Travelling Salesman Problem by 52% (PE) and 30% (P).

Traffic monitoring systems usually make assumptions about the movement of vehicles, such as that they drive in dedicated lanes, and that those lanes rarely include non-vehicle clutter. Urban settings within developing countries often present extremely chaotic traffic scenarios which make these assumptions unrealistic. We show how a standard approach to traffic monitoring can be made more robust by using probabilistic inference, and in such a way that we bypass the need for vehicle segmentation. Instead of tracking individual vehicles but treat a lane of traffic as a fluid and estimate the rate of flow. Our modelling of uncertainty allows us to accurately monitor traffic flow even in the presence of substantial clutter.

In this article we give our contribution to the problem of segmentation with plug-in procedures. We give general sufficient conditions under which plug in procedure are efficient. We also give an algorithm that satisfy these conditions. We give an application of the used algorithm to hyperspectral images segmentation. Hyperspectral images are images that have both spatial and spectral coherence with thousands of spectral bands on each pixel. In the proposed procedure we combine a reduction dimension technique and a spatial regularisation technique. This regularisation is based on the mixlet modelisation of Kolaczyck and Al.

For the most of my life, I have earned my living as a computer vision professional busy with image processing tasks and problems. In the computer vision community there is a widespread belief that artificial vision systems faithfully replicate human vision abilities or at least very closely mimic them. It was a great surprise to me when one day I have realized that computer and human vision have next to nothing in common. The former is occupied with extensive data processing, carrying out massive pixel-based calculations, while the latter is busy with meaningful information processing, concerned with smart objects-based manipulations. And the gap between the two is insurmountable. To resolve this confusion, I had had to return and revaluate first the vision phenomenon itself, define more carefully what visual information is and how to treat it properly. In this work I have not been, as it is usually accepted, biologically inspired . On the contrary, I have drawn my inspirations from a pure mathematical theory, the Kolmogorov s complexity theory. The results of my work have been already published elsewhere. So the objective of this paper is to try and apply the insights gained in course of this my enterprise to a more general case of information processing in human brain and the challenging issue of human intelligence.

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is su- perior in terms of out-of-control average run length, when one is interest in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives which explains that unexpected and interesting behavior. Since real observations are often not independent, the question arises whether these re- sults still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, firstly, to a large class time series models, and, secondly, to locally dependent image data, as we demonstrate by an example.