2,446 research outputs found

    Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems

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    Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify its solution. Deriving efficient strategies which jointly brings into play the primal and the dual problems is however a more recent idea which has generated many important new contributions in the last years. These novel developments are grounded on recent advances in convex analysis, discrete optimization, parallel processing, and non-smooth optimization with emphasis on sparsity issues. In this paper, we aim at presenting the principles of primal-dual approaches, while giving an overview of numerical methods which have been proposed in different contexts. We show the benefits which can be drawn from primal-dual algorithms both for solving large-scale convex optimization problems and discrete ones, and we provide various application examples to illustrate their usefulness

    Line-Field Based Adaptive Image Model for Blind Deblurring

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    Ph.DDOCTOR OF PHILOSOPH

    MAP entropy estimation: Applications in robust image filtering

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    We introduce a new approach for image filtering in a Bayesian framework. In this case the probability density function (pdf) of the likelihood function is approximated using the concept of non-parametric or kernel estimation. The method is based on the generalized Gaussian Markov random fields (GGMRF), a class of Markov random fields which are used as prior information into the Bayesian rule, which principal objective is to eliminate those effects caused by the excessive smoothness on the reconstruction process of images which are rich in contours or edges. Accordingly to the hypothesis made for the present work, it is assumed a limited knowledge of the noise pdf, so the idea is to use a non-parametric estimator to estimate such a pdf and then apply the entropy to construct the cost function for the likelihood term. The previous idea leads to the construction of Maximum a posteriori (MAP) robust estimators, since the real systems are always exposed to continuous perturbations of unknown nature. Some promising results of three new MAP entropy estimators (MAPEE) for image filtering are presented, together with some concluding remarks

    Bayesian image restoration and bacteria detection in optical endomicroscopy

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    Optical microscopy systems can be used to obtain high-resolution microscopic images of tissue cultures and ex vivo tissue samples. This imaging technique can be translated for in vivo, in situ applications by using optical fibres and miniature optics. Fibred optical endomicroscopy (OEM) can enable optical biopsy in organs inaccessible by any other imaging systems, and hence can provide rapid and accurate diagnosis in a short time. The raw data the system produce is difficult to interpret as it is modulated by a fibre bundle pattern, producing what is called the “honeycomb effect”. Moreover, the data is further degraded due to the fibre core cross coupling problem. On the other hand, there is an unmet clinical need for automatic tools that can help the clinicians to detect fluorescently labelled bacteria in distal lung images. The aim of this thesis is to develop advanced image processing algorithms that can address the above mentioned problems. First, we provide a statistical model for the fibre core cross coupling problem and the sparse sampling by imaging fibre bundles (honeycomb artefact), which are formulated here as a restoration problem for the first time in the literature. We then introduce a non-linear interpolation method, based on Gaussian processes regression, in order to recover an interpretable scene from the deconvolved data. Second, we develop two bacteria detection algorithms, each of which provides different characteristics. The first approach considers joint formulation to the sparse coding and anomaly detection problems. The anomalies here are considered as candidate bacteria, which are annotated with the help of a trained clinician. Although this approach provides good detection performance and outperforms existing methods in the literature, the user has to carefully tune some crucial model parameters. Hence, we propose a more adaptive approach, for which a Bayesian framework is adopted. This approach not only outperforms the proposed supervised approach and existing methods in the literature but also provides computation time that competes with optimization-based methods

    Robust partial-learning in linear Gaussian systems

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    International audienceThis paper deals with unsupervised and off-line learning of parameters involved in linear Gaussian systems, i.e. the estimation of the transition and the noise covariances matrices of a state-space system from a finite series of observations only. In practice, these systems are the result of a physical problem for which there is a partial knowledge either on the sensors from which the observations are issued or on the state of the studied system. We therefore propose in this work an " Expectation-Maximization " learning type algorithm that takes into account constraints on parameters such as the fact that two identical sensors have the same noise characteristics, and so estimation procedure should exploit this knowledge. The algorithms are designed for the pairwise linear Gaussian system that takes into account supplementary cross-dependences between observations and hidden states w.r.t. the conventional linear system, while still allowing optimal filtering by means of a Kalman-like filter. The algorithm is made robust through QR decompositions and the propagation of a square-root of the covariance matrices instead of the matrices themselves. It is assessed through a series of experiments that compare the algorithms which incorporate or not partial knowledge, for short as well as for long signals

    A Markov model for blind image separation by a mean-field EM algorithm

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    Image Restoration

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    This book represents a sample of recent contributions of researchers all around the world in the field of image restoration. The book consists of 15 chapters organized in three main sections (Theory, Applications, Interdisciplinarity). Topics cover some different aspects of the theory of image restoration, but this book is also an occasion to highlight some new topics of research related to the emergence of some original imaging devices. From this arise some real challenging problems related to image reconstruction/restoration that open the way to some new fundamental scientific questions closely related with the world we interact with

    Foundations, Inference, and Deconvolution in Image Restoration

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    Image restoration is a critical preprocessing step in computer vision, producing images with reduced noise, blur, and pixel defects. This enables precise higher-level reasoning as to the scene content in later stages of the vision pipeline (e.g., object segmentation, detection, recognition, and tracking). Restoration techniques have found extensive usage in a broad range of applications from industry, medicine, astronomy, biology, and photography. The recovery of high-grade results requires models of the image degradation process, giving rise to a class of often heavily underconstrained, inverse problems. A further challenge specific to the problem of blur removal is noise amplification, which may cause strong distortion by ringing artifacts. This dissertation presents new insights and problem solving procedures for three areas of image restoration, namely (1) model foundations, (2) Bayesian inference for high-order Markov random fields (MRFs), and (3) blind image deblurring (deconvolution). As basic research on model foundations, we contribute to reconciling the perceived differences between probabilistic MRFs on the one hand, and deterministic variational models on the other. To do so, we restrict the variational functional to locally supported finite elements (FE) and integrate over the domain. This yields a sum of terms depending locally on FE basis coefficients, and by identifying the latter with pixels, the terms resolve to MRF potential functions. In contrast with previous literature, we place special emphasis on robust regularizers used commonly in contemporary computer vision. Moreover, we draw samples from the derived models to further demonstrate the probabilistic connection. Another focal issue is a class of high-order Field of Experts MRFs which are learned generatively from natural image data and yield best quantitative results under Bayesian estimation. This involves minimizing an integral expression, which has no closed form solution in general. However, the MRF class under study has Gaussian mixture potentials, permitting expansion by indicator variables as a technical measure. As approximate inference method, we study Gibbs sampling in the context of non-blind deblurring and obtain excellent results, yet at the cost of high computing effort. In reaction to this, we turn to the mean field algorithm, and show that it scales quadratically in the clique size for a standard restoration setting with linear degradation model. An empirical study of mean field over several restoration scenarios confirms advantageous properties with regard to both image quality and computational runtime. This dissertation further examines the problem of blind deconvolution, beginning with localized blur from fast moving objects in the scene, or from camera defocus. Forgoing dedicated hardware or user labels, we rely only on the image as input and introduce a latent variable model to explain the non-uniform blur. The inference procedure estimates freely varying kernels and we demonstrate its generality by extensive experiments. We further present a discriminative method for blind removal of camera shake. In particular, we interleave discriminative non-blind deconvolution steps with kernel estimation and leverage the error cancellation effects of the Regression Tree Field model to attain a deblurring process with tightly linked sequential stages
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