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This paper presents a new method to perform unsupervised band selection (UBS) with hyperspectral data. The method provides a probabilistic clustering approach. The band images are clustered in the image space by computing their posterior class probability. Then, for each cluster, the band exhibiting the highest probability of belonging to it is selected as cluster exemplar. More particularly, the proposed method falls into information-maximization clustering methods, where the posterior class probability is modeled and the parameters of the models are derived by maximizing the information between the data and the unknown cluster labels. In this context, we propose a new image representation for hyperspectral images, based on the first- and second-order statistics of multiple image features. We refer to this representation as multiple-feature local statistical descriptors (MLSD). The descriptors are computed with respect to regular grids, and a special pixel selection procedure reduces the number of samples within each block of the grid. A kernel-based model that embeds the MLSD is then proposed for the posterior class probability. The model is finally optimized according to an information-maximization criterion. We conduct several experiments to determine the best parameters for the proposed approach and compare the latter with other state-of-the-art UBS methods. Quantitative evaluations show that, by employing our band selection method, higher performance in terms of classification accuracy and endmember extraction can be achieved in comparison with the state of the art. [ABSTRACT FROM AUTHOR]

The most common scheme for estimating the orientation field of space-varying directional textures is based on a local nonlinear spatial averaging of the gradient field. This leads to locally biased orientations, especially in regions of nonlinearly distributed convergence, asymmetrically distributed curvature, or geometry superposition. In this paper, we propose an orientation estimation framework that is invariant toward the local geometry. Instead of applying the spatial averaging in the initial space, it is performed in a flattened space which is obtained from a parametric space transformation model deduced from the reconstruction of local hypersurfaces. The flattening can either be applied to the initial gradient field or to the intensity image, on which the flattened gradient field is computed. The process is iterated in order to define more accurate space transformations leading to refined orientation estimation. The computational efficiency is improved without noticeable loss of orientation accuracy by a patch-based approach. Experiments, both on synthetic as well as real-life fingerprint and fibrous material images, exhibit enhanced performance in comparison with conventional methods such as the structure tensor method. [ABSTRACT FROM AUTHOR]

Objective: This paper tackles the problem of transfer learning in the context of electroencephalogram (EEG)-based brain–computer interface (BCI) classification. In particular, the problems of cross-session and cross-subject classification are considered. These problems concern the ability to use data from previous sessions or from a database of past users to calibrate and initialize the classifier, allowing a calibration-less BCI mode of operation. Methods: Data are represented using spatial covariance matrices of the EEG signals, exploiting the recent successful techniques based on the Riemannian geometry of the manifold of symmetric positive definite (SPD) matrices. Cross-session and cross-subject classification can be difficult, due to the many changes intervening between sessions and between subjects, including physiological, environmental, as well as instrumental changes. Here, we propose to affine transform the covariance matrices of every session/subject in order to center them with respect to a reference covariance matrix, making data from different sessions/subjects comparable. Then, classification is performed both using a standard minimum distance to mean classifier, and through a probabilistic classifier recently developed in the literature, based on a density function (mixture of Riemannian Gaussian distributions) defined on the SPD manifold. Results: The improvements in terms of classification performances achieved by introducing the affine transformation are documented with the analysis of two BCI datasets. Conclusion and significance: Hence, we make, through the affine transformation proposed, data from different sessions and subject comparable, providing a significant improvement in the BCI transfer learning problem. [ABSTRACT FROM PUBLISHER]

Rotation Forest (RoF) is a recent powerful decision tree (DT) ensemble classifier of hyperspectral images. RoF exploits random feature selection and data transformation techniques to improve both the diversity and accuracy of DT classifiers. Conventional RoF only considers data transformation on spectral information. To overcome this limitation, we propose a spectral and spatial RoF (SSRoF), to further improve the performance. In SSRoF, pixels are first smoothed by the multiscale (MS) spatial weight mean filtering. Then, spectral–spatial data transformation, which is based on a joint spectral and spatial rotation matrix, is introduced into the RoF. Finally, classification results obtained from each scale are integrated by a majority voting rule. Experimental results on two datasets indicate the competitive performance of the proposed method when compared to other state-of-the-art methods. [ABSTRACT FROM PUBLISHER]

Data, which lie in the space \mathcal Pm\, , of $m \times m$ symmetric positive definite matrices, (sometimes called tensor data), play a fundamental role in applications, including medical imaging, computer vision, and radar signal processing. An open challenge, for these applications, is to find a class of probability distributions, which is able to capture the statistical properties of data in \mathcal Pm\, , as they arise in real-world situations. The present paper meets this challenge by introducing Riemannian Gaussian distributions on \mathcal Pm\, . Distributions of this kind were first considered by Pennec in 2006. However, the present paper gives an exact expression of their probability density function for the first time in existing literature. This leads to two original contributions. First, a detailed study of statistical inference for Riemannian Gaussian distributions, uncovering the connection between the maximum likelihood estimation and the concept of Riemannian centre of mass, widely used in applications. Second, the derivation and the implementation of an expectation-maximisation algorithm, for the estimation of mixtures of Riemannian Gaussian distributions. The paper applies this new algorithm, to the classification of data in \mathcal Pm\, , (concretely, to the problem of texture classification, in computer vision), showing that it yields significantly better performance, in comparison to recent approaches. [ABSTRACT FROM PUBLISHER]

In this paper, we aim at super-resolving a low-resolution texture under the assumption that a high-resolution patch of the texture is available. To do so, we propose a variational method that combines two approaches that are texture synthesis and image reconstruction. The resulting objective function holds a nonconvex energy that involves a quadratic distance to the low-resolution image, a histogram-based distance to the high-resolution patch, and a nonlocal regularization that links the missing pixels with the patch pixels. As for the histogram-based measure, we use a sum of Wasserstein distances between the histograms of some linear transformations of the textures. The resulting optimization problem is efficiently solved with a primal-dual proximal method. Experiments show that our method leads to a significant improvement, both visually and numerically, with respect to the state-of-the-art algorithms for solving similar problems. [ABSTRACT FROM AUTHOR]

To obtain accurate classification results of hyperspectral images, both spectral and spatial information should be fully exploited in the classification process. In this paper, we propose a novel method using independent component analysis (ICA) and edge-preserving filtering (EPF) via an ensemble strategy for the classification of hyperspectral data. First, several subsets are randomly selected from the original feature space. Second, ICA is used to extract spectrally independent components followed by an effective EPF method, to produce spatial features. Two strategies (i.e., parallel and concatenated) are presented to include the spatial features in the analysis. The spectral–spatial features are then classified with a random forest or a rotation forest classifier. Experimental results on two real hyperspectral data sets demonstrate the effectiveness of the proposed methods. A sensitivity analysis of the new classifiers is also performed. [ABSTRACT FROM PUBLISHER]

We consider the problem of recovering a high-resolution image from a pair consisting of a complete low-resolution image and a high-resolution but incomplete one. We refer to this task as the image zoom completion problem. After discussing possible contexts in which this setting may arise, we introduce a nonlocal regularization strategy, giving full details concerning the numerical optimization of the corresponding energy and discussing its benefits and shortcomings. We also derive two total variation-based algorithms and evaluate the performance of the proposed methods on a set of natural and textured images. We compare the results and get with those obtained with two recent state-of-the-art single-image super-resolution algorithms. [ABSTRACT FROM PUBLISHER]

Multivariate generalized Gaussian distribution (MGGD) has been an attractive solution to many signal processing problems due to its simple yet flexible parametric form, which requires the estimation of only a few parameters, i.e., the scatter matrix and the shape parameter. Existing fixed-point (FP) algorithms provide an easy to implement method for estimating the scatter matrix, but are known to fail, giving highly inaccurate results, when the value of the shape parameter increases. Since many applications require flexible estimation of the shape parameter, we propose a new FP algorithm, Riemannian averaged FP (RA-FP), which can effectively estimate the scatter matrix for any value of the shape parameter. We provide the mathematical justification of the convergence of the RA-FP algorithm based on the Riemannian geometry of the space of symmetric positive definite matrices. We also show using numerical simulations that the RA-FP algorithm is invariant to the initialization of the scatter matrix and provides significantly improved performance over existing FP and method-of-moments (MoM) algorithms for the estimation of the scatter matrix. [ABSTRACT FROM PUBLISHER]