Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. The contribution of this paper to the topic is twofold. First, we propose a Gaussian mixture model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, which we call PCA-GMM. To learn the (low dimensional) parameters of the mixture model we propose an EM algorithm whose M-step requires the solution of constrained optimization problems. Fortunately, these constrained problems do not depend on the usually large number of samples and can be solved efficiently by an (inertial) proximal alternating linearized minimization algorithm. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob. Numerical results confirm the moderate influence of the dimensionality reduction on the overall superresolution result.

We present a steered data-analysis approach to measure coherence for fault detection. In contrast with conventional coherence, which detects discontinuities without distinction, our approach aims to identify faults only. Assuming the local linearity of fault geometry, the method performs a continuity test using a steered data-analysis window over a set of dip/azimuth directions. A robust, selective directional continuity test is achieved by combining measures of coherence computed from a few aligned, steered windows. Finally, fault detection consists of finding the maximum directional response and accumulating it into an attribute volume. A comparison between results obtained on both synthetic and real seismic images indicates the new method is superior to the conventional coherence measure in isolating faults from stratigraphic signature and noise. Undesired scale, staircase, and mislocation effects are reduced noticeably.

Remote sensing image scene classification, which consists of labeling remote sensing images with a set of categories based on their content, has received remarkable attention for many applications such as land use mapping. Standard approaches are based on the multi-layer representation of first-order convolutional neural network (CNN) features. However, second-order CNNs have recently been shown to outperform traditional first-order CNNs for many computer vision tasks. Hence, the aim of this paper is to show the use of second-order statistics of CNN features for remote sensing scene classification. This takes the form of covariance matrices computed locally or globally on the output of a CNN. However, these datapoints do not lie in an Euclidean space but a Riemannian manifold. To manipulate them, Euclidean tools are not adapted. Other metrics should be considered such as the log-Euclidean one. This consists of projecting the set of covariance matrices on a tangent space defined at a reference point. In this tangent plane, which is a vector space, conventional machine learning algorithms can be considered, such as the Fisher vector encoding or SVM classifier. Based on this log-Euclidean framework, we propose a novel transfer learning approach composed of two hybrid architectures based on covariance pooling of CNN features, the first is local and the second is global. They rely on the extraction of features from models pre-trained on the ImageNet dataset processed with some machine learning algorithms. The first hybrid architecture consists of an ensemble learning approach with the log-Euclidean Fisher vector encoding of region covariance matrices computed locally on the first layers of a CNN. The second one concerns an ensemble learning approach based on the covariance pooling of CNN features extracted globally from the deepest layers. These two ensemble learning approaches are then combined together based on the strategy of the most diverse ensembles. For validation and comparison purposes, the proposed approach is tested on various challenging remote sensing datasets. Experimental results exhibit a significant gain of approximately $2\%$ in overall accuracy for the proposed approach compared to a similar state-of-the-art method based on covariance pooling of CNN features (on the UC Merced dataset).

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.

The Riemannian geometry of the space P_m, of m × m symmetric positive definite matrices, has provided effective tools to the fields of medical imaging, computer vision and radar signal processing. Still, an open challenge remains, which consists of extending these tools to correctly handle the presence of outliers (or abnormal data), arising from excessive noise or faulty measurements. The present paper tackles this challenge by introducing new probability distributions, called Riemannian Laplace distributions on the space P_m. First, it shows that these distributions provide a statistical foundation for the concept of the Riemannian median, which offers improved robustness in dealing with outliers (in comparison to the more popular concept of the Riemannian center of mass). Second, it describes an original expectation-maximization algorithm, for estimating mixtures of Riemannian Laplace distributions. This algorithm is applied to the problem of texture classification, in computer vision, which is considered in the presence of outliers. It is shown to give significantly better performance with respect to other recently-proposed approaches.