nils-herrmann/clean_scirepeval huggingface dataset:
Transfer Learning: A Riemannian Geometry Framework With Applications to Brain–Computer Interfaces

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.  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.  The improvements in terms of classification performances achieved by introducing the affine transformation are documented with the analysis of two BCI datasets.  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.
Seismic horizon and pseudo-geological time cube extraction based on a riemmanian geodesic search

In this paper we present a new approach for the automatic reconstruction of seismic horizons and the generation of a pseudo-geological time cube. Our method can accomodate user constraints and relies on the computation of a local Riemannian metric on the seismic image, whose geodesic lines correspond to seismic horizons. The parameterization chosen in our method eases some of the restrictions imposed by currently available algorithms and can thus be used with a greater variety of seismc data, such as roll-over folds and salt domes.
Lipschitz Bounds for Noise Robustness in Compressive Sensing: Two Algorithms

The paper deals with numerical estimations of Lipschitz bounds relating locally the reconstruction error to the measurement error in the compressive sensing framework. Most recent theoretical papers in the field parametrize such bounds relatively to certain families of vectors called dual certificates, which are fundamental to several reconstruction criteria. The paper provides two algorithms for computing dual certificates that optimize their related reconstruction error bounds. We give a greedy algorithm that provides a fast approximate solution, and a convex-projection algorithm that computes the exact optimum.
Multiscale skewed heavy tailed model for texture analysis

This paper deals with texture analysis based on multiscale stochastic modeling. In contrast to common approaches using symmetric marginal probability density functions of subband coefficients, experimental manipulations show that the symmetric shape assumption is violated for several texture classes. From this fact, we propose in this paper to exploit this shape property to improve texture characterization. We present Asymmetric Generalized Gaussian density as a model to represent detail subbands resulting from multiscale decomposition. A fast estimation method is presented and closed-form of Kullback-Leibler divergence is provided in order to validate the model into a retrieval scheme. The experimental results indicate that this model achieves higher recognition rates than the conventional approach of using the Generalized Gaussian model where asymmetry was not considered.
Image Zoom Completion

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.
Multidate Divergence Matrices for the Analysis of SAR Image Time Series

The paper provides a spatio-temporal change detection framework for the analysis of image time series. In this framework, the detection of changes in time is addressed at the image level by using a matrix of cross-dissimilarities computed upon wavelet and curvelet image features. This makes possible identifying the acquisitions of interest: the acquisitions that exhibit singular behavior with respect to their neighborhood in the time series, and those that are representatives of some stationary behavior. These acquisitions of interest are compared at the pixel level to detect spatial changes characterizing the evolution of the time series. Experiments carried out over European Remote Sensing (ERS) and TerraSAR-X time series highlight the relevancy of the approach for analyzing synthetic aperture radar image time series.
High Resolution spectral caracterization of sleep spindles

This paper deals with the analysis of the spindle part of the sleep electroencephalogram (EEG). The purpose is to extract pertinent features to caracterize the spindle. Due to the drawback of the previous approaches we propose the use of High Resolution (HR) techniques which permits to precisely caracterlze the spindle spectra. In section one, we provide a quick report of the results given by parametric methods. In section two, we give the main lines of the HR approach and provide in section 3 the obtained results.
Minimum Eigenvalue Based 3-D AR Model Order Selection

This paper deals with the problem of three-dimensional autoregressive (3-D AR) model order estimation. Especially, we develop a practical algorithm to estimate the 3-D AR order (P1,P2,P3) corresponding to the quarter-space (QS) region of support. The proposed method is derived from the minimum description length (MDL) criterion and uses the minimum eigenvalue of the covariance matrix of the underlying 3-D Gaussian process. Numerical simulations are presented to illustrate the performances of the new proposed algorithm and compare it with a recently developed method
Classification approach based on the product of riemannian manifolds from Gaussian parametrization space

This paper presents a novel framework for visual content classification using jointly local mean vectors and covariance matrices of pixel level input features. We consider local mean and covariance as realizations of a bivariate Riemannian Gaussian density lying on a product of submanifolds. We first introduce the generalized Mahalanobis distance and then we propose a formal definition of our product-spaces Gaussian distribution on Rm × SPD(m). This definition enables us to provide a mixture model from a mixture of a finite number of Riemannian Gaussian distributions to obtain a tractable descriptor. Mixture parameters are estimated from training data by exploiting an iterative Expectation-Maximization (EM) algorithm. Experiments in a texture classification task are conducted to evaluate this extended modeling on several color texture databases, namely popular Vistex, 167-Vistex and CUReT. These experiments show that our new mixture model competes with state-of-the-art on the experimented datasets.
A New Riemannian Averaged Fixed-Point Algorithm for MGGD Parameter Estimation

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.
Langevin and hessian with fisher approximation stochastic sampling for parameter estimation of structured covariance

We have studied two efficient sampling methods, Langevin and Hessian adapted Metropolis Hastings (MH), applied to a parameter estimation problem of the mathematical model (Lorentzian, Laplacian, Gaussian) that describes the Power Spectral Density (PSD) of a texture. The novelty brought by this paper consists in the exploration of textured images modeled by centered, stationary Gaussian fields using directional stochastic sampling methods. Our main contribution is the study of the behavior of the previously mentioned two samplers and the improvement of the Hessian MH method by using the Fisher information matrix instead of the Hessian to increase the stability of the algorithm and the computational speed. The directional methods yield superior performances as compared to the more popular Independent and standard Random Walk MH for the PSD described by the three models, but can easily be adapted to any target law respecting the differentiability constraint. The Fisher MH produces the best results as it combines the advantages of the Hessian, i.e., approaches the most probable regions of the target in a single iteration, and of the Langevin MH, as it requires only first order derivative computations.
Rotation-Invariant texture retrieval using a steerable Gaussian copula model

In this paper, we address the problem of rotation invariance in the context of texture retrieval. For this, we propose a framework based on the well-known copula theory which is considered one of the most powerful statistical tools. Prior to apply a such model, we first use the steerable pyramid SP as one of the most relevant transforms. Then, we build a steerable Gaussian copula model which offers a good fitting of the SP coefficients distribution while taking into consideration their rotation invariance property. Finally, we derive a closed-form of the Jefferey divergence as a similarity measure. The latter consists on an angular alignment between the query and the target texture features. Experiments have been conducted on USC database, good performances in term of retrieval rates are achieved compared to previously proposed copula models.
Optical flow estimation using forward-backward constraint equation

This article introduces the estimation of the optical flow, based on the combination of forward and backward constraint motion equations. Among all the existing techniques allowing the retrieval of the motion, many methods start from the assumption of recorded image brightness dependency after displacement. This dependency spans a derivative formulation, so called motion constraint equation, based on the spatial transformation. In this framework, for fixed temporal positions, the motion of a rigid object can be described by a forward and backward exploitation of the motion constraint equation, for the same spatial position. This setting in equation enables us to establish a new relation called a forward-backward optical flow equation.
Bayesian Texture Classification From Indirect Observations Using Fast Sampling

A Bayesian method for texture model choice from blurred and noisy (i.e., indirect) observations is presented. The textures are modeled by stationary Random Fields, with various distribution laws, either Gaussian or Scale Mixtures of Gaussians. The power spectral densities of the fields are modeled by parametric functions and the aim is to select the most appropriate model among a set of candidates. This is achieved by computing the a posteriori model probabilities through parameter marginalization. The marginalization is done by sampling and harmonic mean approach, considering separately each model, in a within-model sampling strategy. The highly nonlinear dependency with respect to the parameters imposes the use of the Metropolis-Hastings sampler. Moreover, to achieve efficient sampling, the paper proposes a new fast algorithm based on the Fisher information matrix, the Fisher Metropolis-Hastings.
A robust framework for GeoTime cube

This paper presents a robust unsupervised framework for 3D seismic data flattening. The resulting volume, called GeoTime cube, brings to light history of sedimentary deposits which is a key issue in petroleum prospecting. The proposed method makes it possible to obtain the transformation by transcribing fundamental principles of geophysics in image processing. The first step is a sedimentary layer reconstruction, the second one consists in numbering them according to their relative geological age and the last one computes a transformation in order to clearly represent them in a flattened way. Finally, the results obtained by our method compared to an existing one show that many relevant information can be extracted from GeoTime cubes and the final flattened data enhances the seismic structures identification.
[ADC Characterization in Time Domain] Frequency Estimation to Linearize Time-Domain Analysis of A/D Converters

Time-domain analysis is a powerful tool for testing A/D converters (ADCs), particularly by incoherent sampling. This sampling is encountered for instance in real application and systems where the clock is generated by an on-board crystal oscillator. In the case of the sine-wave model for ADC output samples, fitting a sine-wave function to the data record is nonlinear with respect to the frequency. To overcome the convergence problem, the authors propose some alternative methods based on frequency estimation by means of fast Fourier transform and eigenanalysis of the autocorrelation matrix. This leads to a simple linear problem. The effectiveness of these methods is proven on both simulation and experimental results
3-D AR model order selection via rank test procedure

This paper deals with the problem of three-dimensional autoregressive (3-D AR) model order estimation. We show that the information for the 3-D AR model order is implicitly contained in an appropriate matrix rank built from the autocorrelation function (ACF) of the underlying 3-D Gaussian process. Exploiting this property, we develop an algorithm to estimate the order (p1,p2,p3) corresponding to the quarter-space (QS) region of support. The proposed method is based upon a rank test procedure (RTP) using singular value decomposition (SVD) and solving nonlinear system equations. Numerical simulations are presented to illustrate the performances of the proposed algorithm
Robust high resolution image spectral analysis

This paper deals with a 2-D high resolution frequency estimation method dedicated to corrupted image by outliers. Outliers are particular data points that do not obey the assumed model. In this framework the well-known model of the sum of complex exponentials fails for the smallest fraction of a data set, which causes the classical estimators to produce inaccurate results. To alleviate this drawback, we propose a new robust iterative Levenberg-Marquardt (LM)-based method. The three main steps of the method we propose are as follows. First, we define a weight function based on the influence function which allows one to detect and correct the "wrong" data. The influence function measures the influence of a datum on the value of the parameter estimate. It is inspired from the so-called M-estimator. Second, a 2-D extension of the large sample approximation of the Maximum likelihood (ML) estimator is developed in order to estimate the image parameters. Third, the Levenberg-Marquardt (LM) technique is used to ensure the convergence of the ML estimator by performing the detection of "wrong" data for each iteration. The effectiveness of the proposed method is illustrated by some numerical simulations.
Texture classification based on the Generalized Gamma distribution and the Dual Tree Complex Wavelet Transform

This paper deals with stochastic texture modeling for classification issue. A generic stochastic model based on three-parameter Generalized Gamma (GG) distribution function is proposed. The GG modeling offers more flexibility parameterization than other kinds of heavy-tailed density devoted to wavelet empirical histograms characterization. Moreover, Kullback-leibler divergence is chosen as similarity measure between textures. Experiments carried out on Vistex texture database show that the proposed approach achieves good classification rates.
Bayesian Texture and Instrument Parameter Estimation From Blurred and Noisy Images Using MCMC

This letter addresses an estimation problem based on blurred and noisy observations of textured images. The goal is jointly estimating the 1) image model parameters, 2) parametric point spread function (semi-blind deconvolution) and 3) signal and noise levels. It is an intricate problem due to the data model non-linearity w.r.t. these parameters. We resort to an optimal estimation strategy based on Mean Square Error, yielding the best (non-linear) estimate, namely the Posterior Mean. It is numerically computed using a Monte Carlo Markov Chain algorithm: Gibbs loop including a Random Walk Metropolis-Hastings sampler. The novelty is double: i) addressing this fully parametric threefold problem never tackled before through an optimal strategy and ii) providing a theoretical Fisher information-based analysis to anticipate estimation accuracy and compare with numerical results.
Copulas based multivariate gamma modeling for texture classification

This paper deals with texture modeling for classification or retrieval systems using multivariate statistical features. The proposed features are defined by the hyperparameters of a copula-based multivariate distribution characterizing the coefficients provided by image decomposition in scale and orientation. As it belongs to the multivariate stochastic models, the copulas are useful to describe pairwise non-linear association in the case of multivariate non-Gaussian density. In this paper, we propose the d-variate Gaussian copula associated to univariate Gamma densities for modeling the texture. Experiments were conducted on the VisTex database aiming to compare the recognition rates of the proposed model with the univariate generalized Gaussian model, the univariate Gamma model, and the generalized Gaussian copula-based multivariate model.
Recursive orientation estimation based on hypersurface reconstruction

Estimating the local orientations of a directional structure may prove to be complicated especially for complex geometries for which conventional methods, including those based on the gradient, are unsuitable. In this paper, we propose a recursive method of orientation estimation based on the reconstruction of hypersurfaces and the definition of a model of the structure in these so-called complex areas. The estimation proves to be more accurate when executed on the flattened data and driven to the initial referential. This process recursively leads to a more accurate orientation field estimation. When applied to synthetic data, the method reduces significantly the estimation bias. For real directional textures, the resulting orientation field coincides better with the perceptual orientation of the directional structures.
Combining time-frequency transforms to create a sequence of instantaneous range-Doppler images in ISAR processing

In ISAR processing, ship classification is usually based on a range-Doppler (RD) image. The RD image is obtained by combining range alignment, phase compensation and short-time Fourier transform. Nevertheless, this leads to sophisticated approaches to weaken unwanted phenomena such as blurred images. In this paper, an alternative approach is proposed based on the time-frequency analysis. In that case, the Wigner-Ville transform provides geometrical structured events which correspond to the scatterers and unstructured ones which are associated to the artefacts and cross-terms. Taking advantage of these geometrical features, we first suggest computing a time-frequency local gradient analysis. This variational analysis provides a confidence map of the time-frequency distribution we can use to remove artefacts. Then, the practitioner can exploit the corresponding time-frequency images to choose the more appropriate instantaneous RD image. Simulation results confirm the effectiveness of this approach.
Global motion estimation from relative measurements using iterated extended Kalman filter on matrix LIE groups

In this paper, we are interested in estimating global motions (homographies, 3D rotations, 3D Euclidean motions, etc.) as well as the covariance of the estimation errors from relative measurements by exploiting the Lie group structure of the motions. We propose a generative model based on the formulation of a concentrated Gaussian distribution on matrix Lie groups. In this context, the global motion estimation problem reduces to the minimization of the sum of squared intrinsic invariant (w.r.t the right action of the Lie group on itself) errors. We derive an iterated extended Kalman filter on matrix Lie groups from the Gauss-Newton formalism on matrix Lie groups, which exhibits a low computational complexity. Experimental results on simulated data, in the context of a consistent pose registration problem, show that the proposed algorithm significantly outperforms the state of the art approaches.
Intrinsic prior for Bayesian classification of texture images

This paper introduces an intrinsic prior distribution for supervised classification of texture images. First, we introduce the intrinsic prior distribution as the normal law on a Riemannian manifold. Next, based on this definition, we derive the estimation and classification schemes. Finally, we propose an application for the classification of texture images. Experiments on the VisTex texture database are conducted and demonstrate the interest of the proposed intrinsic classification algorithm.
An M-Estimator for Robust Centroid Estimation on the Manifold of Covariance Matrices

This letter introduces a new robust estimation method for the central value of a set of N covariance matrices. This estimator, called Huber's centroid, is described starting from the expression of two well-known methods that are the center of mass and the median. In addition, a computation algorithm based on the gradient descent is proposed. Moreover, Huber's centroid performances are analyzed on simulated data to identify the impact of outliers on the estimation process. In the end, the algorithm is applied to brain decoding, based on magnetoencephalography data. For both simulated and real data, the covariance matrices are considered as realizations of Riemannian Gaussian distributions and the results are compared to those given by the center of mass and the median.