Ioana Ilea

Riemannian Laplace Distribution on the Space of Symmetric Positive Definite Matrices

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.

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

Texture image classification with Riemannian fisher vectors issued from a Laplacian model

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Texture image classification with Riemannian fisher vectors

covariance matrices. This estimator, called Hubers 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, Hubers 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.

Statistical hypothesis test for robust classification on the space of covariance matrices

Many signal and image processing applications are based on the classification of covariance matrices. These latter are elements on a Riemannian manifold for which many generative models have been developed in the literature. Recently, the Riemannian Laplace distribution (RLD) has been proposed to model the within-class variability of images. In this context, the present paper proposes an application of RLDs to the definition of Riemannian Fisher vectors issued from this Laplacian model. The expression of these descriptors is derived for mixtures of RLDs and their relation with the Riemannian vectors of locally aggregated descriptors is shown. Some comparisons with the bag of Riemannian words model are also performed. All these aforementioned descriptors are applied to texture image classification to find the most discriminating one. Moreover, to determine the best model for fitting the data, the classification performances are compared to those given by the Riemannian Gaussian distribution.

Classification of oyster habitats by combining wavelet-based texture features and polarimetric SAR descriptors

This paper introduces a generalization of the Fisher vectors to the Riemannian manifold. The proposed descriptors, called Riemannian Fisher vectors, are defined first, based on the mixture model of Riemannian Gaussian distributions. Next, their expressions are derived and they are applied in the context of texture image classification. The results are compared to those given by the recently proposed algorithms, bag of Riemannian words and R-VLAD. In addition, the most discriminant Riemannian Fisher vectors are identified.

Fisher Vector Coding for Covariance Matrix Descriptors Based on the Log-Euclidean and Affine Invariant Riemannian Metrics

This paper introduces a new statistical hypothesis test for robust image classification. First, we introduce the proposed statistical hypothesis test based on the geodesic distance and on the fixed point estimation algorithm. Next, we analyze its properties in the case of the zero-mean multivariate Gaussian distribution by studying its asymptotic distribution under the null hypothesis H0. Then, the performance of the proposed classifier is addressed by analyzing its noise robustness. Finally, the robust classification method is employed for the classification of simulated Polarimetric Synthetic Aperture Radar images of maritime pine forests.

Co-occurrence matrix of covariance matrices: a novel coding model for the classification of texture images

In this study, we propose to evaluate the potential of combining very high resolution optical and SAR images for the classification of oyster habitats in tidal flats. To describe the classes of interest in both data, features are extracted by using wavelet-based texture features and polarimetric inter-band dependencies. A multisensor fusion scheme is then applied by adopting a maximum probability rule based on the outputs of SVM classifiers. Classification results show higher accuracies of detection of cultivated and abandoned oyster fields in comparison to classifications obtained using only texture features. This demonstrate the benefit of using both optical and SAR data for oyster habitats mapping in tidal flats.

PolSAR image denoising using directional diffusion

This paper presents an overview of coding methods used to encode a set of covariance matrices. Starting from a Gaussian mixture model (GMM) adapted to the Log-Euclidean (LE) or affine invariant Riemannian metric, we propose a Fisher Vector (FV) descriptor adapted to each of these metrics: the Log-Euclidean Fisher Vectors (LE FV) and the Riemannian Fisher Vectors (RFV). Some experiments on texture and head pose image classification are conducted to compare these two metrics and to illustrate the potential of these FV-based descriptors compared to state-of-the-art BoW and VLAD-based descriptors. A focus is also applied to illustrate the advantage of using the Fisher information matrix during the derivation of the FV. In addition, finally, some experiments are conducted in order to provide fairer comparison between the different coding strategies. This includes some comparisons between anisotropic and isotropic models, and a estimation performance analysis of the GMM dispersion parameter for covariance matrices of large dimension.

ICA based PolSAR image denoising

This paper introduces a novel local model for the classification of covariance matrices: the co-occurrence matrix of covariance matrices. Contrary to state-of-the-art models (BoRW, R-VLAD and RFV), this local model exploits the spatial distribution of the patches. Starting from the generative mixture model of Riemannian Gaussian distributions, we introduce this local model. An experiment on texture image classification is then conducted on the VisTex and Outex_TC000_13 databases to evaluate its potential.