Riemannian Gaussian distributions on the space of symmetric positive definite matrices

S Said, L Bombrun, Y Berthoumieu… - IEEE Transactions on …, 2017 - ieeexplore.ieee.org
Data, which lie in the space P m, of m× m symmetric positive definite matrices,(sometimes
called tensor data), play a fundamental role in applications, including medical imaging …

A simple approximation method for the Fisher–Rao distance between multivariate normal distributions

F Nielsen - Entropy, 2023 - mdpi.com
We present a simple method to approximate the Fisher–Rao distance between multivariate
normal distributions based on discretizing curves joining normal distributions and …

Ensemble learning approaches based on covariance pooling of CNN features for high resolution remote sensing scene classification

S Akodad, L Bombrun, J Xia, Y Berthoumieu… - Remote Sensing, 2020 - mdpi.com
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 …

Structure tensor Riemannian statistical models for CBIR and classification of remote sensing images

R Rosu, M Donias, L Bombrun, S Said… - … on Geoscience and …, 2016 - ieeexplore.ieee.org
This paper deals with parametric techniques for the description of texture on very high
resolution (VHR) remote sensing images. These techniques focus on the property of …

Parameters estimate of Riemannian Gaussian distribution in the manifold of covariance matrices

P Zanini, M Congedo, C Jutten, S Said… - 2016 IEEE Sensor …, 2016 - ieeexplore.ieee.org
The study of P m, the manifold of m× m symmetric positive definite matrices, has recently
become widely popular in many engineering applications, like radar signal processing …

Covariance matrices encoding based on the log-Euclidean and affine invariant Riemannian metrics

I Ilea, L Bombrun, S Said… - Proceedings of the …, 2018 - openaccess.thecvf.com
This paper presents coding methods used to encode a set of covariance matrices. Starting
from a Gaussian mixture model adapted to the log-Euclidean or affine invariant Riemannian …

Texture image classification with Riemannian Fisher vectors

I Ilea, L Bombrun, C Germain, R Terebes… - … on Image Processing …, 2016 - ieeexplore.ieee.org
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 …

Fisher vector coding for covariance matrix descriptors based on the log-Euclidean and affine invariant Riemannian metrics

I Ilea, L Bombrun, S Said, Y Berthoumieu - Journal of Imaging, 2018 - mdpi.com
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) …

Remote sensing scene classification based on covariance pooling of multi-layer cnn features guided by saliency maps

S Akodad, L Bombrun, C Germain… - … Conference on Pattern …, 2022 - Springer
The new generation of remote sensing imaging sensors enables high spatial, spectral and
temporal resolution images with high revisit frequencies. These sensors allow the …

Cramér-Rao Bound on Lie Groups with Observations on Lie Groups: Application to SE (2)

S Labsir, A Renaux, J Vilà-Valls… - ICASSP 2023-2023 …, 2023 - ieeexplore.ieee.org
In this communication, we derive a new intrinsic Cramér-Rao bound for both parameters and
observations lying on Lie groups. The expression is obtained by using the intrinsic …