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An M-Estimator for Robust Centroid Estimation on the Manifold of Covariance Matrices

Ioana Ilea, Lionel Bombrun, Romulus Terebes, Monica Borda, Christian Germain
2016 IEEE Signal Processing Letters  
This paper introduces a new robust estimation method for the central value of a set of N covariance matrices.  ...  Moreover, the Huber's centroid performances are analyzed on simulated data, to identify the impact of outliers on the estimation process.  ...  The Huber's estimator 1) Definition of the Huber's centroid In this section, we introduce a novel centroid estimator on the manifold of covariance matrices, based on the theory of M-estimators [17] ,  ... 
doi:10.1109/lsp.2016.2594149 fatcat:pjbuglpnrzhbxlbfg5a77vbzu4

An M-estimator for robust centroid estimation on the manifold of covariance matrices: Performance analysis and application to image classification

Ioana Ilea, Hatem Hajri, Salem Said, Lionel Bombrun, Christian Germain, Yannick Berthoumieu
2016 2016 24th European Signal Processing Conference (EUSIPCO)  
Based on the theory of M-estimators, this robust centroid estimator is issued from the socalled Huber's function. We present a gradient descent algorithm to estimate it.  ...  Many signal and image processing applications, including texture analysis, radar detection or EEG signal classification, require the computation of a centroid from a set of covariance matrices.  ...  ACKNOWLEDGMENT This study has been carried out with financial support from the French National Research Agency (ANR) in the frame of the "Investments for the future" Programme IdEx Bordeaux-CPU (ANR-10  ... 
doi:10.1109/eusipco.2016.7760638 dblp:conf/eusipco/IleaHSBGB16 fatcat:rcv2oadyxjepffhqmzkja72liy

Heterogeneous Clutter Suppression for Airborne Radar STAP Based on Matrix Manifolds

Xixi Chen, Yongqiang Cheng, Hao Wu, Hongqiang Wang
2021 Remote Sensing  
First, the distributions of training data in heterogeneous environments are analyzed, while the received data are characterized on a Riemannian manifold of Hermitian positive definite matrices.  ...  Moreover, as exploiting a geometric metric on manifolds to reveal the underlying information of data, experimental results on both simulated and real data validate that the proposed method has a superior  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/rs13163195 fatcat:wbscdol3gzhdrcg6pxhcoz2nfa

Head pose estimation using covariance of oriented gradients

Ligeng Dong, Linmi Tao, Guangyou Xu
2010 2010 IEEE International Conference on Acoustics, Speech and Signal Processing  
In this paper, we propose an image descriptor, covariance of oriented gradients (COG), for head pose estimation.  ...  Experiments show that the proposed method outperforms two other state-of-the-art methods in terms of estimation accuracy and robustness on image resolutions.  ...  Ma for providing the GaFour feature extraction code.  ... 
doi:10.1109/icassp.2010.5495489 fatcat:qbc2xqbdw5b7bprvupp2r4g3am

Bayesian online learning on Riemannian manifolds using a dual model with applications to video object tracking

Zulfiqar Hasan Khan, Irene Yu-Hua Gu
2011 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops)  
The basic idea is to consider the dynamic appearance of an object as a point moving on a manifold, where a dual model is applied to estimate the posterior trajectory of this moving point at each time instant  ...  The dual model uses two state variables for modeling the online learning process on Riemannian manifolds: one is for object appearances on Riemannian manifolds, another is for velocity vectors in tangent  ...  [14] proposes a head pose estimation approach by using covariance matrices of object features and a nearest centroid classifier.  ... 
doi:10.1109/iccvw.2011.6130415 dblp:conf/iccvw/KhanG11 fatcat:hqssxgwgpjggbptilzkltkcpae

Tracking visual and infrared objects using joint Riemannian manifold appearance and affine shape modeling

Zulfiqar Hasan Khan, Irene Yu-Hua Gu
2011 2011 IEEE International Conference on Computer Vision Workshops (ICCV Workshops)  
Main contributions of the paper include: (a) propose an online appearance learning strategy by a particle filter on the manifold; (b) an object tracker that incorporates the manifold appearance for prediction  ...  updated, but also the velocity of dynamic manifold point is estimated.  ...  [14] proposes a head pose estimation approach by using covariance matrices of object features and a nearest centroid classifier.  ... 
doi:10.1109/iccvw.2011.6130473 dblp:conf/iccvw/KhanG11a fatcat:mjrnxfppb5fqxmadnersqn63ku

Riemannian Classification for SSVEP-Based BCI [chapter]

Sylvain Chevallier, Emmanuel K. Kalunga, Quentin Barthélemy, Florian Yger
2018 Brain–Computer Interfaces Handbook  
After reviewing some of the most robust approaches in feature extraction for SSVEP, this chapter will introduce newer tools based on Riemannian geometry.  ...  A recent successful approach in feature extraction and signal processing for BCI is Riemannian geometry, which deals with covariance matrices.  ...  The same goes for Σ − 1 2 . Left: the exponential mapping of Θ i , an element of the tangent space T Σ M C at point Σ, on the manifold M C is Σ i .  ... 
doi:10.1201/9781351231954-19 fatcat:ckjfdf3iardazl45f4vlypf72m

A Geometric Perspective on Variational Autoencoders [article]

Clément Chadebec, Stéphanie Allassonnière
2022 arXiv   pre-print
Since generative models are known to be sensitive to the number of training samples we also stress the method's robustness in the low data regime.  ...  This paper introduces a new interpretation of the Variational Autoencoder framework by taking a fully geometric point of view.  ...  training embeddings and covariance matrices end for Select k centroids c i in the µ i e.g. with k-medoids Get corresponding covariance matrices Σ i ρ ← max i min j =i c i − c j 2 Set ρ to the max distance  ... 
arXiv:2209.07370v1 fatcat:qabahtfdirfmhaiuy55xicwwqa

Re-visiting Riemannian geometry of symmetric positive definite matrices for the analysis of functional connectivity

Kisung You, Hae-Jeong Park
2020 NeuroImage  
Due to its geometric property, the analysis and operation of functional connectivity matrices may well be performed on the Riemannian manifold of the SPD space.  ...  Common representations of functional networks of resting state fMRI time series, including covariance, precision, and cross-correlation matrices, belong to the family of symmetric positive definite (SPD  ...  distance for x, y ∈ M , the length of the shortest curve on M connecting two points.  ... 
doi:10.1016/j.neuroimage.2020.117464 pmid:33075555 fatcat:ubcu5qyydfcwzjnrruknxuorda

Orientation estimation of anatomical structures in medical images for object recognition

Ulaş Bağci, Jayaram K. Udupa, Xinjian Chen, Benoit M. Dawant, David R. Haynor
2011 Medical Imaging 2011: Image Processing  
Motivated from the non-Euclidean nature of the pose information, we propose in this paper the use of non-Euclidean metrics to estimate orientation of the anatomical structures for more accurate recognition  ...  Recognition of anatomical structures is an important step in model based medical image segmentation.  ...  Similarly, for any given subject, the difference between covariance matrices of the mean covariance matrix and intensity structure system is used to estimate the covariance matrix of the shape structure  ... 
doi:10.1117/12.878184 dblp:conf/miip/BagciUC11 fatcat:x4i4vf5hrjfh7enixwwvo4w3vi

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

Ioana Ilea, Lionel Bombrun, Salem Said, Yannick Berthoumieu
2018 Journal of Imaging  
Since these elements do not lie on an Euclidean space but on a Riemannian manifold, a Riemannian metric should be considered.  ...  This paper presents an overview of coding methods used to encode a set of covariance matrices.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/jimaging4070085 fatcat:fveihwbobrb6zawk7r34pc4nh4

Robust statistics on Riemannian manifolds via the geometric median

P. Thomas Fletcher, Suresh Venkatasubramanian, Sarang Joshi
2008 2008 IEEE Conference on Computer Vision and Pattern Recognition  
The geometric median is a classic robust estimator of centrality for data in Euclidean spaces.  ...  Generalizing the Weiszfeld procedure for finding the geometric median of Euclidean data, we present an algorithm for computing the geometric median on an arbitrary manifold.  ...  Noting that the median is an example of an L 1 M-estimator, the techniques presented in this paper can be applied to extend notions of robust covariances and robust PCA to manifold-valued data.  ... 
doi:10.1109/cvpr.2008.4587747 dblp:conf/cvpr/FletcherVJ08 fatcat:l5d5tvhngnfhnbeujqj4nc2dnm

Information Geometry for Radar Target Detection with Total Jensen–Bregman Divergence

Xiaoqiang Hua, Haiyan Fan, Yongqiang Cheng, Hongqiang Wang, Yuliang Qin
2018 Entropy  
be used as the distance-like function on the space of HPD matrices.  ...  On basis of these divergences, definitions of their corresponding median matrices are given.  ...  In the following, we will illustrate the robustness of covariance estimation with respect to the number of samples collected.  ... 
doi:10.3390/e20040256 pmid:33265347 fatcat:42y2l4bn4zapjm23ooddaexjaa

Near out-of-distribution detection for low-resolution radar micro-Doppler signatures [article]

Martin Bauw, Santiago Velasco-Forero, Jesus Angulo, Claude Adnet, Olivier Airiau
2022 arXiv   pre-print
The covariance representation aims at estimating whether dedicated second-order processing is appropriate to discriminate signatures.  ...  This paper puts forward an OODD use case for radar targets detection extensible to other kinds of sensors and detection scenarios.  ...  The authors additionally thank Maxime Bombar and Lev-Arcady Sellem for their constructive comments regarding the mathematical properties of RPO-MEAN.  ... 
arXiv:2205.07869v2 fatcat:hnxfgxi5crcedmnrm7brjbrpzi

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

Ioana Ilea, Lionel Bombrun, Christian Germain, Yannick Berthoumieu
2016 2016 IEEE 12th Image, Video, and Multidimensional Signal Processing Workshop (IVMSP)  
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.  ...  ACKNOWLEDGMENT This study has been carried out in the frame of the Investments for the future Programme IdEx Bordeaux -CPU (ANR-10-IDEX-03-02) of the French National Research Agency (ANR).  ... 
doi:10.1109/ivmspw.2016.7528231 dblp:conf/ivmsp/IleaBGB16 fatcat:rfbdaxkudne4hcn5apjv2v223m
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