Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas
@article{Brunel2010ModelingAU, title={Modeling and Unsupervised Classification of Multivariate Hidden Markov Chains With Copulas}, author={Nicolas J.-B. Brunel and J{\'e}r{\^o}me Lapuyade-Lahorgue and Wojciech Pieczynski}, journal={IEEE Transactions on Automatic Control}, year={2010}, volume={55}, pages={338-349} }
Parametric modeling and estimation of non-Gaussian multidimensional probability density function is a difficult problem whose solution is required by many applications in signal and image processing. A lot of efforts have been devoted to escape the usual Gaussian assumption by developing perturbed Gaussian models such as spherically invariant random vectors (SIRVs). In this work, we introduce an alternative solution based on copulas that enables theoretically to represent any multivariate…
20 Citations
Unsupervised classification using hidden Markov chain with unknown noise copulas and margins
- Computer ScienceSignal Process.
- 2016
Unsupervised data classification using pairwise Markov chains with automatic copulas selection
- Computer ScienceComput. Stat. Data Anal.
- 2013
Unsupervised segmentation of randomly switching data hidden with non-Gaussian correlated noise
- Computer ScienceSignal Process.
- 2011
Copulas for statistical signal processing (Part I): Extensions and generalization
- Computer ScienceSignal Process.
- 2014
Copulas selection in pairwise Markov chain
- Computer Science
- 2012
This work studies the influence of copula shapes on PMC data and the automatic identification of the right copulas from a finite set of admissible copulas, by extending the general “Iterative Conditional Estimation” parameters estimation method to the context considered.
Unsupervised Segmentation by Hidden Markov Chain with Bi-dimensional Observed Process
- Computer Science, Mathematics
- 2011
In unsupervised segmentation context, a bi-dimensional hidden Markov chain model (X,Y) that is seen as a competitive alternative to the Hilbert-Peano scan and a bayesian algorithm to estimate parameters of the considered model is proposed.
Segmenting Multi-Source Images Using Hidden Markov Fields With Copula-Based Multivariate Statistical Distributions
- Computer ScienceIEEE Transactions on Image Processing
- 2017
A novel multi-source fusion method based on the Gaussian copula is proposed, integrated in a statistical framework with the hidden Markov field inference in order to delineate a target volume from multi- source images.
Segmentation of multicorrelated images with copula models and conditionally random fields
- Computer ScienceJournal of medical imaging
- 2022
A method for segmenting multisource images that are statistically correlated and compared with different state-of-the-art methods, which includes supervised (convolutional neural networks) and unsupervised (hierarchical MRF).
Modeling of Multipath Environment Using Copulas for Particle Filtering Based GPS Navigation
- Computer ScienceIEEE Signal Processing Letters
- 2012
This letter suggests taking into account the spatial dependencies between GPS measurements when modeling multipath occurrence/disappearance, and uses a probabilistic tool, namely copulas, to estimate the mobile location and perform the multipath detection/estimation.
Brain MRI segmentation and lesion detection using generalized Gaussian and Rician modeling
- Computer ScienceMedical Imaging
- 2011
Promising results are presented showing that in a multimodal segmentation-detection scheme, this model fits better with the data and increases lesion detection rate.
References
SHOWING 1-10 OF 60 REFERENCES
Copulas in vectorial hidden Markov chains for multicomponent image segmentation
- Computer Science, MathematicsProceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.
- 2005
This work introduces an alternative solution based on a very general class of multivariate models called 'copulas', which are used in the frame of multidimensional mixture estimation arising in the segmentation of multicomponent images, when using a vectorial hidden Markov chain (HMC).
Unsupervised signal restoration using hidden Markov chains with copulas
- Computer ScienceSignal Process.
- 2005
Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation
- Mathematics, Computer ScienceIEEE Trans. Pattern Anal. Mach. Intell.
- 1997
The proposed method is applied to the problem of unsupervised image segmentation and allows one to identify the conditional distribution for each class and each sensor, estimate the unknown parameters in this distribution, estimate priors, and estimate the "true" class image.
Non-Gaussian random vector identification using spherically invariant random processes
- Computer Science
- 1993
E elegant and tractable techniques are presented for characterizing the probability density function (PDF) of a correlated non-Gaussian radar vector and an important result providing the PDF of the quadratic form of a spherically invariant random vector (SIRV) is presented.
The Meta-elliptical Distributions with Given Marginals
- Mathematics
- 2002
Based on an analysis of copulas of elliptically contoured distributions, joint densities of continuous variables with given strictly increasing marginal distributions are constructed. A method…
Pairwise Markov Chains
- Computer Science, MathematicsIEEE Trans. Pattern Anal. Mach. Intell.
- 2003
An original method of parameter estimation, which generalizes the classical iterative conditional estimation (ICE) valid for a classical hidden Markov chain model, and whose extension to possibly non-Gaussian and correlated noise is briefly treated.
Unsupervised multiband image segmentation using hidden Markov quadtree and copulas
- Computer ScienceIEEE International Conference on Image Processing 2005
- 2005
A new approach based on copula theory to compute multivariate density on Markov quadtree for multiband image segmentation with real-time requirements is proposed.
Signal and image segmentation using pairwise Markov chains
- Computer Science, MathematicsIEEE Transactions on Signal Processing
- 2004
The main novelty is an original parameter estimation method that is valid in a general setting, where the form of the possibly correlated noise is not known, and with respect to the classical hidden Markov chain one for supervised and unsupervised restorations.
Non-Gaussian clutter modeling with generalized spherically invariant random vectors
- Computer ScienceIEEE Trans. Signal Process.
- 1996
It is shown how applying this optimum detector to non-Gaussian data leads to a reduction in the false alarm rate when compared to processing with a matched filter alone.
Multisensor triplet Markov chains and theory of evidence
- Mathematics, Computer ScienceInt. J. Approx. Reason.
- 2007