Emmanuel Monfrini

Unsupervised Segmentation of Random Discrete Data Hidden With Switching Noise Distributions

Hidden Markov models are very robust and have been widely used in a wide range of application fields; however, they can prove some limitations for data restoration under some complex situations. These latter include cases when the data to be recovered are nonstationary. The recent triplet Markov models have overcome such difficulty thanks to their rich formalism, that allows considering more complex data structures while keeping the computational complexity of the different algorithms linear to the data size. In this letter, we propose a new triplet Markov chain that allows the unsupervised restoration of random discrete data hidden with switching noise distributions. We also provide genuine parameters estimation and MPM restoration algorithms. The new model is validated through experiments conducted on synthetic data and on real images, whose results show its interest with respect to the standard hidden Markov chain.

Exact fast smoothing in switching models with application to stochastic volatility

We consider the problem of statistical smoothing in nonlinear non-Gaussian systems. Our novel method relies on a Markov-switching model to operate recursively on series of noisy input data to produce an estimate of the underlying system state. We show through a set of experiments that our technique is efficient within the framework of the stochastic volatility model.

Unsupervised segmentation of non stationary data hidden with non stationary noise

Classical hidden Markov chains (HMC) can be inefficient in the unsupervised segmentation of non stationary data. To overcome such involvedness, the more elaborated triplet Markov chains (TMC) resort to using an auxiliary underlying process to model the behavior switches within the hidden states process. However, so far, only this latter was considered non stationary. The aim of this paper is to extend the results of a recently proposed TMC by considering both hidden states and noise non stationary. To show the efficiency of the proposed model, we provide results of non stationary synthetic and real images restoration.

Fast Filtering in Switching Approximations of Non-linear Markov Systems with Applications to Stochastic Volatility

We consider the problem of optimal statistical filtering in general nonlinear non-Gaussian Markov dynamic systems. The novelty of the proposed approach consists in approximating the nonlinear system by a recent Markov switching process, in which one can perform exact and optimal filtering with a linear time complexity. All we need to assume is that the system is stationary (or asymptotically stationary), and that one can sample its realizations. We evaluate our method using two stochastic volatility models and results show its efficiency.

Markov Chains for unsupervised segmentation of degraded NIR iris images for person recognition

Unsupervised statistical models based on Hidden Markov Chain (HMC).Unconstrained segmentation of NIR iris images.Novel method for circular scanning of an image.Improvement of iris verification performance via HMC-based segmentation.New implementation relying down-sampled images for limiting the processing time. The iris segmentation module plays a crucial role in iris recognition system as it allows to define the exact iris texture region in the image of the eye. Usual iris segmentation methods tend to fail on challenging eye images captured in less constrained environment or at-a-distance. In this paper, we propose a new robust model to segment degraded iris images. Its main characteristics are as follows: (1) we explore the use of advanced statistical model for unsupervised iris segmentation and more particularly, we focused on Hidden Markov Chain. (2) Novel adequate image scanning procedure and initialization step for implementing this model are developed. (3) The implementation of the proposed model can be performed on reduced image resolutions allowing limiting the processing time without degradation of the performance. A novel recognition system can therefore be obtained by adding this unsupervised iris segmentation module as a preprocessing in the open-source recognition model OSIRIS-V4. Extensive experiments on two large near infra-red databases ICE2005 and CASIA-IrisV4-distance demonstrate a significant improvement of the recognition performance with this novel system compared to OSIRIS-V4 and recent region-based iris verification systems, showing this way the potential of such statistical models for iris recognition.

Implementation of Unsupervised Statistical Methods for Low-Quality Iris Segmentation

In this paper, we explore the use of advanced statistical models for unsupervised segmentation of challenging eye images. A previous work has shown the superiority of Triplet Markov Field (TMF) over HMF for segmenting challenging eye region but TMF implementation is computationally very expensive. To enable faster processing while preserving performance, we investigate in this paper Hidden Markov Chain (HMC) and Pair wise Markov Chain (PMC). We developed novel adequate image scanning procedures and initialization steps for implementing these models and extensive experiments on challenging images of the ICE2005 database show that the use of HMC with the snail scan and Histogram Initialization enhances the quality of segmentation comparing to OSIRIS-V4 based on contour approach or TMF model.

Optimal SIR algorithm vs. fully adapted auxiliary particle filter: A matter of conditional independence

Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques. In this paper we comparatively analyse the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID) and the fully adapted APF (FA-APF). Both algorithms share the same Sampling (S), Weighting (W) and Resampling (R) steps, and only differ in the order in which these steps are performed. The order of the operations is not unsignificant: starting at time n − 1 from a common set of particles, we show that one single updated particle at time n will marginally be sampled in both algorithms from the same probability density function (pdf), but as a whole the full set of particles will be conditionally independent if created by the FA-APF algorithm, and dependent if created by the SIR algorithm, which results in support degeneracy.

A non asymptotical analysis of the optimal SIR algorithm vs. the fully adapted auxiliary particle filter

Particle filters (PF) and auxiliary particle filters (APF) are widely used sequential Monte Carlo (SMC) techniques for estimating the a posteriori filtering probability density function (pdf) in a Hidden Markov Chain (HMC). These algorithms have been theoretically analysed from an asymptotical statistics perspective. In this paper we provide a non asymptotical, finite number of samples comparative analysis of two particular SMC algorithms : the Sampling Importance Resampling (SIR) PF with optimal conditional importance distribution (CID), and the fully adapted APF (FA). Starting from a common set of N particles, we compute closed form expressions of the mean and variance of the empirical Monte Carlo (MC) estimators of a moment of the a posteriori filtering pdf. Both algorithms have the same mean, but in the case where resampling is used, the variance of the SIR algorithm always exceeds that of the FA algorithm.

Unsupervised Segmentation of Nonstationary Data using Triplet Markov Chains.

An important issue in statistical image and signal segmentation consists in estimating the hidden variables of interest. For this purpose, various Bayesian estimation algorithms have been developed, particularly in the framework of hidden Markov chains, thanks to their efficient theory that allows one to recover the hidden variables from the observed ones even for large data. However, such models fail to handle nonstationary data in the unsupervised context. In this paper, we show how the recent triplet Markov chains, which are strictly more general models with comparable computational complexity, can be used to overcome this limit through two different ways: (i) in a Bayesian context by considering the switches of the hidden variables regime depending on an additional Markov process; and, (ii) by introducing Dempster-Shafer theory to model the lack of precision of the hidden process prior distributions, which is the origin of data nonstationarity. Furthermore, this study analyzes both approaches in order to determine which one is better-suited for nonstationary data. Experimental results are shown for sampled data and noised images.

Pairwise Markov models for stock index forecasting

Common well-known properties of time series of financial asset values include volatility clustering and asymmetric volatility phenomenon. Hidden Markov models (HMMs) have been proposed for modeling these characteristics, however, due to their simplicity, HMMs may lack two important features. We identify these features and propose modeling financial time series by recent Pairwise Markov models (PMMs) with a finite discrete state space. PMMs are extended versions of HMMs and allow a more flexible modeling. A real-world application example demonstrates substantial gains of PMMs compared to the HMMs.