Assessing the segmentation performance of pairwise and triplet Markov models

Gorynin, Ivan; Gangloff, Hugo; Monfrini, Emmanuel; Pieczynski, Wojciech

doi:10.1016/j.sigpro.2017.12.006

Cited by 25 publications

(19 citation statements)

References 25 publications

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“…Hidden Markov Models (HMMs) are a popular family of probabilistic graphical models which have been used in a wide variety of contexts [5]. HMMs are an active research topic where many extensions tend to generalize models so that they can integrate many more dependencies between random variables and thus model more complex phenomena [6] [7] [8]. In particular, Markov Trees (MTs) are generalization of Markov Chains that are particularly suited for modeling multi-resolution data.…”

Section: Context and Related Workmentioning

confidence: 99%

Unsupervised Image Segmentation with Spatial Triplet Markov Trees

Gangloff

Courbot

Monfrini

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Hidden Markov Trees (HMTs) are successful probabilistic models [1] [2] [3] in image segmentation or genetic analysis for example. They offer a good compromise between the random variables that can be modeled and the tractability of the inference within these models. Indeed, the inference procedures can be conducted in a direct, exact fashion [4]. However the conditional independence restrictions in HMTs can be too simplistic with respect to the interactions we wish to model, particularly in the task of natural image segmentation. In this article we study an extension of HMTs called Spatial Triplet Markov Trees (STMTs) which is designed to greatly increase the correlations of the random variables while keeping the possibility of direct and exact inference procedures. The STMT model is tested and compared to other unsupervised segmentation techniques in the case of unsupervised image segmentation. Numerical experiments show that STMTs outperform HMTs and present rich spatial dependencies which are crucial for image segmentation.

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Section: Context and Related Workmentioning

confidence: 99%

Unsupervised Image Segmentation with Spatial Triplet Markov Trees

Gangloff

Courbot

Monfrini

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…For example, to apply it to the so-called triplet Markov models, see e.g. [15,10,23], some additional assumptions are needed. Similarly it is not clear how to apply segmentation EM in HMMs with infinite state spaces (hierarchical Dirichlet processes).…”

Section: Objectives Of the Articlementioning

confidence: 99%

Estimation of Viterbi path in Bayesian hidden Markov models

Lember

Gasbarra

Koloydenko

et al. 2019

METRON

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The article studies different methods for estimating the Viterbi path in the Bayesian framework. The Viterbi path is an estimate of the underlying state path in hidden Markov models (HMMs), which has a maximum joint posterior probability. Hence it is also called the maximum a posteriori (MAP) path. For an HMM with given parameters, the Viterbi path can be easily found with the Viterbi algorithm. In the Bayesian framework the Viterbi algorithm is not applicable and several iterative methods can be used instead. We introduce a new EM-type algorithm for finding the MAP path and compare it with various other methods for finding the MAP path, including the variational Bayes approach and MCMC methods. Examples with simulated data are used to compare the performance of the methods. The main focus is on non-stochastic iterative methods and our results show that the best of those methods work as well or better than the best MCMC methods. Our results demonstrate that when the primary goal is segmentation, then it is more reasonable to perform segmentation directly by considering the transition and emission parameters as nuisance parameters.

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“…The process Z is sometimes called the pairwise Markov model (PMM) [34,5,6,14] and covers many latent variable models used in practice, such as hidden Markov models (HMM) and autoregressive regime-switching models. For a classification and general properties of pairwise models, we refer to [34,6,14]. Generally, neither Y nor X is a Markov chain, although for special cases they might be.…”

Section: Introductionmentioning

confidence: 99%

Exponential forgetting of smoothing distributions for pairwise Markov models

Lember

Sova

2021

Electron. J. Probab.

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We consider a bivariate Markov chain Z = {Z k } k≥1 = {(X k , Y k )} k≥1 taking values on product space Z = X ×Y, where X is possibly uncountable space and Y = {1, . . . , |Y|} is a finite state-space. The purpose of the paper is to find sufficient conditions that guarantee the exponential convergence of smoothing, filtering and predictive probabilities:Here t ≥ s ≥ l ≥ 1, Ks is σ(Xs:∞)-measurable finite random variable and α ∈ (0, 1) is fixed. In the second part of the paper, we establish two-sided versions of the above-mentioned convergence. We show that the desired convergences hold under fairly general conditions. A special case of above-mentioned very general model is popular hidden Markov model (HMM). We prove that in HMM-case, our assumptions are more general than all similar mixing-type of conditions encountered in practice, yet relatively easy to verify.

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Assessing the segmentation performance of pairwise and triplet Markov models

Cited by 25 publications

References 25 publications

Unsupervised Image Segmentation with Spatial Triplet Markov Trees

Unsupervised Image Segmentation with Spatial Triplet Markov Trees

Estimation of Viterbi path in Bayesian hidden Markov models

Exponential forgetting of smoothing distributions for pairwise Markov models

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