2016
DOI: 10.1142/s0219467816500200
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Unsupervised Image Segmentation with Pairwise Markov Chains Based on Nonparametric Estimation of Copula Using Orthogonal Polynomials

Abstract: Copula were introduced in Markov models in the early 2000s to better model the relationship between the observation data involved in these models. However, their estimation is difficult. This paper presents a new approach in the estimation of copula in Markov models. The proposed approach is based on a nonparametric method of estimating the density of the copula. The decomposition of an orthonormal basis of the unit interval support polynomials is used to estimate this density. The family of polynomial used is… Show more

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Cited by 8 publications
(1 citation statement)
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“…Among extensions, hidden semi-Markov chains (HSMCs) can be very useful as they allow the modelling of any sojourn time in a given class, when it is necessarily geometric in HMCs [13], [14], [15], [16]. Hidden bivariate Markov chains [17], [18], double Markov chains [19], or still pairwise Markov chains (PMCs) [20], [21], [22], [23] are other extensions. This paper is related to "triplet Markov chains" (TMCs), which is an extension of PMCs consisting in considering a third stochastic sequence, which might or might not have a practical signification, along the hidden sequence to be estimated and the sequence of observations, and assuming the joint Markovianity of the three sequences.…”
Section: Introductionmentioning
confidence: 99%
“…Among extensions, hidden semi-Markov chains (HSMCs) can be very useful as they allow the modelling of any sojourn time in a given class, when it is necessarily geometric in HMCs [13], [14], [15], [16]. Hidden bivariate Markov chains [17], [18], double Markov chains [19], or still pairwise Markov chains (PMCs) [20], [21], [22], [23] are other extensions. This paper is related to "triplet Markov chains" (TMCs), which is an extension of PMCs consisting in considering a third stochastic sequence, which might or might not have a practical signification, along the hidden sequence to be estimated and the sequence of observations, and assuming the joint Markovianity of the three sequences.…”
Section: Introductionmentioning
confidence: 99%