In the classical hidden Markov chain (HMC) model we have a hidden chain X, which is a Markov one and an observed chain Y. HMC are widely used; however, in some situations they have to be replaced by the more general “hidden semi‐Markov chains” (HSMC) which are particular “triplet Markov chains” (TMC) T = (X, U, Y), where the auxiliary chain U models the semi‐Markovianity of X. Otherwise, non stationary classical HMC can also be modeled by a triplet Markov stationary chain with, as a consequence, the possibility of parameters’ estimation. The aim of this paper is to use simultaneously both properties. We consider a non stationary HSMC and model it as a TMC T = (X, U1, U2, Y), where U1 models the semi‐Markovianity and U2 models the non stationarity. The TMC T being itself stationary, all parameters can be estimated by the general “Iterative Conditional Estimation” (ICE) method, which leads to unsupervised segmentation. We present some experiments showing the interest of the new model and related processing in image segmentation area.
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Research Article| November 29 2006
Unsupervised Segmentation of Hidden Semi‐Markov Non Stationary Chains
AIP Conf. Proc. 872, 347–354 (2006)
Jérôme Lapuyade‐Lahorgue, Wojciech Pieczynski; Unsupervised Segmentation of Hidden Semi‐Markov Non Stationary Chains. AIP Conf. Proc. 29 November 2006; 872 (1): 347–354. https://doi.org/10.1063/1.2423293
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