Unsupervised segmentation of hidden semi-Markov non-stationary chains

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) ) , , ( Y U X T = , 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 ) , , , ( 2 1 Y U U X T = , where 1 U models the semi-Markovianity and 2 U 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.