From turbo hidden Markov models to turbo state-space models

We recently introduced a novel approximation of the intractable two-dimensional hidden Markov model (2-D HMM), the turbo- HMM (T-HMM), which consists of a set of interconnected horizontal and vertical 1-D HMMs. In this paper, we consider the extension of this framework to the continuous state HMM, generally referred to as the state-space model (SSM). We provide efficient approximate answers to the three following problems: 1) how to compute the likelihood of a set of observations, 2) how to find the sequence of states that best "explains" a set of observations and 3) how to estimate the model parameters given a set of observations. The application of this work to the challenging problem of face recognition in the presence of large illumination variations will illustrate the potential of our approach. next section, we provide a brief review of the approximations underlying the T-HMM framework and consider its extension to the T-SSM. In the three following sections, we provide answers to the three previously listed problems. Finally, in section 6, we apply the T-SSM framework to the challenging problem of face recognition in the presence of illumination variation and present experimental results.