Hidden Markov models have been extended in many directions, leading to pairwise Markov models, triplet Markov models, or discriminative random fields, all of which have been successfully applied in many fields covering signal and image processing. The Dempster-Shafer theory of evidence has also shown its interest in a wide range of situations involving reasoning under uncertainty and/or information fusion. There are, however, only few works dealing with both of these modeling tools simultaneously. The aim of this paper, which falls under this category of works, is to propose a general evidential Markov model offering wide modeling and processing possibilities regarding information imprecision, sensor unreliability, and data fusion. The main interest of the proposed model relies in the possibility of achieving, easily, the Dempster-Shafer fusion without destroying the Markovianity.

When the state space dimension increases, the computational burden can become a major challenge for optimal Kalman filtering in Gaussian triplet Markov models (TMMs). In this paper, we introduce a new model order reduction technique applicable to linear time-homogeneous Gaussian TMMs. Taking advantage of the lower state dimension of the resulting approximate model, a low-complexity suboptimal Kalman filter is obtained. The proposed estimator provides complexity reduction without significant accuracy loss and is shown to outperform two classical methods in the case of Markovian process noise.

Purpose: The purpose of this study was to investigate the use of a probabilistic quad‐tree graph (hidden Markov tree, HMT) to provide fast computation, robustness and an interpretational framework for multimodality image processing and to evaluate this framework for single gross tumor target (GTV) delineation from both positron emission tomography (PET) and computed tomography (CT) images.Methods: We exploited joint statistical dependencies between hidden states to handle the data stack using multi‐observation, multi‐resolution of HMT and Bayesian inference. This framework was applied to segmentation of lung tumors in PET/CT datasets taking into consideration simultaneously the CT and the PET image information. PET and CT images were considered using either the original voxels intensities, or after wavelet/contourlet enhancement. The Dice similarity coefficient (DSC), sensitivity (SE), positive predictive value (PPV) were used to assess the performance of the proposed approach on one simulated and 15 clinical PET/CT datasets of non‐small cell lung cancer (NSCLC) cases. The surrogate of truth was a statistical consensus (obtained with the Simultaneous Truth and Performance Level Estimation algorithm) of three manual delineations performed by experts on fused PET/CT images. The proposed framework was applied to PET‐only, CT‐only and PET/CT datasets, and were compared to standard and improved fuzzy c‐means (FCM) multimodal implementations.Results: A high agreement with the consensus of manual delineations was observed when using both PET and CT images. Contourlet‐based HMT led to the best results with a DSC of 0.92 ± 0.11 compared to 0.89 ± 0.13 and 0.90 ± 0.12 for Intensity‐based HMT and Wavelet‐based HMT, respectively. Considering PET or CT only in the HMT led to much lower accuracy. Standard and improved FCM led to comparatively lower accuracy than HMT, even when considering multimodal implementations.Conclusions: We evaluated the accuracy of the proposed HMT‐based framework for PET/CT image segmentation. The proposed method reached good accuracy, especially with pre‐processing in the contourlet domain.

Stationary Jump Markov Linear Systems (JMLSs) model linear systems whose parameters evolve with time according to a hidden finite state Markov chain. We propose an algorithm for parameter estimation of a recent class of JMLSs called Conditionally Gaussian Pairwise Markov Switching Models (CGPMSMs). Our algorithm, named Double-EM (DEM), is based on the Expectation-Maximization (EM) principle applied twice sequentially. The first EM is applied to the couple (switches, observations) temporarily assumed to be a Pairwise Markov Chain (PMC). The second one is used to estimate the remaining conditional transitions and conditional noise matrices of the CGPMSM. The efficiency of the proposed algorithm is studied via unsupervised smoothing on simulated data. In particular, smoothing results, produced with CGPMSM in an unsupervised manner using DEM, can be more efficient than the ones obtained with the nearest classic “Conditionally Gaussian Linear State-Space Model” (CGLSSM) based on true parameters and true switches.