We present the Evidential Hidden Markov Models (EvHMM), an extension of probabilistic HMM for time-series modeling, where conditional belief functions are used in place of probabilities to manage uncertainty on discrete latent variables. Inference and learning mechanisms are described and allow to solve the three problems initially defined for HMM, namely, the classification problem (find the most plausible model), the decoding problem (finding the best sequence of hidden states), and the learning problem based on incomplete and uncertain data (estimate the parameters). Exact inference mechanisms based on the GBT are proposed which allows one to recover standard HMM when probabilities are considered. An EM-like procedure is developed for parameter learning, relying on some approximations suggested to make the solutions tractable. Relationships are discussed with both the learning criterion conjectured by Vannoorenberghe and Smets and the formulation of EMCs by Pieczynski et al. A comparison with standard HMM on simulated data confirms the interest of considering random disjunctive sets to represent data incompleteness in evidential temporal graphical models.

This paper addresses the problem of parameter estimation and state prediction in hidden Markov models (HMMs) based on observed outputs and partial knowledge of hidden states expressed in the belief function framework. The usual HMM model is recovered when the belief functions are vacuous. Parameters are learned using the evidential expectation-maximization algorithm, a recently introduced variant of the expectation-maximization algorithm for maximum likelihood estimation based on uncertain data. The inference problem, i.e., finding the most probable sequence of states based on observed outputs and partial knowledge of states, is also addressed. Experimental results demonstrate that partial information about hidden states, when available, may substantially improve the estimation and prediction performances.

Various approaches for prognostics have been developed, and data-driven methods are increasingly applied. The training step of these methods generally requires huge datasets to build a model of the degradation signal, and estimate the limit under which the degradation signal should stay. Applicability and accuracy of these methods are thereby closely related to the amount of available data, and even sometimes requires the user to make assumptions on the dynamics of health states evolution. Following that, the aim of this paper is to propose a method for prognostics and remaining useful life estimation that starts from scratch, without any prior knowledge. Assuming that remaining useful life can be seen as the time between the current time and the instant where the degradation is above an acceptable limit, the proposition is based on a classification of prediction strategy (CPS) that relies on two factors. First, it relies on the use of an evolving real-time neuro-fuzzy system that forecasts observations in time. Secondly, it relies on the use of an evidential Markovian classifier based on Dempster-Shafer theory that enables classifying observations into the possible functioning modes. This approach has the advantage to cope with a lack of data using an evolving system, and theory of belief functions. Also, one of the main assets is the possibility to train the prognostic system without setting any threshold. The whole proposition is illustrated and assessed by using the CMAPPS turbofan dataset. RUL estimates are shown to be very close to actual values, and the approach appears to accurately estimate the failure instants, even with few learning data.

Forecasting the future states of a complex system is a complicated challenge that is encountered in many industrial applications covered in the community of prognostics and health management. Practically, states can be either continuous or discrete: Continuous states generally represent the value of a signal while discrete states generally depict functioning modes reflecting the current degradation. For each case, specific techniques exist. In this paper, we propose an approach based on case-based reasoning that jointly estimates the future values of the continuous signal and the future discrete modes. The main characteristics of the proposed approach are the following: 1) It relies on the K-nearest neighbor algorithm based on belief function theory; 2) belief functions allow the user to represent his/her partial knowledge concerning the possible states in the training data set, particularly concerning transitions between functioning modes which are imprecisely known; and 3) two distinct strategies are proposed for state prediction, and the fusion of both strategies is also considered. Two real data sets were used in order to assess the performance in estimating future breakdown of a real system.

Moving Object Databases (MOD), although ubiquitous, still call for methods that will be able to understand, search, analyze, and browse their spatiotemporal content. In this paper, we propose a method for trajectory segmentation and sampling based on the representativeness of the (sub)trajectories in the MOD. In order to find the most representative subtrajectories, the following methodology is proposed. First, a novel global voting algorithm is performed, based on local density and trajectory similarity information. This method is applied for each segment of the trajectory, forming a local trajectory descriptor that represents line segment representativeness. The sequence of this descriptor over a trajectory gives the voting signal of the trajectory, where high values correspond to the most representative parts. Then, a novel segmentation algorithm is applied on this signal that automatically estimates the number of partitions and the partition borders, identifying homogenous partitions concerning their representativeness. Finally, a sampling method over the resulting segments yields the most representative subtrajectories in the MOD. Our experimental results in synthetic and real MOD verify the effectiveness of the proposed scheme, also in comparison with other sampling techniques.

We present a shape-based method for automatic people detection and counting without any assumption concerning camera motion. In order to evaluate the robustness of the proposed method, we apply it for classifying athletics videos into two classes: videos of individual and videos of team sports. The videos used are real and characterized by dynamic and unconstrained environment. Moreover, in the case of team sport, we propose a shape deformations based method for running/hurdling discrimination (activity recognition). Robust, adaptive and independent from color, illumination changes and the camera motion, the proposed features are combined in the Transferable Belief Model (TBM) framework providing a two-level (frames and shot) video categorization. Experimental results of 97% of accuracy for individual/team sport categorization using a dataset of 252 real videos of athletic meetings, acquired by moving cameras under varying view angles, indicate the stability and the good performance of the proposed scheme.

We propose a general framework that focuses on automatic individual/multiple people motion-shape analysis and on suitable features extraction that can be used on action/activity recognition problems under real, dynamical and unconstrained environments. We have considered various athletic videos from a single uncalibrated, possibly moving camera in order to evaluate the robustness of the proposed method. We have used an easily expanded hierarchical scheme in order to classify them to videos of individual and team sports. Robust, adaptive and independent from the camera motion, the proposed features are combined within Transferable Belief Model (TBM) framework providing a two level (frames and shot) video categorization. The experimental results of 97% individual/team sport categorization accuracy, using a dataset of more than 250 videos of athletic meetings indicate the good performance of the proposed scheme.

In this paper, we propose a tool called temporal credal filter with conflict-based model change (TCF-CMC) to smooth belief functions online in transferable belief model (TBM) framework. The TCF-CMC takes temporal aspects of belief functions into account and relies on conflict information explicitly modelled in TBM when combining beliefs. TBM fusion, in addition to uncertainty, takes into account imprecision and conflict inherent to features. The TCF-CMC takes part in a wider system for human action recognition in videos. The whole system is tested on 62 videos (11000 images) with moving camera and real conditions where the TCF-CMC improves running, jumping, falling and standing-up actions recognition in high jump, pole vault, long jump and triple jump activities. The TCF-CMC is also compared to hidden Markov models. Lastly, a TBM rules-based modelling is compared to Gaussian mixture.

In the context of human action sequence recognition in video sequences, a scheduler of actions is proposed. The belief scheduler is based on a temporal belief filter ensuring a consistency in the temporal belief evolution as well as temporal constraints. The belief scheduler is inspired from system science and is used to recognize actions in human activity defined as a sequence of actions. This new scheduler is proposed for applications in computer vision. The whole system of action and sequence recognition is based on the transferable belief model proposed and developed by Ph. Smets which allows to explicitly model the doubt between actions. Furthermore, it emphasizes the conflict which is exploited for state change in action sequence. The experiments concern real video sequences with moving camera and several unknown view angles. The temporal belief filter and the belief scheduler show their efficiency to cope with varying video quality and experiment conditions

In the context of human action recognition in video sequences, a temporal belief filter based on the transferable belief model is proposed. It ensures a consistency in the temporal belief evolution. The filter is useful to cope with varying video quality and experiment conditions by smoothing belief on actions and solving conflict due to contradictory parameters. The proposed approach is validated on real video sequences with moving camera under several view angles