Etude d'un modele generatif pour l'analyse en temps reel de trajectoires bidimensionnelles bruitees

Introduction. Video surveillance, cellular telecommunication, global positioning systems and wireless sensor networks are just a few examples among many others of monitoring systems providing real time location data. Objective. The purpose of this work is to develop an activity model in the paradigm of probabilistic graphical models (PGM) and Bayesian networks (BN) to analyze in real time two-dimensional trajectories observed from the displacement of autonomous mobile agents. Method. An HHMM is the hierarchical version of the hidden Markov model (HMM) and is studied and tested here within three contexts of application in order to determine its ability to recognize patterns and sub-patterns of displacement from two-dimensional trajectories. The first context of application resumes to random sequences of Gaussian primitives. The second context of application resumes to random sequences of primitives created from two-dimensional trajectory samples. Finally, two-dimensional trajectories of displacement from real RoboCup competitions are used in the third context of application. An online segmentation model based on PPCA, the probabilistic version of principal component analysis (PCA), is then used to reduce the computation cost involving the HHMM. Results. It is shown that when trained in an unsupervised fashion with the expectation maximization (EM) algorithm, the HHMM as well as the HMM lead to a recognition score of almost 100% in the idealistic case of Gaussian primitives and to a score of 75% in the case of two-dimensional trajectories. The HHMM also has the ability to recognize sub-patterns. However such PGMs might not be tractable in real time because of the high computation cost introduced by potentially complex hierarchical topologies. The computation cost of the HHMM can be reduced by a factor of 102 with the addition of an online PPCA segmentation model, keeping recognition scores approximately the same. Discussion/Conclusion. The online PPCA segmentation model stands as the best trade-off between segmentation efficiency and computation cost. Indeed, the online PPCA segmentation model is 2 to 4 times more efficient than the basic PCA model for the double of the cost. Since the HHMM has a complexity level greater than the HMM the curse of the dimensionality leads to overfitting problems. Results show however that the model is relevant and appropriate for two-dimensional trajectory recognition if a proper regularization is performed. Finally, the achievements on the activity model presented in this work might provide an interesting framework for developments regarding plan recognition, trajectory prediction and anomaly detection.