Advances in probabilistic particle tracking for biomedical imaging. (Avancées en suivi probabiliste de particules pour l'imagerie biologique)

Particle tracking is a method of choice to understand subcellular mechanisms since it provides a robust and accurate means to characterize the dynamics of moving objects at the micro- and nano-metric scale. This thesis addresses several aspects related to the problem of tracking several hundreds of particles in cluttered conditions. We present novel techniques based on robust mathematical methods which allow us to track subresolutive particles in the wealth of conditions which are met in cellular imaging. Particle detection: we have first addressed the issue of detecting particles in fluorescence images containing a structured background. The key idea of the proposed method is to use a blind source separation technique: the Morphological Component Analysis (MCA) algorithm, to separate the background from the particle signal by exploiting the differences between their morphologies in the image. We have made a number of adaptations to the MCA to comply with the characteristics of biological fluorescence images. For instance, we have proposed to use the curvelet dictionary and a wavelet dictionary with sparsity priors to split the background and the particles signals. After source separation, the background-free image can be reliably analyzed to identify the particle locations and track them through time. Particle tracking problem modeling: we have proposed a global statistical framework which accounts for every aspect of the particle tracking problem in cluttered conditions. The designed probabilistic framework includes several models which are dedicated to biological imaging, such as statistical models of motion of particles. We have also defined the concept of target perceivability for biological particles. By doing so, the existence of particles is explicitly modeled and statistically quantified, thereby addressing the issues of track termination/creation within the statistical framework for tracking. As a result, the proposed framework enjoys a high degree of flexibility since every parameter and model involved finds a simple and intuitive interpretation. The proposed probabilistic framework has consequently allowed us to exhaustively model a wealth of different biological cases. Tracking algorithm design: we have reformulated the Multiple Hypothesis Tracking (MHT) algorithm to include the probabilistic framework for tracking biological particles, and proposed an efficient implementation which allows one to track numerous particles in poor imaging conditions. The Enhanced MHT (E-MHT) we propose takes full advantage of the tracking model by incorporating the knowledge from future frames, whereby the significance of statistical scores is increased. As a result, the E-MHT is able to automatically identify false detections and detect target appearance/disappearance events. We address the complexity of the tracking task by an efficient design of the algorithm which exploits the tree organization of the solutions and the ability to make the computations in a parallel manner. A series of comparative tests between the E-MHT and a number of state-of-the-art techniques have been performed with synthetic 2D image sequences and real 2D and 3D data sets. In every case the E-MHT has proved superior performance over standard techniques, with a remarkable capability to handle very poor imaging conditions. We have applied the proposed tracking techniques in a number of biological projects, leading to novel biological results. The flexibility and robustness of the proposed methods have allowed us to track prions infecting cell, characterize protein transport during the Drosophila oocyte development, and to study the mRNA trafficking in a Drosophila ovocyte.