This paper is concerned with the tracking of multiple moving objects in an image sequence and the reconstruction of the entire trajectories of these objects all over the sequence. More specifically, we address the joint issue of trajectory estimation and measurement-to-trajectory associations, which is the key problem in that context due to the occurrence of object occlusions or crossings. An original and efficient scheme is proposed, that adapts the Probabilistic Multiple Hypothesis Tracking (PMHT) technique to the case of tracking of regions in video, for which geometry and motion models can be introduced. Moreover, reliable partial associations can be obtained as an initialization. Data association and trajectory estimation are conducted within a probabilistic framework. The latter relies on Kalman filtering, while the former is solved with an EM algorithm for which a suitable initial configuration can be defined. The proposed tracking method is validated by experiments carried out on real image sequences depicting complex situations.