We address the problem of computing the three-dimensional motions of objects in a long sequence of stereo frames. Our approach is bottom-up and consists of two levels. The first level deals with the tracking of 3D tokens from frame to frame and the estimation of their kinematics. The processing is completely parallel for each token. The second level groups tokens into objects based on their kinematic parameters, controls the processing at the low level to cope with problems such as occlusion, disappearance, and appearance of tokens, and provides information to other components of the system. We have implemented this approach using 3D line segments obtained from stereo as the tokens. We use classical kinematics and derive closed-form solutions for some special, but useful, cases of motions. The motion computation problem is then formulated as a tracking problem in order to apply the extended Kalman filter. The tracking is performed in a prediction-matching-update loop in which multiple matches can be handled. Tokens are labeled by a number called its support of existence which measures their adequation to the measurements. If this number goes beyond a threshold, the token disappears. The individual line segments can be grouped into rigid objects according to the similarity of their kinematic parameters. Experiments using synthetic and real data have been carried out and the results found to be quite good.