Deformable contours, based on energy minimization, have been widely used for tracking purposes. This paper proposes a novel type of constraint for the energy minimization problem: the use of motion models. Such an approach greatly reduces the sliding effects occurring during tracking: thus tracking provides point-to-point correspondence between the tracked B- spline based curves and reliably estimates their apparent motion. For a calibrated camera system, the stereo correspondences provided by this matching method can be used to reconstruct a 3-D curve point by point. This set of 3-D points is then approximated and refined by a 3-D deformable curve, in order to improve consistency with image observations. Furthermore, the bases of this tracking approach, i.e., B-splines and the estimation of 2-D motion models, provide an efficient way of estimating time-to-collision, and recovering the spatio-temporal surface of a moving contour, which has been proven to supply valuable information about its 3-D structure and motion. A large set of experimental results illustrates the different parts of this work.