We propose a new approach for integrating geometric scene knowledge into a level-set tracking framework. Our approach is based on a novel constrained-homography transformation model that restricts the deformation space to physically plausible rigid motion on the ground plane. This model is especially suitable for tracking vehicles in automotive scenarios. Apart from reducing the number of parameters in the estimation, the 3D transformation model allows us to obtain additional information about the tracked objects and to recover their detailed 3D motion and orientation at every time step. We demonstrate how this information can be used to improve a Kalman filter estimate of the tracked vehicle dynamics in a higher-level tracker, leading to more accurate object trajectories. We show the feasibility of this approach for an application of tracking cars in an inner-city scenario.