This paper proposes a new front propagation method to deal accurately with the challenging problem of tracking non-rigid moving objects. This is obtained by employing a Geodesic Active Region model where the designed objective function is composed of boundary and region-based terms and optimizes the curve position with respect to motion and intensity properties. The main novelty of our approach is that we deal with the motion estimation (linear models are assumed) and the tracking problem simultaneously. In other words, the optimization problem contains a coupled set of unknown variables; the curve position and the corresponding motion model. The designed objective function is minimized using a gradient descent method; the curve is propagated towards the object boundaries under the influence of boundary, intensity and motion-based forces, while given the curve position an analytical solution is obtained for the motion model. Besides, the PDE is implemented using a level set approach where topological changes are naturally handled. Very promising experimental results are provided using real video sequences.