Feature point tracking over a video sequence fails when the points go out of the field of view or behind other objects. In this paper, we extend such interrupted tracking by imposing the constraint that under the affine camera model all feature trajectories should be in an affine space. Our method consists of iterations for optimally extending the trajectories and for optimally estimating the affine space, coupled with an outlier removal process. Using real video images, we demonstrate that our method can restore a sufficient number of trajectories for detailed 3-D reconstruction.