In this paper we address the problem of projective reconstruction for deformable objects. Recent work in non-rigid factorization has proved that it is possible to model deformations as a linear combination of basis shapes, allowing the recovery of camera motion and 3D shape under weak perspective viewing conditions. However, the performance of these methods degrades when the object of interest is close to the camera and strong perspective distortion is present in the data. The main contribution of this work is the proposal of a practical method for the recovery of projective depths, camera motion and non-rigid 3D shape from a sequence of images under strong perspective conditions. Our approach is based on minimizing 2D reprojection errors, solving the minimization as four {\em weighted least squares} problems. Results using synthetic and real data are given to illustrate the performance of our method.