We show how to automatically acquire similarity-invariant shape representations of objects from noisy image sequences under weak perspective. The proposed method is linear and incremental, requiring no more than pseudo-inverse. It is based on the observation that the trajectories that points on the object form in weak-perspective image sequences are linear combinations of three of the trajectories themselves, and that the coefficients of the linear combinations represent shape in an affine-invariant basis. A nonlinear but numerically sound preprocessing state is added to improve the accuracy of the results even further. Experiments show that attention to noise and computational techniques improve the shape results substantially with respect to previous methods proposed.