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This paper address the problem of automatically extracting the 3D configurations of deformable objects from 2D features. Our focus in this work is to build on the observation that the subspace spanned by the motion parameters is a subset of a smooth manifold, and therefore we hunt for the solution in this space, rather than use heuristics (as previously attempted earlier). We succeed in this by attaching a canonical Riemannian metric, and using a variant of the non-rigid factorisation algorithm for structure from motion. We qualitatively and quantitatively show that our algorithm produces better results when compared to the state of art.