Re-thinking non-rigid structure from motion

We present a novel approach to non-rigid structure from motion (NRSFM) from an orthographic video sequence, based on a new interpretation of the problem. Existing ap- proaches assume the object shape space is well-modeled by a linear subspace. Our approach only assumes that small neighborhoods of shapes are well-modeled with a linear subspace. This constrains the shapes to belong to a man- ifold of dimensionality equal to the number of degrees of freedom of the object. After showing that the problem is still overconstrained, we present a solution composed of a novel initialization algorithm, followed by a robust exten- sion of the Locally Smooth Manifold Learning algorithm tailored to the NRSFM problem. We finally present some test cases where the linear basis method fails (and is ac- tually not meant to work) while the proposed approach is successful.