A Direct Method for 3D Factorization of Nonrigid Motion Observed in 2D

The nonrigid structure-from-motion (NSFM) problem seeks to recover a sequence of 3D shapes, shape articulation parameters, and camera view matrices from 2D correspondence data. Factorization approaches relate the principal subspaces of the data matrix to the desired parameters through a linear corrective transform. Current methods for finding this transform are heuristic or depend on strong assumptions about the data. We show how to solve for this transform by directly minimizing deviation from the required orthogonal structure of the projection/articulation matrix. The solution is exact for noiseless data and an order of magnitude more accurate than state-of-the-art methods for noisy data.