Uncalibrated Non-Rigid Factorisation by Independent Subspace Analysis

We propose a general, prior-free approach for the uncalibrated non-rigid structure-from-motion problem for modelling and analysis of non-rigid objects such as human faces. We recover the non-rigid affine structure and motion from 2D point correspondences by assuming that (1) the non-rigid shapes are generated by a linear combination of rigid 3D basis shapes, (2) that the non-rigid shapes are affine in nature, i.e., they can be modelled as deviations from the mean, rigid shape, (3) and that the basis shapes are statistically independent. In contrast to the majority of existing works, no statistical prior is assumed for the structure and motion apart from the assumption that underlying basis shapes are statistically independent. The independent 3D shape bases are recovered by independent subspace analysis (ISA). Likewise, in contrast to the most previous approaches, no calibration information is assumed for affine cameras; the reconstruction is solved up to a global affine ambiguity that makes our approach simple and efficient. In the experiments, we evaluated the method with several standard data sets including a real face expression data set of 7200 faces with 2D point correspondences and unknown 3D structure and motion for which we obtained promising results.