Procrustean Normal Distribution for Non-Rigid Structure from Motion

A well-defined deformation model can be vital for non-rigid structure from motion (NRSfM). Most existing methods restrict the deformation space by assuming a fixed rank or smooth deformation, which are not exactly true in the real world, and they require the degree of deformation to be predetermined, which is impractical. Meanwhile, the errors in rotation estimation can have severe effects on the performance, i.e., these errors can make a rigid motion be misinterpreted as a deformation. In this paper, we propose an alternative to resolve these issues, motivated by an observation that non-rigid deformations, excluding rigid changes, can be concisely represented in a linear subspace without imposing any strong constraints, such as smoothness or low-rank. This observation is embedded in our new prior distribution, the Procrustean normal distribution (PND), which is a shape distribution exclusively for non-rigid deformations. Because of this unique characteristic of the PND, rigid and non-rigid changes can be strictly separated, which leads to better performance. The proposed algorithm, EM-PND, fits a PND to given 2D observations to solve NRSfM without any user-determined parameters. The experimental results show that EM-PND gives the state-of-the-art performance for the benchmark data sets, confirming the adequacy of the new deformation model.