Nonrigid structure-from-motion: Estimating shape and motion with hierarchical priors

This paper describes methods for recovering time-varying shape and motion of nonrigid 3D objects from uncalibrated 2D point tracks. For example, given a video recording of a talking person, we would like to estimate the 3D shape of the face at each instant and learn a model of facial deformation. Time-varying shape is modeled as a rigid transformation combined with a nonrigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed, and thus additional assumptions about deformations are required. We first suggest restricting shapes to lie within a low-dimensional subspace and describe estimation algorithms. However, this restriction alone is insufficient to constrain reconstruction. To address these problems, we propose a reconstruction method using a Probabilistic Principal Components Analysis (PPCA) shape model and an estimation algorithm that simultaneously estimates 3D shape and motion for each instant, learns the PPCA model parameters, and robustly fills-in missing data points. We then extend the model to represent temporal dynamics in object shape, allowing the algorithm to robustly handle severe cases of missing data.