Non-Rigid Structure-From-Motion: Estimating
Shape and Motion with Hierarchical Priors

Lorenzo Torresani, Aaron Hertzmann, Chris Bregler


We present methods for recovering time-varying shape and motion of non-rigid 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 non-rigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed, and thus additional assumptions about deformations are required. We propose using a Probabilistic Principal Components Analysis (PPCA) shape model, and describe a reconstruction 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 model temporal dynamics in object shape, allowing the algorithm to robustly handle severe cases of missing data.


Revised from earlier conference papers:


A Matlab implementation of our algorithm can be downloaded here.


The datasets used in the experiments of the journal article are available here as Matlab files: