Combining Local-Physical and Global-Statistical Models for Sequential Deformable Shape from Motion

In this paper, we simultaneously estimate camera pose and non-rigid 3D shape from a monocular video, using a sequential solution that combines local and global representations. We model the object as an ensemble of particles, each ruled by the linear equation of the Newton’s second law of motion. This dynamic model is incorporated into a bundle adjustment framework, in combination with simple regularization components that ensure temporal and spatial consistency. The resulting approach allows to sequentially estimate shape and camera poses, while progressively learning a global low-rank model of the shape that is fed back into the optimization scheme, introducing thus, global constraints. The overall combination of local (physical) and global (statistical) constraints yields a solution that is both efficient and robust to several artifacts such as noisy and missing data or sudden camera motions, without requiring any training data at all. Validation is done in a variety of real application domains, including articulated and non-rigid motion, both for continuous and discontinuous shapes. Our on-line methodology yields significantly more accurate reconstructions than competing sequential approaches, being even comparable to the more computationally demanding batch methods.