  Non-Rigid Structure-from-Motion (NRSfM) problem aims to recover 3D geometry
of a deforming object from its 2D feature correspondences across multiple
frames. Classical approaches to this problem assume a small number of feature
points and, ignore the local non-linearities of the shape deformation, and
therefore, struggles to reliably model non-linear deformations. Furthermore,
available dense NRSfM algorithms are often hurdled by scalability,
computations, noisy measurements and, restricted to model just global
deformation. In this paper, we propose algorithms that can overcome these
limitations with the previous methods and, at the same time, can recover a
reliable dense 3D structure of a non-rigid object with higher accuracy.
Assuming that a deforming shape is composed of a union of local linear subspace
and, span a global low-rank space over multiple frames enables us to
efficiently model complex non-rigid deformations. To that end, each local
linear subspace is represented using Grassmannians and, the global 3D shape
across multiple frames is represented using a low-rank representation. We show
that our approach significantly improves accuracy, scalability, and robustness
against noise. Also, our representation naturally allows for simultaneous
reconstruction and clustering framework which in general is observed to be more
suitable for NRSfM problems. Our method currently achieves leading performance
on the standard benchmark datasets.
