Non-rigid Structure from Motion with Diffusion Maps Prior

In this paper, a novel approach based on a non-linear manifold learning technique is proposed to recover 3D non-rigid structures from 2D image sequences captured by a single camera. Most of the existing approaches assume that 3D shapes can be accurately modelled in a linear subspace. These techniques perform well when the deformations are relatively small or simple, but fail when more complex deformations need to be recovered. The non-linear deformations are often observed in highly flexible objects for which the use of the linear model is impractical. A specific type of shape variations might be governed by only a small number of parameters, therefore can be well-represented in a low dimensional manifold. We learn a non-linear shape prior using diffusion maps method. The key contribution in this paper is the introduction of the shape prior that constrain the reconstructed shapes to lie in the learned manifold. The proposed methodology has been validated quantitatively and qualitatively on 2D points sequences projected from the 3D motion capture data and real 2D video sequences. The comparisons of the proposed manifold based method against several state-of-the-art techniques are shown on different types of deformable objects.