Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
A multi-body factorization method for motion analysis
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A Direct Method for 3D Factorization of Nonrigid Motion Observed in 2D
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Articulated Structure from Motion by Factorization
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Non-Rigid Stereo Factorization
International Journal of Computer Vision
Implicit Non-Rigid Structure-from-Motion with Priors
Journal of Mathematical Imaging and Vision
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Perspective Nonrigid Shape and Motion Recovery
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Tensor Decompositions and Applications
SIAM Review
Sequential non-rigid structure-from-motion with the 3D-implicit low-rank shape model
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
3D reconstruction of a moving point from a series of 2D projections
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Reconstruction of non-rigid 3D shapes from stereo-motion
Pattern Recognition Letters
Trajectory Space: A Dual Representation for Nonrigid Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-rigid structure from motion with complementary rank-3 spaces
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Multiview structure from motion in trajectory space
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Automated articulated structure and 3D shape recovery from point correspondences
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
International Journal of Computer Vision
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Multiple-view geometry and structure-from-motion are well established techniques to compute the structure of a moving rigid object. These techniques are all based on strong algebraic constraints imposed by the rigidity of the object. Unfortunately, many scenes of interest, e.g. faces or cloths, are dynamic and the rigidity constraint no longer holds. Hence, there is a need for non-rigid structure-from-motion (NRSfM) methods which can deal with dynamic scenes. A prominent framework to model deforming and moving non-rigid objects is the factorization technique where the measurements are assumed to lie in a low-dimensional subspace. Many different formulations and variations for factorization-based NRSfM have been proposed in recent years. However, due to the complex interactions between several subspaces, the distinguishing properties between two seemingly related approaches are often unclear. For example, do two approaches just vary in the optimization method used or is really a different model beneath? In this paper, we show that these NRSfM factorization approaches are most naturally modeled with tensor algebra. This results in a clear presentation which subsumes many previous techniques. In this regard, this paper brings several strings of research together and provides a unified point of view. Moreover, the tensor formulation can be extended to the case of a camera network where multiple static affine cameras observe the same deforming and moving non-rigid object. Thanks to the insights gained through this tensor notation, a closed-form and an efficient iterative algorithm can be derived which provide a reconstruction even if there are no feature point correspondences at all between different cameras. An evaluation of the theory and algorithms on motion capture data show promising results.