Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Structure from Planar Motions with Small Baselines
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
A Factorization Method for Structure from Planar Motion
WACV-MOTION '05 Proceedings of the IEEE Workshop on Motion and Video Computing (WACV/MOTION'05) - Volume 2 - Volume 02
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
Wide Baseline Matching between Unsynchronized Video Sequences
International Journal of Computer Vision
On Single-Sequence and Multi-Sequence Factorizations
International Journal of Computer Vision
A convenient multicamera self-calibration for virtual environments
Presence: Teleoperators and Virtual Environments
Rotation constrained power factorization for structure from motion of nonrigid objects
Pattern Recognition Letters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Tensor Decompositions and Applications
SIAM Review
5D motion subspaces for planar motions
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Trajectory Space: A Dual Representation for Nonrigid Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Camera networks have gained increased importance in recent years. Existing approaches mostly use point correspondences between different camera views to calibrate such systems. However, it is often difficult or even impossible to establish such correspondences. But even without feature point correspondences between different camera views, if the cameras are temporally synchronized then the data from the cameras are strongly linked together by the motion correspondence: all the cameras observe the same motion. The present article therefore develops the necessary theory to use this motion correspondence for general rigid as well as planar rigid motions. Given multiple static affine cameras which observe a rigidly moving object and track feature points located on this object, what can be said about the resulting point trajectories? Are there any useful algebraic constraints hidden in the data? Is a 3D reconstruction of the scene possible even if there are no point correspondences between the different cameras? And if so, how many points are sufficient? Is there an algorithm which warrants finding the correct solution to this highly non-convex problem? This article addresses these questions and thereby introduces the concept of low-dimensional motion subspaces. The constraints provided by these motion subspaces enable an algorithm which ensures finding the correct solution to this non-convex reconstruction problem. The algorithm is based on multilinear analysis, matrix and tensor factorizations. Our new approach can handle extreme configurations, e.g. a camera in a camera network tracking only one single point. Results on synthetic as well as on real data sequences act as a proof of concept for the presented insights.