Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
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
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
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
A convenient multicamera self-calibration for virtual environments
Presence: Teleoperators and Virtual Environments
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
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Tensor Decompositions and Applications
SIAM Review
Multilinear Factorizations for Multi-Camera Rigid Structure from Motion Problems
International Journal of Computer Vision
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In practice, rigid objects often move on a plane. The object then rotates around a fixed axis and translates in a plane orthogonal to this axis. For a concrete example, think of a car moving on a street. Given multiple static affine cameras which observe such a rigidly moving object and track feature points located on this object, what can be said about the resulting feature point trajectories in the camera views? Are there any useful algebraic constraints hidden in the data? Is a 3D reconstruction of the scene possible even if there are no feature point correspondences between the different cameras? And if so, how many points are sufficient? Does a closed-form solution to this shape from motion reconstruction problem exist? This paper addresses these questions and thereby introduces the concept of 5 dimensional planar motion subspaces: the trajectory of a feature point seen by any camera is restricted to lie in a 5D subspace. The constraints provided by these motion subspaces enable a closed-form solution for the reconstruction. The solution is based on multilinear analysis, matrix and tensor factorizations. As a key insight, the paper shows that already two points are sufficient to derive a closed-form solution. Hence, even two cameras where each of them is just tracking one single point can be handled. Promising results of a real data sequence act as a proof of concept of the presented insights.