Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Damped Newton Algorithms for Matrix Factorization with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Lessons from the Netflix prize challenge
ACM SIGKDD Explorations Newsletter - Special issue on visual analytics
Implicit Non-Rigid Structure-from-Motion with Priors
Journal of Mathematical Imaging and Vision
An iterative image registration technique with an application to stereo vision
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 2
Non-rigid structure from motion with complementary rank-3 spaces
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
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Matrices that collect the image coordinates of point features tracked through video --- one column per feature --- have often low rank, either exactly or approximately. This observation has led to many matrix factorization methods for 3D reconstruction, motion segmentation, or regularization of feature trajectories. However, temporary occlusions, image noise, and variations in lighting, pose, or object geometry often confound trackers. A feature that reappears after a temporary tracking failure --- whatever the cause --- is regarded as a new feature by typical tracking systems, resulting in very sparse matrices with many columns and rendering factorization problematic. We propose a method to simultaneously factor and compact such a matrix by merging groups of columns that correspond to the same feature into single columns. This combination of compaction and factorization makes trackers more resilient to changes in appearance and short occlusions. Preliminary experiments show that imputation of missing matrix entries --- and therefore matrix factorization --- becomes significantly more reliable as a result. Clean column merging also required us to develop a history-sensitive feature reinitialization method we call feature snapping that aligns merged feature trajectory segments precisely to each other.