Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Multibody Grouping from Motion Images
International Journal of Computer Vision
EM algorithms for PCA and SPCA
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Incremental Singular Value Decomposition of Uncertain Data with Missing Values
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Factorization with Uncertainty
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A multi-body factorization method for motion analysis
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
3D motion segmentation using intensity trajectory
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
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Matrix factorization is a fundamental building block in many computer vision and machine learning algorithms. In this work we focus on the problem of ”structure from motion” in which one wishes to recover the camera motion and the 3D coordinates of certain points given their 2D locations. This problem may be reduced to a low rank factorization problem. When all the 2D locations are known, singular value decomposition yields a least squares factorization of the measurements matrix. In realistic scenarios this assumption does not hold: some of the data is missing, the measurements have correlated noise, and the scene may contain multiple objects. Under these conditions, most existing factorization algorithms fail while human perception is relatively unchanged. In this work we present an EM algorithm for matrix factorization that takes advantage of prior information and imposes strict constraints on the resulting matrix factors. We present results on challenging sequences.